Blog Block 2A
(Most recent entry listed first)
(Most recent entry listed first)
Friday March 13 - School has been suspended due to the Coronavirus until further notice, please be safe and I will provide you an update of the status of our learning when we find out when school will be back in session. We will pick up with the lesson outlined below that was intended for Friday 3/13 upon our return to school
* Journal Alert - The journals will be due at 2pm on the first day that we return to school. I encourage you to send them while we are on hiatus, I have plenty of time to read them and have a conversation with you (and you have plenty of time too).
* Journal Alert - The journals will be due at 2pm on the first day that we return to school. I encourage you to send them while we are on hiatus, I have plenty of time to read them and have a conversation with you (and you have plenty of time too).
Friday March 13 (Mr. Harris was absent today)
On the way in, the sub distributed lesson 4.2. This lesson is fairly short and has three key points:
* Homework - Make sure BOTH lessons 4.1 and 4.2 are completed (will be checked for a HW grade Tuesday). Note any questions you may have for review on Tuesday.
* Journal Alert - Your 3Q journals are due on Monday 3/23 at 2pm
On the way in, the sub distributed lesson 4.2. This lesson is fairly short and has three key points:
- Coterminal angles are angles that have the same initial and terminal side. For example, 3∏/2 and -∏/2 are coterminal. We also discussed how there are an infinite number of coterminal angles for a given angle since we can always add/subtract another revolution (2∏ around the circle.
- Complementary angles are angles that add to right angles. Previously a right angle was alway measured as 90 degrees, however now, we are measuring angles as ∏/2 radians. Remember, angles that are > than right angles do not have compliments
- Supplementary angles are angles that add to 180 degrees or ∏ radians
- CLICK HERE for a video that demonstrates how to find coterminal angles of a given angle
- CLICK HERE for a video that demonstrates how to determine complementary/supplementary angles given in radians
* Homework - Make sure BOTH lessons 4.1 and 4.2 are completed (will be checked for a HW grade Tuesday). Note any questions you may have for review on Tuesday.
* Journal Alert - Your 3Q journals are due on Monday 3/23 at 2pm
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Wednesday March 11
On the way in, everyone received the 3Q Journal assignment. We reviewed the assignment for about 5-8 minutes. The journal is due on Monday 3/23 at 2pm. Also on the way in everyone received lesson 4.1. To start Unit 4, I gave a preview that this unit was primarily about the unit circle, one of the most important concepts that is a prerequisite for Calculus. To start, we reviewed the concept the difference between arc measure and arc length. We also reviewed the theorem that the measure of an arc is the same as the measure of the central angle that creates it. Then we introduced that there is a different way to quantify angle measures called "radians" (which relates to arc length). We reviewed how to sketch/find angles that are measured in radians. Remember, that positive angle direction is counterclockwise and negative angle direction is clockwise. Also remember, that is is possible to have an angle that is more than one revolution around the circle. We also reviewed how to convert angles measured in radians to degree measure and vice versa.
* Homework - Complete all of lesson 4.1, please email me with questions, will be checked for a HW grade (I took the answers off the blog).
* Journal Alert - Your 3Q journals are due on Monday 3/23 at 2pm
On the way in, everyone received the 3Q Journal assignment. We reviewed the assignment for about 5-8 minutes. The journal is due on Monday 3/23 at 2pm. Also on the way in everyone received lesson 4.1. To start Unit 4, I gave a preview that this unit was primarily about the unit circle, one of the most important concepts that is a prerequisite for Calculus. To start, we reviewed the concept the difference between arc measure and arc length. We also reviewed the theorem that the measure of an arc is the same as the measure of the central angle that creates it. Then we introduced that there is a different way to quantify angle measures called "radians" (which relates to arc length). We reviewed how to sketch/find angles that are measured in radians. Remember, that positive angle direction is counterclockwise and negative angle direction is clockwise. Also remember, that is is possible to have an angle that is more than one revolution around the circle. We also reviewed how to convert angles measured in radians to degree measure and vice versa.
- CLICK HERE for today's video that defines radian angle measures and demonstrates the relationship radian's have to the arc length created by a central angle
- CLICK HERE for a video that demonstrates how to sketch angles in radians
- CLICK HERE for a video that demonstrates how to convert from degrees to radians and vice versa.
* Homework - Complete all of lesson 4.1, please email me with questions, will be checked for a HW grade (I took the answers off the blog).
* Journal Alert - Your 3Q journals are due on Monday 3/23 at 2pm
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Monday March 9
For the first 20 minutes of class I took final questions regarding material for today's unit test. Those who did not have questions used their notes. For the last hour of class, students completed the Unit 3 test. When finished I asked students to watch the following video that provides an overview of the "unit circle". The unit circle and periodic (circular) functions are the crux of unit 4, this is a very good introduction on the IDEA of how the unit circle is constructed and the relationship between sine and cosine to coordinates on the unit circle.
For the first 20 minutes of class I took final questions regarding material for today's unit test. Those who did not have questions used their notes. For the last hour of class, students completed the Unit 3 test. When finished I asked students to watch the following video that provides an overview of the "unit circle". The unit circle and periodic (circular) functions are the crux of unit 4, this is a very good introduction on the IDEA of how the unit circle is constructed and the relationship between sine and cosine to coordinates on the unit circle.
- CLICK HERE for a video that provides an overview of the unit circle
Thursday March 5
At the start of class, we played a Kahoot related to special right triangles as a review for the upcoming unit test. After the Kahoot, students worked on:
* Homework - There is no specific HW due on Monday however...
* Unit Test Alert - Your Unit 3 test will be on Monday March 9.
At the start of class, we played a Kahoot related to special right triangles as a review for the upcoming unit test. After the Kahoot, students worked on:
- The review guide (answers below this post)
- The bearing supplement to the review guide (answers also below this post)
- Corrections from the 3.11 - 3.14 quiz (I updated grades in real time)
* Homework - There is no specific HW due on Monday however...
* Unit Test Alert - Your Unit 3 test will be on Monday March 9.
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Tuesday March 3
For the first 30 minutes or so of class, students completed a warm up related to lessons 3.11 - 3.14. I answered questions about the warm up and about lessons 3.11 - 3.14. Then, everyone completed a quiz on lessons 3.11 - 3.14. After the quiz, students exchanged papers for the unit 3 Review Guide and worked on the guide for the remainder of the period. The Unit Test is on Monday 3/9. Thursday will be a review day and will include a warm up on bearings, possibly a short Kahoot and the class working to complete the guide. Please communicate with me/come to flex if there is anything I can do to help your preparation.
* Homework - There is no specific HW due on Thursday however...
* Unit Test Alert - Your Unit 3 test will be on Monday March 9. It is up to you to manage your time to prepare, see above for how we will be spending class time on Thursday.
For the first 30 minutes or so of class, students completed a warm up related to lessons 3.11 - 3.14. I answered questions about the warm up and about lessons 3.11 - 3.14. Then, everyone completed a quiz on lessons 3.11 - 3.14. After the quiz, students exchanged papers for the unit 3 Review Guide and worked on the guide for the remainder of the period. The Unit Test is on Monday 3/9. Thursday will be a review day and will include a warm up on bearings, possibly a short Kahoot and the class working to complete the guide. Please communicate with me/come to flex if there is anything I can do to help your preparation.
* Homework - There is no specific HW due on Thursday however...
* Unit Test Alert - Your Unit 3 test will be on Monday March 9. It is up to you to manage your time to prepare, see above for how we will be spending class time on Thursday.
unit 3 review |
Friday February 28
At the start of class, I collected everyone's Unit 3 Project. On the way in, students received lessons 3.13 and 3.14. To start the day, completed a warm up related to lessons 3.11 and 3.12. I resolved any questions pertaining to lessons 3.11 and 3.12 and then we started 3.13 and 3.14. Lesson 3.13 shows us another way of writing vectors using a notation called a "linear combination". This is fairly straight forward.
* Homework - Complete lessons 3.13 and 3.14. 3.14 will be checked for a HW grade. Check answers and prepare questions (better yet, email me!) because...
* Quiz Alert - On Tuesday 3/3, there will be a quiz on lessons 3.11 - 3.14 (you will have a mini warm up quiz first)
* Unit Test Alert - Lesson 3.14 is the last lesson in Unit 3. Your Unit 3 test will be on Monday March 9. You will receive a review guide after your quiz on Tuesday. We will review on Thursday 3/5. On Thursday you will also receive your quizzes back and be allowed to make corrections if necessary.
At the start of class, I collected everyone's Unit 3 Project. On the way in, students received lessons 3.13 and 3.14. To start the day, completed a warm up related to lessons 3.11 and 3.12. I resolved any questions pertaining to lessons 3.11 and 3.12 and then we started 3.13 and 3.14. Lesson 3.13 shows us another way of writing vectors using a notation called a "linear combination". This is fairly straight forward.
- CLICK HERE for a video that reviews how to write a vector as a linear combination.
- Directions angles always open counter clockwise from "east direction". Think 3:15 on a clock is an angle of 0 degrees. 3:00 is an angle of 90 degrees. 3:30 is 270 degrees. One full revolution is an angle of 360 degrees.
- The quadrant of the direction angle and the +/- signs of the vector are related.
- Given a vector, the direction angle can be determined by using SOH CAH TOA. CLICK HERE for a video that demonstrates this
- Given a direction angle and magnitude, the vector can be determined by using SOH CAH TOA. CLICK HERE for a video that demonstrates this.
* Homework - Complete lessons 3.13 and 3.14. 3.14 will be checked for a HW grade. Check answers and prepare questions (better yet, email me!) because...
* Quiz Alert - On Tuesday 3/3, there will be a quiz on lessons 3.11 - 3.14 (you will have a mini warm up quiz first)
* Unit Test Alert - Lesson 3.14 is the last lesson in Unit 3. Your Unit 3 test will be on Monday March 9. You will receive a review guide after your quiz on Tuesday. We will review on Thursday 3/5. On Thursday you will also receive your quizzes back and be allowed to make corrections if necessary.
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Wednesday February 26
I started class by collecting quiz corrections. On the way in to class, everyone received lessons 3.11 and 3.12. Because these lessons are both fairly short, I reviewed both topics before students started practicing. For the first 7 minutes or so we watched a short video about the greatest mathematical super villain of all time and then we reviewed the basics of vectors... what they are, how to write them, how to determine magnitude and direction. I modeled an example and then I turned to lesson 3.12. This lesson is about performing operations with vectors (multiplication, addition and subtraction). Lastly I modeled the "unit vector" problems on the last page of 3.12.
* Homework - Complete Lessons 3.11 and 3.12, check answers, come in on Friday with questions/issues
* Project Alert - The Bearings project is due at the start of class on Friday 2/28
I started class by collecting quiz corrections. On the way in to class, everyone received lessons 3.11 and 3.12. Because these lessons are both fairly short, I reviewed both topics before students started practicing. For the first 7 minutes or so we watched a short video about the greatest mathematical super villain of all time and then we reviewed the basics of vectors... what they are, how to write them, how to determine magnitude and direction. I modeled an example and then I turned to lesson 3.12. This lesson is about performing operations with vectors (multiplication, addition and subtraction). Lastly I modeled the "unit vector" problems on the last page of 3.12.
- CLICK HERE for a video that shows how to perform operations with vectors.
- CLICK HERE for a video that demonstrates what a unit vector is and that models a problem similar to those in the lesson.
* Homework - Complete Lessons 3.11 and 3.12, check answers, come in on Friday with questions/issues
* Project Alert - The Bearings project is due at the start of class on Friday 2/28
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Monday February 24
On the way in, students received a supplement related to lesson 3.10 - Bearings. I had students do problem #2 and Problem #7 as a warm up that I reviewed/checked with each student individually. After completing the warm up, students were directed to check their answers to lesson 3.10 and note questions/problems. When finished checking and while waiting for the others to finish the warm up, students were directed to complete the remainder of the supplement. With about 30 minutes left in the period, I allowed students to work on their 3Q projects for the remainder of the period. On Wednesday, we will complete lessons 3.11 and 3.12.
* Homework - Complete the 3.10 supplement, check answers, let me know if you have any questions
* Project Alert - The Bearings project is due at the start of class on Friday 2/28
On the way in, students received a supplement related to lesson 3.10 - Bearings. I had students do problem #2 and Problem #7 as a warm up that I reviewed/checked with each student individually. After completing the warm up, students were directed to check their answers to lesson 3.10 and note questions/problems. When finished checking and while waiting for the others to finish the warm up, students were directed to complete the remainder of the supplement. With about 30 minutes left in the period, I allowed students to work on their 3Q projects for the remainder of the period. On Wednesday, we will complete lessons 3.11 and 3.12.
* Homework - Complete the 3.10 supplement, check answers, let me know if you have any questions
* Project Alert - The Bearings project is due at the start of class on Friday 2/28
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Thursday February 20
For the first 30 minutes or so of class, I demonstrated what bearing angles are and how diagram a navigation problem that uses bearing angles. Remember, the most important thing to remember is that a bearing angles originate from the NORTH SOUTH line. I demonstrated the example on the front page as well as the 4 problems on the first practice page. Students then worked with their partners/groups to solve the treasure map problem and complete the practice from the lesson. Please note, you can skip any problem that has an angle measure of more than 90 degrees. These problems are:
* Homework - Complete lesson 3.10 all problems except the ones listed above, email me questions
* Project Alert - The Bearings project is due at the start of class on Friday 2/28
For the first 30 minutes or so of class, I demonstrated what bearing angles are and how diagram a navigation problem that uses bearing angles. Remember, the most important thing to remember is that a bearing angles originate from the NORTH SOUTH line. I demonstrated the example on the front page as well as the 4 problems on the first practice page. Students then worked with their partners/groups to solve the treasure map problem and complete the practice from the lesson. Please note, you can skip any problem that has an angle measure of more than 90 degrees. These problems are:
- Page 2 - Skip 2 and 3 (we did #1 in class together)
- Page 3 - Skip problem 1 and 2 (we did the treasure map problem together, answer is posted below)
- Page 4 - Skip problem 4 only, for problem 3, ignore the "minutes" given in the problem
- Page 5 - All problems are good
- Page 6 - Skip Problem #180
- With about 20 minutes left, I stopped the class and distributed the Unit 3 "Bearings project". There are two versions of this project and I know which students have version A vs. version B. Please only do the version you were assigned.
- People who were absent today: Gerina do Version A, Samantha do version B
* Homework - Complete lesson 3.10 all problems except the ones listed above, email me questions
* Project Alert - The Bearings project is due at the start of class on Friday 2/28
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Tuesday February 18
For the first 15-20 minutes of class, students reviewed their 3.7 - 3.9 notes and the practice quiz. I answered questions as needed. After this short review, everyone completed a quiz on lessons 3.7 - 3.9. After the quiz, students exchanged papers for lesson 3.10 - Bearings. Students were asked to read the notes on the first page (summary of notes below) and watch the videos posted below:
For the first 15-20 minutes of class, students reviewed their 3.7 - 3.9 notes and the practice quiz. I answered questions as needed. After this short review, everyone completed a quiz on lessons 3.7 - 3.9. After the quiz, students exchanged papers for lesson 3.10 - Bearings. Students were asked to read the notes on the first page (summary of notes below) and watch the videos posted below:
- COMPASS bearings are acute angles that are always drawn from the NORTH/SOUTH line of the compass. The bearing angle will always "touch" the north south line of the compass. When writing a compass bearing, the first letter always notes North and South and the last letter denotes east and west.
- TRUE bearings are always drawn from the north and the angle always follows a clockwise path. It is possible for a true bearing to be an angle measuring greater than 90, 180, 270 or even 360 degrees CLICK HERE for a video that explains the difference between compass bearings and true bearings. In this lesson, we will be working with COMPASS bearings.
- CLICK HERE for a video that demonstrates how to use bearings to solve a navigation problem.
- CLICK HERE for a different example
lesson 3.10 - Bearings |
Thursday February 13
On the way in, everyone received a warm up pertaining to lessons 3.8 and 3.9. I quickly checked/logged completion of lesson 3.8 for a HW grade. Students brought their warm ups to me as they completed them (or questions if they were struggling) and I reviewed one by one checking work, giving tips when necessary. When finished with the warm up, students continued to complete lesson 3.9 and check answers vs. the key below this post. When everyone finished the warm up, I answered answered any questions about lesson 3.9. Students who finished 3.9 received a "practice quiz" in preparation for the actual quiz during the next class. Before the period ended, everyone received the practice quiz. The practice quiz is your HW for our next meeting. You will have 20-25 minutes of practice time at the start of the next class prior to the quiz, it is up to you to complete the practice quiz on your own time, come prepared with questions (or better yet, email me.
* Homework - Complete 3.7 - 3.9 practice quiz (you MUST communicate with me if you are struggling)
* Quiz Alert - There will be a quiz on Tuesday 2/18 on lessons 3.7 - 3.9 (I will provide you with the Law of Sines, Law of Cosines and Area formulas)
On the way in, everyone received a warm up pertaining to lessons 3.8 and 3.9. I quickly checked/logged completion of lesson 3.8 for a HW grade. Students brought their warm ups to me as they completed them (or questions if they were struggling) and I reviewed one by one checking work, giving tips when necessary. When finished with the warm up, students continued to complete lesson 3.9 and check answers vs. the key below this post. When everyone finished the warm up, I answered answered any questions about lesson 3.9. Students who finished 3.9 received a "practice quiz" in preparation for the actual quiz during the next class. Before the period ended, everyone received the practice quiz. The practice quiz is your HW for our next meeting. You will have 20-25 minutes of practice time at the start of the next class prior to the quiz, it is up to you to complete the practice quiz on your own time, come prepared with questions (or better yet, email me.
* Homework - Complete 3.7 - 3.9 practice quiz (you MUST communicate with me if you are struggling)
* Quiz Alert - There will be a quiz on Tuesday 2/18 on lessons 3.7 - 3.9 (I will provide you with the Law of Sines, Law of Cosines and Area formulas)
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Tuesday February 11
At the start of class I polled everyone regarding the following:
At the start of class I polled everyone regarding the following:
- How was your understanding/completion of lesson 3.7 practice
- How was your understanding/completion of lesson 3.8
- CLICK HERE for a video that demonstrates how to use the law of cosines in a SSS situation to solve for a missing angle
- CLICK HERE for a video that demonstrates how to use the law of cosines in a SAS situation to solve for the third side
- CLICK HERE for a video that further clarifies the various situations in which you would use the law of cosines vs. the law of sines
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Friday February 7 (Mr. Harris was out ill today)
Your HW assignment for today was to complete the first page of the Law of sines "practice" packet. I have provided the answers below. Please check and work together to resolve any issues. After resolving the first page, please complete the remainder of the practice (and again, check answers). Make note of any questions/issues for review at our next meeting (or you can email me questions). Once complete with the lesson 3.7 practice packet, the sub will have lesson 3.8 ready for you. Lesson 3.8 is all about using formulas to determine the area of an oblique triangle. There are two formulas. "Heron's Formula" is used to solve for area when SSS information is given. The other formula(s) are used when you have SAS information. NOTE, if the problem does NOT provide complete SAS information, use the law of sines to solve for missing measures until you DO have SAS information.
* Homework - Complete lessons 3.7 (practice) and lesson 3.8. Please email me any questions/issues you may be having.
Thank you for your hard work and professionalism during my absence.
Your HW assignment for today was to complete the first page of the Law of sines "practice" packet. I have provided the answers below. Please check and work together to resolve any issues. After resolving the first page, please complete the remainder of the practice (and again, check answers). Make note of any questions/issues for review at our next meeting (or you can email me questions). Once complete with the lesson 3.7 practice packet, the sub will have lesson 3.8 ready for you. Lesson 3.8 is all about using formulas to determine the area of an oblique triangle. There are two formulas. "Heron's Formula" is used to solve for area when SSS information is given. The other formula(s) are used when you have SAS information. NOTE, if the problem does NOT provide complete SAS information, use the law of sines to solve for missing measures until you DO have SAS information.
- CLICK HERE for a video that reviews BOTH formulas that determine the area of an oblique triangle. The video is about 6 minutes long
- As with any problem involving area, please make sure your answer is in square units
* Homework - Complete lessons 3.7 (practice) and lesson 3.8. Please email me any questions/issues you may be having.
Thank you for your hard work and professionalism during my absence.
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Wednesday February 5
To start class we reviewed the "your turn" problem from lesson 3.7 that I assigned for HW. After, I flashed one more problem similar to this one to ensure everyone was understanding. Then we reviewed the how to use the law of sines if we are given SSA information. When given SSA information it is possible that one, two or no triangles can be made with the given information. The following is the process that makes this determination:
CLICK HERE for a link to a "triangle calculator" that you can use for the purpose of checking answers as you work. This is NOT a substitute for showing your setups/calculations.
After reviewing the examples from the lesson, Students completed all "your turns" from the "notes" portion of lesson 3.7. I then distributed the "practice" from lesson 3.7 and assigned the first page as HW for our next meeting. A blank copy is below this post.
* Homework - Complete all problems from lesson 3.7 (notes) and completed first page from lesson 3.7 (practice)
To start class we reviewed the "your turn" problem from lesson 3.7 that I assigned for HW. After, I flashed one more problem similar to this one to ensure everyone was understanding. Then we reviewed the how to use the law of sines if we are given SSA information. When given SSA information it is possible that one, two or no triangles can be made with the given information. The following is the process that makes this determination:
- Assume that a triangle can be made. Use the Law of Sines to solve the triangle. If, you get an error on your calculator while solving for "c" then you know that no triangles exist with the given measures.
- Once you have successfully solved the triangle (establishing that at least one triangle does exist), assume that a second triangle can be made.
- Begin to diagram the second triangle by including all of the given information for the first triangle.
- Then, take the SUPPLEMENT of angle B (the first angle you solved for in the first triangle) and put it on your diagram
- Add the two angles that are on your diagram of the second triangle. If the sum of the angles is greater than or equal to 180 degrees, then a second triangle can not exist.
CLICK HERE for a link to a "triangle calculator" that you can use for the purpose of checking answers as you work. This is NOT a substitute for showing your setups/calculations.
After reviewing the examples from the lesson, Students completed all "your turns" from the "notes" portion of lesson 3.7. I then distributed the "practice" from lesson 3.7 and assigned the first page as HW for our next meeting. A blank copy is below this post.
* Homework - Complete all problems from lesson 3.7 (notes) and completed first page from lesson 3.7 (practice)
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Monday February 3
At the start of class I answered one or two questions about lessons 3.1 - 3.6 and then everyone completed a quiz. After the quiz, students exchanged papers for lesson 3.7. While waiting for others to finish, students watched the following video on the proof of the law of sines:
* Homework - Complete the first "your turn" problem from lesson 3.7
At the start of class I answered one or two questions about lessons 3.1 - 3.6 and then everyone completed a quiz. After the quiz, students exchanged papers for lesson 3.7. While waiting for others to finish, students watched the following video on the proof of the law of sines:
- CLICK HERE for a video that shows the derivation/proof of the law of sines
- The law of sines is used to solve for missing angles/sides of an OBLIQUE (non-right) triangle
- The law of sines is only used if you are given AAS, ASA or SSA information in the problem
- If you are given AAS or ASA information, then we know only one triangle can be created with the information given.
- CLICK HERE for a video that provides a basic example of how to use the Law of sines to solve a right triangle similar to the first "your turn" problem from the lesson
* Homework - Complete the first "your turn" problem from lesson 3.7
lesson 3.7 - the law of sine (notes) |
Thursday January 30
At the start of class everyone received a warm up related to lesson 3.6 - Special right triangles. These diagrams were similar to those at the end of lesson 3.6 where two triangles are "connected" by a side. Some students struggled with the process of solving one side to the next but everyone improved after the warm up. There were several questions about lesson 3.6 that I was happy to answer. The vast majority of students in 2A did not complete the practice quiz so I allowed everyone time to complete and review answers. The answers to the practice quiz are attached here (I also sent them earlier today). Since everyone was still wrapping up the practice quiz with about 20 minutes left, I decided to postpone the actual quiz until Monday (as I mentioned, I was a bit disappointed but I was not mad). I reminded everyone that I had provided links to extra practice on Tuesday's blog post. You should complete this practice on your own (answers are provided) and email me with questions. The quiz will be Monday at the beginning of class.
* Homework - There is no HW that will be checked, however I strongly recommend that everyone review their lessons/notes/practice quiz and complete the extra practice that using the link I provided on Tuesday's blog. Email me with questions, I am happy to help you
* Quiz Alert - The quiz originally scheduled for today will take place on Monday no later than 7:30, we need to get into lesson 3.7.
At the start of class everyone received a warm up related to lesson 3.6 - Special right triangles. These diagrams were similar to those at the end of lesson 3.6 where two triangles are "connected" by a side. Some students struggled with the process of solving one side to the next but everyone improved after the warm up. There were several questions about lesson 3.6 that I was happy to answer. The vast majority of students in 2A did not complete the practice quiz so I allowed everyone time to complete and review answers. The answers to the practice quiz are attached here (I also sent them earlier today). Since everyone was still wrapping up the practice quiz with about 20 minutes left, I decided to postpone the actual quiz until Monday (as I mentioned, I was a bit disappointed but I was not mad). I reminded everyone that I had provided links to extra practice on Tuesday's blog post. You should complete this practice on your own (answers are provided) and email me with questions. The quiz will be Monday at the beginning of class.
* Homework - There is no HW that will be checked, however I strongly recommend that everyone review their lessons/notes/practice quiz and complete the extra practice that using the link I provided on Tuesday's blog. Email me with questions, I am happy to help you
* Quiz Alert - The quiz originally scheduled for today will take place on Monday no later than 7:30, we need to get into lesson 3.7.
3.1 - 3.6 practice quiz answers |
Tuesday January 28
On the way in, everyone received lesson 3.6. To start class everyone completed a warm up on the board related to the Khan Academy HW assignment. We briefly discussed the logistics of the assignment and their effectiveness in helping you remember how to work with radicals. I then asked if there were any lingering questions related to lesson 3.5 and resolved them as needed. We then turned to Lesson 3.6. This lesson is about "special right triangles"...the 45-45-90 and the 30-60-90. We completed a brief discovery activity which led us to understand the patterns associated with each and modeled several simple examples:
* Quiz Alert - There will be a quiz at the end of the block on Thursday on lessons 3.1 - 3.6. You need to KNOW SOH CAH TOA and the patterns associated with special right triangles.
On the way in, everyone received lesson 3.6. To start class everyone completed a warm up on the board related to the Khan Academy HW assignment. We briefly discussed the logistics of the assignment and their effectiveness in helping you remember how to work with radicals. I then asked if there were any lingering questions related to lesson 3.5 and resolved them as needed. We then turned to Lesson 3.6. This lesson is about "special right triangles"...the 45-45-90 and the 30-60-90. We completed a brief discovery activity which led us to understand the patterns associated with each and modeled several simple examples:
- CLICK HERE for a web lesson that demonstrates the properties of 45-45-90 and 30-60-90 right triangles
- CLICK HERE for a video that demonstrates how to use the properties of 45-45-90 right triangles
- CLICK HERE for a video that demonstrates how to use the properties of 30-60-90 right triangles
- CLICK HERE for a link to extra practice for lessons 3.2 - 3.5
- CLICK HERE for a link to extra practice for lesson 3.6
* Quiz Alert - There will be a quiz at the end of the block on Thursday on lessons 3.1 - 3.6. You need to KNOW SOH CAH TOA and the patterns associated with special right triangles.
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Friday January 24
To start class I quickly passed back (and then collected) the Unit 2 test. I also asked if there were any lingering questions from lesson 3.4. Prior to moving to lesson 3.5, I mentioned to everyone that gave the class three short Khan Academy assignments that are due for our next meeting (first HW grade of 3Q). These assignments are a prelude to lesson 3.6 and involve operating with and simplifying radicals (specifically square roots). Everyone should have received an email with this assignment, check your school email account. We then started 3.5. This lesson is about applications (real world problems) involving Trigonometry. We discussed that the key to success with these problems is being able to draw/label an accurate diagram prior to solving whatever the problem is asking for. I reviewed the examples on the front page of the lesson and explained the difference between angles of elevation and depression.
* Homework - Complete lesson 3.5 if you did not do so in class. Complete Khan Academy Assignment. Watch all videos and complete all practice. I will be informed through Khan that you have completed the assignment. If there are any obstacles for completing this they must be communicated to me in advance of class on Tuesday.
To start class I quickly passed back (and then collected) the Unit 2 test. I also asked if there were any lingering questions from lesson 3.4. Prior to moving to lesson 3.5, I mentioned to everyone that gave the class three short Khan Academy assignments that are due for our next meeting (first HW grade of 3Q). These assignments are a prelude to lesson 3.6 and involve operating with and simplifying radicals (specifically square roots). Everyone should have received an email with this assignment, check your school email account. We then started 3.5. This lesson is about applications (real world problems) involving Trigonometry. We discussed that the key to success with these problems is being able to draw/label an accurate diagram prior to solving whatever the problem is asking for. I reviewed the examples on the front page of the lesson and explained the difference between angles of elevation and depression.
- CLICK HERE for a video that explains how to solve problems involving angles of elevation and depression.
* Homework - Complete lesson 3.5 if you did not do so in class. Complete Khan Academy Assignment. Watch all videos and complete all practice. I will be informed through Khan that you have completed the assignment. If there are any obstacles for completing this they must be communicated to me in advance of class on Tuesday.
lesson_3.5_-_answers.pdf |
Wednesday January 22
On the way in, students received Lessons 3.3 and 3.4. After a quick warm up to remember SOH CAH TOA from the last class, I asked if there were any questions pertaining to lessons 3.1 and 3.2 (there were a couple). Once we resolved these questions we turned to lesson 3.3. This lesson requires us to use the INVERSE trig function to solve for a missing ANGLE of a right triangle.
* Homework - Complete lessons 3.3 and 3.4, check answers (below this post) and come in on Friday with questions. Also, complete problems 1 & 2 from lesson 3.5, we will do the rest in class on Friday.
* Journal Update - I have replied to 100% of the journals in this class although there are a few of you who do not have grades because you owe me one more reply. If I do not receive your reply by 2pm tomorrow, you will be deducted as late.
*END OF SEMESTER REMINDER - The 2Q and Semester 1 end at 2pm on Friday 1/24. If you are missing any work, I will be forced to put a zero in the grade book for the assignment, it is up to you to know the status of your grade/missing work. I will not be hunting anyone down to make up work. Please communicate with me immediately if there is something you need to make up.
On the way in, students received Lessons 3.3 and 3.4. After a quick warm up to remember SOH CAH TOA from the last class, I asked if there were any questions pertaining to lessons 3.1 and 3.2 (there were a couple). Once we resolved these questions we turned to lesson 3.3. This lesson requires us to use the INVERSE trig function to solve for a missing ANGLE of a right triangle.
- CLICK HERE for a video that reviews using inverse trig functions for solving for an acute angle of a right triangle
- CLICK HERE for a video that reviews how to solve a right triangle for all missing sides/angles.
* Homework - Complete lessons 3.3 and 3.4, check answers (below this post) and come in on Friday with questions. Also, complete problems 1 & 2 from lesson 3.5, we will do the rest in class on Friday.
* Journal Update - I have replied to 100% of the journals in this class although there are a few of you who do not have grades because you owe me one more reply. If I do not receive your reply by 2pm tomorrow, you will be deducted as late.
*END OF SEMESTER REMINDER - The 2Q and Semester 1 end at 2pm on Friday 1/24. If you are missing any work, I will be forced to put a zero in the grade book for the assignment, it is up to you to know the status of your grade/missing work. I will not be hunting anyone down to make up work. Please communicate with me immediately if there is something you need to make up.
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Friday January 17
At the start of class I reminded everyone that if I did not receive your journal by 7:20am it is now late (not many of you). If you have not submitted your journal, your "lateness" deduction will depend on when I finally receive it. For the first 30 or so minutes of class, students completed the STAR test. Those who had completed STAR in another math class worked to complete lesson 3.1 (I helped/answered questions as needed). As students finished STAR, they jumped in and also worked to complete 3.1. Students who completed 3.1 and checked answers then grabbed lessons 3.2 AND 3.3. When everyone was finished with STAR, I spend a few minutes discussing lesson 3.1 and advised everyone to finish this lesson on their own because I wanted to start/focus on lesson 3.2, SOH CAH TOA. Lesson 3.2 begins our review of Right Triangle Trigonometry, specifically using SOH CAH TOA to determine the measure of missing sides of a right triangle. I modeled the example problems in class, emphasizing the importance of labelling the sides "opposite", "adjacent" and "Hypotenuse" prior to setting up and solving your trig equations.
* Homework - Complete lessons 3.1 AND lesson 3.2 for Wednesday, check answers vs. the keys below and make note of any questions (or my mistakes on key).
At the start of class I reminded everyone that if I did not receive your journal by 7:20am it is now late (not many of you). If you have not submitted your journal, your "lateness" deduction will depend on when I finally receive it. For the first 30 or so minutes of class, students completed the STAR test. Those who had completed STAR in another math class worked to complete lesson 3.1 (I helped/answered questions as needed). As students finished STAR, they jumped in and also worked to complete 3.1. Students who completed 3.1 and checked answers then grabbed lessons 3.2 AND 3.3. When everyone was finished with STAR, I spend a few minutes discussing lesson 3.1 and advised everyone to finish this lesson on their own because I wanted to start/focus on lesson 3.2, SOH CAH TOA. Lesson 3.2 begins our review of Right Triangle Trigonometry, specifically using SOH CAH TOA to determine the measure of missing sides of a right triangle. I modeled the example problems in class, emphasizing the importance of labelling the sides "opposite", "adjacent" and "Hypotenuse" prior to setting up and solving your trig equations.
- CLICK HERE for a video that provides an overview of SOH CAH TOA and how to create each ratio from a right triangle.
- CLICK HERE for a video that demonstrates how to determine the length of a missing side of a right triangle given one acute angle and one other side length (similar to the problems in the lesson).
* Homework - Complete lessons 3.1 AND lesson 3.2 for Wednesday, check answers vs. the keys below and make note of any questions (or my mistakes on key).
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Wednesday January 15
For the first 20-25 mins of class, I answered as many review questions as I could about Unit 2. After, students completed the Unit 2 test. After the test, students exchanged papers for lesson 3.1 (blank copy below this post). Students were instructed to read the notes, watch the videos below and attempt the first two example problems.
* Journal Alert - The 2Q journal is due at 7:20 am on Friday 1/17
For the first 20-25 mins of class, I answered as many review questions as I could about Unit 2. After, students completed the Unit 2 test. After the test, students exchanged papers for lesson 3.1 (blank copy below this post). Students were instructed to read the notes, watch the videos below and attempt the first two example problems.
- CLICK HERE for a video that demonstrates how to convert an angle given in decimal degrees to Degrees/minutes/seconds
- CLICK HERE for a video that demonstrates how to convert an angle given in degrees/minutes/seconds to decimal degrees
- CLICK HERE for a video that demonstrates how to add two angle measures both given in degrees/minutes/seconds
- CLICK HERE for a video that demonstrates how to subtract two angle measure both given in degrees/minutes/seconds
* Journal Alert - The 2Q journal is due at 7:20 am on Friday 1/17
lesson 3.1 - degrees minutes seconds |
Monday January 13
At the start of class, I collected quiz corrections. For the first 20 minutes of class, students worked to complete/check answers to the supplementary practice that was provided at the end of the previous class (I entered the corrections into the grade book). After, we played a Kahoot as a means of reviewing for Wednesday's unit test (this took about the last 50 minutes of the period). The Unit 2 test is on Wednesday.
* Unit Test Alert - The Unit 2 test will be on Wednesday 1/15. See Tuesday 1/7 blog for details.
* Journal Alert - The 2Q journal is due at 7:20 am on Friday 1/17
At the start of class, I collected quiz corrections. For the first 20 minutes of class, students worked to complete/check answers to the supplementary practice that was provided at the end of the previous class (I entered the corrections into the grade book). After, we played a Kahoot as a means of reviewing for Wednesday's unit test (this took about the last 50 minutes of the period). The Unit 2 test is on Wednesday.
* Unit Test Alert - The Unit 2 test will be on Wednesday 1/15. See Tuesday 1/7 blog for details.
* Journal Alert - The 2Q journal is due at 7:20 am on Friday 1/17
answers - supplementary log/exponential practice (equations & applications) |
Thursday January 9
On the way in, students received the Q2 Journal Assignment (due 7am on Friday 1/17). For the first 5 or so minutes of class, students read the journal assignment and I answered any questions. Then, everyone completed a two part warm up while I checked/logged HW completion (Your turn #3 from 2.10). The first warm up was a True/False style review some of the properties of Logs, and the second was specific to lesson 2.10 and the HW problem. After the warm up, students spent the balance of the period completing 2.10 and checking answers below this post. At the end of class I handed back the most recent quiz (corrections due on Monday) as well as some extra Log equations/applications practice (blank copy below this post). On Tuesday, we will Kahoot as Unit test review.
* Homework - There is no specific HW for Tuesday, however I strongly suggest that you start preparation/practice for...
* Unit Test Alert - The Unit 2 test will be on Wednesday 1/15. See Tuesday 1/7 blog for details.
* Journal Alert - The 2Q journal is due at 7:20 am on Friday 1/17
On the way in, students received the Q2 Journal Assignment (due 7am on Friday 1/17). For the first 5 or so minutes of class, students read the journal assignment and I answered any questions. Then, everyone completed a two part warm up while I checked/logged HW completion (Your turn #3 from 2.10). The first warm up was a True/False style review some of the properties of Logs, and the second was specific to lesson 2.10 and the HW problem. After the warm up, students spent the balance of the period completing 2.10 and checking answers below this post. At the end of class I handed back the most recent quiz (corrections due on Monday) as well as some extra Log equations/applications practice (blank copy below this post). On Tuesday, we will Kahoot as Unit test review.
* Homework - There is no specific HW for Tuesday, however I strongly suggest that you start preparation/practice for...
* Unit Test Alert - The Unit 2 test will be on Wednesday 1/15. See Tuesday 1/7 blog for details.
* Journal Alert - The 2Q journal is due at 7:20 am on Friday 1/17
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Tuesday January 7
On the way in, I collected any quiz corrections from the 2.1 - 2.5 quiz. Before class started I made an announcement about the date/expectations for your unit 2 test (see end of post for details). At the start of class everyone completed a short warm up related to lesson 2.8 and 2.9. After the warm up, we reviewed questions from the lesson practice as well as the 2.6 - 2.9 quiz review (answers to both were on previous blog entries). About 30 minutes into class students completed a quiz on lessons 2.6 - 2.9. Upon completion of the quiz, students exchanged papers for lesson 2.10. Lesson 2.10 is the last new lesson of Unit 2. Students watched the following video after completing the quiz:
* Homework - watch the video above and attempt (at minimum) the "your turn #3" from the lesson as well as problems #2 and #3 on the bottom of page 5 of the lesson. We will complete the remainder of the lesson in class on Thursday.
* Unit Test Alert - Your Unit test will be on Wednesday 1/15. There will be no formal review guide. All problems on this test (with the exception of the problem relating to 2.10) are problems that you have done before that have been part of your lessons, quiz reviews, warm ups or the quizzes themselves. For the Unit test you will need to be able to:
On the way in, I collected any quiz corrections from the 2.1 - 2.5 quiz. Before class started I made an announcement about the date/expectations for your unit 2 test (see end of post for details). At the start of class everyone completed a short warm up related to lesson 2.8 and 2.9. After the warm up, we reviewed questions from the lesson practice as well as the 2.6 - 2.9 quiz review (answers to both were on previous blog entries). About 30 minutes into class students completed a quiz on lessons 2.6 - 2.9. Upon completion of the quiz, students exchanged papers for lesson 2.10. Lesson 2.10 is the last new lesson of Unit 2. Students watched the following video after completing the quiz:
- CLICK HERE for a video that demonstrates how to use logarithms to solve a compound interest problem in which we are trying to determine the amount of time (in years) it takes an investment to grow to a specific dollar figure.
* Homework - watch the video above and attempt (at minimum) the "your turn #3" from the lesson as well as problems #2 and #3 on the bottom of page 5 of the lesson. We will complete the remainder of the lesson in class on Thursday.
* Unit Test Alert - Your Unit test will be on Wednesday 1/15. There will be no formal review guide. All problems on this test (with the exception of the problem relating to 2.10) are problems that you have done before that have been part of your lessons, quiz reviews, warm ups or the quizzes themselves. For the Unit test you will need to be able to:
- Determine the domain and range of a logarithmic OR exponential function (one problem)
- Write the equation of the asymptote of a transformed logarithmic OR exponential function (one problem)
- Determine the correct graph of transformed logarithmic OR exponential function given its equation (one problem, multiple choice)
- Expand and condense Logarithmic expressions (one problem each for expanding/condensing)
- Solve exponential equations (one problem with and one problem without using logs)
- Solve logarithmic equations (one problem using one to one property, one using the change of base formula, one that requires expanding/condensing as a first step)
- Solve a compounding interest problem (I will give you formulas)
- Solve a problem similar to those from 2.10 (I will give you formula)
lesson 2.10 - logarithmic applications |
Friday January 3
At the start of class everyone completed a short warm up related to lesson 2.8 (solving exponential equations). After the warm up, we resolved reviewed any questions and resolved any issues related to lesson 2.8. On the way into class everyone received lesson 2.9. In this lesson we are solving logarithmic equations. Strategically, the process of solving is similar to exponentials.
* Homework - Complete lesson 2.9, check answers and communicate questions to me. I strongly suggest completing the quiz review because....
* Quiz Alert - There will be quiz on Tuesday 1/7 on lessons 2.6 - 2.9. You will have about 30 minutes prior to the quiz to interact with the review guide and ask questions.
* Unit Test Alert - Lesson 2.10 (which you will receive after the quiz) is the last new lesson of Unit 2. You will not be quizzed on this lesson only but there will be an application problem on the unit test The Unit test will be on Wednesday 1/15, you will receive a study guide after your quiz.
At the start of class everyone completed a short warm up related to lesson 2.8 (solving exponential equations). After the warm up, we resolved reviewed any questions and resolved any issues related to lesson 2.8. On the way into class everyone received lesson 2.9. In this lesson we are solving logarithmic equations. Strategically, the process of solving is similar to exponentials.
- The goal for solving exponentials was to isolate the exponential term
- The goal for logs is to isolate the logarithmic term.
- CLICK HERE for a video that models several problems solving logarithmic equations including those with extraneous solutions
* Homework - Complete lesson 2.9, check answers and communicate questions to me. I strongly suggest completing the quiz review because....
* Quiz Alert - There will be quiz on Tuesday 1/7 on lessons 2.6 - 2.9. You will have about 30 minutes prior to the quiz to interact with the review guide and ask questions.
* Unit Test Alert - Lesson 2.10 (which you will receive after the quiz) is the last new lesson of Unit 2. You will not be quizzed on this lesson only but there will be an application problem on the unit test The Unit test will be on Wednesday 1/15, you will receive a study guide after your quiz.
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Friday December 20
At the start of class everyone completed a short warm up related to lesson 2.7 (expanding/condensing logarithmic expressions). After the warm up I flashed answers to the HW and students completed the right hand column. After resolving any issues/questions pertaining to lesson 2.7, we turned to lesson 2.8 (everyone received on way in). Lesson 2.8 is about solving exponential equations. Part 1 of the lesson used the "one to one" property of exponentials to create a "like base" for all terms. Then we use the "one to one" rule to set the exponents into their own equation to solve for x. (remember, if the bases are multiplying each other, the exponents are added to each other. CLICK HERE for a video to help you solve basic exponential equations that do not require logs. Part 2 of the lesson uses logarithms to solve exponentials (remember, logs and exponents are inverse processes of each other just like multiplication and division are). We reviewed the examples on page 3 of the lesson for solving exponentials that require the use of logarithms. Here are some strategies that we discussed:
* Homework - Complete lesson 2.8
HAVE A HAPPY AND SAFE HOLIDAY! IT IS A PRIVILEGE TO BE YOUR TEACHER, YOU ARE WONDERFUL KIDS AND I COULD NOT BE PROUDER OF YOU!!
At the start of class everyone completed a short warm up related to lesson 2.7 (expanding/condensing logarithmic expressions). After the warm up I flashed answers to the HW and students completed the right hand column. After resolving any issues/questions pertaining to lesson 2.7, we turned to lesson 2.8 (everyone received on way in). Lesson 2.8 is about solving exponential equations. Part 1 of the lesson used the "one to one" property of exponentials to create a "like base" for all terms. Then we use the "one to one" rule to set the exponents into their own equation to solve for x. (remember, if the bases are multiplying each other, the exponents are added to each other. CLICK HERE for a video to help you solve basic exponential equations that do not require logs. Part 2 of the lesson uses logarithms to solve exponentials (remember, logs and exponents are inverse processes of each other just like multiplication and division are). We reviewed the examples on page 3 of the lesson for solving exponentials that require the use of logarithms. Here are some strategies that we discussed:
- If you ever have the number "e" as the base of your exponential term, you will ulitimately need to use a natural log to solve the problem
- The first step(s) in solving is to isolate the exponential term FOLLOWED BY using logs to solve for x
- CLICK HERE for a video that model several problems similar to those on the Practice 2 set.
* Homework - Complete lesson 2.8
HAVE A HAPPY AND SAFE HOLIDAY! IT IS A PRIVILEGE TO BE YOUR TEACHER, YOU ARE WONDERFUL KIDS AND I COULD NOT BE PROUDER OF YOU!!
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Wednesday December 18 (2 hour delay)
At the start of class, students completed a quiz on lessons 2.1 - 2.5. After the quiz, students received lesson 2.6 (The change of base formula) and lesson 2.7 (properties of Logarithmic Operations). Lesson 2.6 is about how the change of base formula allows us to calculate a specific number value for a logarithm of any base.
* Homework - Complete lesson 2.6 if you did not do so in class (and check answers) AND complete the left hand column of practice on pages 3 and 4 from lesson 2.7
At the start of class, students completed a quiz on lessons 2.1 - 2.5. After the quiz, students received lesson 2.6 (The change of base formula) and lesson 2.7 (properties of Logarithmic Operations). Lesson 2.6 is about how the change of base formula allows us to calculate a specific number value for a logarithm of any base.
- CLICK HERE for a video on what the change of base formula is and how it is used to solve a problem similar to those in this lesson.
- NOTE, many students with graphing calculators were able to learn how to use the calculator to evaluate logs that are not base 10, if your calculator has a function that does this, that is fine. If it does not, then you need to know the change of base formula
- The POWER property for exponents means that when multiplying similar bases, we add the exponents. For logs, when the log has multiplication going on, we expand by adding the logs of each item being multiplied
- The QUOTIENT property for exponents means that when dividing similar bases, we subtract the exponents. For logs, when the log has division going on, we expand by subtracting the logs of each item being divided (the numerator always goes on the left
- The POWER property for exponents means that when we raise a base to a power and then again to another power, we multiply the exponents. For logs, when the log is being raised to a power, we expand by multiplying the log by the exponent
- CLICK HERE for a video that models expanding/condensing problems that use these properties similar to those we are practicing in this lesson
* Homework - Complete lesson 2.6 if you did not do so in class (and check answers) AND complete the left hand column of practice on pages 3 and 4 from lesson 2.7
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Monday December 16
On the way in, students received lesson warm up related to lessons 2.3 and 2.4 as well as a fresh copy of lesson 2.5. Students completed the warm up and I checked answers/helped students as needed. After the warm up, we turned to lesson 2.5. This lesson is VERY short like lesson 2.3 was. The topic is the "natural log". Here is what you need to know about the natural log
Students worked to complete lesson 2.5. When finished, they received a "practice quiz" for lessons 2.1 - 2.5. At the start of class on Wednesday, there will be a quiz on lessons 2.1 - 2.5.
* Homework - There is no specific HW for Wednesday however...
* Quiz Alert - There will be a quiz on lessons 2.1 - 2.5 on Wednesday. See blog from 12/12 for details/expectations.
On the way in, students received lesson warm up related to lessons 2.3 and 2.4 as well as a fresh copy of lesson 2.5. Students completed the warm up and I checked answers/helped students as needed. After the warm up, we turned to lesson 2.5. This lesson is VERY short like lesson 2.3 was. The topic is the "natural log". Here is what you need to know about the natural log
- It is simply a log with a base of "e" (just like any other log will have a base)
- It is used to "undo" the exponential function e^x
- All of the properties of the natural log are identical to the properties of any other log with any base from lesson 2.4.
Students worked to complete lesson 2.5. When finished, they received a "practice quiz" for lessons 2.1 - 2.5. At the start of class on Wednesday, there will be a quiz on lessons 2.1 - 2.5.
* Homework - There is no specific HW for Wednesday however...
* Quiz Alert - There will be a quiz on lessons 2.1 - 2.5 on Wednesday. See blog from 12/12 for details/expectations.
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Thursday December 12
On the way in, students received lesson 2.3 and a warm up related to lesson 2.2. After reviewing the warm up, questions from lesson 2.2 and a loose end or two from lesson 2.1, we started lesson 2.3. This is a very SHORT lesson that reviews what logarithmic functions are and their relationship to exponential functions (they are inverses of each other). We defined inverses as "flipping upside down" (inverting) rather than "opposites". Logarithms and Exponentials are inverse"processes" just as addition and subtraction are. We reviewed how to convert a function in exponential form to logarithmic form and vice versa.
* Quiz Alert - There will be a quiz on Wednesday 12/18 on lessons 2.1 - 2.5 (we will complete lesson 2.5 on Monday). Here is what you will need to know/be able to do:
On the way in, students received lesson 2.3 and a warm up related to lesson 2.2. After reviewing the warm up, questions from lesson 2.2 and a loose end or two from lesson 2.1, we started lesson 2.3. This is a very SHORT lesson that reviews what logarithmic functions are and their relationship to exponential functions (they are inverses of each other). We defined inverses as "flipping upside down" (inverting) rather than "opposites". Logarithms and Exponentials are inverse"processes" just as addition and subtraction are. We reviewed how to convert a function in exponential form to logarithmic form and vice versa.
- CLICK HERE for video that reviews how to convert from exponential form to logarithmic form
- CLICK HERE for video that reviews how to convert from logarithmic form to exponential form
- All parent Logarithmic functions have a VERTICAL asymptote at x = 0
- All parent Logarithmic functions have an x intercept of (1, 0)
- The domain of all parent log function is x > 0
- The Range of all parent log function is all real numbers (all the time)
- CLICK HERE for a video on the inverse relationship between the graph of logs and the graph of exponentials
- CLICK HERE for a video on the transformations of log function graphs
- CLICK HERE for a video on the basic properties of logarithms and how they are used to simplify/solve basic logarithmic equations/expressions
* Quiz Alert - There will be a quiz on Wednesday 12/18 on lessons 2.1 - 2.5 (we will complete lesson 2.5 on Monday). Here is what you will need to know/be able to do:
- Convert expressions from logarithmic form to exponential and vice versa (lesson 2.3)
- Determine the asymptotes and domain/range given a logarithmic/exponential equation (Lessons 2.1 and 2.4)
- Write the equation of a logarithmic/exponential function given its transformations (Lessons 2.1 and 2.4)
- Identify the transformations present given the equation of a logarithmic/exponential function (lessons 2.1 and 2.4)
- Calculate compounding interest and continually compounding interest (I will provide the formulas) (lesson 2.2)
- Use the basic properties of logs/natural logs (lesson 2.5)
lesson 2.3 - answers |
Tuesday December 10
At the start of class everyone completed a warm up related to lesson 2.1. After the warm up, we continued with lesson 2.2 from our last meeting (we only completed page 1 on Friday). We did a discovery activity on the second page of the lesson designed to show what happens as you increase the frequency of which you compound interest. Given a base investment of one dollar, as we increased the compounding frequency, the value of the investment approaches the number 2.71828...... This is the number "e". This number is analogous to what Pi is in geometry. An irrational number that exists in math that is prevalent in many exponential equations. Using "e" we can determine the value of investments that are compounding CONTINUOUSLY all the time by using the continuously compounding interest formula on the bottom of page 2 of the lesson.
CLICK HERE for video that outlines what the number "e" is and its properties
CLICK HERE for a video that demonstrates a continuously compounding interest problem
Students spent the last 10-15 minutes completing all problems from the lesson, I directed everyone to skip problems 61-64
* Homework - Complete lesson 2.2, skip problems 61-64. Check answers vs. the key below and come in Thursday prepared with questions. (or mistakes on my key)
At the start of class everyone completed a warm up related to lesson 2.1. After the warm up, we continued with lesson 2.2 from our last meeting (we only completed page 1 on Friday). We did a discovery activity on the second page of the lesson designed to show what happens as you increase the frequency of which you compound interest. Given a base investment of one dollar, as we increased the compounding frequency, the value of the investment approaches the number 2.71828...... This is the number "e". This number is analogous to what Pi is in geometry. An irrational number that exists in math that is prevalent in many exponential equations. Using "e" we can determine the value of investments that are compounding CONTINUOUSLY all the time by using the continuously compounding interest formula on the bottom of page 2 of the lesson.
CLICK HERE for video that outlines what the number "e" is and its properties
CLICK HERE for a video that demonstrates a continuously compounding interest problem
Students spent the last 10-15 minutes completing all problems from the lesson, I directed everyone to skip problems 61-64
* Homework - Complete lesson 2.2, skip problems 61-64. Check answers vs. the key below and come in Thursday prepared with questions. (or mistakes on my key)
lesson 2.2 answers |
Friday December 6
At the start of class, I quickly. reviewed everyone's video HW for a 2pt HW grade. We reviewed the answers to the video questions and used Desmos to explore the graph and basic attributes of exponential functions.. Here is what you need to know:
* Homework - There is no HW for Tuesday, enjoy your weekend.
At the start of class, I quickly. reviewed everyone's video HW for a 2pt HW grade. We reviewed the answers to the video questions and used Desmos to explore the graph and basic attributes of exponential functions.. Here is what you need to know:
- Exponential functions have a variable in the exponent
- The part of the expression that is being raised to a power is called the base
- The parent function for exponentials is a^x where a is a real number >1. There are an infinite number of parent functions for exponentials because there are an infinite numbers that can be plugged in for a
- The two distinct characteristics of all parent exponential functions graphs (regardless of the base) are
- They all have a y intercept of (0, 1) because if you raise any number to the zero power, it = 1
- They all have a horizontal asymptote at y = 0
- The domain of all exponential functions is All real numbers all the time
- The range of the function depends on where the horizontal asymptote is. For the parent function the range is all positive real numbers (numbers > but not including 0), however if the function is translated vertically or reflected over the x axis, the range will change
- Exponential function with positive slope are GROWTH functions, Exponential function with negative slope are DECAY functions
- Horizontal actions occur "inside" the function, using "opposite logic". In this case, "inside the function" means "within the exponent"
- Vertical actions occur "outside" the function using "normal logic"
- We reviewed the "order of transformations" on the bottom of page 2 from lesson 2.1 and did a short experiment to prove that the order of transformations matters.
- CLICK HERE for a video that demonstrates a simple compound interest problem using the formula on the first page of lesson 2.2.
* Homework - There is no HW for Tuesday, enjoy your weekend.
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Wednesday December 4
For the first 15 minutes or so of class, students reviewed in preparation for the unit test. Then, students completed the unit test. Afterwards, students exchanged papers for lesson 2.1 (video activity and lesson). After a short break, students were instructed to complete the video activity and attempt the problems in lesson 2.1. The video activity at minimum is HW for our next meeting.
For the first 15 minutes or so of class, students reviewed in preparation for the unit test. Then, students completed the unit test. Afterwards, students exchanged papers for lesson 2.1 (video activity and lesson). After a short break, students were instructed to complete the video activity and attempt the problems in lesson 2.1. The video activity at minimum is HW for our next meeting.
- CLICK HERE for a video that takes a very detailed look at the transformations of exponential function graphs. (use this video for the activity in lesson 2.1)
lesson 2.1 - basics of exponential functions |
Monday December 2 (school cancelled due to weather)
Today we were supposed to play family feud as preparation for Wednesday's unit test. The snow day will cancel (not postpone) this activity. Your unit test will still be on Wednesday 12/4. Your assignment for the snow day today is to:
* Homework - there is no specific HW for Wednesday however...
* Unit Test Alert - The unit 1B test will be on Wednesday 12/4
DID YOU KNOW - Mr Harris's first client in Advertising was Nabisco cookies. During a tour of the Nabisco factory in New Jersey, I ate Oreos that were hot out of the oven (and they were yummy)
Today we were supposed to play family feud as preparation for Wednesday's unit test. The snow day will cancel (not postpone) this activity. Your unit test will still be on Wednesday 12/4. Your assignment for the snow day today is to:
- Complete the review guide if you have not done so already
- Check answers on key posted last Tuesday. I have a few mistakes, please email me if you find one, you will get a lollipop as a reward
- Email me with questions, I will respond to all emails today
- If you have finished/checked the key, please review your notes/study what you need to in order to be prepared for Wednesday's Unit Test. If there is a particular topic for which you need extra practice, email me and I will send you.
* Homework - there is no specific HW for Wednesday however...
* Unit Test Alert - The unit 1B test will be on Wednesday 12/4
DID YOU KNOW - Mr Harris's first client in Advertising was Nabisco cookies. During a tour of the Nabisco factory in New Jersey, I ate Oreos that were hot out of the oven (and they were yummy)
Tuesday November 26
For the first third of the period, everyone completed a short quiz on lessons 1.24 - 1.27. I graded the quiz in real time which allowed students to make any necessary corrections also in real time. After the quiz everyone exchanged papers for the study guide for the Unit 1B test. Students spent the balance of the block working on the study guide. I helped/checked answers as needed. On Monday, we will complete review and play a Kahoot.
* Homework - There is no specific HW for Monday however...
* Unit Test Alert - The unit 1B test will be on Wednesday 12/4. It is strongly recommended that you complete part/all of the review guide over the break. The unit test will cover lessons 1.12 - 1.27. Please see Wednesday 11/20 blog for details on expectations for the unit test.
For the first third of the period, everyone completed a short quiz on lessons 1.24 - 1.27. I graded the quiz in real time which allowed students to make any necessary corrections also in real time. After the quiz everyone exchanged papers for the study guide for the Unit 1B test. Students spent the balance of the block working on the study guide. I helped/checked answers as needed. On Monday, we will complete review and play a Kahoot.
* Homework - There is no specific HW for Monday however...
* Unit Test Alert - The unit 1B test will be on Wednesday 12/4. It is strongly recommended that you complete part/all of the review guide over the break. The unit test will cover lessons 1.12 - 1.27. Please see Wednesday 11/20 blog for details on expectations for the unit test.
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Friday November 22
On the way into class everyone received lesson 1.27. To start class everyone completed a 5 question warm up related to lesson 1.25. After the warm up, we reviewed HW answers and I resolved questions/issues as needed. We then turned to lesson 1.27. Here are key points for solving Absolute Value inequalities
* Homework - As long as you finished lesson 1.27 there is no specific HW however...
* Quiz Alert - There will be a very short quiz on lessons 1.24 - 1.27 on Tuesday 11/26. One problem from each lesson.
* Unit Test Alert - The unit 1B test will be on Wednesday 12/4. You will receive your review guide after the quiz on Tuesday. The unit test will cover lessons 1.12 - 1.27. Please see Wednesday's blog for details on expectations for the unit test.
On the way into class everyone received lesson 1.27. To start class everyone completed a 5 question warm up related to lesson 1.25. After the warm up, we reviewed HW answers and I resolved questions/issues as needed. We then turned to lesson 1.27. Here are key points for solving Absolute Value inequalities
- The process of solving is similar to equations in that you isolate the AV terms and solve by breaking up into two separate inequalities (one positive, one negative).
- In addition to the above, the negative inequality also has a flipped inequality sign
- A number line graph is part of the answer for these problems (requirement). The points found in the process above set the boundaries for the solution range
- When it is a LESS THAN inequality, the solution range is BETWEEN the two boundary points
- When it is a GREATER than inequality, the solution range is OUTSIDE the two boundary points
- The boundary points themselves may be part of the solution if the inequality has the equal sign
- After isolating the AV term:
- if the result is greater than a negative number (or zero), then the solution is all real numbers
- if the result is less than a negative number (or zero), then there is no solution
- CLICK HERE for a video on how to solve AV Inequality (LESS THAN).
- CLICK HERE for a video on how to solve an AV inequality (GREATER THAN).
* Homework - As long as you finished lesson 1.27 there is no specific HW however...
* Quiz Alert - There will be a very short quiz on lessons 1.24 - 1.27 on Tuesday 11/26. One problem from each lesson.
* Unit Test Alert - The unit 1B test will be on Wednesday 12/4. You will receive your review guide after the quiz on Tuesday. The unit test will cover lessons 1.12 - 1.27. Please see Wednesday's blog for details on expectations for the unit test.
lesson 1.27 - answers |
Wednesday November 20
Class began today with 3 warm up problems related to lesson 1.25. I checked/logged completion of HW (left hand column of 1.25) as students worked on the warm up. After the warm up I assigned the right hand column for 1.25, students worked to complete these problems and check their answers vs. the key below this post. With about 30-35 minutes left in the period, I distributed lesson 1.26. We reviewed the process of how to solve absolute value equations:
* Homework - Complete lesson 1.26, check answers, note/email me questions
* Quiz Alert - There will be a very short quiz on lessons 1.24 - 1.27 on Tuesday 11/26. One problem from each lesson.
* Unit Test Alert - The unit 1B test will be on Wednesday 12/4. You will receive your review guide after the quiz on Tuesday. The unit test will cover lessons 1.12 - 1.27. Here is an overview:
1 question Lesson 1.16
Class began today with 3 warm up problems related to lesson 1.25. I checked/logged completion of HW (left hand column of 1.25) as students worked on the warm up. After the warm up I assigned the right hand column for 1.25, students worked to complete these problems and check their answers vs. the key below this post. With about 30-35 minutes left in the period, I distributed lesson 1.26. We reviewed the process of how to solve absolute value equations:
- Remember, that Absolute value is always positive. The absolute value of both positive and negative numbers results in a positive absolute value.
- Because of this, AV equations will almost always have TWO solutions (think of the "V" nature of the AV graph, there are two y coordinates)
- The first step to solving an AV equation is to isolate the AV term by "undoing" all other numbers outside the AV term. Use standard math operations to isolate the AV Term
- Once the AV term is isolated, you are going to create and then solve TWO equations. For the first equation You will take the expression inside the AV term and solve it normally. For the second equation, you will take the same expression inside the AV term and set it equal to the "negative" of the expression. Please note, if the other expression is a binomial, you must change all signs to make it negative.
- Because AV must be positive, it is possible to get an extraneous solution when solving AV equations. To check/identify an extraneous solution, plug it into the ORIGINAL equation. If the isolated AV term equals a negative number, then your solution is extraneous.
- CLICK HERE for a video that shows how to solve an AV equation and check for extraneous solutions.
* Homework - Complete lesson 1.26, check answers, note/email me questions
* Quiz Alert - There will be a very short quiz on lessons 1.24 - 1.27 on Tuesday 11/26. One problem from each lesson.
* Unit Test Alert - The unit 1B test will be on Wednesday 12/4. You will receive your review guide after the quiz on Tuesday. The unit test will cover lessons 1.12 - 1.27. Here is an overview:
1 question Lesson 1.16
- Multiply/Divide complex numbers
- Solve a polynomial that has complex solutions
- Given a complex zero, determine all other zeros of a polynomial
- Given a rational function, identify, domain, VA's, HA's, SA's, Hole, x intercepts, y interceps
- Solve a rational equation and check for extraneous solutions
- Solve a polynomial inequality, answer in interval notation
- Solve a rational inequality, answer in interval notation
- Solve AV equation, check for extraneous solutions
- Solve AV inequality, graph solution on a number line
- See review guide for potential topics
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Monday November 18
To start class everyone completed a warm up related to lesson 1.24 (solving polynomial inequalities). Students completed the warm up while I checked/logged completion of the HW from lesson 1.24 (left hand column). For the next 30 minutes or so, students checked their HW answers and completed the right hand column (answers below this post). I answered questions/checked work as needed. We then turned to lesson 1.25 (everyone received lesson 1.25 on the way into class). This lesson is similar to lesson 1.24, however now we are working with RATIONAL inequalities. For these here is what is different from 1.24:
* Homework - Complete the left hand column of practice from lesson 1.25
* Quiz Alert - The next quiz will be after lesson 1.27, I am projecting Tuesday 11/26
* Unit Test Alert - The last new lesson of Unit 1B-C is lesson 1.27 so a unit test will happen fairly soon after. I am projecting Wednesday 12/4
To start class everyone completed a warm up related to lesson 1.24 (solving polynomial inequalities). Students completed the warm up while I checked/logged completion of the HW from lesson 1.24 (left hand column). For the next 30 minutes or so, students checked their HW answers and completed the right hand column (answers below this post). I answered questions/checked work as needed. We then turned to lesson 1.25 (everyone received lesson 1.25 on the way into class). This lesson is similar to lesson 1.24, however now we are working with RATIONAL inequalities. For these here is what is different from 1.24:
- Because we have a denominator, excluded values also help set the boundaries of our intervals in addition to the zeros from the numerator
- Because excluded values are undefined, they will ALWAYS be an open circle on the number line
- Do not attempt to graph these, always use the +/- method to determine the intervals on a number line
- All other parts of this process mirror lesson 1.24, including how we quantify our answer using interval notation.
- CLICK HERE for a video that demonstrates how to solve a rational inequality.
* Homework - Complete the left hand column of practice from lesson 1.25
* Quiz Alert - The next quiz will be after lesson 1.27, I am projecting Tuesday 11/26
* Unit Test Alert - The last new lesson of Unit 1B-C is lesson 1.27 so a unit test will happen fairly soon after. I am projecting Wednesday 12/4
lesson 1.25 - rational inequalities |
Thursday November 14
For the first 15 minutes of class I answered questions about practice set you all received at the end of the last class in preparation for today's quiz. Students then spent 30-35 minutes completing a quiz on lessons 1.20 - 1.23. After the quiz, students exchanged their papers for lesson 1.24. Lesson 1.24 was NOT covered in Algebra 2. While students were waiting for others to finish the quiz, I asked that everyone watch the following video: CLICK HERE for a video that demonstrates how to solve a polynomial inequality. After everyone completed the quiz, I demonstrated the process for solving a polynomial inequality. We started by looking at the difference in the nature of the solutions between an equation and an inequality
* Homework - Complete the left hand column of problems (both pages) from lesson 1.24 (will be checked for a HW grade
For the first 15 minutes of class I answered questions about practice set you all received at the end of the last class in preparation for today's quiz. Students then spent 30-35 minutes completing a quiz on lessons 1.20 - 1.23. After the quiz, students exchanged their papers for lesson 1.24. Lesson 1.24 was NOT covered in Algebra 2. While students were waiting for others to finish the quiz, I asked that everyone watch the following video: CLICK HERE for a video that demonstrates how to solve a polynomial inequality. After everyone completed the quiz, I demonstrated the process for solving a polynomial inequality. We started by looking at the difference in the nature of the solutions between an equation and an inequality
- Equations have solutions that are single points
- Inequalities have solutions that are an infinite number of points (within intervals on the x axis)
* Homework - Complete the left hand column of problems (both pages) from lesson 1.24 (will be checked for a HW grade
lesson 1.24 - solving polynomial inequalities |
Tuesday November 12
At the start of class, everyone completed a warm up related to lessons 1.20-1.23. On the way in, everyone received lesson 1.23. This lesson is review from algebra 2 of solving rational equations. The key to solving these equation is to set them = 0, then determine the common denominator. Once combined, the numerator leads us to the solution. IMPORTANT: if the solution is also an excluded value, then it is extraneous (toss it out). CLICK HERE for a video that demonstrates how to solve rational equations using common denominators (and how to check for extraneous solutions). I modeled the example from page 2 of the lesson that had an extraneous solution. as well as a few others from the lesson. Students worked for the last 40 minutes or so to complete the lesson. Everyone completed the lesson in class. There will be a quiz on Monday on lessons 1.20 - 1.23. After completing lesson 1.23, everyone received some "extra practice" in preparation for Thursday's quiz on lessons 1.20 - 1.23
* Homework - There is no specific HW for Thursday, however it is highly recommended that you complete the 1.20 - 1.23 practice you received at the end of class because....
* Quiz Alert - There will be a quiz on Thursday 11/14 on lessons 1.20 - 1.23
At the start of class, everyone completed a warm up related to lessons 1.20-1.23. On the way in, everyone received lesson 1.23. This lesson is review from algebra 2 of solving rational equations. The key to solving these equation is to set them = 0, then determine the common denominator. Once combined, the numerator leads us to the solution. IMPORTANT: if the solution is also an excluded value, then it is extraneous (toss it out). CLICK HERE for a video that demonstrates how to solve rational equations using common denominators (and how to check for extraneous solutions). I modeled the example from page 2 of the lesson that had an extraneous solution. as well as a few others from the lesson. Students worked for the last 40 minutes or so to complete the lesson. Everyone completed the lesson in class. There will be a quiz on Monday on lessons 1.20 - 1.23. After completing lesson 1.23, everyone received some "extra practice" in preparation for Thursday's quiz on lessons 1.20 - 1.23
* Homework - There is no specific HW for Thursday, however it is highly recommended that you complete the 1.20 - 1.23 practice you received at the end of class because....
* Quiz Alert - There will be a quiz on Thursday 11/14 on lessons 1.20 - 1.23
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Thursday November 8
To start class, everyone completed a warm up related to lessons 1.20 and 1.21. After the warm up and through the next 30 minutes, students worked to complete lesson 1.21. Answers are below this post, I helped students and answered questions as needed. With about 20 minutes left, everyone received lesson 1.22 (Slant Asymptotes). I reviewed the process of how to determine a slant asymptote: Slant asymptotes only exist for rational functions only when the degree of the numerator is EXACTLY 1 larger then the degree of the denominator. To determine the equation of a slant asymptote, divide the denominator into the numerator using long division. The answer (excluding the remainder) is the equation of the slant asymptote. CLICK HERE for a video that reviews how to find slant asymptotes. I modeled the example, the your turn and a few others from the lesson. The class worked for the balance of the period to complete lesson 1.22, I helped/checked as necessary. Your HW is to complete through lesson 1.22 for our next meeting
* Homework - Complete through lesson 1.22 for Tuesday.
* Quiz Alert - The next quiz will be after lesson 1.23 which we will cover Tuesday. Quiz will be on Thursday 11/14
To start class, everyone completed a warm up related to lessons 1.20 and 1.21. After the warm up and through the next 30 minutes, students worked to complete lesson 1.21. Answers are below this post, I helped students and answered questions as needed. With about 20 minutes left, everyone received lesson 1.22 (Slant Asymptotes). I reviewed the process of how to determine a slant asymptote: Slant asymptotes only exist for rational functions only when the degree of the numerator is EXACTLY 1 larger then the degree of the denominator. To determine the equation of a slant asymptote, divide the denominator into the numerator using long division. The answer (excluding the remainder) is the equation of the slant asymptote. CLICK HERE for a video that reviews how to find slant asymptotes. I modeled the example, the your turn and a few others from the lesson. The class worked for the balance of the period to complete lesson 1.22, I helped/checked as necessary. Your HW is to complete through lesson 1.22 for our next meeting
* Homework - Complete through lesson 1.22 for Tuesday.
* Quiz Alert - The next quiz will be after lesson 1.23 which we will cover Tuesday. Quiz will be on Thursday 11/14
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Monday November 4
At the start of class, everyone completed a quiz on lessons 1.17 - 1.19. After the quiz everyone received lessons 1.20 and 1.21. These two lessons are review of from Algebra two of Rational Functions and their attributes such as values that are excluded from the domain result in discontinuities (asymptotes, holes) in the functions graph. After a short break from the quiz, we reviewed how to use the denominator to determine each type of discontinuity including how to find the y coordinate of the hole (this was new to most students). We reviewed the three circumstances that defines the existence of horizontal asymptotes. Lastly we reviewed how we look to the numerator, to determine the function's zeros. Students worked to complete the left hand column of lesson 1.20 (answers below this post). We reviewed the Your turn examples from lesson 1.21 but time ran out before we could practice. I did not assign the lesson for HW, we will complete it in class on Monday. In the meantime, here are some videos that can help you remember these concepts from Algebra 2:
At the start of class, everyone completed a quiz on lessons 1.17 - 1.19. After the quiz everyone received lessons 1.20 and 1.21. These two lessons are review of from Algebra two of Rational Functions and their attributes such as values that are excluded from the domain result in discontinuities (asymptotes, holes) in the functions graph. After a short break from the quiz, we reviewed how to use the denominator to determine each type of discontinuity including how to find the y coordinate of the hole (this was new to most students). We reviewed the three circumstances that defines the existence of horizontal asymptotes. Lastly we reviewed how we look to the numerator, to determine the function's zeros. Students worked to complete the left hand column of lesson 1.20 (answers below this post). We reviewed the Your turn examples from lesson 1.21 but time ran out before we could practice. I did not assign the lesson for HW, we will complete it in class on Monday. In the meantime, here are some videos that can help you remember these concepts from Algebra 2:
- CLICK HERE for a video that reviews how to determine the domain of a rational function. Lesson 1.20 was exclusively about domain. Lesson 1.21 reviews all of the other attributes below
- CLICK HERE for a video that reviews how to determine the locations of Vertical Asymptotes and holes (see the 3:20 mark for how to determine the y coordinate of the hole)
- CLICK HERE for a video that reviews how to determine the existence (and location) of Horizontal Asymptotes
- CLICK HERE for a video that reviews how to determine the zeros (x intercepts)
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Thursday October 31
To start class everyone completed a warm up related to lesson 1.18. Students were given a partial list of zeros and were required to use the multiplication of linear factors to determine a polynomial. Students needed to remember that all complex zeros have a conjugate. After the warm up I distributed lesson 1.19. Lesson 1.19 is about finding all other zeros of a polynomial equation if we are given a complex zero. This process is also about remembering that complex zeros have a conjugate. Multiply the two conjugates together to get a quadratic and then use long division to divide the quadratic into the original polynomial. Factor the result of your long division (or use quadratic formula) to determine the remaining zeros. CLICK HERE for a video that demonstrates how to solve a polynomial equation given a complex zero. Students worked for the balance of the period to complete the lesson, just about everyone finished before the bell. Answers are below this post, students checked answers and I provides support/help as needed.
* Homework - As long as you have completed lesson 1.19 and checked your answers, there is no specific HW for Thursday, however...
* Quiz Alert - There will be a short quiz on Monday 11/4 on lessons 1.17 - 1.19. There will be one problem from each lesson (1.17, 1.18, 1.19).
* Journal Alert - Your 1Q journal is due on Friday November 1 at 2pm
To start class everyone completed a warm up related to lesson 1.18. Students were given a partial list of zeros and were required to use the multiplication of linear factors to determine a polynomial. Students needed to remember that all complex zeros have a conjugate. After the warm up I distributed lesson 1.19. Lesson 1.19 is about finding all other zeros of a polynomial equation if we are given a complex zero. This process is also about remembering that complex zeros have a conjugate. Multiply the two conjugates together to get a quadratic and then use long division to divide the quadratic into the original polynomial. Factor the result of your long division (or use quadratic formula) to determine the remaining zeros. CLICK HERE for a video that demonstrates how to solve a polynomial equation given a complex zero. Students worked for the balance of the period to complete the lesson, just about everyone finished before the bell. Answers are below this post, students checked answers and I provides support/help as needed.
* Homework - As long as you have completed lesson 1.19 and checked your answers, there is no specific HW for Thursday, however...
* Quiz Alert - There will be a short quiz on Monday 11/4 on lessons 1.17 - 1.19. There will be one problem from each lesson (1.17, 1.18, 1.19).
* Journal Alert - Your 1Q journal is due on Friday November 1 at 2pm
lesson 1.19 - answers |
Tuesday October 29
To start class everyone completed a warm up related to lesson 1.17, finding both real and complex zeros of a polynomial. When solving these problems, we use the techniques that we used in the previous series of lessons (breaking down the polynomial into linear factors by factoring or using synthetic division to test possible zeros). The only difference is that we may now have zeros that are complex. CLICK HERE for a video that demonstrates examples of how to solve for the complex zeros of a polynomial. Students worked prior to lunch and for the first 30 minutes after lunch to complete 1.17. With about 25 minutes left in the class I distributed and models examples from lesson 1.8.
Lesson 1.8 lesson is about working "backwards" to turn zeros that we are given into a polynomial equation. The process is similar to what we did in lesson 1.11, however now we are given complex zeros. The key is to always remember that complex (or irrational) zeros ALWAYS come in conjugate pairs. So, if they give us one complex zero, we automatically know that the conjugate is also a zero. CLICK HERE for a video that demonstrates how to write an equation of a polynomial given a complex zero. Students worked for the balance of the period to complete lesson 1.8, whatever was not finished in class is HW for Tuesday.
* Homework - Complete lessons 1.17 and 1.18 if you did not do so in class. Check answers and come in on Thursday prepared with any question you might have.
* Quiz Alert - There will be a short quiz after lesson 1.19, I am projecting it will be Monday 11/4
To start class everyone completed a warm up related to lesson 1.17, finding both real and complex zeros of a polynomial. When solving these problems, we use the techniques that we used in the previous series of lessons (breaking down the polynomial into linear factors by factoring or using synthetic division to test possible zeros). The only difference is that we may now have zeros that are complex. CLICK HERE for a video that demonstrates examples of how to solve for the complex zeros of a polynomial. Students worked prior to lunch and for the first 30 minutes after lunch to complete 1.17. With about 25 minutes left in the class I distributed and models examples from lesson 1.8.
Lesson 1.8 lesson is about working "backwards" to turn zeros that we are given into a polynomial equation. The process is similar to what we did in lesson 1.11, however now we are given complex zeros. The key is to always remember that complex (or irrational) zeros ALWAYS come in conjugate pairs. So, if they give us one complex zero, we automatically know that the conjugate is also a zero. CLICK HERE for a video that demonstrates how to write an equation of a polynomial given a complex zero. Students worked for the balance of the period to complete lesson 1.8, whatever was not finished in class is HW for Tuesday.
* Homework - Complete lessons 1.17 and 1.18 if you did not do so in class. Check answers and come in on Thursday prepared with any question you might have.
* Quiz Alert - There will be a short quiz after lesson 1.19, I am projecting it will be Monday 11/4
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Friday October 25
On the way in, everyone received a practice quiz related to lessons 1.12 - 1.16. Students worked on this while I checked/logged HW completion for lesson 1.16. I stopped the practice quiz to flash answers/resolve issues with lesson 1.16. Once questions were exhausted, students resumed the practice quiz. With 40 minutes left students completed a quiz on lessons 1.12 - 1.16. After the quiz, students exchanged their papers for lesson 1.17, The fundamental Theorem of Algebra (part 1). The Fundamental theorem of Algebra states that the degree of a polynomial will ALWAYS equal the sum of its real AND complex zeros. This includes repeated zeros with multiplicity greater than one. Lesson 1.17 requires us using the FTOA to solve for ALL zeros of a polynomial, zero or complex. NOTE, in many of these problems, complex zeros will be the result of using the quadratic formula where the discriminant will be negative.
* CLICK HERE for a video that outlines what the Fundamental Theorem of Algebra is
* CLICK HERE for a video that demonstrates how to use the FTOA to solve for real and complex zeros
In the packet, you will use quadratic formula and the other techniques for finding real/rational zeros to determine ALL zeros. I directed everyone to watch the videos above and complete problems 9-14 on page 2 of the lesson as HW for Friday.
* Homework - Watch the videos above and complete problems 9-14 on page 2 of lesson 1.17
* Journal Alert - Your 1Q journal is due on Friday November 1 at 2pm
On the way in, everyone received a practice quiz related to lessons 1.12 - 1.16. Students worked on this while I checked/logged HW completion for lesson 1.16. I stopped the practice quiz to flash answers/resolve issues with lesson 1.16. Once questions were exhausted, students resumed the practice quiz. With 40 minutes left students completed a quiz on lessons 1.12 - 1.16. After the quiz, students exchanged their papers for lesson 1.17, The fundamental Theorem of Algebra (part 1). The Fundamental theorem of Algebra states that the degree of a polynomial will ALWAYS equal the sum of its real AND complex zeros. This includes repeated zeros with multiplicity greater than one. Lesson 1.17 requires us using the FTOA to solve for ALL zeros of a polynomial, zero or complex. NOTE, in many of these problems, complex zeros will be the result of using the quadratic formula where the discriminant will be negative.
* CLICK HERE for a video that outlines what the Fundamental Theorem of Algebra is
* CLICK HERE for a video that demonstrates how to use the FTOA to solve for real and complex zeros
In the packet, you will use quadratic formula and the other techniques for finding real/rational zeros to determine ALL zeros. I directed everyone to watch the videos above and complete problems 9-14 on page 2 of the lesson as HW for Friday.
* Homework - Watch the videos above and complete problems 9-14 on page 2 of lesson 1.17
* Journal Alert - Your 1Q journal is due on Friday November 1 at 2pm
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Wednesday October 23
On the way in, everyone received the 1Q Journal Assignment. Since it is your first one, I reviewed the purpose of journaling as well as the details of this assignment. The key to getting a 100% is:
* Homework - Complete lesson 1.16 all problems (will be checked for a HW grade, please email me with questions)
* Quiz Alert - There will be a quiz on Friday 10/25 on lessons 1.12 - 1.16
* Journal Alert - Your 1Q Journal is due on Friday November 1 at 2pm
On the way in, everyone received the 1Q Journal Assignment. Since it is your first one, I reviewed the purpose of journaling as well as the details of this assignment. The key to getting a 100% is:
- Meeting the due date
- Being honest with me/yourself. Complete the assignment in the spirit it is intended
- Remember that the assignment isn't over until you get your grade. If I reply with a question about your reflection, you need to respond back in a timely manner. So check your email daily
- An imaginary number ("i") is a representation of the square root of -1. It is not a real number because it can not be drawn on a number line
- A complex number is a number that is composed of both real and imaginary parts. The standard form is a + bi where a and b are both real numbers. We reviewed that all real numbers are ALSO complex numbers because they can be written in the form a + 0i.
- CLICK HERE for a video that reviews adding/subtracting complex numbers
- CLICK HERE for a video that reviews multiplying complex numbers
- CLICK HERE for a video that reviews how to divide complex numbers using conjugates
* Homework - Complete lesson 1.16 all problems (will be checked for a HW grade, please email me with questions)
* Quiz Alert - There will be a quiz on Friday 10/25 on lessons 1.12 - 1.16
* Journal Alert - Your 1Q Journal is due on Friday November 1 at 2pm
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Monday October 21
At the start of class, everyone completed a warm up related to lessons 1.14 (using the remainder/factor theorem to find the zeros of a polynomial). After the warm up, we reviewed the answers to all of 1.14 and I answered questions/resolved issues as needed. I then distributed lesson 1.15, the Rational Zero Test. We reviewed the Rational Zero test which helps us determine the "possible" rational zeros for larger degree polynomials that have a lead coefficient > 1. After we list the possible rational zeros, we "test" the zeros (by using synthetic division) to determine if they are zeros (if there is no remainder, they are). If there is a remainder, we eliminate the value as a possible value and then we test the next one.
* Homework - There is no specific HW for Wednesday, however...
* Quiz Alert - There will be a quiz on Friday 10/25 on lessons 1.12 - 1.16
At the start of class, everyone completed a warm up related to lessons 1.14 (using the remainder/factor theorem to find the zeros of a polynomial). After the warm up, we reviewed the answers to all of 1.14 and I answered questions/resolved issues as needed. I then distributed lesson 1.15, the Rational Zero Test. We reviewed the Rational Zero test which helps us determine the "possible" rational zeros for larger degree polynomials that have a lead coefficient > 1. After we list the possible rational zeros, we "test" the zeros (by using synthetic division) to determine if they are zeros (if there is no remainder, they are). If there is a remainder, we eliminate the value as a possible value and then we test the next one.
- CLICK HERE for a video on how the Rational Zero test helps break down a large polynomial into factors that lead to determine zeros.
* Homework - There is no specific HW for Wednesday, however...
* Quiz Alert - There will be a quiz on Friday 10/25 on lessons 1.12 - 1.16
lesson_1.15_answers.pdf |
Thursday October 17
On the way in, everyone received lesson 1.14. At the start of class, everyone completed a warm up related to lessons 1.12 and 1.13 (polynomial long/synthetic division). I checked/logged HW completion while students worked on the warm up. Today's HW was for a 4 pt grade as opposed to 2 since you were to complete two lessons. After reviewing the warm up, students checked their HW answers vs. the answer keys below. I resolved issues/answered questions related to these lessons as needed. We then turned to lesson 1.14. we briefly reviewed the remainder and factor theorems:
* Homework - Complete lesson 1.14, check answers, prepare questions for our next meeting.
* Quiz Alert - The next quiz will be after lesson 1.16
On the way in, everyone received lesson 1.14. At the start of class, everyone completed a warm up related to lessons 1.12 and 1.13 (polynomial long/synthetic division). I checked/logged HW completion while students worked on the warm up. Today's HW was for a 4 pt grade as opposed to 2 since you were to complete two lessons. After reviewing the warm up, students checked their HW answers vs. the answer keys below. I resolved issues/answered questions related to these lessons as needed. We then turned to lesson 1.14. we briefly reviewed the remainder and factor theorems:
- The remainder theorem states that if you divide a polynomial by a number and there is a remainder (not zero), then the number you are dividing by and the value of the remainder represent a coordinate (x, y) on the graph of the polynomial.
- CLICK HERE for a video that reviews the remainder theorem and what it is used for.
- The factor theorem states that if you divide a polynomial by a number and there is NOT a remainder, then the quotient is a factor of the polynomial
- CLICK HERE for a video that reviews the factor theorem and demonstrates how to use the factor theorem to break down a large degree polynomial into its linear factors
* Homework - Complete lesson 1.14, check answers, prepare questions for our next meeting.
* Quiz Alert - The next quiz will be after lesson 1.16
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Tuesday October 15
`For the first 8 minutes of class, students reviewed their guides/notes as last second prep for the Unit 1A test. For the next 40 minutes or so everyone completed the Unit 1A test. After finishing, students exchanged their papers for Lessons 1.12 - (Polynomial long Division) and 1.13 (synthetic division). These lessons are a straight review from Algebra 2. I asked students to watch the videos below and begin to complete both of these lessons
* Homework - Complete lessons 1.12 and lesson 1.13, will be checked for a HW grade.
`For the first 8 minutes of class, students reviewed their guides/notes as last second prep for the Unit 1A test. For the next 40 minutes or so everyone completed the Unit 1A test. After finishing, students exchanged their papers for Lessons 1.12 - (Polynomial long Division) and 1.13 (synthetic division). These lessons are a straight review from Algebra 2. I asked students to watch the videos below and begin to complete both of these lessons
- CLICK HERE for a video that reviews polynomial long division (with remainder, no missing exponents)
- CLICK HERE for a video that reviews polynomial long division (with missing exponents)
- CLICK HERE for a video that reviews synthetic division
* Homework - Complete lessons 1.12 and lesson 1.13, will be checked for a HW grade.
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Thursday October 10
On the way into class I returned the quizzes from last Monday (they were excellent). To start class, the pairs/groups in the room had a discussion regarding each of the four "big idea" review questions from the guide you received last week. We did a "share out" where we all agreed on a summary for each topic. If you missed anyting, my answer key attached has what I believe to be the key ideas for that discussion. There will be one question related to one of these four topics on your unit test Thursday. After our discussion, students spent 20 minutes checking their review guide work vs. the answer key below this post. Some students who did not complete the entire review guide worked on it. I answered as many student questions as possible. With 30 minutes left, the class completed a Kahoot as a review for the unit test on Tuesday 10/15
* Homework - There is no specific HW due for Monday however...
* Unit Test Alert - The Unit 1A test will be on Monday 10/15. It will cover lessons 1.1 - 1.11
On the way into class I returned the quizzes from last Monday (they were excellent). To start class, the pairs/groups in the room had a discussion regarding each of the four "big idea" review questions from the guide you received last week. We did a "share out" where we all agreed on a summary for each topic. If you missed anyting, my answer key attached has what I believe to be the key ideas for that discussion. There will be one question related to one of these four topics on your unit test Thursday. After our discussion, students spent 20 minutes checking their review guide work vs. the answer key below this post. Some students who did not complete the entire review guide worked on it. I answered as many student questions as possible. With 30 minutes left, the class completed a Kahoot as a review for the unit test on Tuesday 10/15
* Homework - There is no specific HW due for Monday however...
* Unit Test Alert - The Unit 1A test will be on Monday 10/15. It will cover lessons 1.1 - 1.11
Answers - Unit 1A Review guide |
Monday October 7
Class started today with a warm up related to lesson 1.11. There were a few problems with many in terms of your execution for this lesson so I assigned a few of the "odd" problems from the lesson as a means of getting more practice. Students worked on this for about 20-25 minutes practicing the even problems as needed. After that, the class completed a quiz on lessons 1.8 - 1.11. After the quiz, students exchanged papers for the study/review guide for the unit test next week. Thursday will be a review day and the Unit 1A test will be on Tuesday 10/15.
* Homework - The review guide is not assigned specifically as HW, however you should review it and prioritize the topics that you need to practice/ask questions about
* Unit Test Alert - Your Unit 1A test will be on Tuesday 10/15. It will cover lessons 1.1 - 1.11
Class started today with a warm up related to lesson 1.11. There were a few problems with many in terms of your execution for this lesson so I assigned a few of the "odd" problems from the lesson as a means of getting more practice. Students worked on this for about 20-25 minutes practicing the even problems as needed. After that, the class completed a quiz on lessons 1.8 - 1.11. After the quiz, students exchanged papers for the study/review guide for the unit test next week. Thursday will be a review day and the Unit 1A test will be on Tuesday 10/15.
* Homework - The review guide is not assigned specifically as HW, however you should review it and prioritize the topics that you need to practice/ask questions about
* Unit Test Alert - Your Unit 1A test will be on Tuesday 10/15. It will cover lessons 1.1 - 1.11
Unit 1A Review Guide |
Thursday October 3
On the way in, everyone received and completed a warm up related to lesson 1.10. We reviewed the warm up and then I took questions regarding lesson 1.10. After we wrapped up all issues/questions regarding 1.10, I distributed lesson 1.11. This lesson is all about "working backwards" to turn zeros into polynomial equations. This is a two step process:
* CLICK HERE for a video that models the process writing polynomial equations given real zeros (fairly easy example with rational zeros)
* CLICK HERE for a video that models the same process but with "nasty square roots" (irrational numbers) as zeros.
After reviewing these examples and the "your turn" problem on the bottom of the front page, I assigned the class the even numbered problems At minimum, I am expecting everyone to have the evens complete by our next meeting.
* Homework - Complete the even # problems from lesson 1.11, check answers vs. key below and come prepared with questions for our next meeting
* Quiz Alert - You will be having a quiz on Monday 10/7. It will cover lessons 1.8 - 1.11
* Unit Test Alert - Your Unit 1A test will be on Tuesday 10/15. It will cover lessons 1.1 - 1.11. I will provide a review guide after your quiz on Tuesday, however you should also review your previous quizzes. There will be a short answer question or two that will require you to know/explain vocabulary or key ideas related to a particular topic (such as the excluded value question from the first quiz).
On the way in, everyone received and completed a warm up related to lesson 1.10. We reviewed the warm up and then I took questions regarding lesson 1.10. After we wrapped up all issues/questions regarding 1.10, I distributed lesson 1.11. This lesson is all about "working backwards" to turn zeros into polynomial equations. This is a two step process:
- Turn zeros into factors
- Multiply factors to create the equations
* CLICK HERE for a video that models the process writing polynomial equations given real zeros (fairly easy example with rational zeros)
* CLICK HERE for a video that models the same process but with "nasty square roots" (irrational numbers) as zeros.
After reviewing these examples and the "your turn" problem on the bottom of the front page, I assigned the class the even numbered problems At minimum, I am expecting everyone to have the evens complete by our next meeting.
* Homework - Complete the even # problems from lesson 1.11, check answers vs. key below and come prepared with questions for our next meeting
* Quiz Alert - You will be having a quiz on Monday 10/7. It will cover lessons 1.8 - 1.11
* Unit Test Alert - Your Unit 1A test will be on Tuesday 10/15. It will cover lessons 1.1 - 1.11. I will provide a review guide after your quiz on Tuesday, however you should also review your previous quizzes. There will be a short answer question or two that will require you to know/explain vocabulary or key ideas related to a particular topic (such as the excluded value question from the first quiz).
lesson 1.11 - answers |
Tuesday October 1
On the way into class, everyone received a warm up related to lesson 1.9 as well as lesson 1.10. I started class by announcing that the 7:20am due date for the project has passed and that if you have not submitted your video it is now late. Students then completed the warm up while I checked completion of your HW from 1.9. Not everyone had completed the lesson due to the project so I gave everyone a few extra minutes to complete a bit more practice. We then answered any remaining questions pertaining to lesson 1.9 (there were several). After, we turned to lesson 1.10. This lesson requires us to graph polynomials by hand (rough sketch). When you are assessed on this type of graphing, a graphing calculator (or desmos), will not be allowed. The key to making these graphs is to use the attributes we discovered in lessons 1.8 and 1.9. These include end behavior, # of turns, zeros (x intercepts), multiplicity and y intercepts. When graphing by hand, here are my expectations:
* Homework - Complete lesson 1.10, check answers and come in Thursday with Questions
* Quiz Alert - I am projecting a quiz on lessons 1.8 - 1.11 on Monday 10/7 (we will complete 1.11 on Thursday)
* Unit Test Alert - Lesson 1.11 is the last new lesson of Unit 1A. I am projecting your first Unit test on Tuesday 10/15
On the way into class, everyone received a warm up related to lesson 1.9 as well as lesson 1.10. I started class by announcing that the 7:20am due date for the project has passed and that if you have not submitted your video it is now late. Students then completed the warm up while I checked completion of your HW from 1.9. Not everyone had completed the lesson due to the project so I gave everyone a few extra minutes to complete a bit more practice. We then answered any remaining questions pertaining to lesson 1.9 (there were several). After, we turned to lesson 1.10. This lesson requires us to graph polynomials by hand (rough sketch). When you are assessed on this type of graphing, a graphing calculator (or desmos), will not be allowed. The key to making these graphs is to use the attributes we discovered in lessons 1.8 and 1.9. These include end behavior, # of turns, zeros (x intercepts), multiplicity and y intercepts. When graphing by hand, here are my expectations:
- You must show all real zeros on the graph (please label the x value on the graph)
- You must show how the graph interacts with the zeros (pass, bounce or wiggle)
- You must show y intercept
- You must show end behavior
- You must show each turn of the graph between the real zeros, however you can not identify any specific maxima/minima without calculus
- CLICK HERE for a video that shows how to graph polynomials by hand
* Homework - Complete lesson 1.10, check answers and come in Thursday with Questions
* Quiz Alert - I am projecting a quiz on lessons 1.8 - 1.11 on Monday 10/7 (we will complete 1.11 on Thursday)
* Unit Test Alert - Lesson 1.11 is the last new lesson of Unit 1A. I am projecting your first Unit test on Tuesday 10/15
lesson 1.10 - Answers |
Thursday September 25
On the way in, everyone received warm up that had two parts. The first part involved factoring (a variety of methods), the second part was related to lesson 1.8. To start class, I collected quiz corrections. Students then completed the warm up as I helped/checked work as needed. After resolving any lingering questions issues with 1.8, we turned to lesson 1.9 (blank copy below this post). We reviewed what the "zeros" of a polynomial are and how they are directly related to "factors", "solutions" and "x intercepts" of polynomial graphs. We also reviewed what multiplicity is and how it affects the way the graph interacts with the x axis (pass, bounce).
* Homework - Complete Lesson 1.9 (all problems), check answers, prepare questions/email me with any issues
* Project Alert - Your 1Q project is due on Tuesday 10/1 @ 7:20 am.
On the way in, everyone received warm up that had two parts. The first part involved factoring (a variety of methods), the second part was related to lesson 1.8. To start class, I collected quiz corrections. Students then completed the warm up as I helped/checked work as needed. After resolving any lingering questions issues with 1.8, we turned to lesson 1.9 (blank copy below this post). We reviewed what the "zeros" of a polynomial are and how they are directly related to "factors", "solutions" and "x intercepts" of polynomial graphs. We also reviewed what multiplicity is and how it affects the way the graph interacts with the x axis (pass, bounce).
- CLICK HERE for a video that reviews what multiplicity is and its effect on the graph of a polynomial
- CLICK HERE for a video that reviews how to find the real zeros and multiplicity of a polynomial
* Homework - Complete Lesson 1.9 (all problems), check answers, prepare questions/email me with any issues
* Project Alert - Your 1Q project is due on Tuesday 10/1 @ 7:20 am.
lesson 1.9 - answers |
Tuesday September 24
On the way in, everyone received/completed a factoring "pre-assessment". Starting with Lesson 1.9, factoring will be a critical skill. The purpose of the "pre-assessment" is to establish who does/does not need extra help prior to starting lesson 1.9. As I reviewed papers, I assigned a Khan Academy module to a small group of you that is designed to take you through whichever type of factoring you had difficulty with in the pre-assessment. The due date to complete the module is at the start of class Thursday. After the pre-assessment students worked to complete the Transformations worksheet as well as lesson 1.8. Students used their notes from the previous class as a guide. Almost everyone completed both assignments, if you did not finish, this is also HW for our next meeting. with 5 minutes left I handed back the 1.4 - 1.7 quiz. If you have corrections, they are due on Thursday.
* Homework - Complete both assignments from lesson 1.8 if you did not do so in class. Check answers and bring questions to our next meeting (or better yet, email me). If you were assigned a Khan academy Module, this is due at the start of class on Tuesday (will count for a HW grade)
* Project Alert - Your 1Q project is due on Tuesday 10/1 @ 7:20 am.
* Quiz Corrections - For the 1.4 - 1.7 quiz are due at the start of class on Thursday.
On the way in, everyone received/completed a factoring "pre-assessment". Starting with Lesson 1.9, factoring will be a critical skill. The purpose of the "pre-assessment" is to establish who does/does not need extra help prior to starting lesson 1.9. As I reviewed papers, I assigned a Khan Academy module to a small group of you that is designed to take you through whichever type of factoring you had difficulty with in the pre-assessment. The due date to complete the module is at the start of class Thursday. After the pre-assessment students worked to complete the Transformations worksheet as well as lesson 1.8. Students used their notes from the previous class as a guide. Almost everyone completed both assignments, if you did not finish, this is also HW for our next meeting. with 5 minutes left I handed back the 1.4 - 1.7 quiz. If you have corrections, they are due on Thursday.
* Homework - Complete both assignments from lesson 1.8 if you did not do so in class. Check answers and bring questions to our next meeting (or better yet, email me). If you were assigned a Khan academy Module, this is due at the start of class on Tuesday (will count for a HW grade)
* Project Alert - Your 1Q project is due on Tuesday 10/1 @ 7:20 am.
* Quiz Corrections - For the 1.4 - 1.7 quiz are due at the start of class on Thursday.
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Friday September 20
To start class, everyone completed a warm up related to lesson 1.7 (even/odd functions). After the warm up I answered questions/resolved issues from lessons 1.4 - 1.7 as prep for today's quiz. After all questions were answered, everyone completed a quiz on lessons 1.4 - 1.7. After the quiz, students exchanged their papers for lesson 1.8 and a transformations worksheet. When everyone was done with the quiz and as a prelude to lesson 1.8, we reviewed the concept of transforming functions. I told the class that they needed to know (study/memorize) the "parent function" equations, graphs (shape/end behavior) for the following function types:
* Homework - There is no specific HW for Tuesday however...
* Project Alert - Your 1Q project is due on Tuesday 10/1 @ 7:20 am. The deadline to request an extension (for a 2/4 due date grade) was today. If I haven't heard from you, I expect your project by the due date above.
To start class, everyone completed a warm up related to lesson 1.7 (even/odd functions). After the warm up I answered questions/resolved issues from lessons 1.4 - 1.7 as prep for today's quiz. After all questions were answered, everyone completed a quiz on lessons 1.4 - 1.7. After the quiz, students exchanged their papers for lesson 1.8 and a transformations worksheet. When everyone was done with the quiz and as a prelude to lesson 1.8, we reviewed the concept of transforming functions. I told the class that they needed to know (study/memorize) the "parent function" equations, graphs (shape/end behavior) for the following function types:
- Quadratic (even degree polynomial)
- Cubic (odd degree polynomial)
- Absolute Value
- Square Root
- VERTICAL transformations occur "inside the function" while HORIZONTAL transformations occur "outside the function"
- All transformations that are "inside the function" work with opposite logic. For example, if we have the function f(x) = |x + 5| + 4, there would be a horizontal translations 5 units LEFT and a vertical translation 4 units UP.
- * If the exponent is EVEN than the end behavior will rise/fall in the SAME direction
- * If the exponent is ODD then the end behavior will rise/fall in OPPOSITE directions
- * If the lead coefficient is POSITIVE than the end behavior models the parent function
- * If the lead coeffieient is NEGATIVE then the end behavior is reflected from the parent function
* Homework - There is no specific HW for Tuesday however...
* Project Alert - Your 1Q project is due on Tuesday 10/1 @ 7:20 am. The deadline to request an extension (for a 2/4 due date grade) was today. If I haven't heard from you, I expect your project by the due date above.
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Wednesday September 18
On the way in, students received a warm up related to lesson 1.6. At the start of class I collected any quiz corrections. I checked/logged completion of HW as students worked on the warm up. After the warm up Students spent 20 minutes continuing to practice from 1.6 and checking the answers below this post (I helped/checked/modeled problems as needed). If you are still having difficulty with 1.6, please communicate with me if you need help. After a short break and with about 40 minutes left in the period everyone received lesson 1.7 (even/odd functions. The key idea to understanding even/odd functions is as follows:
1. If a function is EVEN, then its graph reflects over the y axis. If you change the sign of x, then the sign of y (and the numerical value of y) also stays the same
2. If a function is ODD, then its graph reflects over the origin. If you change the sign of x, then the sign of y also changes (the numerical value stays the same
3. The function is NEITHER even or odd, if you change the sign of x and the numerical value of y changes in any way
* CLICK HERE for a video that reviews the process of how to test for whether a function is even, odd or neither both algebraically and graphically.
Students spent the remainder of the period completing lesson 1.7 and checking answers on the key below this post. I announced that there will be quiz on Friday on lessons 1.4 - 1.7.
* Homework - Complete lessons 1.6 and 1.7 and check answers. We will have a Q&A on Friday before the quiz so bring any questions you may have (or come to flex)
* Quiz Alert - The next quiz will be on Friday 9/20, it will cover lessons 1.4 - 1.7.
* Project Alert - Your 1Q project is due on Tuesday 10/1 @ 7:20 am. Do not wait until the last minute to start/ask a question.
On the way in, students received a warm up related to lesson 1.6. At the start of class I collected any quiz corrections. I checked/logged completion of HW as students worked on the warm up. After the warm up Students spent 20 minutes continuing to practice from 1.6 and checking the answers below this post (I helped/checked/modeled problems as needed). If you are still having difficulty with 1.6, please communicate with me if you need help. After a short break and with about 40 minutes left in the period everyone received lesson 1.7 (even/odd functions. The key idea to understanding even/odd functions is as follows:
1. If a function is EVEN, then its graph reflects over the y axis. If you change the sign of x, then the sign of y (and the numerical value of y) also stays the same
2. If a function is ODD, then its graph reflects over the origin. If you change the sign of x, then the sign of y also changes (the numerical value stays the same
3. The function is NEITHER even or odd, if you change the sign of x and the numerical value of y changes in any way
* CLICK HERE for a video that reviews the process of how to test for whether a function is even, odd or neither both algebraically and graphically.
Students spent the remainder of the period completing lesson 1.7 and checking answers on the key below this post. I announced that there will be quiz on Friday on lessons 1.4 - 1.7.
* Homework - Complete lessons 1.6 and 1.7 and check answers. We will have a Q&A on Friday before the quiz so bring any questions you may have (or come to flex)
* Quiz Alert - The next quiz will be on Friday 9/20, it will cover lessons 1.4 - 1.7.
* Project Alert - Your 1Q project is due on Tuesday 10/1 @ 7:20 am. Do not wait until the last minute to start/ask a question.
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Monday September 16
On the way in everyone received a warm up related lessons 1.4 (domain/range and interval notation) and 1.5 (defining increasing/decreasing intervals. Students also received lesson 1.6 (Piecewise functions, blank copy below this post). Students completed the warm up while I helped/checked work. After reviewing the warm up, we resolved any final questions pertaining to lessons 1.4 and 1.5. We then started 1.6. I modeled the "your turn" example on the front page of the lesson as well as #5 from the "first group" of practice. I also modeled #1 from the "second group" of practice as a way of demonstrating how to graph if one of the pieces is a quadratic. For the remainder of the period, I assigned problems 1-4 from the "first group of 8" (non-quadratic) and problems 2-4 from the "second group of 8" (with quadratics). Whatever is not finished in class is HW for our next meeting.
* Quiz Corrections Due - If you have corrections for the 1.1 - 1.3 quiz they are due at the start of class on Wednesday
* Quiz Alert - The next quiz will be after lesson 1.7 which we will cover on Wednesday, therefore the quiz will be on Friday 9/20 and it will cover lessons 1.4 - 1.7.
* Project Alert - Your 1Q project is due on Tuesday 10/1 @ 7:20 am. Do not wait until the last minute to start/ask a question.
On the way in everyone received a warm up related lessons 1.4 (domain/range and interval notation) and 1.5 (defining increasing/decreasing intervals. Students also received lesson 1.6 (Piecewise functions, blank copy below this post). Students completed the warm up while I helped/checked work. After reviewing the warm up, we resolved any final questions pertaining to lessons 1.4 and 1.5. We then started 1.6. I modeled the "your turn" example on the front page of the lesson as well as #5 from the "first group" of practice. I also modeled #1 from the "second group" of practice as a way of demonstrating how to graph if one of the pieces is a quadratic. For the remainder of the period, I assigned problems 1-4 from the "first group of 8" (non-quadratic) and problems 2-4 from the "second group of 8" (with quadratics). Whatever is not finished in class is HW for our next meeting.
- CLICK HERE for a video that demonstrates how to graph a piecewise function by hand (fairly easy example)
- CLICK HERE for a video that demonstrates more complex examples (with quadratic intervals)
- CLICK HERE for a video that demonstrates how to write the equation of a piecewise function given its graph
- Quiz redos are optional (but strongly recommended
- You may only redo problems for which I specifically write "redo" on your paper
- You must do redos on separate sheet and attach/staple to your original quiz
- You must show all work whenever possible
- If your correction is good, you will receive 50% of the points back to your quiz score
- Quiz corrections are due at the start of class the following block
- If you are not sure how to do your corrections, please communicate with me so I can help you!
* Quiz Corrections Due - If you have corrections for the 1.1 - 1.3 quiz they are due at the start of class on Wednesday
* Quiz Alert - The next quiz will be after lesson 1.7 which we will cover on Wednesday, therefore the quiz will be on Friday 9/20 and it will cover lessons 1.4 - 1.7.
* Project Alert - Your 1Q project is due on Tuesday 10/1 @ 7:20 am. Do not wait until the last minute to start/ask a question.
lesson 1.6 - piecewise functions |
Thursday September 12
At the start of class, I did a short Q & A to answer any questions related to Lessons 1.1 - 1.3 and the pending quiz. Then, students completed a quiz on lessons 1.1 - 1.3 (20-30 mins). After the quiz (and a short break), students worked to complete Lesson 1.4 (Using interval notation to define domain and range). This is a straight review of Algebra 2, but in case you are rusty:
* Homework - Complete lessons 1.4 and 1.5, check answers bring a list of questions and/or email me, it is my hope that we will start 1.6 at our next meeting, the topic will be new to you.
* Project Alert - Your 1Q project is due on Tuesday 10/1 @ 7:20 am. Do not wait until the last minute to start/ask a question.
At the start of class, I did a short Q & A to answer any questions related to Lessons 1.1 - 1.3 and the pending quiz. Then, students completed a quiz on lessons 1.1 - 1.3 (20-30 mins). After the quiz (and a short break), students worked to complete Lesson 1.4 (Using interval notation to define domain and range). This is a straight review of Algebra 2, but in case you are rusty:
- CLICK HERE for a video that reviews how to quantify domain/range using interval notation.
- CLICK HERE for a video that reviews how to identify increasing/decreasing intervals
- CLICK HERE for a video that reviews how to identify relative maxima/minima
* Homework - Complete lessons 1.4 and 1.5, check answers bring a list of questions and/or email me, it is my hope that we will start 1.6 at our next meeting, the topic will be new to you.
* Project Alert - Your 1Q project is due on Tuesday 10/1 @ 7:20 am. Do not wait until the last minute to start/ask a question.
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Tuesday September 10
On the way into class everyone received a warm up related to lesson 1.2. To start class, students completed the warm up, I checked everyone's work (was very pleased). After the warm up I answered final questions regarding lesson 1.2. Most questions pertaining to lesson 1.2 had to do with finding the domain when a rational or square root was present so I have included more practice for those who need it.
CLICK HERE for a link to extra practice finding the domain of square root functions (with notes/explanations)
CLICK HERE for a link to extra practice finding the domain of a rational function (with notes/explanations)
After putting 1.2 to bed, I outlined expectations for your quiz on Thursday (details provided below). Then, we turned to lesson 1.3, evaluating difference quotients. I modeled the problem (primarily step 4) and then students used the balance of the period completing the lesson and checking answers (below this post). Again, I thought the quality of the work was very good but in case you need extra practice CLICK HERE for a link that models several problems (with work). Several students received and started lesson 1.4 (not too many). Everyone will begin lesson 1.4 after the quiz on Thursday.
* Homework - There is no specific HW for Thursday however...
* Quiz Alert - Your first quiz will be on Thursday 9/12 and will cover lessons 1.1 - 1.3. Please make sure you communicate with me if there is anything you are unsure about. Here is what you need to know/be able to do:
On the way into class everyone received a warm up related to lesson 1.2. To start class, students completed the warm up, I checked everyone's work (was very pleased). After the warm up I answered final questions regarding lesson 1.2. Most questions pertaining to lesson 1.2 had to do with finding the domain when a rational or square root was present so I have included more practice for those who need it.
CLICK HERE for a link to extra practice finding the domain of square root functions (with notes/explanations)
CLICK HERE for a link to extra practice finding the domain of a rational function (with notes/explanations)
After putting 1.2 to bed, I outlined expectations for your quiz on Thursday (details provided below). Then, we turned to lesson 1.3, evaluating difference quotients. I modeled the problem (primarily step 4) and then students used the balance of the period completing the lesson and checking answers (below this post). Again, I thought the quality of the work was very good but in case you need extra practice CLICK HERE for a link that models several problems (with work). Several students received and started lesson 1.4 (not too many). Everyone will begin lesson 1.4 after the quiz on Thursday.
* Homework - There is no specific HW for Thursday however...
* Quiz Alert - Your first quiz will be on Thursday 9/12 and will cover lessons 1.1 - 1.3. Please make sure you communicate with me if there is anything you are unsure about. Here is what you need to know/be able to do:
- Know how to determine whether a relation is a function given each of the ways listed in lesson 1.1 (graph, chart, equation, ordered pairs).
- Know how to evaluate a piecewise function for given input values. (1.2)
- Know what an excluded value is and how to determine he excluded values of a function (1.2)
- Know how to determine the domain of any function equation (1.2)
- Evaluate a difference quotient (1.3)
lesson 1.3 - answers |
Friday September 6
On the way into class everyone received a warm up related to lesson 1.1 as well as lesson 1.2. The warm up was a real world application that required students to evaluate a function for a variety of inputs. Afterwards, I flashed a second warm up related to lesson 1.1 that requried students to identify functions ( or not a function) given equations, ordered pairs and graphs. After the warm ups, we resolved any questions/issues from lesson 1.1. We then turned to lesson 1.2. Lesson 1.2 has two parts:
1) Identifying the domain of a function (this is very much review)
A piece wise function is a function who's domain is defined by more than one equation.
* Homework - Watch the video above and attempt the "step 4" problem on the bottom the front page of lesson 1.3.
* Quiz Alert - Your first quiz will be on Thursday 9/12 and will cover lessons 1.1 - 1.3. Please make sure you communicate with me if there is anything you are unsure about
* Project Alert - Your 1Q project is due on Tuesday 10/1 @ 7:20 am. Do not wait until the last minute to start/ask a question.
On the way into class everyone received a warm up related to lesson 1.1 as well as lesson 1.2. The warm up was a real world application that required students to evaluate a function for a variety of inputs. Afterwards, I flashed a second warm up related to lesson 1.1 that requried students to identify functions ( or not a function) given equations, ordered pairs and graphs. After the warm ups, we resolved any questions/issues from lesson 1.1. We then turned to lesson 1.2. Lesson 1.2 has two parts:
1) Identifying the domain of a function (this is very much review)
- CLICK HERE for a video that explains how to define the domain of a function
A piece wise function is a function who's domain is defined by more than one equation.
- CLICK HERE for a video that explains what a piecewise function is
- CLICK HERE for a video that demonstrates how to evaluate a piecewise function
* Homework - Watch the video above and attempt the "step 4" problem on the bottom the front page of lesson 1.3.
* Quiz Alert - Your first quiz will be on Thursday 9/12 and will cover lessons 1.1 - 1.3. Please make sure you communicate with me if there is anything you are unsure about
* Project Alert - Your 1Q project is due on Tuesday 10/1 @ 7:20 am. Do not wait until the last minute to start/ask a question.
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VIDEOS FOR QUADRATIC FORMULA PROJECT (Due 7:20 am on Tues. 10/1)
- EXAMPLE VIDEO #1
- EXAMPLE VIDEO #2
- EXAMPLE VIDEO #3 (Khan)
- EXAMPLE VIDEO #4 (Virtual Nerd), personally, I like this one best
Wednesday September 4
On the way into class, everyone picked up lesson 1.1. This lesson is mostly a repeat from Algebra 2. We reviewed how to tell if a relation is a function (in various forms such as graphs, tables and ordered pairs). I demonstrated the process of how to tell an equation is/is not a function using algebra (solve for y, if you take a square root during the process it is not a function b/c the result will result in two x values from the +/-). I also reminded everyone what evaluating functions is (plug in the value given for x to determine the resulting y value.
After 30 minutes, we took a break from the lessons and I distributed/reviewed the directions for your first unit project (directions and rubric are attached below this post). Here is what you need to know about the project:
* Homework - If you did not complete/check lesson 1.1, please do so. Email me or come in on Friday with any questions. Also, complete problems 53, 54, 57 and 58 from lesson 1.2.
* Project Alert - Your 1Q project is due on Tuesday 10/1 @ 7:20 am. Do not wait until the last minute to start/ask a question.
On the way into class, everyone picked up lesson 1.1. This lesson is mostly a repeat from Algebra 2. We reviewed how to tell if a relation is a function (in various forms such as graphs, tables and ordered pairs). I demonstrated the process of how to tell an equation is/is not a function using algebra (solve for y, if you take a square root during the process it is not a function b/c the result will result in two x values from the +/-). I also reminded everyone what evaluating functions is (plug in the value given for x to determine the resulting y value.
- CLICK HERE for a video that reviews the basics of functions and relations
- CLICK HERE for a video that demonstrates the process of how to determine whether an equation is a function using algebra
- CLICK HERE for a video that demonstrates how to evaluate functions (some harder examples)
After 30 minutes, we took a break from the lessons and I distributed/reviewed the directions for your first unit project (directions and rubric are attached below this post). Here is what you need to know about the project:
- The due date for the project is Tuesday 10/1 at 7:20 am regardless of A/B day (be sure to read the details about the due date and the rules for requesting an extension)
- For the project you ARE NOT solving a problem using the quadratic formula, you ARE deriving the quadratic formula from an equation in standard form (you WILL be explaining where the formula comes from, NOT doing a problem)
- The videos that you can use to learn the derivation (and model your own video after) are listed at the top of the blog and will remain there until the due date passes
- Make sure you read the rubric carefully and use it as a check list before submitting your project.
- When I receive your project, I will reply to your submission confirming that I can open your file. Please see the formats in which you can submit it. Emailing as an attachment is sometimes difficult because of the file size and download/upload time. Please keep an eye on your email in case I reply with a technical difficulty.
- DO NOT wait until the last minute to start this project and ask me questions.
- Projects/Unit Tests are 40% of your grade.
- CLICK HERE for a video that explains how to define the domain of a function
* Homework - If you did not complete/check lesson 1.1, please do so. Email me or come in on Friday with any questions. Also, complete problems 53, 54, 57 and 58 from lesson 1.2.
* Project Alert - Your 1Q project is due on Tuesday 10/1 @ 7:20 am. Do not wait until the last minute to start/ask a question.
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Friday August 29
On the way into class, all students received a handout titled "Library of Parent Functions". I started class by reviewing the class's status regarding the email HW and the Khan Summer Work. We then started our Math year by creating a definition of what "pre-calculus" is: The branch of math associated with the properties of functions. We then transitioned to the Library of functions handout. We created a list of the types of functions that students were familiar with from Algebra 1 and Algebra 2 and I explained how we will be studying all other function on this list throughout the course of the year. We reviewed the "Library of Parent Functions" tab on the lessons button to review the common properties that we will be studying with all functions. CLICK HERE for a link to go directly to this page and to see the details of this part of the discussion. As a means of demonstrating all of the attributes we will be studying, I handed out an "Algebra 2 Skills" sheet. The first side was completed as a class as an interactive discussion. Using the example of a fairly simple quadratic:
* We reviewed how to use the general shape and key attributes of the function to create a sketch of the graph by hand
* We reviewed the process of how to determine the vertex of the parabola,the x and y intercepts
* We reviewed how to identify domain and range (and various notations of quantification)
* We reviewed how to identify transformations from the parent function
For the last 30 minutes of the class, students completed the back side of this sheet which involved factoring/solving some fairly simple equations that the class would have encountered in Algebra 2. After completing these problems, students checked their answers using the key below this post and then completed/submitted an exit slip in which they communicated to me which types of problems were easy/difficult and what they may need to practice.
* Homework - There is no specific HW for the weekend, enjoy your Labor Day.
On the way into class, all students received a handout titled "Library of Parent Functions". I started class by reviewing the class's status regarding the email HW and the Khan Summer Work. We then started our Math year by creating a definition of what "pre-calculus" is: The branch of math associated with the properties of functions. We then transitioned to the Library of functions handout. We created a list of the types of functions that students were familiar with from Algebra 1 and Algebra 2 and I explained how we will be studying all other function on this list throughout the course of the year. We reviewed the "Library of Parent Functions" tab on the lessons button to review the common properties that we will be studying with all functions. CLICK HERE for a link to go directly to this page and to see the details of this part of the discussion. As a means of demonstrating all of the attributes we will be studying, I handed out an "Algebra 2 Skills" sheet. The first side was completed as a class as an interactive discussion. Using the example of a fairly simple quadratic:
* We reviewed how to use the general shape and key attributes of the function to create a sketch of the graph by hand
* We reviewed the process of how to determine the vertex of the parabola,the x and y intercepts
* We reviewed how to identify domain and range (and various notations of quantification)
* We reviewed how to identify transformations from the parent function
For the last 30 minutes of the class, students completed the back side of this sheet which involved factoring/solving some fairly simple equations that the class would have encountered in Algebra 2. After completing these problems, students checked their answers using the key below this post and then completed/submitted an exit slip in which they communicated to me which types of problems were easy/difficult and what they may need to practice.
* Homework - There is no specific HW for the weekend, enjoy your Labor Day.
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Wednesday August 28
All students received a 2019-2020 syllabus on their way into class (attached below this post). The following is a summary of our "Welcome back" discussion:
* Class Overview: - I provided a brief overview of the syllabus to the class as well as discussing class expectations, routines and policies.
* Class Website: I had everyone bookmark your blog page and gave a tour of this website, its resources and how we will use it during our day to day learning.
* Summer Work - On Monday, I sent everyone a link to sign up for a Khan Academy class linked to your particular block. We spent a few minutes making sure everyone had an account and was "connected" to the correct class. I will review everyone's productivity and assign grades from 0-4 for the assignment.
It was my intent that after all of the "Welcome back" items above were discussed and questions answered, we would discuss some math but we did not get to that today. I did inform everyone of the HW assignment listed below:
* Homework (all classes) - Send me an email to [email protected] with the following information. Please follow ALL directions and answer all questions completely and honestly (remember, I am trying to get to know you).
In the subject box of the email, include your name and block 2A
All students received a 2019-2020 syllabus on their way into class (attached below this post). The following is a summary of our "Welcome back" discussion:
* Class Overview: - I provided a brief overview of the syllabus to the class as well as discussing class expectations, routines and policies.
* Class Website: I had everyone bookmark your blog page and gave a tour of this website, its resources and how we will use it during our day to day learning.
* Summer Work - On Monday, I sent everyone a link to sign up for a Khan Academy class linked to your particular block. We spent a few minutes making sure everyone had an account and was "connected" to the correct class. I will review everyone's productivity and assign grades from 0-4 for the assignment.
It was my intent that after all of the "Welcome back" items above were discussed and questions answered, we would discuss some math but we did not get to that today. I did inform everyone of the HW assignment listed below:
* Homework (all classes) - Send me an email to [email protected] with the following information. Please follow ALL directions and answer all questions completely and honestly (remember, I am trying to get to know you).
In the subject box of the email, include your name and block 2A
- What math class(es) did you take last year and who was your teacher(s) (please note if honors)
- Are you taking any other math class besides Honors Precalc this year (if yes, please state the class/teacher)
- Do you think you are good at math (why or why not)?
- Do you like Math (why are why not)
- What extra curricular activities are you involved in at DHS? If you are an athlete, which sport(s )do you play
- What career might you want to do some day?
- Name two things you are passionate about outside of school
- Did you work over the summer? If so, what kind of job did you have? If you are still working during the school year, tell me approximately how many hours a week.
- Please provide the name and email of a parent/guardian
- Due date for email HW assignment is 7:20 am on Friday 8/28 :
2019 - 2020 Honors Precalc syllabus |