Blog Block 1B
(Most recent entry listed first)
(Most recent entry listed first)
Thursday March 12
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 students exchanged papers for the Q3 Journal assignment. The journal is due at 2pm on Monday 3/23. I also 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.
* Journal Alert - The 3Q journal is due on Monday 3/23 at 2pm
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 students exchanged papers for the Q3 Journal assignment. The journal is due at 2pm on Monday 3/23. I also 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
* Journal Alert - The 3Q journal is due on Monday 3/23 at 2pm
3Q journal assignment |
Tuesday March 10
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 Thursday March 12.
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 Thursday March 12.
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Friday March 6
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 Thursday 3/12. Tuesday will be a review day and will include a warm up on bearings, 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 Thursday March 12. 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 Thursday 3/12. Tuesday will be a review day and will include a warm up on bearings, 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 Thursday March 12. It is up to you to manage your time to prepare, see above for how we will be spending class time on Thursday.
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Wednesday March 4
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 Friday 3/4, 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 Thursday March 12. You will receive a review guide after your quiz on Friday. We will review on Tuesday 3/10. On Tuesday 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 Friday 3/4, 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 Thursday March 12. You will receive a review guide after your quiz on Friday. We will review on Tuesday 3/10. On Tuesday you will also receive your quizzes back and be allowed to make corrections if necessary.
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Monday March 2
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 Wednesday with questions/issues
* Project Alert - The Bearings project is due at the start of class on Wednesday 3/4
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 Wednesday with questions/issues
* Project Alert - The Bearings project is due at the start of class on Wednesday 3/4
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Thursday February 27
To start class I collected quiz corrections. 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 Wednesday 3/4
To start class I collected quiz corrections. 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 Wednesday 3/4
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Tuesday February 25
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 Wednesday 3/4
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: Savanna and Patrick, please do version A
* 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 Wednesday 3/4
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Friday February 21
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 |
Wednesday February 19
On the way in, everyone received a warm up pertaining to lessons 3.8 and 3.9. 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 Friday 2/21 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. 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 Friday 2/21 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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Friday February 14
On the way into class everyone received lesson 3.9. To start class everyone completed a warm up related to lesson 3.8 while I checked/logged HW completion (you must have shown work to get full credit). After the warm up, I resolved any issues/questions pertaining to lesson 3.8 and we moved to lesson 3.9 - Law of Cosines. I made an analogy of the law of cosines to the three area formulas. Both sets of formulas are simply different ways of re-writing the same one formula depending on the information we are given in the problem. We reviewed the examples on the front page of the lesson (as well as the mistake on example 2 and I assigned the practice (all problems) as classwork/HW. Lesson 3.9 is the last lesson before the next quiz
* Quiz Alert - There will be a quiz next Friday 2/21 on lessons 3.7 - 3.9 (there will be a practice quiz Wednesday).
On the way into class everyone received lesson 3.9. To start class everyone completed a warm up related to lesson 3.8 while I checked/logged HW completion (you must have shown work to get full credit). After the warm up, I resolved any issues/questions pertaining to lesson 3.8 and we moved to lesson 3.9 - Law of Cosines. I made an analogy of the law of cosines to the three area formulas. Both sets of formulas are simply different ways of re-writing the same one formula depending on the information we are given in the problem. We reviewed the examples on the front page of the lesson (as well as the mistake on example 2 and I assigned the practice (all problems) as classwork/HW. Lesson 3.9 is the last lesson before the next quiz
- 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
* Quiz Alert - There will be a quiz next Friday 2/21 on lessons 3.7 - 3.9 (there will be a practice quiz Wednesday).
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Wednesday February 12
To begin class,. I did NOT check HW as I wanted to since a number of you did not complete it fully. I advised the class that this is the last time this will happen. For those who were confused about the ambiguous case from the last class, we completed the warm up together (and then reviewed it). The understanding for the group was much better after reviewing the example. I advised everyone that I posted a link to extra law of sines practice below for those who need it.
* Homework - Complete lessons 3.7 and 3.8 (check answers) and communicate with me if you have any questions. WILL BE CHECKED FOR A HW GRADE!
To begin class,. I did NOT check HW as I wanted to since a number of you did not complete it fully. I advised the class that this is the last time this will happen. For those who were confused about the ambiguous case from the last class, we completed the warm up together (and then reviewed it). The understanding for the group was much better after reviewing the example. I advised everyone that I posted a link to extra law of sines practice below for those who need it.
- CLICK HERE for extra practice using the law of signs and identifying the ambiguous case
- 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 and 3.8 (check answers) and communicate with me if you have any questions. WILL BE CHECKED FOR A HW GRADE!
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Monday February 10
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 (Practice). When everyone was finished with the quiz, we reviewed the key points from lesson 3.7 regarding the Law of Sines including the proof. I had the class complete one very basic problem to make sure everyone understood how to set up and solve the ratios. Then we turned to the ambiguous case which can occur if you are provided SSA information in the problem. I provided an alternative (better, quicker) way of of making the determination of whether there are one, two or no triangles that can be make with the SSA information you are given. The following is the process that makes this determination:
* Homework - Complete all of lesson 3.7 (practice), will be checked for a 2 pt grade, it is urgent that you communicate with me if you are having difficulty with the process outlined above.
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 (Practice). When everyone was finished with the quiz, we reviewed the key points from lesson 3.7 regarding the Law of Sines including the proof. I had the class complete one very basic problem to make sure everyone understood how to set up and solve the ratios. Then we turned to the ambiguous case which can occur if you are provided SSA information in the problem. I provided an alternative (better, quicker) way of of making the determination of whether there are one, two or no triangles that can be make with the SSA information you are given. 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 video that shows the ambiguous case and how to solve for two possible triangles.
- 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.
* Homework - Complete all of lesson 3.7 (practice), will be checked for a 2 pt grade, it is urgent that you communicate with me if you are having difficulty with the process outlined above.
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Thursday February 6 (Mr. Harris is out ill today)
The quiz that was supposed to be today is postponed until Monday due to my illness. The sub directed everyone to do one of two things today:
1. For those who would benefit from extra practice for the quiz:
* Homework - There is no specific HW due on Monday, however...
* Quiz Alert - There will be a quiz on lessons 3.1 - 3.6 on Monday (first thing). I do hope to be in school tomorrow, please email me if you would like me to put you in my flex for tomorrow as I will be checking my email. Thank you all for your professionalism in my absence today
The quiz that was supposed to be today is postponed until Monday due to my illness. The sub directed everyone to do one of two things today:
1. For those who would benefit from extra practice for the quiz:
- 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
- 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 - There is no specific HW due on Monday, however...
* Quiz Alert - There will be a quiz on lessons 3.1 - 3.6 on Monday (first thing). I do hope to be in school tomorrow, please email me if you would like me to put you in my flex for tomorrow as I will be checking my email. Thank you all for your professionalism in my absence today
lesson 3.7 - The Law of sines (notes) |
Tuesday February 4
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. On the way in, everyone also received a "practice quiz" as a means for preparing for the "real" quiz on Thursday. Students worked for the balance of the period completing the practice quiz, I helped/checked student work as necessary. A blank copy and the answers to the practice quiz are below this post. Also, I am reposting the "extra practice" links from the other day
* 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. Email me with questions, I am happy to help you
* Quiz Alert - There will be a quiz on Thursday that begins 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. On the way in, everyone also received a "practice quiz" as a means for preparing for the "real" quiz on Thursday. Students worked for the balance of the period completing the practice quiz, I helped/checked student work as necessary. A blank copy and the answers to the practice quiz are below this post. Also, I am reposting the "extra practice" links from the other day
- 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
* 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. Email me with questions, I am happy to help you
* Quiz Alert - There will be a quiz on Thursday that begins no later than 7:30, we need to get into lesson 3.7.
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Friday January 31
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 start of the block on Thursday 2/6 on lessons 3.1 - 3.6. You need to KNOW SOH CAH TOA and the patterns associated with special right triangles. We will have a practice quiz on Tuesday and you will also practice using the above links.
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 start of the block on Thursday 2/6 on lessons 3.1 - 3.6. You need to KNOW SOH CAH TOA and the patterns associated with special right triangles. We will have a practice quiz on Tuesday and you will also practice using the above links.
lesson 3.6 - answers |
Wednesday January 29
To start class 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. For the first 30 or so minutes of class, students completed the STAR test. Those who completed STAR in another math class started 3.5 (everyone moved to 3.5 as they completed STAR. 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 Friday
To start class 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. For the first 30 or so minutes of class, students completed the STAR test. Those who completed STAR in another math class started 3.5 (everyone moved to 3.5 as they completed STAR. 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 Friday
lesson 3.5 - answers |
Monday January 27
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 Wednesday with questions. Also, complete problems 1 & 2 from lesson 3.5, we will do the rest in class on Wednesday.
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 Wednesday with questions. Also, complete problems 1 & 2 from lesson 3.5, we will do the rest in class on Wednesday.
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Thursday January 23
On the way in everyone received lesson 3.2. I spend a few minutes at the start of class reviewing the status of your unit test grades, journal submissions and "setting up" Unit 3 which led to a discussion of lesson 3.1. I reviewed the process of converting to/from degrees/minutes/seconds as well as how to add/subtract angle measures that are given in DMS. Students practiced this lesson for the next 30 minutes or so (answers below this post). After 30 minutes, I 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 Monday, check answers vs. the keys below and make note of any questions (or my mistakes on key).
* Journal Update - I will be replying to journals within the next 48 hours, some conversations may spill into next week, they all need to be over by Tuesday.
*END OF SEMESTER REMINDER - The 2Q and Semester 1 end at 2pm tomorrow 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 everyone received lesson 3.2. I spend a few minutes at the start of class reviewing the status of your unit test grades, journal submissions and "setting up" Unit 3 which led to a discussion of lesson 3.1. I reviewed the process of converting to/from degrees/minutes/seconds as well as how to add/subtract angle measures that are given in DMS. Students practiced this lesson for the next 30 minutes or so (answers below this post). After 30 minutes, I 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 Monday, check answers vs. the keys below and make note of any questions (or my mistakes on key).
* Journal Update - I will be replying to journals within the next 48 hours, some conversations may spill into next week, they all need to be over by Tuesday.
*END OF SEMESTER REMINDER - The 2Q and Semester 1 end at 2pm tomorrow 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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Tuesday January 21
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 is Journal is due at 2pm on Wednesday 1/22 (original copies said Tuesday 1/22, it is due WED 1/22)
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 is Journal is due at 2pm on Wednesday 1/22 (original copies said Tuesday 1/22, it is due WED 1/22)
lesson 3.1 - degrees/minutes/seconds |
Thursday January 16
At the start of class, I collected quiz corrections. For most of the class we played a Kahoot as a means of reviewing for Wednesday's unit test (this took about the last 50 minutes of the period).
* Unit Test Alert - Your Unit test will be on Tuesday 1/21. There will be no formal review guide. See post from 1/10 for details/expectations.
* Journal Alert - The 2Q is Journal is due at 2pm on Wednesday 1/22 (original copies said Tuesday 1/22, it is due WED 1/22)
At the start of class, I collected quiz corrections. For most of the class we played a Kahoot as a means of reviewing for Wednesday's unit test (this took about the last 50 minutes of the period).
- CLICK HERE to access the Kahoot that we completed in class today
* Unit Test Alert - Your Unit test will be on Tuesday 1/21. There will be no formal review guide. See post from 1/10 for details/expectations.
* Journal Alert - The 2Q is Journal is due at 2pm on Wednesday 1/22 (original copies said Tuesday 1/22, it is due WED 1/22)
answers - supplementary log/exponential practice (equations & applications |
Tuesday January 14
To start class I asked if there were any questions about the journal assignment. Then, everyone completed a two part warm up. 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, I modeled examples from the lesson in which we had to determine the amount of time it takes to grow an investment (see video last blog) as well as a "half life" problem.
* Homework - There is no specific HW for Thursday, however I strongly suggest that you start preparation/practice for...
* Unit Test Alert - Your Unit test will be on Tuesday 1/21. There will be no formal review guide. See post from 1/10 for details/expectations.
* Journal Alert - The 2Q is Journal is due at 2pm on Wednesday 1/22 (original copies said Tuesday 1/22, it is due WED 1/22)
To start class I asked if there were any questions about the journal assignment. Then, everyone completed a two part warm up. 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, I modeled examples from the lesson in which we had to determine the amount of time it takes to grow an investment (see video last blog) as well as a "half life" problem.
- CLICK HERE for a video that reviews the process of using logs to solve a half life problem (several examples).
* Homework - There is no specific HW for Thursday, however I strongly suggest that you start preparation/practice for...
* Unit Test Alert - Your Unit test will be on Tuesday 1/21. There will be no formal review guide. See post from 1/10 for details/expectations.
* Journal Alert - The 2Q is Journal is due at 2pm on Wednesday 1/22 (original copies said Tuesday 1/22, it is due WED 1/22)
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Friday January 10
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 40 minutes into class students completed a quiz on lessons 2.6 - 2.9. Upon completion of the quiz, students exchanged papers for the 2Q Journal Assignment and lesson 2.10. Lesson 2.10 is the last new lesson of Unit 2. NOTE - I was short copies so about 8 of you did not get a printed packet. Please use the attached lesson copy below this post to complete the assignment if you were absent or did not get a lesson. 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 (on bottom of page 3) 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. The above will be checked for a HW grade.
* Journal Alert - The 2Q is Journal is due at 2pm on Wednesday 1/22 (original copies said Tuesday 1/22, it is due WED 1/22)
* Unit Test Alert - Your Unit test will be on Tuesday 1/21. 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:
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 40 minutes into class students completed a quiz on lessons 2.6 - 2.9. Upon completion of the quiz, students exchanged papers for the 2Q Journal Assignment and lesson 2.10. Lesson 2.10 is the last new lesson of Unit 2. NOTE - I was short copies so about 8 of you did not get a printed packet. Please use the attached lesson copy below this post to complete the assignment if you were absent or did not get a lesson. 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 (on bottom of page 3) 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. The above will be checked for a HW grade.
* Journal Alert - The 2Q is Journal is due at 2pm on Wednesday 1/22 (original copies said Tuesday 1/22, it is due WED 1/22)
* Unit Test Alert - Your Unit test will be on Tuesday 1/21. 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)
- Answer a short answer question about Inverses OR extraneous solutions OR the graphs of the exponential/Logarithmic parent functions
- Solve a problem similar to those from 2.10 (I will give you formula)
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Wednesday January 8
On the way in, students received lesson 2.9. After collecting quiz corrections, we started class with a short warm up related to lesson 2.8 (part 1) while I checked/logged HW completion. After reviewing the warm up, I provided everyone some strategies for part 2 of the lesson when logs must be used to solve the equation (remember, logs and exponents are inverse processes of each other just like multiplication and division are). We reviewed the examples on page 3 of lesson 2.8 for solving exponentials that require the use of logarithms. Here are some strategies that we discussed:
* Homework - Complete lesson 2.9 and the 2.6 - 2.9 quiz review (answers to both below). Please communicate with me regarding your status because...
* Quiz Alert - There will be a quiz at the end of class on Friday on lessons 2.6 - 2.9
* Unit Test Alert - Lesson 2.10 is the last lesson in Unit 2. I am projecting your unit test to be on Tuesday 1/21 (more details to come)
On the way in, students received lesson 2.9. After collecting quiz corrections, we started class with a short warm up related to lesson 2.8 (part 1) while I checked/logged HW completion. After reviewing the warm up, I provided everyone some strategies for part 2 of the lesson when logs must be used to solve the equation (remember, logs and exponents are inverse processes of each other just like multiplication and division are). We reviewed the examples on page 3 of lesson 2.8 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.
- 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 and the 2.6 - 2.9 quiz review (answers to both below). Please communicate with me regarding your status because...
* Quiz Alert - There will be a quiz at the end of class on Friday on lessons 2.6 - 2.9
* Unit Test Alert - Lesson 2.10 is the last lesson in Unit 2. I am projecting your unit test to be on Tuesday 1/21 (more details to come)
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Monday January 6
On the way in, students received lesson 2.7 (blank copy below this post). This lesson is all about properties of operations with logarithms and using them to expand /condense logarithmic expressions (as a prelude to solving which is the next lesson). These properties are "born" from the properties of exponents (makes sense, b/c logarithms are an inverse process of exponential equations):
Lesson 2.8 is about solving exponential equations. Part 1 of the lesson uses 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. I assigned the problems on "Practice part 1" of lesson 2.8 as classwork for the last 10 minutes, what is not finished is HW for Wednesday. On the way out of class, I handed back the quizzes you completed last Thursday, any corrections are due on Wednesday.
* Homework - Complete all problems from lesson 2.7, check answers, ask me questions if it is not working out (almost all of you finished this in class). Also, complete practice part 1 from lesson 2.8 (this will be checked for a HW grade on Wednesday).
* Quiz Alert - The next quiz will be after lesson 2.9, I am hoping it is at the end of class on Friday (we will get to 2.9 on Wednesday), if not, it will be on Tuesday 1/14 the latest.
On the way in, students received lesson 2.7 (blank copy below this post). This lesson is all about properties of operations with logarithms and using them to expand /condense logarithmic expressions (as a prelude to solving which is the next lesson). These properties are "born" from the properties of exponents (makes sense, b/c logarithms are an inverse process of exponential equations):
- 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
Lesson 2.8 is about solving exponential equations. Part 1 of the lesson uses 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. I assigned the problems on "Practice part 1" of lesson 2.8 as classwork for the last 10 minutes, what is not finished is HW for Wednesday. On the way out of class, I handed back the quizzes you completed last Thursday, any corrections are due on Wednesday.
* Homework - Complete all problems from lesson 2.7, check answers, ask me questions if it is not working out (almost all of you finished this in class). Also, complete practice part 1 from lesson 2.8 (this will be checked for a HW grade on Wednesday).
* Quiz Alert - The next quiz will be after lesson 2.9, I am hoping it is at the end of class on Friday (we will get to 2.9 on Wednesday), if not, it will be on Tuesday 1/14 the latest.
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Thursday January 2
At the start of class, everyone received a warm up and extra practice related to lessons 2.1 - 2.5. I put a summary of key points/notes to help jog any memories for those who had trouble remembering before the break. Students completed both the warm up and additional practice (answers to both below this post). At about 8:05, everyone completed a quiz on lessons 2.1 - 2.5. After the quiz, students received lesson 2.6 (The change of base formula). Lesson 2.6 VERY short 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, check answers, email me questions and come in Tuesday ready to start lesson 2.7.
At the start of class, everyone received a warm up and extra practice related to lessons 2.1 - 2.5. I put a summary of key points/notes to help jog any memories for those who had trouble remembering before the break. Students completed both the warm up and additional practice (answers to both below this post). At about 8:05, everyone completed a quiz on lessons 2.1 - 2.5. After the quiz, students received lesson 2.6 (The change of base formula). Lesson 2.6 VERY short 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.
- IMPORTANT NOTE: 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
* Homework - Complete lesson 2.6, check answers, email me questions and come in Tuesday ready to start lesson 2.7.
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Thursday December 19
At the start of class, everyone received a warm up related to lesson 2.2 (blank warm up attached below). Students completed the warm up while I checked the snow day HW assignment (glad that almost all of you completed the assignment). After the 2.2 warm up I flashed a second warm up related to lesson 2.3 on the board. We then reviewed the snow day assignment (lesson 2.4) and used desmos to demonstrate the graphs of transformed logarithmic functions. Please see notes from previous blog post for details. We then turned to the other part of lesson 2.4, the basic properties of logarithms.
Lesson 2.5 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
* Homework - If you did not do so in class, complete lessons 2.4 and 2.5, check answers, email me questions because...
* Quiz Alert - There will be a quiz on Thursday January 2 on lessons 2.1 - 2.5. I apologize for doing this the day we get back but we need to keep pace (as mentioned, the snow days are causing us to be way behind). We WILL have a practice quiz to warm up before taking the real quiz. Please make sure you review your notes/practice on the evening of 1/1 if at all possible.
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 received a warm up related to lesson 2.2 (blank warm up attached below). Students completed the warm up while I checked the snow day HW assignment (glad that almost all of you completed the assignment). After the 2.2 warm up I flashed a second warm up related to lesson 2.3 on the board. We then reviewed the snow day assignment (lesson 2.4) and used desmos to demonstrate the graphs of transformed logarithmic functions. Please see notes from previous blog post for details. We then turned to the other part of lesson 2.4, the basic properties of logarithms.
- CLICK HERE for a video on the basic properties of logarithms and how they are used to simplify/solve basic logarithmic equations/expressions
Lesson 2.5 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
- CLICK HERE for a video that reviews what the natural log is and its properties
* Homework - If you did not do so in class, complete lessons 2.4 and 2.5, check answers, email me questions because...
* Quiz Alert - There will be a quiz on Thursday January 2 on lessons 2.1 - 2.5. I apologize for doing this the day we get back but we need to keep pace (as mentioned, the snow days are causing us to be way behind). We WILL have a practice quiz to warm up before taking the real quiz. Please make sure you review your notes/practice on the evening of 1/1 if at all possible.
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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Tuesday December 17 (school canceled due to weather)
Hello class 1B, once again you guys get hosed in terms of learning due to the weather (I'm sure you are all disappointed). That being said, as you know, the learning doesn't stop in Mr. Harris's class. Here is your snow day assignment:
* Homework - Check answers to lesson 2.3, complete page 3 of lesson 2.4. I am available over email the entire day if you have any questions or problems, I am happy to help you. As I have mentioned several times, it is MANDATORY that you check the blog on days school is canceled. I am expecting that everyone will do so and will have the HW ready to go on Thursday. If you email me with questions, problems or for any other reason, I am happy to help you. Please be safe and have a good snow day.
Hello class 1B, once again you guys get hosed in terms of learning due to the weather (I'm sure you are all disappointed). That being said, as you know, the learning doesn't stop in Mr. Harris's class. Here is your snow day assignment:
- When we left our last meeting, you were directed to complete lesson 2.3. I have posted the answers below, please check, and note any questions/mistakes (better yet, email me)
- Below is a blank copy of lesson 2.4. This lesson is about the graphs and basic properties of logarithmic functions. The key attributes of Logarithmic functions are as follows:
- 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 domain will only change if the function is translated left or right
- The Range of all parent log function is all real numbers (all the time).
- You will notice that all of the above are INVERSES of the attributes of graphs of exponential functions.
- The transformations of Logarithmic function graphs work similarly to the transformations of all the other functions we have studied (such as "horizontal actions are inside the function (with opposite logic), vertical actions are outside the function" (with normal logic)
- 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
* Homework - Check answers to lesson 2.3, complete page 3 of lesson 2.4. I am available over email the entire day if you have any questions or problems, I am happy to help you. As I have mentioned several times, it is MANDATORY that you check the blog on days school is canceled. I am expecting that everyone will do so and will have the HW ready to go on Thursday. If you email me with questions, problems or for any other reason, I am happy to help you. Please be safe and have a good snow day.
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Friday December 6
On the way in, everyone received lesson 2.2. At the start of class everyone completed a warm up related to lesson 2.1. After reviewing the warm up and the HW answers from 2.1 (any my many mistakes on the key), we turned to lesson 2.2. This lesson applies exponential growth to financial investments. After reviewing the simple compounding interest formula on the first page, 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 increase 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 CONTINUALLY all the time by using the continuously compounding interest formula on the bottom of page 2 of the lesson.
* Homework - Complete lesson 2.2, skip problems 61-64, check answers with key below, note questions/problems (better yet, email me). ALSO, complete lesson 2.3 all problems.
On the way in, everyone received lesson 2.2. At the start of class everyone completed a warm up related to lesson 2.1. After reviewing the warm up and the HW answers from 2.1 (any my many mistakes on the key), we turned to lesson 2.2. This lesson applies exponential growth to financial investments. After reviewing the simple compounding interest formula on the first page, 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 increase 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 CONTINUALLY 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 simple compound interest problem
- CLICK HERE for a video that demonstrates a continuously compounding interest problem
- 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
* Homework - Complete lesson 2.2, skip problems 61-64, check answers with key below, note questions/problems (better yet, email me). ALSO, complete lesson 2.3 all problems.
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Wednesday December 11 (3 hr delay)
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 - Complete lesson 2.1 all problems
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.
* Homework - Complete lesson 2.1 all problems
Monday December 9
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 provides an overview of exponential function graphs and their transformations. (use this video for the activity in lesson 2.1)
lesson 2.1 - Basics of exponential functions |
Thursday December 5
Today we played "Family Feud Review in preparation for Monday's Unit Test. Several of you asked for the questions/answers after the game so I posted them below. If you have ANY questions whatsoever about the unit test, please email me (many of you are coming to flex tomorrow).
* Homework - Complete the review guide, check answers (on Tuesday's blog), communicate questions to me (will NOT be checked for a grade)
* Unit Test Alert - The unit 1B test will be on Monday 12/9. The unit test will cover lessons 1.12 - 1.27. See 11/25 blog for details/expectations
Today we played "Family Feud Review in preparation for Monday's Unit Test. Several of you asked for the questions/answers after the game so I posted them below. If you have ANY questions whatsoever about the unit test, please email me (many of you are coming to flex tomorrow).
* Homework - Complete the review guide, check answers (on Tuesday's blog), communicate questions to me (will NOT be checked for a grade)
* Unit Test Alert - The unit 1B test will be on Monday 12/9. The unit test will cover lessons 1.12 - 1.27. See 11/25 blog for details/expectations
unit 1b family feud |
Tuesday December 3 (3 hr Delay)
On the way in to class everyone received the review guide for the Unit 1B test. I started class by making the following reminders/announcements:
* Homework - Complete the review guide, check answers, communicate questions to me (will NOT be checked for a grade)
* Unit Test Alert - The unit 1B test will be on Monday 12/9. The unit test will cover lessons 1.12 - 1.27. See 11/25 blog for details/expectations
On the way in to class everyone received the review guide for the Unit 1B test. I started class by making the following reminders/announcements:
- There will be no quiz on 1.24 - 1.27
- The Unit Test is on Monday (see 11/25 blog for details/expectations)
- Any problems/lessons from 1.24 - 1.27 that were not complete/fully understood
- The Unit Test Review Guide (answers are below, there are a couple of mistakes)
* Homework - Complete the review guide, check answers, communicate questions to me (will NOT be checked for a grade)
* Unit Test Alert - The unit 1B test will be on Monday 12/9. The unit test will cover lessons 1.12 - 1.27. See 11/25 blog for details/expectations
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Wednesday November 27
On the way into class everyone received lesson 1.27 as well as a warm up related to lesson 1.26. Students completed the warm up and then 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 - Complete lesson 1.27, all problems, check answers, email me with questions
* Quiz News - Because of the consecutive early dismissals on B days today/next Tuesday and in an effort not fall WAY behind my other classes, there will NOT be a quiz on lessons 1.24 - 1.27. After 1.27, we will go straight into "Unit Test Review Mode". There will be problems from 1.24 - 1.27 on the unit test.
* Unit Test Alert - The unit 1B test will be on Monday 12/9. You will receive your review guide on Tuesday. The unit test will cover lessons 1.12 - 1.27. See 11/25 blog for details/expectations
On the way into class everyone received lesson 1.27 as well as a warm up related to lesson 1.26. Students completed the warm up and then 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 - Complete lesson 1.27, all problems, check answers, email me with questions
* Quiz News - Because of the consecutive early dismissals on B days today/next Tuesday and in an effort not fall WAY behind my other classes, there will NOT be a quiz on lessons 1.24 - 1.27. After 1.27, we will go straight into "Unit Test Review Mode". There will be problems from 1.24 - 1.27 on the unit test.
* Unit Test Alert - The unit 1B test will be on Monday 12/9. You will receive your review guide on Tuesday. The unit test will cover lessons 1.12 - 1.27. See 11/25 blog for details/expectations
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Monday November 25
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 12/3. One problem from each lesson.
* Unit Test Alert - The unit 1B test will be on Monday 12/9. 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 12/3. One problem from each lesson.
* Unit Test Alert - The unit 1B test will be on Monday 12/9. 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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Thursday November 21
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 12/3
* 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 Monday 12/9
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 12/3
* 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 Monday 12/9
lesson 1.24 - answers |
Tuesday November 19
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 approximately 40 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 approximately 40 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 |
Friday November 15
At the start of class, everyone completed a warm up related to lessons 1.20-1.22. 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 Tuesday on lessons 1.20 - 1.23. After completing lesson 1.23, everyone received some "extra practice" in preparation for Tuesday's quiz on lessons 1.20 - 1.23
* Homework - There is no specific HW for Tuesday, 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 Tuesday 11/14 on lessons 1.20 - 1.23
At the start of class, everyone completed a warm up related to lessons 1.20-1.22. 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 Tuesday on lessons 1.20 - 1.23. After completing lesson 1.23, everyone received some "extra practice" in preparation for Tuesday's quiz on lessons 1.20 - 1.23
* Homework - There is no specific HW for Tuesday, 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 Tuesday 11/14 on lessons 1.20 - 1.23
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Wednesday November 13
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. At the end of class I handed back the quizzes from last week, corrections are due Friday.
* Homework - Complete through lesson 1.22 for Friday.
* Quiz Alert - The next quiz will be after lesson 1.23 which we will cover Friday. Quiz will be on Tuesday 11/19
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. At the end of class I handed back the quizzes from last week, corrections are due Friday.
* Homework - Complete through lesson 1.22 for Friday.
* Quiz Alert - The next quiz will be after lesson 1.23 which we will cover Friday. Quiz will be on Tuesday 11/19
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Friday November 8
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 assigned problems 1-4 as HW, we will complete the remainder of the lesson in class on Wednesday. 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 assigned problems 1-4 as HW, we will complete the remainder of the lesson in class on Wednesday. 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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Wednesday November 6
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 Friday 11/8 on lessons 1.17 - 1.19. There will be one problem from each lesson (1.17, 1.18, 1.19).
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 Friday 11/8 on lessons 1.17 - 1.19. There will be one problem from each lesson (1.17, 1.18, 1.19).
lesson 1.19 - answers |
Friday November 1
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 for about 35 minutes to complete 1.17. With about 25 minutes left in the class I distributed and modeld 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
* Journal Alert - Your 1Q journal is/was due today at 2pm. If I don't have it it is now late
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 for about 35 minutes to complete 1.17. With about 25 minutes left in the class I distributed and modeld 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
* Journal Alert - Your 1Q journal is/was due today at 2pm. If I don't have it it is now late
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Wednesday October 30
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 to use 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 (will be checked for HW grade)
* 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 to use 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 (will be checked for HW grade)
* Journal Alert - Your 1Q journal is due on Friday November 1 at 2pm
1.12 - 1.16 practice quiz answers |
Monday October 28
To start of class, everyone completed a warm up related to lessons 1.15 (using the rational zero theorem to test and then find the zeros of a polynomial). After the warm up, we reviewed the answers to all of 1.15 and I answered questions/resolved issues as needed. On the way in, everyone received lesson 1.16 (blank copy below this post). We started the lesson by reviewing the difference between an imaginary number and a complex number
* 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 Wednesday 10/29 on lessons 1.12 - 1.16
* Journal Alert - Your 1Q Journal is due on Friday November 1 at 2pm
To start of class, everyone completed a warm up related to lessons 1.15 (using the rational zero theorem to test and then find the zeros of a polynomial). After the warm up, we reviewed the answers to all of 1.15 and I answered questions/resolved issues as needed. On the way in, everyone received lesson 1.16 (blank copy below this post). We started the lesson by reviewing the difference between an imaginary number and a complex number
- 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 Wednesday 10/29 on lessons 1.12 - 1.16
* Journal Alert - Your 1Q Journal is due on Friday November 1 at 2pm
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Thursday October 24
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, check answers, come Monday prepared with questions (better yet, email me)
* Quiz Alert - There will be a quiz on Wednesday 10/29 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.
- 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 - Complete lesson 1.16, check answers, come Monday prepared with questions (better yet, email me)
* Quiz Alert - There will be a quiz on Wednesday 10/29 on lessons 1.12 - 1.16
* Journal Alert - Your 1Q Journal is due on Friday November 1 at 2pm
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Tuesday October 22
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, I am projecting Wednesday 10/30
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, I am projecting Wednesday 10/30
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Friday October 18
For the first 10 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 10 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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Friday October 11
On the way into class I returned the quizzes from last Tuesday (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 anything, 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 Friday 10/18. REMINDER, today is our last meeting prior to the test (PSAT's are next Wednesday). It is up to you to communicate with me if there is anything that you do not understand/need help with, it is my pleasure.
* Homework - There is no specific HW due for next Friday however...
* Unit Test Alert - The Unit 1A test will be on Friday 10/18. It will cover lessons 1.1 - 1.11
On the way into class I returned the quizzes from last Tuesday (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 anything, 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 Friday 10/18. REMINDER, today is our last meeting prior to the test (PSAT's are next Wednesday). It is up to you to communicate with me if there is anything that you do not understand/need help with, it is my pleasure.
* Homework - There is no specific HW due for next Friday however...
* Unit Test Alert - The Unit 1A test will be on Friday 10/18. It will cover lessons 1.1 - 1.11
Answers - unit 1A Review guide |
Tuesday October 8
Class started today with a warm up related to lesson 1.11. There were a few issues with understanding so I did a brief demonstration, emphasizing the "short cut" in creating the difference of squares step of the process. After the demonstration, I had everyone complete an additional problem to ensure understanding (the class improved). For the next 20-25 minutes, students reviewed their notes from lessons 1.8 - 1.11 and I answered specific questions about any problems that may be on the quiz. 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. Friday will be a review day, next Wednesday (the next B day) are the PSAT's so there is no meeting. Your Unit 1A test will be on Friday 10/18.
* 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 Friday 10/18. It will cover lessons 1.1 - 1.11
Class started today with a warm up related to lesson 1.11. There were a few issues with understanding so I did a brief demonstration, emphasizing the "short cut" in creating the difference of squares step of the process. After the demonstration, I had everyone complete an additional problem to ensure understanding (the class improved). For the next 20-25 minutes, students reviewed their notes from lessons 1.8 - 1.11 and I answered specific questions about any problems that may be on the quiz. 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. Friday will be a review day, next Wednesday (the next B day) are the PSAT's so there is no meeting. Your Unit 1A test will be on Friday 10/18.
* 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 Friday 10/18. It will cover lessons 1.1 - 1.11
Unit 1A Review Guide |
Friday October 4 (Mr. Harris was absent today)
The sub was instructed to distribute 2 handouts:
* 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.
The class was instructed to complete all problems and check answers using the key below this post (note, I have a couple of minor mistakes including with the "your turn" problem on the front page. Hopefully, you worked with your partners and were able to help each other. We will warm up/review from 1.10 and 1.11 on Tuesday and then there will be a quiz on lessons 1.8 - 1.11 the last 30 minutes of the period.
* Homework - Complete lesson 1.11, check answers and prepare questions for Tuesday
* Quiz Alert - There will be a quiz on lessons 1.8 - 1.11 on Tuesday 10/8
* Unit Test Alert - Lesson 1.11 is the last new lesson of Unit 1A. I am projecting your first Unit test on Friday 10/18. You will receive a review/study guide after your quiz on Tuesday.
The sub was instructed to distribute 2 handouts:
- A warm up related to lesson 1.10
- Lesson 1.11
- 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.
The class was instructed to complete all problems and check answers using the key below this post (note, I have a couple of minor mistakes including with the "your turn" problem on the front page. Hopefully, you worked with your partners and were able to help each other. We will warm up/review from 1.10 and 1.11 on Tuesday and then there will be a quiz on lessons 1.8 - 1.11 the last 30 minutes of the period.
* Homework - Complete lesson 1.11, check answers and prepare questions for Tuesday
* Quiz Alert - There will be a quiz on lessons 1.8 - 1.11 on Tuesday 10/8
* Unit Test Alert - Lesson 1.11 is the last new lesson of Unit 1A. I am projecting your first Unit test on Friday 10/18. You will receive a review/study guide after your quiz on Tuesday.
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Tuesday October 2
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 prepare questions for Tuesday (I will be absent on Friday)
* Quiz Alert - I am projecting a quiz on lessons 1.8 - 1.11 on Tuesday 10/8 (You will complete lesson 1.11 on Friday)
* Unit Test Alert - Lesson 1.11 is the last new lesson of Unit 1A. I am projecting your first Unit test on Friday 10/18
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 prepare questions for Tuesday (I will be absent on Friday)
* Quiz Alert - I am projecting a quiz on lessons 1.8 - 1.11 on Tuesday 10/8 (You will complete lesson 1.11 on Friday)
* Unit Test Alert - Lesson 1.11 is the last new lesson of Unit 1A. I am projecting your first Unit test on Friday 10/18
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Friday September 26
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 - zeros and multiplicity |
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 Friday.
* 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 Friday.
* 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 Friday.
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 Friday.
* 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 Friday.
* 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 Friday.
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Monday September 23
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 the quiz after lunch. After resolving any issues 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 Wednesday however...
* Project Alert - Your 1Q project is due on Tuesday 10/1 @ 7:20 am. You may submit your project early if you wish.
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 the quiz after lunch. After resolving any issues 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 Wednesday however...
* Project Alert - Your 1Q project is due on Tuesday 10/1 @ 7:20 am. You may submit your project early if you wish.
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Thursday September 19
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 helped/checked student answers as needed as everyone was working. After the warm up Students spent 20 minutes continuing to practice from 1.6 and checking the answers below this post (I continued to help/check/model 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 Monday 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 Monday 9/23, it will cover lessons 1.4 - 1.7.
* Project Alert - Your 1Q project is due on Tuesday 10/1 @ 7:20 am. The deadline to request an extension is tomorrow.
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 helped/checked student answers as needed as everyone was working. After the warm up Students spent 20 minutes continuing to practice from 1.6 and checking the answers below this post (I continued to help/check/model 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 Monday 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 Monday 9/23, it will cover lessons 1.4 - 1.7.
* Project Alert - Your 1Q project is due on Tuesday 10/1 @ 7:20 am. The deadline to request an extension is tomorrow.
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Tuesday September 17
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 checked completion of the 1.5 HW from Friday. 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 Thursday
* Quiz Alert - The next quiz will be after lesson 1.7 which we will cover on Thursday, therefore the quiz will be on Monday 9/23 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 checked completion of the 1.5 HW from Friday. 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 Thursday
* Quiz Alert - The next quiz will be after lesson 1.7 which we will cover on Thursday, therefore the quiz will be on Monday 9/23 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.
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Friday September 13
At the start of class, I did 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. Completion of Lesson 1.5 will be checked for a HW grade.
* 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 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. Completion of Lesson 1.5 will be checked for a HW grade.
* 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 1.4 - answers |
Wednesday September 11
At the start of class, I told everyone my September 11th story. I thank you for listening, it meant a lot to share with you. 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. I was pleased with the Piece wise function part of the warm up; but there were several questions about finding domain. I gave a brief demonstration and told everyone that I have provided links below for 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 improved as you practiced, but in case you need extra practice 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 Friday.
* Homework - There is no specific HW for Friday however...
* Quiz Alert - Your first quiz will be on Friday 9/13 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:
At the start of class, I told everyone my September 11th story. I thank you for listening, it meant a lot to share with you. 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. I was pleased with the Piece wise function part of the warm up; but there were several questions about finding domain. I gave a brief demonstration and told everyone that I have provided links below for 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 improved as you practiced, but in case you need extra practice 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 Friday.
* Homework - There is no specific HW for Friday however...
* Quiz Alert - Your first quiz will be on Friday 9/13 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 |
Monday September 9
At the start of class I collected the "half sheet" regarding the A2 skills worksheet from the other day. 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 required 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 - Complete lesson 1.2, check answers and ask me questions (email or bring to next class). ALSO, 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 Friday 9/13 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.
At the start of class I collected the "half sheet" regarding the A2 skills worksheet from the other day. 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 required 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 - Complete lesson 1.2, check answers and ask me questions (email or bring to next class). ALSO, 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 Friday 9/13 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)
Thursday September 5
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 (part 2) - Complete the "back side" of the Algebra 2 skills check. Check your answers using the key below and use the half sheet of paper to answer the questions listed above. I will be collecting this first thing at our next meeting.
* 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.
- Which question(s) were easiest?
- Which question(s) were hardest?
- Which question(s) did you not remember how to do but then when you checked the key, you remembered how to do it?
- Which question(s) do you think you need to practice some more.
- Was there anything you have not seen before?
* Homework (part 2) - Complete the "back side" of the Algebra 2 skills check. Check your answers using the key below and use the half sheet of paper to answer the questions listed above. I will be collecting this first thing at our next meeting.
* 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 3
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. There are 5 of you who did not send me an email, you are now late. Please send to me asap so you can receive partial credit . 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
Our discussion of the above ran a bit longer than I would have liked, so we did not get to complete the back side of the Algebra 2 skills sheet. We will do that first thing on Thursday, please do NOT complete this side of the handout for HW
* Homework - There is no specific HW for Thursday, however if you are one of the few that have not submitted the email HW from last week, please do so asap so you can receive partial credit. (see below for the details of the assignment).
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. There are 5 of you who did not send me an email, you are now late. Please send to me asap so you can receive partial credit . 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
Our discussion of the above ran a bit longer than I would have liked, so we did not get to complete the back side of the Algebra 2 skills sheet. We will do that first thing on Thursday, please do NOT complete this side of the handout for HW
* Homework - There is no specific HW for Thursday, however if you are one of the few that have not submitted the email HW from last week, please do so asap so you can receive partial credit. (see below for the details of the assignment).
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Thursday August 29th
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 1B
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 1B
- 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 Tuesday 9/2:
2019-2020 Honors Precalc Syllabus |