Algebra 2 5-8 Guided Practice: Polynomial Models in the Real World

Last updated over 3 years ago

19 questions

3

10

3

10

F.IF.4

F.IF.5

3

7

10

14

F.IF.5

F.IF.6

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Algebra 2 5-8 Guided Practice: Polynomial Models in the Real World

Last updated over 3 years ago

19 questions

3

You are designing a patio. Square A is where you will place your grill. You are experimenting with your design by varying the size of square B. 

10

F.IF.5

10

F.IF.5

F.IF.6

3

10

Take Note: Restate The (n + 1) Point Principle in your own words.

10

Draggable item		Corresponding Item

10

3

10

Take Note: Summarize the process of modeling data that is used in Problem 2.

10

F.IF.5

3

10

F.IF.4

F.IF.5

3

5

Take Note: Define interpolation. You may use the canvas to help illustrate your written definition.

5

7

10

Problem 4 Got It?
Create a table at desmos.com and use it to find a linear regression model of the cheese consumption data. Let x = years since 1900. Recall Desmos' linear regression notation: y1~ax1+b.
Zoom and pan your graph to establish an appropriate viewing window that contains all data points and the regression line.
Take a screenshot of your graph and upload or paste it to the Formative canvas.

14

F.IF.5

F.IF.6

10

🧠 Retrieval Practice:
Summarize the mathematical content of this lesson. What topics, ideas, and vocabulary were introduced?

Video Check: Select all that apply with regards to the video embedded directly above this item.

🕵️ I carefully watched the entire video.

📵 I removed distractions from my field of view while watching the entire video.

🎧 I used headphones (or earbuds) to listen to the entire video as I watched it.

✋ I sought clarification, as needed, to understand each concept in the video.

🎓 I understand each concept in the video and feel ready to move on.

🎯 I feel prepared to complete challenging problems related to the video.

❌ None of these statements apply.

You are designing a patio. Square A is where you will place your grill. You are experimenting with your design by varying the size of square B. 

The table shows the total patio area for each of five different lengths x.

10

F.IF.5

10

F.IF.5

F.IF.6

Video Check: Select all that apply with regards to the video embedded directly above this item.

🕵️ I carefully watched the entire video.

📵 I removed distractions from my field of view while watching the entire video.

🎧 I used headphones (or earbuds) to listen to the entire video as I watched it.

✋ I sought clarification, as needed, to understand each concept in the video.

🎓 I understand each concept in the video and feel ready to move on.

🎯 I feel prepared to complete challenging problems related to the video.

❌ None of these statements apply.

10

Take Note: Restate The (n + 1) Point Principle in your own words.

Take Note: Match each Desmos regression notation with the appropriate model.

Draggable item		Corresponding Item

10

Video Check: Select all that apply with regards to the video embedded directly above this item.

🕵️ I carefully watched the entire video.

📵 I removed distractions from my field of view while watching the entire video.

🎧 I used headphones (or earbuds) to listen to the entire video as I watched it.

✋ I sought clarification, as needed, to understand each concept in the video.

🎓 I understand each concept in the video and feel ready to move on.

🎯 I feel prepared to complete challenging problems related to the video.

❌ None of these statements apply.

10

Take Note: Summarize the process of modeling data that is used in Problem 2.

10

F.IF.5

Video Check: Select all that apply with regards to the video embedded directly above this item.

🕵️ I carefully watched the entire video.

📵 I removed distractions from my field of view while watching the entire video.

🎧 I used headphones (or earbuds) to listen to the entire video as I watched it.

✋ I sought clarification, as needed, to understand each concept in the video.

🎓 I understand each concept in the video and feel ready to move on.

🎯 I feel prepared to complete challenging problems related to the video.

❌ None of these statements apply.

Problem 3 Got It? If four data points are given, which type of regression function can guarantee a perfect fit?
HINT: Recall The (n+1) Point Principle.

constant

linear

quadratic

cubic

Video Check: Select all that apply with regards to the video embedded directly above this item.

🕵️ I carefully watched the entire video.

📵 I removed distractions from my field of view while watching the entire video.

🎧 I used headphones (or earbuds) to listen to the entire video as I watched it.

✋ I sought clarification, as needed, to understand each concept in the video.

🎓 I understand each concept in the video and feel ready to move on.

🎯 I feel prepared to complete challenging problems related to the video.

❌ None of these statements apply.

5

Take Note: Define interpolation. You may use the canvas to help illustrate your written definition.

5

Take Note: Define extrapolation. You may use the canvas to help illustrate your written definition.

Take Note: Consider modeling the data in the table.
Classify each year in the left column below based on whether estimating cheese consumption that year is an example of interpolation or extrapolation.

1995
2000
2019
1950
2050
1890
2005

Interpolation
Extrapolation

Problem 4 Got It?
Create a table at desmos.com and use it to find a linear regression model of the cheese consumption data. Let x = years since 1900. Recall Desmos' linear regression notation: y1~ax1+b.
Zoom and pan your graph to establish an appropriate viewing window that contains all data points and the regression line.
Take a screenshot of your graph and upload or paste it to the Formative canvas.

Problem 4 Got It? Use the model you created above to estimate cheese consumption for 1980, 2000, and 2012 algebraically and/or graphically. Remember that you were instructed to let x represent years since 1900.
Also, identify the prediction years in which you can have the most and least confidence.
Hint: Consider interpolation vs extrapolation.

26.31 lb
23.07 lb
21.53 lb
17.7 lb
1980
2000
2012

Estimated consumption in 1980
Estimated consumption in 2000
Estimated consumption in 2012
Two prediction years with greatest confidence
Prediction year with least confidence

10

🧠 Retrieval Practice:
Summarize the mathematical content of this lesson. What topics, ideas, and vocabulary were introduced?

Video Check: Select all that apply with regards to the video embedded directly above this item.

🕵️ I carefully watched the entire video.

📵 I removed distractions from my field of view while watching the entire video.

🎧 I used headphones (or earbuds) to listen to the entire video as I watched it.

✋ I sought clarification, as needed, to understand each concept in the video.

🎓 I understand each concept in the video and feel ready to move on.

🎯 I feel prepared to complete challenging problems related to the video.

❌ None of these statements apply.

The table shows the total patio area for each of five different lengths x.

Solve It! Based on the pattern in the table, find the total area when x is 5.

43 m²

58 m²

60 m²

53 m²

Solve It! What type of polynomial function does the data fit? Explain.

The data fit a linear function because the first differences are constant.

The data fit a quadratic function because the second differences are constant and the first are not.

The data fit a cubic function because the third differences are constant and the second are not.

The data fit a quartic function because the fourth differences are constant and the third are not.

Video Check: Select all that apply with regards to the video embedded directly above this item.

🕵️ I carefully watched the entire video.

📵 I removed distractions from my field of view while watching the entire video.

🎧 I used headphones (or earbuds) to listen to the entire video as I watched it.

✋ I sought clarification, as needed, to understand each concept in the video.

🎓 I understand each concept in the video and feel ready to move on.

🎯 I feel prepared to complete challenging problems related to the video.

❌ None of these statements apply.

Take Note: Match each Desmos regression notation with the appropriate model.

Problem 1 Got It?

A

B

C

D

Video Check: Select all that apply with regards to the video embedded directly above this item.

🕵️ I carefully watched the entire video.

📵 I removed distractions from my field of view while watching the entire video.

🎧 I used headphones (or earbuds) to listen to the entire video as I watched it.

✋ I sought clarification, as needed, to understand each concept in the video.

🎓 I understand each concept in the video and feel ready to move on.

🎯 I feel prepared to complete challenging problems related to the video.

❌ None of these statements apply.

Problem 2 Got It?

A

B

C

D

Video Check: Select all that apply with regards to the video embedded directly above this item.

🕵️ I carefully watched the entire video.

📵 I removed distractions from my field of view while watching the entire video.

🎧 I used headphones (or earbuds) to listen to the entire video as I watched it.

✋ I sought clarification, as needed, to understand each concept in the video.

🎓 I understand each concept in the video and feel ready to move on.

🎯 I feel prepared to complete challenging problems related to the video.

❌ None of these statements apply.

Problem 3 Got It? If four data points are given, which type of regression function can guarantee a perfect fit?
HINT: Recall The (n+1) Point Principle.

constant

linear

quadratic

cubic

Video Check: Select all that apply with regards to the video embedded directly above this item.

🕵️ I carefully watched the entire video.

📵 I removed distractions from my field of view while watching the entire video.

🎧 I used headphones (or earbuds) to listen to the entire video as I watched it.

✋ I sought clarification, as needed, to understand each concept in the video.

🎓 I understand each concept in the video and feel ready to move on.

🎯 I feel prepared to complete challenging problems related to the video.

❌ None of these statements apply.

Take Note: Define extrapolation. You may use the canvas to help illustrate your written definition.

Take Note: Consider modeling the data in the table. 
Classify each year in the left column below based on whether estimating cheese consumption that year is an example of interpolation or extrapolation.

1995

2000

2019

1950

2050

1890

2005

Interpolation

Extrapolation

Problem 4 Got It? Use the model you created above to estimate cheese consumption for 1980, 2000, and 2012 algebraically and/or graphically. Remember that you were instructed to let x represent years since 1900. 
Also, identify the prediction years in which you can have the most and least confidence. 
Hint: Consider interpolation vs extrapolation.

26.31 lb

23.07 lb

21.53 lb

17.7 lb

1980

2000

2012

Estimated consumption in 1980

Estimated consumption in 2000

Estimated consumption in 2012

Two prediction years with greatest confidence

Prediction year with least confidence

Solve It! Based on the pattern in the table, find the total area when x is 5.

43 m²

58 m²

60 m²

53 m²

Solve It! What type of polynomial function does the data fit? Explain.

The data fit a linear function because the first differences are constant.

The data fit a quadratic function because the second differences are constant and the first are not.

The data fit a cubic function because the third differences are constant and the second are not.

The data fit a quartic function because the fourth differences are constant and the third are not.

Problem 1 Got It?

A

B

C

D

Problem 2 Got It?

A

B

C

D

Algebra 2 5-8 Guided Practice: Polynomial Models in the Real World

Algebra 2 5-8 Guided Practice: Polynomial Models in the Real World

Take Note: Restate The (n + 1) Point Principle in your own words.

Take Note: Summarize the process of modeling data that is used in Problem 2.

Take Note: Define interpolation. You may use the canvas to help illustrate your written definition.

🧠 Retrieval Practice:Summarize the mathematical content of this lesson. What topics, ideas, and vocabulary were introduced?

Video Check: Select all that apply with regards to the video embedded directly above this item.

Video Check: Select all that apply with regards to the video embedded directly above this item.

Take Note: Restate The (n + 1) Point Principle in your own words.

Take Note: Match each Desmos regression notation with the appropriate model.

Video Check: Select all that apply with regards to the video embedded directly above this item.

Take Note: Summarize the process of modeling data that is used in Problem 2.

Video Check: Select all that apply with regards to the video embedded directly above this item.

Problem 3 Got It? If four data points are given, which type of regression function can guarantee a perfect fit?HINT: Recall The (n+1) Point Principle.

Video Check: Select all that apply with regards to the video embedded directly above this item.

Take Note: Define interpolation. You may use the canvas to help illustrate your written definition.

Take Note: Define extrapolation. You may use the canvas to help illustrate your written definition.

Take Note: Consider modeling the data in the table. Classify each year in the left column below based on whether estimating cheese consumption that year is an example of interpolation or extrapolation.

🧠 Retrieval Practice:Summarize the mathematical content of this lesson. What topics, ideas, and vocabulary were introduced?

Solve It! Based on the pattern in the table, find the total area when x is 5.

Solve It! What type of polynomial function does the data fit? Explain.

Problem 1 Got It?

Problem 2 Got It?

Take Note: Define extrapolation. You may use the canvas to help illustrate your written definition.

🧠 Retrieval Practice:
Summarize the mathematical content of this lesson. What topics, ideas, and vocabulary were introduced?

Problem 3 Got It? If four data points are given, which type of regression function can guarantee a perfect fit?
HINT: Recall The (n+1) Point Principle.

Take Note: Consider modeling the data in the table.
Classify each year in the left column below based on whether estimating cheese consumption that year is an example of interpolation or extrapolation.

🧠 Retrieval Practice:
Summarize the mathematical content of this lesson. What topics, ideas, and vocabulary were introduced?