How Does it Change?: IM Alg1.6.2
[url=https://im.kendallhunt.com/HS/teachers/1/6/2/preparation.html]“How Does it Change?”[/url] from IM Algebra I © 2019 [url=https://www.illustrativemathematics.org/]Illustrative Mathematics[/url]. Licensed under the [url=https://creativecommons.org/licenses/by/4.0/]Creative Commons Attribution 4.0[/url] license.
Table of Contents
- Alg1.6.2 Lesson
- IM Alg1.6.2 Lesson: How Does it Change?
- Alg1.6.2 Practice
- IM Alg1.6.2 Practice: How Does it Change?
IM Alg1.6.2 Lesson: How Does it Change?
How does each expression represent the number of small squares in the figure?
[img]data:image/png;base64,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[/img][br]Expression A: [math]6\cdot8-2\cdot3[/math]
Expression B: [math]4\cdot8+2\cdot5[/math]
Expression C: [math]8+8+8+8+5+5[/math]
Expression D: [math]5\cdot6+3\cdot4[/math]
Study the 2 patterns of dots.
[img]data:image/png;base64,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[/img][br][img]data:image/png;base64,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[/img][br][br]How are the number of dots in each pattern changing?
How would you find the number of dots in the 5th step in each pattern?[br]
Complete the table with the number of dots in each pattern.
Plot the number of dots at each step number for Pattern 1.
Plot the number of dots at each step number for Pattern 2.
Explain why the graphs of the 2 patterns look the way they do.
Here is a pattern of squares.
[img]data:image/png;base64,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[/img][br]Is the number of small squares growing linearly? Explain how you know.
Complete the table.
Is the number of small squares growing exponentially? Explain how you know.[br]
[size=150]Han wrote [math]n\left(n+2\right)-2\left(n-1\right)[/math] for the number of small squares in the design at Step [math]n[/math].[/size][br][br]Explain why Han is correct.[br]
Label the picture in a way that shows how Han saw the pattern when writing his expression.
IM Alg1.6.2 Practice: How Does it Change?
[br][img]data:image/png;base64,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[/img][br]How many small squares are in Step 10?
Here are 2 patterns of dots.
[size=150]Pattern A[br][img]data:image/png;base64,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[/img][br][br]Pattern B[/size][br][br][img]data:image/png;base64,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[/img][br][br]How many dots will there be in Step 4 of each pattern?
Which pattern shows a quadratic relationship between the step number and the number of dots? Explain how you know.[br]
Here are descriptions for how two dot patterns are growing.
[list][size=150][*]Pattern A: Step 2 has 10 dots. It grows by 3 dots at each additional step.[/*][*]Pattern B: The total number of dots can be expressed by [math]2n^2+1[/math], where [math]n[/math] is the step number.[/*][/size][/list]
For each pattern, draw a diagram of Step 0 to Step 3.
[size=150]Each expression represents the total number of dots in a pattern where n represents the step number. [br][br]Select [b]all[/b] the expressions that represent a quadratic relationship between the step number and the total number of dots. (If you get stuck, consider sketching the first few steps of each pattern as described by the expression.)[/size]
[size=150]The function [math]C[/math] gives the percentage of homes using only cell phone service [math]x[/math] years after 2004. Explain the meaning of each statement.[/size][br][br][math]C\left(10\right)=35[/math]
[math]C\left(x\right)=10[/math]
How is [math]C\left(10\right)[/math] different from [math]C\left(x\right)=10[/math]?
Here are some lengths, widths, and areas of a garden whose perimeter is 40 feet. Complete the table with the missing measurements.
What lengths and widths do you think will produce the largest possible area? Explain how you know.
A bacteria population is 10,000 when it is first measured and then doubles each day. Use this information to complete the table.
Which is the first day, after the antibiotic is given, that the bacteria population is more than 1,000,000?[br]
Write an equation relating [math]p[/math], the bacteria population, to [math]d[/math], the number of days since it was first measured.