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9-12 Extra Support Materials for Algebra 1 Unit 3 Lesson 5

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Algebra 1 Geometry Algebra 2 •Extra Support Materials for Algebra 1

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Extra Support Materials for Algebra 1

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Lesson 5

5.1 Warm-up 5.2 Activity 5.3 Activity

Unit 3, Lesson 5

Goodness of Fit

Extra Support Materials for Algebra 1

5.1

Warm-up

Each situation can be modeled using a linear equation. Describe the rate of change for each situation.

Andre started his no-interest savings account with \$1,000. He made the same deposit each week, and there was \$1,600 in the account after 6 weeks. How much money did Andre deposit each week?
Kiran started with \$748 in his checking account. After 4 weeks of spending the same amount each week, he had \$716 left. How much money did Kiran spend each week?

5.2

Activity

Here are 3 copies of the same scatter plot. Each student tries to draw a line that models the data well.

Noah says his line fits the data well because the line connects the leftmost point to the rightmost point.

Scatter plot on grid, origin O. Horizontal x axis from 0 to 12 by 1’s. Vertical y axis from 0 to 14 by 1’s. 11 data points at 1 comma 7, 2 comma 12, 4 comma 9, 5 comma 12, 6 comma 8, 7 comma 11, 8 cooma 6, 9 comma 11, 10 comma 8, 11 comma 4 and 12 comma 2. A line is drawn from 1 comma 7, downward and to the right to 12 comma 2. 9 points fall above the line.

Lin says her line fits the data well because the points are somewhat evenly arranged around the line with about half the points above the line and half the points below the line.

Scatter plot on grid, origin O. Horizontal x axis from 0 to 12 by 1’s. Vertical y axis from 0 to 14 by 1’s. 11 data points at 1 comma 7, 2 comma 12, 4 comma 9, 5 comma 12, 6 comma 8, 7 comma 11, 8 comma 6, 9 comma 11, 10 comma 8, 11 comma 4 and 12 comam 2. A line is drawn from 2 comma 14, downward and to the right to 12 comma 3. 6 points fall below the line, 4 points fall above the line

Andre says his line fits the data well because it passes directly through as many points as possible.

Scatter plot on grid, origin O. Horizontal x axis from 0 to 12 by 1’s. Vertical y axis from 0 to 14 by 1’s. 11 data points at 1 comma 7, 2 comma 12, 4 comma 9, 5 comma 12, 6 comma 8, 7 comma 11, 8 comma 6, 9 comma 11, 10 comma 8, 11 comma 4 and 12 comam 2. A line is drawn from 2 comma 12, downward and to the right to 12 comma 2. 2 points fall below the line, 5 points fall above the line.

Do you agree with any of these students? Explain your reasoning.

5.3

Activity

Look at the scatter plots and figure out which one is best modeled by a linear model.

A
Scatter plot with 19 points plotted. Points at 0 comma 23, 1 comma 25, 2 comma 24, 5 comma 17, 7 comma 17, 10 comma 15, 10 comma 18, 12 comma 16, 13 comma 14, 14 comma 14, 16 comma 8, 16 comma 9, 16 comma 11, 17 comma 5, 18 comma 9, 19 comma 9, 20 comma 4, 20 comma 5, 20 comma 6.

B
Scatter plot with 18 points plotted. Points plotted at 0 comma 19, 0 comma 20, 2 comma 20, 3 comma 20, 4 comma 19, 5 comma 18, 5 comma 19, 7 comma 17, 9 comma 14, 9 comma 15, 10 comma 13, 10 comma 14, 11 comma 13, 12 comma 11, 13 comma 10, 14 comma 8, 17 comma 1, 17 comma 2.

C
Scatter plot with 20 points plotted. Points at 1 comma 25, 2 comma 20, 2 comma 21, 3 comma 18, 4 comma 15, 6 comma 14, 7 comma 12, 8 comma 11, 8 comma 12, 10 comma 9, 10 comma 10, 11 comma 9, 13 comma 8, 14 comma 8, 17 comma 7, 18 comma 6, 18 comma 7, 19 comma 5, 19 comma 6, 20 comma 5.
Draw a linear model that fits the data well on the appropriate scatter plot. Compare your line with a partner’s. If your lines are different, determine which line is the better fit line.

None