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Unit 3, Lesson 7

Confident Models

Extra Support Materials for Algebra 1

7.1

Warm-up

Mentally order the numbers from least to greatest.

20.2, 18.2, 19.2
-14.6, -16.7, -15.1
-0.43, -0.87, -0.66
0.50, -0.52, 0.05

7.2

Activity

Here are scatter plots that represent various situations. Order the scatter plots from “A linear model is not a good fit for the data” to “A linear model is an excellent fit for the data.”

A

B

C

Scatter plot on grid, origin O. Horizontal axis, men’s ages, from 0 to 40, by 10’s. Vertical axis, length of beard, centimeters, from 0 to 35, by 5’s. 39 data points at 15 comma 15, 18 comma 0, 19 comma 6, 19 comma 14, 20 comma 7, 20 comma 4, 22 comma 0, 22 comma 12, 23 comma 3, 25 comma 22, 25 comma 25, 26 comma 26, 26 comma 9, 27 comma 14, 27 comma 25, 27 comma 27, 28 comma 18, 28 comma 25, 29 comma 22, 29 comma 20, 30 comma 13, 32 comma 11, 32 comma 12, 34 comma 22, 32 comma 19, 35 comma 22, 25 comma 28, 36 comma 15, 36 comma 17, 36 comma 18, 36 comma 23, 37 comma 14, 37 comma 20, 38 comma 16, 38 comma 23, 38 comma 33, 39 comma 16, 39 comma 19 and 39 comma 32.

D

Scatter plot on grid, origin O. Horizontal axis, time eating lunch, minutes, from 0 to 45 by 5’s. Vertical axis, number of absences, from 0 to 20, by 5’s. 50 data points. 1 comma 3, 1 comma 14, 3 comma 14, 4 comma 5, 5 comma 17, 7 comma 1, 10 comma 2, 11 comma 10, 12 comma 3, 12 comma 19, 13 comma 11, 15 comma 8, 15 comma 12, 15 comma 14, 19 comma 5, 19 comma 15, 20 comma 4, 20 comma 13, 20 comma 17, 21 comma 5, 21 comma 10, 21 comma 10, 22 comma 7, 23 comma 1, 23 comma 6, 25 comma 10, 26 comma 7, 27 comma 0, 29 comma 6, 30 comma 1, 30 comma 3, 30 comma 8, 30 comma 17, 32 comma 3, 33 comma 0, 33 comma 8, 35 comma 11, 37 comma 11, 38 comma 2, 38 comma 15, 38 comma 19, 39 comma 8, 39 comma 18, 40 comma 0, 40 comma 12, 40 comma 18, 42 comma 12, 43 comma 7, 43 comma 7, 43 comma 15.

E

Scatter plot on grid, origin O. Horizontal axis, time sharpening the pencil, seconds, from 0 to 30 by 5’s. Vertical axis, length of pencil, millimeters, from 0 to 150 by 30’s. 50 data points. 1 comma 148, 2 comma 133, 3 comma 139, 4 comma 123, 4 comma 127, 5 comma 117, 7 comma 132, 8 comma 102, 8 comma 106, 9 comma 98, 9 comma 119, 9 comma 123, 10 comma 108, 10 comma 108, 11 comma 110, 12 comma 75, 12 comma 76, 12 comma 78, 15 comma 56, 15 comma 89, 16 comma 50, 16 comma 56, 17 comma 46, 17 comma 48, 17 comma 64, 19 comma 57, 19 comma 60, 19 comma 60, 19 comma 66, 20 comma 38, 22 comma 22, 22 comma 24, 22 comma 24, 22 comma 41, 22 comma 43, 23 comma 50, 24 comma 32, 24 comma 33, 25 comma 5, 25 comma 10, 25 comma 43, 26 comma 19, 26 comma 23, 26 comma 27, 27 comma 6, 27 comma 9, 27 comma 31, 28 comma 18, 29 comma 10, 29 comma 18.
Here are two scatter plots including a linear model. For each model, determine the when is 15. Which model prediction do you think is closer to the real data? Explain your reasoning.

<p>Scatter plot and line on grid.</p> — Graph F.

A first quadrant scatter plot comparing time for dog haircut (minutes) with dog hair length after grooming (mm) with the line of best fit. — Graph G.

7.3

Activity

Here are situations represented with graphs and linear models of the data. Use the information given to complete the missing fields for each situation.

The model predicts how much money, in dollars, the coach will make based on how many athletes sign up for one-on-one training. The model is represented with the equation .
Scatter plot and line on grid, origin O. Horizontal axis, number of athletes, from 0 to 35 by 5’s. Vertical axis, amount, dollars, from 0 to 1400 by 200’s. Line, moving upwards and to the right, passes through 5 comma 325, 10 comma 450, 15 comma 575, 20 comma 700, 25 comma 825, and 30 comma 950. 10 data points, located at 4 comma 300, 5 comma 375, 9 comma 410, 10 comma 420, 13 comma 525, 15 comma 60, 20 comma 700, 25 comma 820, 27 comma 830, and 30 comma 950.
- The slope of the model is (positive or negative).
- What does the model predict would be the amount the coach makes when there are 10 athletes present?
- Using the data points and the model as a reference, what is a reasonable range of money the coach will make when there are 10 athletes present?
- This model is a (great, good, okay, or bad) fit for the data.
- Using numbers between 0 and 1, rate your confidence in the model where 0 is no confidence and 1 is total confidence.
The model predicts the annual salary of a worker in a certain government position based on years of experience. The model is represented with the equation .
Scatter plot and line on grid, origin O. Horizontal axis, years of experience, from 0 to 20 by 5’s. Vertical axis, salary, thousands of dollars, from 0 to 70 by 10’s. Line moving upwards and to the right, passes through 3 comma 39 point 5, 10 comma 50, and ends at 15 comma 57 point 5. 9 data points at 3 comma 40, 5 comma 30, 7 comma 50, 9 comma 48, 10 comma 60, 11 comma 58, 12 comma 61 and 14 comma 59. 6 points fall above the line, 2 points fall on the line, 1 point falls well below the line.
- The slope of the model is (positive or negative).
- What does the model predict would be the employee’s salary when the employee has 10 years of experience?
- Using the data points and the model as a reference, what is a reasonable range for the salary of a worker based on 10 years of experience?
- This model is a (great, good, okay, or bad) fit for the data.
- Using numbers between 0 and 1, rate your confidence in the model where 0 is no confidence and 1 is total confidence.
The model predicts the number of absences a school will have based on the number of incentives given per month. The model is represented with the equation .
Scatter plot and line on grid, origin O. Horizontal axis, number of incentives, from 0 to 20 by 5’s. Vertical axis, number of absences, from 0 to 70 by 10’s. Line, moving downward and to the right, passes through 0 comma 54 point 78, 5 comma 65 point 68, 10 comma 76 point 58 and 15 comma 87 point 48. 30 data points at 0 comma 48, 1 comma 60, 2 comma 42, 3 comma 51, 5 comma 55, 6 comma 32, 6 comma 46, 6 comma 60, 7 comma 30, 7 comma 37, 7 comma 5, 8 comma 13, 8 comma 33, 9 comma 22, 9 comma 32, 9 comma 46, 10 comma 25, 10 comma 37, 10 comma 52, 11 comma 28, 11 comma 30, 11 comma 33, 12 comma 0, 13 comma 28, 13 comma 33, 13 comma 40, 13 comma 53, 14 comma 6, 14 comma 15 and 15 comma 28.
- The slope of the model is (positive or negative).
- What does the model predict would be the number of absences when 10 incentives are given for the month?
- Using the data points and the model as a reference, what is a reasonable number of absences when there are 10 incentives given?
- This model is a (great, good, okay, or bad) fit for the data.
- Using numbers between 0 and 1, rate your confidence in the model where 0 is no confidence and 1 is total confidence.