MidSchoolMath 1

If a set of data shows a linear trend, a line can be drawn through the data, and the line (and its equation) can be used to make predictions and answer questions. During The Slope of Sprouts, Delta Team Geologist Kim O’Hara has lost touch with NASA and is concerned about having enough food. She is experimenting with growing her own food under special lights to increase the growth rate. The data provided is a scatter plot, which shows the daily height of various sprouts.

LESSON: THE SLOPE OF SPROUTSHow much do the sprouts grow each day under the lights?

The Slope of Sprouts

Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height.

The Math SimulatorTM

ImmersionPlay The Slope of Sprouts Immersion video, whole-class. Restate the question: How much do the sprouts grow each day under the lights?Facilitate classroom discussion; ask students: "What do we need to know?"

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2 Data & ComputationPrint the Data Artifact and distribute to students. Allow students work time. Ask students: "Does your answer make sense?"Consider using a sharing protocol leading to mathematical insights and/or highlighting misconceptions. Allow students to revise their work.

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3 ResolutionPlay The Slope of Sprouts Resolution video, whole-class. Prepare and give brief lecture (Teacher Instruction).

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Download the Detailed Lesson PlanAvailable on the Teacher Dashboard

+ Simulation TrainerAssign the Simulation Trainer.Use protocols that encourage students to help each other.Use Progress Monitoring to access real-time data for the classroom.Provide individual help for students who are not making progress.

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(Use student headphones.)

8.SP.A.3Statistics & Probability

Clicker QuizLaunch the Clicker Quiz, whole-class.

MidSchoolMath 2The Slope of Sprouts

8.SP.A.3Statistics & Probability

Gladys: A review of linear functions and slope-intercept form may be helpful for this standard.

Kevin: When interpreting the slope of a linear model, be sure students are referenc-ing the variables correctly – the dependent variable (y) as a function of the indepen-dent variable (x).

Megan: Make sure students understand that linear models should only be used for data that suggest a linear association.

KevinSimpson

GladysGraham

MeganLeBleu

Ex. Clicker Quiz #5Standard Math Procedures

Instruction at a Glance

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Interpret slope.

Select appropriate option.

∆ Life Expectancy (y) = 2=

D: All of these are true.

∆ Year of Birth (x) 7

2 Compare to each option.

True. 2-year increase in life expectancy for every 7 years that pass

A: 27

True. ≈ 0.285 0.285 years increase in life expectancy for every one year that passes

B: 27

True. = 4-year increase in life expectancy for every 14 years that pass

C: 27

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THE SLOPE OF SPROUTSHow much do the sprouts grow each day under the lights?Delta Team Geologist Kim O’Hara has lost touch with NASA so she is experimenting with growing her own food.

Using her super-powered grow lights, O’Hara has already begun growing potatoes, tomatoes and peas, but she has just planted some basil, so she can give her potatoes some fl avor. She has tracked the growth of her basil sprouts over the last fi ve days and has determined that the height of the sprouts and the number of days they have been growing is linearly related.

Draw a line of best fi t for O’Hara’s data. Write an equation for the line, and use it to determine the daily growth rate of the basil sprouts.

8.SP.A.3

Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height.

About this standard

Date PeriodName

MidSchoolMath The Slope of Sprouts 1 of 2

Equation: _________________ Daily Growth Rate: _________________

APPLYING THE STANDARD

For each problem below, an equation is given that models the linear relationship of two variables. Interpret the slope and y-intercept (if reasonable) within the context of the two variables.

MidSchoolMath The Slope of Sprouts 2 of 2

Date PeriodName

How might this standard appear on a test?

y = -4.3x + 80.5

x: Exercise per week (hrs)y: Resting Heart Rate (bpm)

1) y = 19.35x - 870

x: Temperature (°F)y: Ice Cream Sales ($)

2)

A pediatrician has measured and recorded Alysha’s height every year since she was 4 years old.4)

The scatter plot shows a relationship between Study Time and GPA.3)

Meaning of slope:

Meaning of y-intercept:

Meaning of slope:

Meaning of y-intercept:

Draw a line of best fi t, and write an equation that models the relationship.

a)

Use the points (4, 2.25) and (7, 3.25) to write a linear equation that models the data.

a)

What does the slope mean in this context?

b) What does the y-intercept mean in this context?

c)

Use your equation to predict Alysha’s height when she is 16 years old.

b)

Use your equation to predict Alysha’s age when she was 27 inches tall.

c)

Check out my worked example #1

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