MidSchoolMath 1

A word problem, a graph, a table of values, and an algebraic equation can all be used to express the same idea. Translating these ideas from one form to another can be useful, especially when two different representations of functions have to be compared. In Happy Trails, cowgirl Dallas Sparks is looking for the quickest way to get to Jalisco, México for work. She comes across a drifter, Cornelius Defray, who gives her information about two possible trails that run the same distance, but with unknown rates of travel: Old Pico’s Way and Brogan’s Trail. The data provided is a travel logbook which Dallas will use to find the rate of travel for each trail: one from a verbal description and one from a table.

LESSON: HAPPY TRAILSWhich trail is faster?

Happy Trails

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.

The Math SimulatorTM

ImmersionPlay Happy Trails Immersion video, whole-class. Restate the question: Which trail is faster?Facilitate classroom discussion; ask students: "What do we need to know?"

•

••

1

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.

•

•

•

•

3 ResolutionPlay Happy Trails Resolution video, whole-class. Prepare and give brief lecture (Teacher Instruction).

••

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.

•

•

••

(Use student headphones.)

8.F.A.2Functions

Clicker QuizLaunch the Clicker Quiz, whole-class.

MidSchoolMath 2Happy Trails

8.F.A.2Functions

Gladys: When describing a function and discussing its properties, consider answering questions like these: What is the slope? Is the function increasing or decreasing? What is the y-intercept? Is the function proportional? For what x-values is the function positive or negative?

Kevin: As often as possible, have students explain how the same information can be found in verbal, tabular, graphic, and equation forms.

Megan: Consider showing one form of a function and asking students to write down everything they know about that function, including details about its other forms. Share out ideas as a class. Repeat with the various forms of different functions.

KevinSimpson

GladysGraham

MeganLeBleu

Ex. Clicker Quiz #2Standard Math Procedures

Instruction at a Glance

1 Determine the rate of change (slope) of Function A.

∆y = 3 =

∆y = 3 =

∆x 2

∆x 1

2

3

Determine the rate of change (slope) of Function B.

Select function with greater rate of change.B: Function B

= = 1.5

= = 3

8.F

Stan

dard

s &

Les

sons

8.F

Ass

essm

ents

8.F

Dom

ain

Revi

ew

HAPPY TRAILSWhich trail is faster?Dallas “Do-Right” Sparks was successful as a cowhand in México, but is ready to come back home. She decides to try out a new trail, as Old Pico’s Way was a bit slow for her liking. She estimates the new trail will be the same distance as Old Pico’s way.

Dallas keeps her travel details in the logbook she bought from the drifter. That way, the Do-Right Passage will never be forgotten.

Use the logbook to determine if Old Pico’s Way or the Do-Right Passage is faster.

8.F.A.2

Compare properties of two functions each represented in a diff erent way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.

About this standard

Date PeriodName

MidSchoolMath Happy Trails 1 of 2

Draw Function D with a

rate of change (slope)

of and a y-intercept

of 1.

APPLYING THE STANDARD

Which statements about the properties of Function A, Function B, and Function C are true?

Mark each true statement with an ‘X’.

MidSchoolMath Happy Trails 2 of 2

Date PeriodName

How might this standard appear on a test?

_______ 1a) Functions A, B, and C are linear._______ 1b) Functions A, B, and C have y-intercepts below the x-axis._______ 1c) Functions B is proportional._______ 1d) The rate of change (slope) of Function A is less than the rate of change (slope) of Function C._______ 1e) Function A and Function B both have a positive rate of change (slope)._______ 1f) Function C is neither increasing nor decreasing._______ 1g) At x = 1, the value of Function B is greater than the value of Function A and Function C._______ 1h) The equation for Function C is y = -5.

23

2a) For Function E, write a linear equation with a greater rate of change (slope) than Function D and a y-intercept that is below the x-axis.

2b) Create a table of values that shows Function F is proportional and has a rate of change (slope) of -3.

2c)

Check out my worked example #1b

8.F

Stan

dard

s &

Les

sons

8.F

Ass

essm

ents

8.F

Dom

ain

Revi

ew