MidSchoolMath 1

Interpreting graphs and sketching them to tell an accurate story is often a difficult skill for students, so it’s helpful for them to experience the many characteristics of a graph. In Twin Tactics, twins Jon and Jordan Wonder are about to have an important business meeting about the stock of their company, Wonder Toys. Jon tells Jordan that, today, he’s going to have to handle the meeting himself. Jordan is nervous, but Jon has the idea to feed Jordan the stock information through an earpiece while Jordan makes a graph live for the meeting attendees. Jon gives Jordan the first piece of information, and Jordan draws the first line. The data provided are Jordan’s graph and the stock information that Jon is providing to him.

LESSON: TWIN TACTICSHow will Jordan draw the rest of the graph?

Twin Tactics

Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g. where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

The Math SimulatorTM

ImmersionPlay Twin Tactics Immersion video, whole-class. Restate the question: How will Jordan draw the rest of the graph?Facilitate classroom discussion; ask students: "What do we need to know?"

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2 Data & ComputationPrint the Data Artifact, cut into halves, 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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Download the Detailed Lesson PlanAvailable on the Teacher Dashboard

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

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+ 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.F.B.5Functions

MidSchoolMath 2Twin Tactics

8.F.B.5Functions

Clicker QuizLaunch the Clicker Quiz, whole-class.

Gladys: When students are interpreting a graph, it is imperative that they know what variables are represented on the two axes.

Kevin: Students may need extra practice reading, writing, and interpreting inequalities representing intervals on a graph (e.g. -2 < x ≤ 6).

Megan: Consider giving small groups the same graph, with axes labeled (time/distance, time/speed, time/height). Set up the context (a car driving to a gas station, a boy walking to school, a ball being thrown in the air, etc.). Ask groups to write the story of what is happening. Have groups share out and respectfully critique each other's stories until arriving at a consensus about what occurred according to the graph.

KevinSimpson

GladysGraham

MeganLeBleu

Ex. Clicker Quiz #5Standard Math Procedures

Instruction at a Glance

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Analyze the table.

Select the appropriate answer.

Discuss the result in the context of a diver, maybe sketching a graph.

D: Non-linear function that increases then decreases.

A diver begins on the diving board at a height above the water. She jumps up, increasing her height above the water. She reaches a peak, then begins to come down, decreasing her height above the water, until she hits the water at height 0.

Even though time is increasing by a constant rate, the height above the water is not changing by a constant amount. Therefore it is not a linear function.As time increases, the height above the water increases, but somewhere between 0.5 and 0.75 seconds, it changes direction and begins to decrease.

2 Interpret the rate of change.

Time(sec)

Height abovewater (ft)

0 100.25 10.10.5 11.20.75

110.910

+ 0.1

+ 1.1– 0.3– 0.9

+ 0.25

+ 0.25+ 0.25+ 0.25

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TWIN TACTICSHow will Jordan draw the rest of the graph?

Twins Jon and Jordan Wonder are about to have an important business meeting about the stock of their company, Wonder Toys. Normally they present together, but Jon tells Jordan that he’s going to have to handle the meeting himself, as his fl ight has been canceled and he won’t make it back for the meeting.

Jordan is nervous, but Jon decides to feed Jordan the stock information through a Bluetooth earpiece, while Jordan makes a graph live for the meeting attendees. Jon tells Jordan the fi rst piece of information, and Jordan draws the fi rst part of the graph.

How will Jordan draw the rest of the graph?

8.F.B.5

Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

About this standard

Date PeriodName

MidSchoolMath Twin Tactics 1 of 2

APPLYING THE STANDARD

MidSchoolMath 2 of 2

Date PeriodName

How might this standard appear on a test?

Twin Tactics

Consider the following function. Decide if each statement is true or false. Write T or F in the blank next to the statement.

1)

Match each scenario with the graph that it describes. Write the graph number in the blank next to the statement.

2)

Ben washed dishes when he got home from school. Using the details provided, sketch a graph depicting Ben’s experience.

3)

The function is constant for -5 < x < -1 and 6 < x < 7.a)

A bathtub is fi lled at a constant rate of 2 gallons per minute.

a)

A bathtub contains 4 gallons of water.b)

A bathtub is drained at a constant rate of 1 gallon per minute.

c)

A bathtub is fi lled at a constant rate of 1 gallon per minute.

d)

The function increases for 3 < x < 8.c)

When x ≥ ¼ , y ≤ 0.e)

When x ≤ 0, y > 0.f)

The function has one x-intercept.i)

The y-intercept is greater than 0.j)

The function decreases at a variable rate for -8 < x < -5.

b)

The maximum value is y = 4, and the minimum value is y = -7.

d)

For -5 < x < -1 and 6 < x < 7, the function has zero slope.

g)

For -1 < x < 3 the function has a negative slope. For 7 < x < 8 the function has a positive slope.

h)

Ben took two minutes to fi ll the sink to half-full. He then washed the dishes for 8 minutes. He took about 3 minutes to drain half the water out and to fi ll it back up to half-full with new warm water. It took him four minutes to fi nish washing the rest of the dishes. Then he drained the water. It took Ben 20 minutes in total from start to fi nish.

Check out my worked example #1a

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