MidSchoolMath 1

Knowing more than one method for solving a system of equations will help students "work smarter, not harder." During Mars Rocks!, Delta Team Geologist Kim O’Hara is away from base on a long mission and is running out of supplies. Her teammate, Decker, tells her that a supply vehicle is on the way to meet her but that communications have been spotty, so they used her last known position to set the course for the supply vehicle. O’Hara decides to use the radar to determine whether or not her explo-ration vehicle and the supply vehicle will meet. The data provided is a radar graph showing the position of each vehicle over the last three hours.

LESSON: MARS ROCKS!Will the two vehicles meet?

Mars Rocks!

Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.

The Math SimulatorTM

ImmersionPlay Mars Rocks! Immersion video, whole-class. Restate the question: Will the two vehicles meet?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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Download the Detailed Lesson PlanAvailable on the Teacher Dashboard

3 ResolutionPlay Mars Rocks! 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.EE.C.8bExpressions & Equations

MidSchoolMath Mars Rocks!

Clicker QuizLaunch the Clicker Quiz, whole-class.

8.EE.C.8bExpressions & Equations

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Gladys: Review with students the process for determining the equation of a line using two points. It will be helpful for The Math SimulatorTM task for this standard.

Kevin: Remind students that putting equa-tions in the same form (slope-intercept form, for example), will help them analyze the system for similarities and differences. It makes the system easier to work with.

Megan: Encourage students to check their solutions by substituting the ordered pair back into both original equations.

KevinSimpson

GladysGraham

MeganLeBleu

Ex. Clicker Quiz #3Standard Math Procedures

Instruction at a Glance

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4

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Because both equations are solved for y, set them equal to each other.

Determine the y-coordinate by substitution.

Choose the correct ordered pair.

- x + 4 = 2x – 3

y = 2(2.8) – 3

D: (2.8, 2.6)

y = 5.6 – 3y = 2.6

- x + 4 + x = 2x – 3 + x

7 • = x • = x x = 2 = 2.8

4 = x – 3 7 = x

4 + 3 = x – 3 + 3

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Isolate the variable using inverse operations and addition property of equality.

Isolate the variable using inverse operations and multiplication property of equality.

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12

25

52

25

45

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52

52

52

12

145

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MARS ROCKS!Will the two vehicles meet?Delta Team Geologist Kim O’Hara is out in the E.V. on another mission. She is running out of supplies, so her teammate, Decker, is sending a supply vehicle to meet her.

As frequently happens, weather is causing communications to be unreliable. They used O’Hara’s last known position to set the course for the supply vehicle and are not certain it will get to her. She may have to alter her course.

Use the radar graph to help O’Hara determine if the two vehicles will meet. If so, determine the coordinates where they will meet.

8.EE.C.8b

Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.

About this standard

Date PeriodName

MidSchoolMath Mars Rocks! 1 of 2

Will the vehicles meet?Yes at ( , )

No

APPLYING THE STANDARD

Determine how many solutions each system of equations will have: ONE SOLUTION, NO SOLUTION, or INFINITE SOLUTIONS.

y = 3x + 1

-4x + y = 9

1) y = 3x + 2

2y = 6x + 4

2) y = 2

x = 3

3)

Solve each system of equations.

x = 5y – 4

-8x – 2y = -52

7) 3x – 0.6y = -0.9

-0.5x + 0.12y = 0.16

8) x + 2y = 8

3x = -4y + 16

9)

4) Write your own system of equations with infi nite solutions.

Write your own system of equations with no solution.

5) 6)

MidSchoolMath Mars Rocks! 2 of 2

Date PeriodName

How might this standard appear on a test?

Braydon ran at a rate of 6 mph on his treadmill and then took a walk outside at a rate of 2 mph. He went a total distance of 10 miles and it took him 2 hours.

How long did he run on the treadmill and how long did he walk outside?

32

Check out my worked example #7

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