Baseball Helmets Day 2 of 2

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Objective

SWBAT connect solving systems of equations by graphing to solving systems by substitution and discuss when using an equation is more accurate.

Big Idea

Connect solving systems of equations to real life baseball helmets and reading tables to find the equations for solving by substitution.

Lesson Author

Christa Lemily

Bowling Green, KY

Grade Level

Eighth grade

Subjects

Math

solving equations

Algebra

Linear and Nonlinear Equations

Systems of Equations and Inequalities

substitution method

Standards

8.EE.C.8

Analyze and solve pairs of simultaneous linear equations.

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.

MP1

Make sense of problems and persevere in solving them.

MP3

Construct viable arguments and critique the reasoning of others.

MP4

Model with mathematics.

MP6

Attend to precision.

MP7

Look for and make use of structure.

Bellringer: Warm-up

10 minutes

Write the following on the board:

Martha and Winston (I like to use odd names just for fun) agree to meet at the park and go for a jog. Martha arrives on time and begins to run at a pace of six miles per hour. Winston is about five minutes late and seeing Martha already in the park he begins to jog at a pace of six miles per hour. How long will it take Winston to catch up to Martha?

Allow students to discuss among themselves the answer, it shouldn't take very long, and then allow groups to share out their thinking. Challenge the class to sketch a graph of Distance over time for both Martha and Winston. Display a graph under the document camera and discuss what it means when the lines are parallel. Bring this discussion back to systems and that this is an example of a system of equations that has "no solution."

If you have time and want to extend this activity, you could challenge the class by asking them how fast Winston would have to run in order to catch up to Martha in 10 minutes. Hint, they could graph it to find the slope or use an equation.