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Algebraic Storytelling and Problem-Solving

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Algebraic Storytelling and Problem-Solving

Use variables to represent unknown quantities. Write equations from each story, solve them, and check your answers in the original equations. Show your working.

Build and solve a system

At a football tournament, teams can enter either a five-a-side or a seven-a-side division. There are 9 teams altogether, with 53 players in total.

1.Choose variables for the numbers of five-a-side teams and seven-a-side teams. State what each variable represents.

2.Write an equation for the 9 teams entered in total.

3.Write an equation for the 53 players. Use 5 players per five-a-side team and 7 players per seven-a-side team.

4.Solve the two equations to find how many teams entered each division. Show your working.

5.Check the team numbers by substituting them into both equations. Show that each equation is true.

Tell the story with equations

A tournament stall sells player meal vouchers and supporter meal vouchers. Player vouchers cost $8 each and supporter vouchers cost $5 each. The stall sells 12 vouchers and takes in $81.

6.Write a short story sentence describing the unknown numbers in the voucher problem. Include the total vouchers and total money collected.

7.Let p be the number of player vouchers and t be the number of supporter vouchers. Write one equation for the total vouchers and one for the total money collected.

8.Solve the voucher equations. How many of each type were sold? Verify your result using both totals.

Explain your mathematical thinking

Use clear mathematical language to communicate how you set up and solved the stories.

9.In the team problem, explain how using variables and equations helped you find the numbers of teams.

10.Which strategies are useful when explaining a system of equations? Select all that apply.

Show the calculation steps in order
Substitute the solution into the original equations to check it
Explain what each variable represents
Use words to connect the equations to the story

11.Name one way you could make a spoken or written explanation of a solution clearer for someone else.

3 printable pages

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Page 3

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3 printable pages

About This Worksheet

Free in Kuraplan

Print-Ready

AI-Generated

For Teachers & Parents

Need a custom version of this worksheet?

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