Creating Equations, Tables & Graphs

Creating Equations, Tables & Graphs

Model with Mathematics

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Model With Mathematics

Watch the video to see Karen and Maya use a table and set up an equation to model the mathematics in a problem.

  • How did setting up a table help Karen and Maya solve the problem?
  • Karen and Maya modeled the problem with an equation. Does their equation reflect the problem?

VIDEO: Mathematical Practice 4

Math Mission

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Create equations, tables, and graphs to show the proportional relationships in sales tax situations.

Chen’s Pair of Shoes

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Chen’s Pair of Shoes

Chen bought a pair of shoes and paid a total of $32.40. The sales tax was 8%. What was the price of the shoes?

  • Copy and complete the table. Show the information given in the problem, and what you need to find.
  • Write an equation to find the price of the shoes.
  • Solve the equation.
  • Complete the given table to show the final amounts for different starting amounts.
  • Make a graph that shows the relationship between the starting amounts and the final amounts.

Hint:

  • When you write the equation, how do you change the 8% to a decimal? What do you need to account for in your equation?
  • Marcus wrote this equation: 1.08 • p = 32.40. Why did he multiply by 1.08? How could he write the equation differently?
  • Once you have filled in the table with $32.40 including the 8% tax, how do you extend the table? What stays constant? What varies?

Sophie’s Book

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Sophie’s Book

Recall the problem from the video:

Sophie bought a book at the bookstore. The price of the book was $18, and the total amount she paid was $19.08. What percent was the sales tax?

  • Make a table of the relationships and fill in the first few rows.
  • Make a graph that shows the relationship between the price of a book and the total amount paid.

HANDOUT: Sales Tax

Hint:

  • Try filling in a table of different starting and final amounts that reflect a 6% tax. What stays constant? What varies?
  • Once you have filled in several rows of the table, use the values to create your graph.

Prepare a Presentation

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Prepare a Presentation

Prepare a presentation comparing what is similar and what is different between the book problem and the shoe problem.

Challenge Problem

  • Look back at the graph you made in the previous lesson representing the relationship between the price and total cost of items at a 5% tax. Compare it to the two graphs you made in this lesson. If the scales on the axes of any of the graphs are different, re-create the three graphs on the same coordinate plane.
  • How does the steepness of each graph compare with the steepness of the other graphs? Identify the constant of proportionality in each relationship.

Make Connections

Performance Task

Ways of Thinking: Make Connections

Take notes about your classmates’ graphs and comparisons.

Hint:

As your classmates present, ask questions such as:

  • How did the table help you make a graph of the situation?
  • How does the line change as the sales tax changes in the different graphs? Can you explain the change?
  • Why did you multiply by 1 plus the sale tax?
  • Does your solution make sense in this situation?
  • Could you have predicted what the graph would look like before you made it? How?
  • Why do you think you found those similarities between the graphs?
  • Why do you think you found those differences between the graphs?
  • Are there any conclusions you can make based on comparing the graphs?

Percent Change

Formative Assessment

Summary of the Math: Percent Change

Read and Discuss

  • A percent can describe a change in a value—for example, a percent increase.
  • If a value increases by x%, you can calculate the new value in two ways:
    • Calculate x% of the original amount and add the result to the original amount.
    • Calculate (100% + x%) of the original amount.
  • For example, if the percent increase is 5% and the original amount is m, then:
    0.05 + m = the total amount, or 1.05m = the total amount
  • These two equations are equivalent because:
    0.05m + m = 1.05m
    0.05m + 1m = 1.05m(0.05 + 1)m = 1.05m

Hint:

Can you:

  • For a problem about a sales tax situation, create a table that can help you organize what is given and what you need to find?
  • Use a table to make a graph?
  • Determine one of the amounts in a sales tax situation—the price of an item, the amount of the sales tax, or the total cost—if you know the other two amounts?

Reflect On Your Work

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Reflection

Write a reflection about the ideas discussed in class today. Use the sentence starter below if you find it to be helpful.

What helped me most in solving today’s sales tax problems was …