# Creating Equations, Tables & Graphs # 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

## Opening

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

# 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

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.

# Ways of Thinking: Make Connections

## Hint:

• 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?

# Summary of the Math: Percent Change

• 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?