Gallery Problems Exercise

Gallery Problems Exercise

Represent a Math Problem

Work Time

Represent a Math Problem

Explore each of these math representations: a ratio table tool, a double number line tool, and a tape diagram tool.

  1. Research each type of representation and explore how to use it. Select one representation to describe to the class.
  2. Solve this problem. Represent it using a double number line or a ratio table.

    Three types of nails are for sale:

  • It costs 5¢ to buy 3 type A nails.
  • It costs 8¢ to buy 6 type B nails.
  • It costs 10¢ to buy 8 type C nails.

Which type of nails costs the least per nail?

  1. Jack says:

    “The rates are 35 for type A, 68 for type B, and 810 for type C. Type A costs the least per nail." Jack is wrong. Explain his mistake.

Research Ratios and Rates

Work Time

Research Ratios and Rates

Do some research to learn about how ratios and rates are related to proportional relationships.

  • Search using a few different keywords to find resources. Follow any links that look useful.
  • Watch video tutorials about proportional relationships.
  • Review worked examples of problems using proportional relationships.
  • Look up ratios and rates in the dictionary.

Write your answers to the following questions.

  1. How are ratios and rates related to proportional relationships?
  2. What are five things you think you will learn about proportional relationships this year?
  3. When is it useful to research a concept?

Louisiana Purchase

Work Time

Louisiana Purchase

  • Solve this problem.

In 1803, the United States negotiated the Louisiana Purchase with France and purchased approximately 800,000 sq mi of land west of the Mississippi River for $15 million.

Reminder: An acre is a measure of area. There are 640 acres in a square mile.

  1. How much did the land cost per acre?
  2. Make an estimate.
  3. Create a diagram to represent the situation.