Constructing Proportions to Solve Real World Problems Lesson Plan

Instructor: Heather Jenkins

Heather has a bachelor's degree in elementary education and a master's degree in special education. She was a public school teacher and administrator for 11 years.

While students study probability and statistics, consider using this lesson to help students learn how to use proportions to solve real-world problems. A hands-on activity involving candy and word problems are included in this lesson.

Learning Objectives

Upon completion, students will be able to:

  • write proportions for a given situation
  • understand how to use cross multiplication to solve problems involving proportions
  • utilize proportions to solve real world problems

Length

1.5-2 hours

Materials

  • Copies of lesson/lesson quiz
  • Colored candies
  • Dry-erase markers
  • Dry-erase boards
  • Chart paper
  • Markers
  • Word problem creation materials (help wanted ads, road maps, recipes, store catalogs)
  • Circle graphs (extension activity)

Curriculum Standards

  • CCSS.MATH.CONTENT.6.RP.A.1

Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.

  • CCSS.MATH.CONTENT.6.RP.A.3.B

Solve unit rate problems including those involving unit pricing and constant speed.

Instructions

  • Provide students (individually or with partners) with a couple handfuls of colored circular candies.
  • Have students sort the candies by color.
  • Tell students that they will using these candies as they learn about ratios and proportions. Ask students to predict how these candies could relate to ratios and proportions.
  • Provide students with copies of the lesson Constructing Proportions to Solve Real World Problems.
  • Read the first section, 'Proportion', together.
  • Have students use their sorted candies to set up ratios to describe the relationships between the different colors of candy.
    • Provide students with dry-erase boards and markers.
    • Have students write ratios to describe the relationship between various colors. For example, if students had 3 red candies and 8 orange candies, they would write the ratio of 3/8. This means that for every 3 red candies there are 8 orange candies.
  • Read the 'Cross Multiplication' section together.
  • Have students use their ratios to set up proportions to predict how many of a certain color of candy would be present given a definitive quantity of another color.
    • Tell students there are a certain number of one of the candy colors, such as 15 red candies.
    • Have students set up proportions and use cross multiplication to figure out how many of the other colors would be present given the known amount of candy. For example, if the ratio of the students' candies was 4/5 for yellow to red candies (4 yellows for every 5 reds), then students would set up the proportion 4/5 = x/15 (x is the unknown amount of yellows).
    • Repeat the same process for other colors of candies.
  • Read through the 'Constructing Proportions to Solve Real World Problems' together.
  • Provide students with the chance to practice using proportions in real-life situations by having them complete a few problems on their dry-erase boards. Consider using the same scenarios as presented in the lesson, but changing the numbers around.
  • Provide students with paper copies of the lesson quiz to complete.

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