Author:
Chris Adcock
Subject:
Ratios and Proportions
Material Type:
Lesson Plan
Level:
Middle School
Grade:
6
Provider:
Pearson
Tags:
6th Grade Mathematics, Division, Fractions
License:
Creative Commons Attribution Non-Commercial
Language:
English
Media Formats:
Text/HTML

Education Standards

Cooking with Fractions

Cooking with Fractions

Overview

Students determine how many times they would need to fill a quarter cup to measure the ingredients in a recipe.

Key Concepts

This lesson informally introduces the idea of dividing by a fraction. Students must figure out how many times a quarter cup must be filled to measure the ingredients in a recipe. This involves dividing each amount by 14. Here are some methods students might use:

  • Add 14 repeatedly until the sum is the desired amount. Count the number of 14s that were added.
  • Start with the amount in the recipe. Subtract 14 repeatedly until the difference is 0. Count the 14s that were subtracted.
  • Draw a model (e.g., a bar or a number line model) to represent the amount in the recipe. Divide it into fourths and count the number of fourths.

Goals and Learning Objectives

  • Learn how to divide by a fraction.

Make Apricot Bread

Lesson Guide

Have students discuss with their partner whether Denzel can make the recipe using only his 14-cup measuring cup.

Mathematics

Before students begin the Work Time problems, be sure they see that Denzel can make the recipe—he just needs to fill his measuring cup several times for each ingredient.

ELL: When working with ELLs, it is important to link new concepts to students’ prior knowledge and experiences. This allows students to make more meaningful connections with the new mathematical concepts they are learning.

Opening

Make Apricot Bread

Here is the list of ingredients for a recipe Denzel wants to make.

Apricot Bread

1 cup chopped almonds
112 cups dried apricots
114 cups water
12 cup honey
212 cups flour
2 tablespoons butter
2 teaspoons baking powder
1 egg
1 teaspoon vanilla
1 teaspoon salt

As Denzel is about to measure out the ingredients, he realizes that the only size measuring cup he has is a 14-cup measuring cup. The first five ingredients are given in cups.

Discuss:

  • Can Denzel measure the first five ingredients using only his 14-cup measuring cup?

Math Mission

Lesson Guide

Discuss the Math Mission. Students will explore how to measure the ingredients for a recipe using only a
14-cup measuring cup.

Opening

Explore how to measure the ingredients for a recipe using only a 14-cup measuring cup.

How Much of Each Ingredient?

Lesson Guide

Have students work in pairs. Be sure students understand what to do. For each of the first five ingredients, they need to enter the number of times Denzel will have to fill the 14-cup measuring cup.

ELL: Model or demonstrate the activity step by step. This modeling will ensure that ELL students understand the task and therefore focus on the mathematics of the activity rather than on trying to figure out the directions. (To check for understanding, have students retell the steps of the task to a partner.)

SWD: Decide how you will partner students together for this task. Partnering students by skill level will allow for more efficient provision of teacher support, while partnering students heterogeneously will promote cooperative teaching and learning opportunities for students with varying mathematical skills. Monitor partnerships to ensure all students’ progress. It is often best practice to have students with disabilities be partners with typically developing peers.

Interventions

Student has difficulty getting started.

  • Describe the task in your own words to your partner.
  • What do you know?
  • What are you trying to find?

Student is not working systematically.

  • How can you organize your work to keep track of how many 14-cups you are combining (or subtracting)?
  • Can you draw a diagram?

Student is making guesses rather than using reasoning.

  • Before you answer the problem, think about how big the answer should be.
  • Can you make a sketch to help you reason about the answer?
  • Will your answer for 112 cups be more or less than your answer for 1 cup?

Mathematical Practices

Mathematical Practice 7: Look for and make use of structure.

Students may use the fact that 212 cups is 1 cup + 1 cup + 12 cup and use their earlier answers to reason that Denzel would have to fill the 14-cup measuring cup 4 + 4 + 2 (or 10) times to measure the flour. Be sure to discuss this practice in Ways of Thinking.

Answers

  • Rewritten recipes will vary in format, but should include the following information:

1 cup chopped almonds: Fill the 14-cup 4 times.

112 cups dried apricots: Fill the 14-cup 6 times.

114 cups water: Fill the 14-cup 5 times.

12 cup honey: Fill the 14-cup 2 times.

212 cups flour: Fill the 14-cup 10 times.

  • Discussions will vary.

Work Time

How Much of Each Ingredient?

Determine how many times Denzel needs to fill his 14-cup measuring cup to get the right amount of each of the first five ingredients.

  • Rewrite the recipe so that it shows how many 14-cups are needed of each of the ingredients.
    • 1 cup chopped almonds = [   ] 14-cups
    • 112 cups dried apricots = [   ] 14-cups
    • 114 cups water = [   ] 14-cups
    • 12 cup honey = [   ] 14-cups
    • 212 cups flour = [   ] 14-cups
  • Discuss your answers with your partner.

Try making a diagram to represent the amount of each ingredient. How many 1/4 -cups does your diagram represent?

Prepare a Presentation

Preparing for Ways of Thinking

Look for student pairs using different methods for determining how many times Denzel will have to fill the 14-cup measuring cup. Choose a variety of strategies to present during Ways of Thinking.

Some possible strategies to highlight:

  • Add 14 repeatedly until the sum is the desired amount. Count the number of fourths that were added.
  • Start with the amount in the recipe. Subtract 14 repeatedly until the difference is 0. Count the fourths that were subtracted.
  • Draw a model (e.g., a bar or a number line model) to represent the amount in the recipe. Divide it into fourths and count the number of fourths.

Select students who solved the Challenge Problem to present during Ways of Thinking.

Presentations will vary.

Challenge Problem

Answers

  • 14 cup honey; 114 cups flour

Work Time

Prepare a Presentation

  • Present your rewritten recipe.
  • Describe the strategy you used to rewrite the recipe so that it could be followed using only a 14-cup measuring cup.

Challenge Problem

Suppose that Denzel decides to make only half of the recipe.

Remember the recipe called for:

  • 12 cup of honey
  • 212 cups of flour

How much honey will he need? How much flour?

Think about what you did to solve the problem. Did you use the same approach for each ingredient?

Make Connections

Lesson Guide

Have students present the various strategies they used. Discuss these strategies as a class.

Mathematics

Students who solved the Challenge Problem should share their solutions and methods. Some students might recognize that the problem requires finding 12 of a given amount and recall that “of” means “times.” So, for the flour: 12 of 212 cups = 12⋅212 c = 54 c = 114 c. Other students might use less formal methods, such as drawing a diagram.

Performance Task

Ways of Thinking: Make Connections

Take notes about your classmates’ strategies for converting the quantities in the recipe.

As your classmates present, ask questions such as:

  • Can you explain why your strategy makes sense?
  • Where can I see the total amount of the ingredient in your model?
  • Where can I see the 1 4 -cups in your model?
  • How are your representations for the different ingredients alike? How are they different?
  • How is your strategy similar to other strategies that your classmates presented? How is it different?

Reflect On Your Work

Lesson Guide

Have students write a brief reflection before the end of class. Review the reflections to find out their understanding of fraction division.

Work Time

Reflection

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

Something I wonder about dividing by a fraction is …