No Matter How You Slice It

Sixth Grade Poster Problem
The Number System

This poster problem creates the need for fraction division using a realistic setting. Through repeatedly solving problems about slicing blocks of cheese using different fractional thicknesses, students will be motivated to use division to make calculations easier.

Understanding fraction division can take a significant amount of time, and it may be valuable to plan enough time for you and your students to get comfortable with the slicing context using other operations (e.g., repeated subtraction) before using division. Teaching this poster problem may take more time than other poster problems, but we think this will be time well used.

Materials:

Consider using a hand-operated slicer (or a mandoline) to demonstrate how the thickness of each slice and the dimensions of the object being sliced determine the number of slices that can be made.

Learning Objectives:

  • Interpret and compute quotients of fractions.
  • Solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem.

Common Core State Standards for Mathematics:

6.RP.A.1

  • Note:

    In this poster problem, students need to understand some “slicing” situations. Students will probably develop strategies for solving the problems without division, but we want to go beyond that. First, they need to recognize that division is a good operation to use in similar situations. Then, they need to learn how to perform the division-by-fractions computation.

    There are several ways for students to do such a calculation: using common denominators, multiplying by one strategically, and so forth. The danger comes when we tell students to “invert and multiply” too early, and they start doing this without (a) understanding why division is the right operation or (b) understanding why the procedure gives the right answer. See the tune-ups below for more details.

The Lesson Plan:

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Lesson Plan

Slides

Handouts

Project funding provided by The William and Flora Hewlett Foundation and S.D. Bechtel Jr. Foundation.

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