Let’s Be Rational Investigation 2 (Multiplying Fractions) Overview

Investigation 2 focuses on developing computational skill with and understanding of fraction multiplication. Various

contexts and models are introduced to help students make sense of when multiplication is appropriate.

In Problem 2.1, students develop an understanding of multiplication with simple fractions. Problems 2.2 and 2.3 focus

on multiplication with fractions, mixed numbers, and whole number combinations.

Estimation is used across the Problems so that students can determine the reasonableness of their answers. Also,

students develop the idea that multiplication does not always lead to a larger product. Within these Problems, students

form a general algorithm for fraction multiplication.

Investigation 2.1-Finding Parts of Parts

This investigation introduces students to finding the part of a part (multiplying a fraction by a fraction). We do not go

straight to the multiplication algorithm; instead we focus on using an area model to demonstrate how much is left after

taking part of a part. Your child will not be seeing the multiplication symbol until the next investigation; instead we will

use the word “of” to imply multiplication. The problem is presented with the context of serving brownies from a pan

that starts out partially full. An example is below, including how to illustrate it with an area model:

Example: Mr. Williams asks to buy 12 of a pan of brownies that is

23 full. What fraction of the whole pan has Mr.

Williams bought?

The models below show the thinking behind solving this problem. Part I shows the initial pan before Mr.

Williams makes his purchase, you can see that the entire pan is split into three equal parts, two of which are

shaded to represent the 23 . Since Mr. Williams is buying

12 of the pan, which is illustrated in part 2. When you

combine them, the gold color represents the overlap of the grey and blue, you can see that Mr. Williams is

buying 26 or

13 of the entire pan.

Investigation 2.2-Modeling Multiplication Situations

In this investigation, students extend their understanding of multiplication by modeling situations that involve fractions, mixed numbers, and whole numbers. A model is simply a drawing or diagram to illustrate the problem. This is where students will transition from using the word “of” to the traditional multiplication symbols and begin to develop the algorithm for multiplying fractions, mixed numbers and whole numbers. A series of examples are below.

Example 1: Multiplying a part by a whole

A recipe calls for 23 of a 16-ounce bag of chocolate chips. How many ounces are needed?

Below is a possible diagram for solving and the answer. You can see there are 16 squares that are then split into

three equal amounts. The shaded part represents the 23 of 16.

Example 2: Multiplying a part by a mixed number

Mr. Flansburgh buys a 2 12 pound block of cheese. His family eats 13 of the block. How much cheese has Mr.

Flansburgh’s family eaten?

Below is a possible diagram for solving and the answer.

Example 3: Multiplying a Mixed Number by a Mixed Number

2 13×1 12

Below is a possible diagram for solving and the answer

Investigation 2.3-Multiplication of Fractions, Mixed Numbers and Whole Numbers

In this investigation, we bring together all of the ideas from the first two to develop an algorithm for multiplying fractions, mixed numbers and whole numbers. The most common strategy that most students will use will be to change all mixed numbers to improper fractions and then multiply the numerator by the numerator, then the denominator by the denominator and finish by simplifying. An example is below.