Lesson 10

Multiplying Fractions by a Whole

Est. Class Sessions: 2–3
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Mathematical Standards

4.NF.B
Build fractions from unit fractions. (4.NF.B.4)

Standards for Mathematical Practice

MP1.
Make sense of problems and persevere in solving them.
MP2.
Reason quantitatively.
MP3.
Construct viable arguments and critique the reasoning of others.
MP4.
Model with mathematics.

Students use a variety of models to multiply fractions by a whole number. They build on the models (fraction strips, circle pieces, and number lines) they have been developing. Students also represent fractions of sets of discrete objects (e.g., boxes of apples). Further, they look for patterns in tables and parallel problems to start to develop generalized procedures based on the properties of multiplication.

Content in this Lesson

  • Multiplying fractions by a whole number using models (e.g., fraction strips, fraction circle pieces, number lines, and set of objects) [E11].
  • Looking for patterns in tables and parallel problems to develop a generalized procedure.
  • Using the distributive property of multiplication to multiply fractions [E11].
  • Connecting repeated addition of fractions to multiplication of fractions [E11].
  • Representing multiplication with area models and with models of sets
    [E1, E11].
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Materials for Students

Daily Practice and Problems Lesson Homework Assessment

Student Books

 Student Guide
Student Activity Book

Teacher Resources

 Teacher Guide - digital

Supplies for Students

fraction strips from Lessons 1 and 2
fraction circle pieces, 1 set
ruler or straight edge to draw number lines

Materials for Teachers

copy of the Strategies for 4 × 1/2 Master (Teacher Guide)
Display of Questions 1 and 2 (Student Guide) Page 348
Display of the vignette after Question 3 (Student Guide) Page 349
Display of Questions 5–6 (Student Guide) Pages 350–351
Unit 8 Assessment Record
Math Facts Class Record
chart paper. See Materials Preparation.
ingredients for Famous Trail Mix (Student Guide) Page 348, optional
collection of measuring cups (1/8, 1/4, 1/8, 1 cup), optional

Materials Preparation

Chart Paper. Prepare 5 sheets of chart paper for a class discussion in Part 1 and then in Part 3. Write the following titles on each sheet: Irma's Strategy, Roberto's Strategy, Shannon's Strategy, Jacob's Strategy, and Ming's Strategy. Copy and cut apart the examples on the Strategies for 4 × 1/2 Master. Attach to the corresponding chart for easy reference. The first four charts will be displayed in Part 1. Ming's chart will be displayed during Summarizing the Lesson.

Assessment in this Lesson

Assessment Expectation Assessed

Multiply Fractions
with Feedback Box
Teacher Guide - digital
E1.
Represent fractions using area models (circle pieces, fraction strips, drawings) and number lines.
E11.
Multiply fractions by a whole number
(e.g., 1/3 × 3 = 1, 2/3 × 6 = 1/3 × 6 × 2).

DPP Item II
Division Quiz: 9s
Teacher Guide - digital
E12.
Demonstrate fluency with the division facts for the 9s.

Vocabulary in this Lesson