Lesson 10

Break-Apart Products with Larger Numbers

Est. Class Sessions: 2–3
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Mathematical Standards

4.NBT.B
Use place value understanding and properties of operations to perform multi-digit arithmetic. (4.NBT.B.5, 4.NBT.B.6)

Standards for Mathematical Practice

MP1.
Make sense of problems and persevere in solving them.
MP2.
Reason abstractly and quantitatively.
MP3.
Construct viable arguments and critique the reasoning of others.
MP8.
Look for and express regularity in repeated reasoning.

Students extend the break-apart method to one-digit by 2-digit multiplication problems. For example, 6 × 32 is broken into 6 × 30 + 6 × 2. To model this idea, they draw a rectangular array on grid paper to represent a product, divide the array into two smaller arrays that represent easier products, and add the easier products to get their answers. They then make connections between using rectangles and using expanded form to multiply.

Content in this Lesson

  • Representing and solving multiplication problems using rectangular arrays [E1, MPE5].
  • Breaking products into the sum of simpler products to solve one-digit by two-digit multiplication problems (applying the distributive property) [E9].
  • Communicating reasoning [MPE5].
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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

crayons or colored markers (to draw borders of rectangles), optional

Supplies for Student Groups

one student work sample of Question 11 on the Unit 3 Test. See Materials Preparation.

Materials for the Teacher

Display of Exploring Break-Apart Products with Larger Numbers pages (Student Activity Book) Pages 85–86
Display of Question 11 Number Riddle Masters (Teacher Guide)
Unit 3 Assessment Record
Math Facts Class Record
Unit 3 Individual Assessment Record

Materials Preparation

Student Work Samples. Choose student work samples for small groups to evaluate and provide feedback on Question 11 on the Unit 3 Test Assessment Master. Samples are provided on the Question 11 Number Riddle Masters. If you choose samples from your class, ask students' permission and prepare to provide one copy of student work to each group of students.

Assessment in this Lesson

Assessment Expectation Assessed Math Practices
Expectation Assessed
Break-Apart Products with Larger Numbers
Check-In:
Questions
9–10
Student Guide
Page 105
E9.
Break products into the sum of simpler products to solve multiplication problems (applying the distributive property of multiplication over addition).
DPP Item EE
Quiz on 5s and 10s
Teacher Guide - digital
Page 36
E10.
Demonstrate fluency with the multiplication facts for the 5s, 10s, and square numbers.
Unit 3 Test
with Feedback Box
Teacher Guide - digital
E1.
Represent and solve multiplication and division problems using rectangular arrays.
E2.
Determine whether one number is a multiple of another number.
E3.
Find the factors of a number.
E4.
Identify prime numbers.
E5.
Identify square numbers.
E6.
Find the prime factorization of a number.
E9.
Break products into the sum of simpler products to solve multiplication problems (applying the distributive property of multiplication over addition).
MPE5.
Show my work. I show or tell how I arrived at my answer so someone else can understand my thinking.