Lesson 1

Break-Apart Products with Larger Numbers

Est. Class Sessions: 1
X

Mathematical Standards

3.OA.A
Represent and solve problems involving multiplication and division. (3.OA.A.3)
3.OA.B
Understand properties of multiplication and the relationship between multiplication and division. (3.OA.B.5)
3.OA.C
Multiply and divide within 100. (3.OA.C.7)

Standards for Mathematical Practice

MP1.
Make sense of problems and persevere in solving them.
MP2.
Reason quantitatively.
MP5.
Use appropriate tools strategically.
MP7.
Look for and make sense of structure.

Students break products, such as 6 × 12, into the sum of simpler products, e.g., 6 × 10 + 6 × 2. To do this, they divide a rectangular array representing a product into two smaller arrays that represent easier products. Then they add the easier products to get their answers. Students begin with a review of this method with one-digit by one-digit problems and move to two-digit by one-digit problems. In doing this activity, students develop an understanding of the distributive property of multiplication over addition although they do not study it formally.

Content in this Lesson

  • Representing and solving multiplication problems using rectangular arrays [E1].
  • Writing number sentences for multiplication situations [E1].
  • Using the distributive property of multiplication over addition to solve multiplication problems [E7].
  • Demonstrating partial products using a rectangle model for multiplication [E2].
  • Multiplying one-digit whole numbers by multiples of ten [E5].
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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 pencils

Materials for the Teacher

Display of Rectangular Arrays (Student Activity Book) Page 511
Display of Centimeter Grid Paper Master (Teacher Guide)
Display of Break Apart and Multiply Check-In: Question 4 (Student Activity Book) Page 516
Unit 13 Assessment Record
Math Facts Class Record

Materials Preparation

Copy Centimeter Grid Paper. Have copies of the Centimeter Grid Paper Master available for students. They might use them to show additional solutions to the problems discussed in class or need an extra copy on which to draw rectangles to solve problems. Extra copies may also be used for students who need more practice with the break-apart method.

Materials Preparation

Triangle Flash Cards. Triangle Flash Cards: Last Six Facts were provided in Unit 12. If needed, prepare copies of the Triangle Flash Cards on heavier paper or card stock. Have students cut apart each set and store them in an envelope. You may want to provide each student with two sets, one to use at school and one to take home.

Assessment in this Lesson

Assessment Expectation Assessed

Break Apart and Multiply
Check-In: Questions 4–5
with Feedback Box
Student Activity Book
Pages 516–517
E1.
Represent 2-digit by 1-digit multiplication problems using counters, tiles, rectangular arrays, drawings, stories, and number sentences.
E2.
Show connections between models and strategies for multiplication (e.g., demonstrate partial products using a rectangle model for multiplication).
E3.
Solve multidigit multiplication problems using mental math strategies (e.g., composing and decomposing numbers, and doubling and halving).
E5.
Multiply one-digit whole numbers by multiples of ten.
E7.
Solve multiplication problems by breaking products into the sum of simpler products (applying the distributive property of multiplication over addition) using a rectangle model, and paper-and-pencil methods (e.g., all-partials).
E14.
Demonstrate fluency with the multiplication facts for the last six facts (4 × 6, 4 × 7, 4 × 8, 6 × 7, 6 × 8, 7 × 8).

DPP Item A
Triangle Flash Cards: Last Six Facts
Teacher Guide - digital
E14.
Demonstrate fluency with the multiplication facts for the last six facts (4 × 6, 4 × 7, 4 × 8, 6 × 7, 6 × 8, 7 × 8).

Vocabulary in this Lesson