Lesson 6

Paper-and-Pencil Division

Est. Class Sessions: 2–3
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Mathematical Standards

4.NBT.A
Generalize place value understanding for multi-digit whole numbers. (4.NBT.A.3)
4.NBT.B
Use place value understanding and properties of operations to perform multi-digit arithmetic. (4.NBT.B.6)
4.OA.A
Use the four operations with whole numbers to solve problems. (4.OA.A.3)

Standards for Mathematical Practice

MP1.
Make sense of problems and persevere in solving them.
MP2.
Reason quantitatively.
MP4.
Model with mathematics.
MP5.
Use appropriate tools strategically.

This lesson introduces a paper-and-pencil method of division called the partial quotients method. Students build on the methods and models they learned in Lessons 3 and 4 to develop the procedures in the partial quotients method. They continue to estimate quotients and interpret remainders.

Content in this Lesson

  • Using models and methods to solve division problems [E1].
  • Showing connections between models of multidigit division and paper-and-pencil methods [E2].
  • Dividing with 1-digit divisors using paper and pencil [E7].
  • Interpreting remainders [E4].
  • Estimating quotients of larger numbers [E5].
  • Checking division with multiplication [E3].
  • Writing a multiplication sentence for quotient, divisor, and remainder [E3].
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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

calculator
Small Multiplication Tables or Facts I Know charts
scissors
envelope to store Digit Cards 0–9

Materials for the Teacher

Unit 12 Assessment Record
Unit 12 Individual Assessment Record
Math Facts Class Record

Materials Preparation

Digit Cards. Ask students to cut apart the Digit Cards 0–9 and store them in an envelope.

Assessment in this Lesson

Assessment Expectation Assessed Math Practices Expectation Assessed

Paper and Pencil Division
Check-In: Questions 6–9
Student Guide
pages 550–551
E2.
Show connections between models and strategies for multidigit division.
E4.
Interpret remainders from division of multidigit numbers.
E7.
Divide multidigit numbers by 1-digit divisors using paper and pencil.

Paper-and-Pencil Division Quiz
with Feedback Box
Teacher Guide - digital
E2.
Show connections between models and strategies for multidigit division.
E3.
Show connections between multiplication and division (e.g., fact families, using multiplication to divide).
E4.
Interpret remainders from division of multidigit numbers.
E7.
Divide multidigit numbers by 1-digit divisors using paper and pencil.
MPE3.
Check for reasonableness. I look back at my solution to see if my answer makes sense. If it does not, I try again.
MPE4.
Check my calculations. If I make mistakes, I correct them.
MPE5.
Show my work. I show or tell how I arrived at my answer so someone else can understand my thinking.

DPP Item O
Division Fact Inventory Test
Teacher Guide - digital
E8.
Demonstrate fluency with the division facts in all groups.