Lesson 6

Paper-and-Pencil Subtraction: Compact Method

Est. Class Sessions: 2–3
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Mathematical Standards

2.NBT.A
Understand place value. (2.NBT.A.1, 2.NBT.A.2)
2.NBT.B
Use place value understanding and properties of operations to add and subtract. (2.NBT.B.6, 2.NBT.B.8, 2.NBT.B.9)
2.MD.B
Relate addition and subtraction to length. (2.MD.B.6)
2.OA.A
Represent and solve problems involving addition and subtraction. (2.OA.A.1)

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.
MP5.
Use appropriate tools strategically.
MP7.
Look for and make use of structure.
MP8.
Look for and express regularity in repeated reasoning.

In this lesson, students solve subtraction problems using paper and pencil. They begin by recording their work with base-ten pieces on base-ten recording sheets. Then they use a standard paper-and-pencil subtraction algorithm, the compact method, to solve problems. They check their work with addition.

Content in this Lesson

  • Using and applying place value concepts to make connections among representations of multidigit numbers using base-ten pieces, number lines, expanded form, and standard form [E1].
  • Subtracting multidigit numbers using mental math strategies [E3].
  • Subtracting multidigit numbers using paper-and-pencil methods
    (e.g., expanded form, compact) [E4].
  • Checking work for reasonable answers [MPE3].
  • Checking calculations [MPE4].
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Materials for Students

Daily Practice and Problems Lesson Homework Assessment

Student Book

 Student Activity Book

Teacher Resources

 Teacher Guide - digital

Supplies for Students

base-ten pieces (21 bits, 20 skinnies, 5 flats)
desk number line (0–100)

Materials for the Teacher

Display of Base-Ten Recording Sheet Master (Teacher Guide), several copies
Unit 9 Assessment Record
Display set of base-ten pieces
class number line (0–130)

Assessment in this Lesson

Assessment Expectation Assessed MATH PRACTICES EXPECTATION ASSESSED
Subtraction My Way
with Feedback Box
Student Activity Book
Pages 467–468
E1.
Use and apply place value concepts to make connections among representations of numbers to the thousands using base-ten pieces, number lines, expanded form, and standard form.
E3.
Subtract multidigit numbers using mental math strategies (e.g., composing and decomposing numbers and counting up) with number lines, a 200 Chart, and base-ten pieces.
E4.
Subtract multidigit numbers using paper-and-pencil methods (e.g., expanded form, compact).
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.

Vocabulary in this Lesson