Lesson 11

Analyze Subtraction Algorithms

Lesson Purpose

The purpose of this lesson is for students to consider subtraction algorithms in more detail, with a focus on decomposing as needed and on cases when it is necessary to decompose multiple units to subtract across zeros.

Lesson Narrative

In a previous lesson, students used a subtraction algorithm in which single digits were used to record the result of subtraction in any place value position and one or two digits were used to record any decompositions. They did any necessary decompositions before beginning to subtract. In this lesson, students make sense of and use an algorithm in which subtraction begins with the ones, decomposing units as needed as they work from right to left. Students also consider a case in which it is necessary to decompose a hundred and a ten in order to get more ones because there is a zero in the tens place.

  • Engagement
  • MLR8

Learning Goals

Teacher Facing

  • Analyze different steps in subtraction algorithms and reason about when certain steps might be more productive.

Student Facing

  • Let’s think about subtraction algorithms in more detail.

Required Preparation

CCSS Standards


Lesson Timeline

Warm-up 10 min
Activity 1 20 min
Activity 2 15 min
Lesson Synthesis 10 min
Cool-down 5 min

Teacher Reflection Questions

How did your students use their prior understanding of subtracting with an algorithm to solve problems in which they have to decompose place value units across zeros?

Suggested Centers

  • How Close? (1–5), Stage 4: Add to 1,000 (Addressing)
  • Number Puzzles: Addition and Subtraction (1–4), Stage 5: Within 1,000 (Addressing)
  • Five in a Row: Multiplication (3–5), Stage 2: Factors 1–9 (Supporting)

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