Mathematics · Year 2

Active learning ideas

Subtracting Two-Digit Numbers (No Regrouping)

Active learning works well for subtracting two-digit numbers without regrouping because it turns abstract place value into visible actions. When students physically remove blocks or jump backward on a number line, they see why tens and ones are handled separately and how the answer forms step by step.

• ACARA Content Descriptions
• AC9M2N03

• 25–40 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Think-Pair-Share
• 30 min · Pairs

Base-10 Blocks: Partition and Subtract

Provide base-10 blocks and place value mats. Students build the larger number, then remove tens and ones blocks for the subtrahend. They draw or record the remaining blocks and explain the steps to a partner before checking with a calculator.

Explain how to subtract two-digit numbers by subtracting tens then ones.

Facilitation Tip

During Base-10 Blocks: Partition and Subtract, have students write the equation next to their block model to connect concrete and symbolic representations.

What to look for

Present students with three subtraction problems: 47 - 23, 58 - 31, and 65 - 18. Ask students to solve the first two using the tens and ones strategy and circle the problem that would require regrouping.

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

Activity 02

• Think-Pair-Share
• 25 min · Pairs

Number Line Jumps: Floor Model

Tape a large number line on the floor. Pairs select a problem, stand on the starting number, and jump back tens first then ones. They mark landings with tape and record the equation with jumps shown.

Predict when a subtraction problem will not require regrouping.

Facilitation Tip

While using the Number Line Jumps: Floor Model, ask students to call out each jump aloud so peers can follow the backward movement by tens and then ones.

What to look for

Pose the problem: 'Sarah has 36 stickers and gives 12 to her friend. How many stickers does she have left?' Ask students to explain their strategy using place value language, and then have another student explain it using a number line model.

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

Activity 03

• Think-Pair-Share
• 35 min · Small Groups

Subtraction Card Game: Strategy Share

Deal cards with two-digit subtraction problems (no regrouping). Pairs draw, solve using tens-ones method on whiteboards, then share strategies with another pair. Winning pair explains their quickest method.

Construct a number line model to demonstrate subtraction without regrouping.

Facilitation Tip

In the Subtraction Card Game: Strategy Share, circulate and prompt pairs to explain their chosen method before swapping cards, so reasoning becomes public.

What to look for

Give each student a card with the problem 59 - 35. Ask them to write down the steps they would take to solve this problem without regrouping, and then write the final answer.

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

Activity 04

• Stations Rotation
• 40 min · Small Groups

Stations Rotation: Visual Strategies

Set up stations: blocks, number lines, drawings, and digit cards. Groups rotate every 7 minutes, solving 3 problems per station and noting which strategy works best for each.

Explain how to subtract two-digit numbers by subtracting tens then ones.

What to look for

Present students with three subtraction problems: 47 - 23, 58 - 31, and 65 - 18. Ask students to solve the first two using the tens and ones strategy and circle the problem that would require regrouping.

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

A few notes on teaching this unit

Teachers should emphasize partitioning first and subtracting within places before recombining. Avoid rushing to the standard algorithm; instead, build mental images through repeated hands-on practice. Research shows that students who visualize subtraction as movement along a number line or as removal of grouped objects develop stronger place value reasoning and fewer misconceptions later.

By the end of these activities, students will confidently partition two-digit numbers, subtract tens and ones in order, and explain their steps using place value language. They will also recognize when regrouping is not needed and justify that choice with models or drawings.

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Watch Out for These Misconceptions

• During Base-10 Blocks: Partition and Subtract, watch for students who try to subtract 45 - 28 by removing 8 ones first from 5 ones.

  Redirect them to model 45 with 4 tens and 5 ones, then remove exactly 2 tens and 8 ones. Ask them to count the remaining blocks to see why removing 8 ones first leaves a negative result, reinforcing the need to subtract within place values in order.

• During Number Line Jumps: Floor Model, watch for students who jump by ones first instead of tens.

  Have them trace the number line with you, marking jumps of 10 first from 45 to 35, then smaller jumps of 1 from 35 to 32. Ask them to describe why grouping the larger jumps together matches the tens place subtraction.

• During Station Rotation: Visual Strategies, watch for students who assume regrouping is always needed for two-digit subtraction.

  Set up a station with a place value chart and problems like 59 - 35. Ask students to predict whether regrouping is needed before solving and have them justify their prediction by showing safe cases using the chart.

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Methods used in this brief

• Think-Pair-Share
• Stations Rotation