Subtracting Two-Digit Numbers (With Regrouping)

Active learning works for subtracting two-digit numbers with regrouping because children need to see and touch the exchange of tens and ones. Concrete tools like base ten blocks let students physically trade a ten rod for ten unit cubes, making the abstract concept of regrouping visible and memorable.

• Year 2
• Mathematics
• 4 activities
• 20 min–45 min

Learning Objectives

1. Calculate the difference between two two-digit numbers when regrouping is required, showing the steps.
2. Compare the efficiency of using base ten blocks versus a number line for solving subtraction problems with regrouping.
3. Explain the necessity of regrouping when the ones digit in the minuend is smaller than the ones digit in the subtrahend.
4. Construct a word problem involving a real-world scenario that can be solved using subtraction with regrouping.
5. Demonstrate the process of regrouping by exchanging one ten for ten ones using concrete manipulatives.

Stations Rotation

⏱ 45 min·Small Groups

Stations Rotation: Regrouping Blocks

Prepare stations with base ten blocks and subtraction cards like 43 - 28. Students model the top number, exchange a ten for ones if needed, subtract bottom number, and record. Rotate groups every 10 minutes, then share one insight as a class.

Prepare & details

Explain the process of regrouping (borrowing) when the ones digit in the top number is smaller.

Facilitation Tip: During Station Rotation: Regrouping Blocks, circulate and ask each pair to explain their exchange step aloud before writing the number sentence.

Setup: Tables/desks arranged in 4-6 distinct stations around room

Materials: Station instruction cards, Different materials per station, Rotation timer

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

Problem-Based Learning

⏱ 25 min·Pairs

Pairs: Number Line Borrow

Give pairs a large number line and cards like 52 - 37. Jump back tens first, then ones, borrowing by partitioning the top number. Partners check by adding back up. Draw their jumps on mini whiteboards.

Prepare & details

Critique different methods for subtracting with regrouping, such as using a number line or base ten blocks.

Facilitation Tip: During Pairs: Number Line Borrow, remind students to mark the borrow point on the number line with a small arrow to show the shift in value.

Setup: Groups at tables with access to research materials

Materials: Problem scenario document, KWL chart or inquiry framework, Resource library, Solution presentation template

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management
• Relationship Skills

Problem-Based Learning

⏱ 30 min·Whole Class

Whole Class: Word Problem Chain

Start with a scenario like '45 apples minus 28 eaten.' Students in a circle add details requiring regrouping, solve using drawings or blocks, pass to next. Teacher scribes on board for all to see.

Prepare & details

Construct a word problem that requires subtraction with regrouping to solve.

Facilitation Tip: During Whole Class: Word Problem Chain, pause after each problem to ask a volunteer to restate the problem in their own words before solving it.

Setup: Groups at tables with access to research materials

Materials: Problem scenario document, KWL chart or inquiry framework, Resource library, Solution presentation template

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management
• Relationship Skills

Problem-Based Learning

⏱ 20 min·Individual

Individual: Pictorial Match-Up

Provide worksheets with pictorial subtractions and mixed methods. Students match problems to correct drawings showing regrouping, then create one themselves. Collect for quick plenary feedback.

Prepare & details

Explain the process of regrouping (borrowing) when the ones digit in the top number is smaller.

Setup: Groups at tables with access to research materials

Materials: Problem scenario document, KWL chart or inquiry framework, Resource library, Solution presentation template

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management
• Relationship Skills

Teaching This Topic

Teach this topic by moving from concrete to pictorial to abstract, using base ten blocks first to model regrouping. Avoid rushing to abstract methods before students can explain the exchange in their own words. Research shows that students who verbalise their steps while using manipulatives develop stronger number sense. Use consistent language like 'trade one ten for ten ones' to reinforce place value understanding.

What to Expect

Students will confidently explain and perform regrouping when subtracting two-digit numbers. They will use base ten blocks, number lines, and pictorial methods to solve problems accurately, showing their steps with clear reasoning. Misconceptions about borrowing will be corrected through guided practice and discussion.

Watch Out for These Misconceptions

Common Misconception

During Station Rotation: Regrouping Blocks, watch for students who subtract the ones without exchanging a ten. Redirect them by asking, 'Can you take away 8 ones from 3 ones? What can we trade to make this possible?'

What to Teach Instead

During Station Rotation: Regrouping Blocks, pair students to verbalise the exchange step before writing the number sentence. Listen for language like 'We trade one ten for ten ones because we need more ones to subtract.' This builds correct habits through peer explanation.

Common Misconception

During Station Rotation: Regrouping Blocks, watch for students who believe trading a ten for ones reduces the number's total value. Ask them to count the total value before and after the exchange to see it remains the same.

What to Teach Instead

During Station Rotation: Regrouping Blocks, guide students to recount the value of the blocks after trading one ten for ten ones. Ask, 'How many tens and ones do we have now? Is the total still the same?' This reinforces place value invariance through hands-on comparison.

Common Misconception

During Individual: Pictorial Match-Up, watch for students who doubt pictorial representations can represent regrouping. Ask them to match their drawing to a base ten block arrangement and explain how both show the same exchange.

What to Teach Instead

During Individual: Pictorial Match-Up, have students pair their drawings with base ten block setups and explain how the exchange looks in both forms. Discuss how the pictures prove consistency across tools, bridging to mental math.

Assessment Ideas

Quick Check

After Station Rotation: Regrouping Blocks, present students with the problem 73 - 28. Ask them to solve it using base ten blocks and draw a picture of their steps, including the regrouping. Observe if they correctly exchange a ten for ten ones.

Discussion Prompt

After Whole Class: Word Problem Chain, pose the question: 'Why do we sometimes need to 'borrow' from the tens place when subtracting?' Use the example 51 - 24 to prompt explanations that involve the ones digit being too small to subtract.

Exit Ticket

After Individual: Pictorial Match-Up, give each student a card with a word problem like: 'Sarah had 35 stickers. She gave 17 stickers to her friend. How many stickers does Sarah have left?' Students must write the number sentence and solve it, showing their regrouping steps.

Extensions & Scaffolding

• Challenge: Provide a set of three-digit subtraction problems (e.g., 205 - 138) using base ten blocks for students who finish early.
• Scaffolding: Offer pre-grouped base ten blocks (pre-traded tens for ones) for students who struggle, so they can focus on the subtraction process.
• Deeper exploration: Ask students to create their own word problem involving regrouping and solve it using all three methods (blocks, drawings, mental math).

Key Vocabulary

Regrouping	The process of exchanging a 'ten' for ten 'ones' (or vice versa) to make subtraction easier when the top digit in a place value column is smaller than the bottom digit.
Minuend	The number from which another number is to be subtracted. In a problem like 52 - 17, 52 is the minuend.
Subtrahend	The number that is to be subtracted from another number. In a problem like 52 - 17, 17 is the subtrahend.
Place Value	The value of a digit based on its position within a number, such as the tens place or the ones place.