Mathematical Explorers: Building Foundations · 2nd Class

Active learning ideas

Subtracting Two-Digit Numbers Without Renaming

Active learning turns abstract subtraction into concrete steps students can touch and see. When students physically separate tens and units with blocks or hop along a number line, they build mental images that make place value subtraction automatic. These hands-on methods prevent the common mistake of treating two-digit numbers as single units and make correct alignment second nature.

• NCCA Curriculum Specifications
• NCCA: Junior Cycle - Number - N.1.6
• NCCA: Junior Cycle - Problem Solving

• 20–35 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Stations Rotation
• 30 min · Pairs

Manipulative Station: Base-10 Blocks

Provide base-10 blocks for pairs to model subtractions like 64 minus 32. Students build both numbers, remove units first then tens, and record the difference. Partners check each other's work and explain the steps verbally.

How do you subtract two-digit numbers by working with tens and units separately?

Facilitation Tip

During the Base-10 Blocks station, have students verbally label each piece as 'tens' or 'units' before removing them to reinforce place value vocabulary.

What to look for

Present students with a worksheet containing 5 subtraction problems without renaming (e.g., 67 - 32, 89 - 54). Ask them to solve each problem using the column method and write down one mental strategy they used for at least two problems.

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

Activity 02

• Stations Rotation
• 25 min · Small Groups

Number Line Hops: Relay Race

Mark a large floor number line. In small groups, one student starts at the minuend (e.g., 53), hops back the subtrahend (3 units, then 2 tens for 23), landing on the difference. Group records and discusses the path.

What mental strategies can help you subtract numbers like 56 − 23 quickly?

Facilitation Tip

For the Number Line Hops relay, stand at the finish line to observe if students hop the units first, then the tens, and call out the sequence to correct any reversals immediately.

What to look for

Give each student a card with a subtraction problem like 58 - 25. Ask them to write the answer and then explain in one sentence how they would teach a classmate to solve it using the tens and units separately.

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

Activity 03

• Stations Rotation
• 20 min · Individual

Column Match-Up Game: Individual Challenge

Distribute cards with subtraction problems and answers. Students set up columns, compute without renaming, and match to answers. Swap cards with a partner to verify and note mental shortcuts used.

Can you set out a subtraction sum in columns and find the correct answer?

Facilitation Tip

In the Column Match-Up Game, provide mats with labeled columns (Tens, Units) and color-coded digits so students practice proper alignment before matching answers.

What to look for

Pose the question: 'Imagine you have 75 stickers and give 30 to a friend. How can you figure out how many stickers you have left?' Facilitate a class discussion where students share different strategies, including partitioning tens and units, and using the column method.

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

Activity 04

• Stations Rotation
• 35 min · Small Groups

Shopping Budget: Role-Play Scenarios

In small groups, give play money and price tags (e.g., €45 minus €21). Students subtract costs from budgets in columns, discuss if they have enough, and share strategies for quick checks.

How do you subtract two-digit numbers by working with tens and units separately?

Facilitation Tip

During the Shopping Budget role-play, hand students play money in exact denominations so they experience subtracting tens and units directly without needing to 'make change' from smaller bills.

What to look for

Present students with a worksheet containing 5 subtraction problems without renaming (e.g., 67 - 32, 89 - 54). Ask them to solve each problem using the column method and write down one mental strategy they used for at least two problems.

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

A few notes on teaching this unit

Teachers should model the column method explicitly, writing each digit in the correct column and saying the place value aloud ('5 tens minus 2 tens equals 3 tens'). Avoid shortcuts like subtracting the whole number at once, which can mask misunderstandings. Use think-alouds to show how the units are subtracted before the tens, and encourage students to do the same during partner talks. Research shows that students who verbalize each step internalize the process faster than those who work silently.

By the end of these activities, students will subtract two-digit numbers without renaming quickly and accurately, explaining each step aloud. They will use the column method with confidence and identify when no renaming is needed, showing their reasoning clearly on paper or in discussion. Peer corrections during games will reinforce correct place-value language like 'tens minus tens' and 'ones minus ones'.

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Watch Out for These Misconceptions

• During the Base-10 Blocks station, watch for students who remove all blocks at once instead of separating tens and units first.

  Prompt them to count out the tens and units separately, then remove the exact amount for the units before the tens. Ask, 'How many tens blocks should stay on the table after subtracting 23?' to redirect their focus to place value.

• During the Number Line Hops relay, watch for students who hop the tens first or mix the order of the subtrahend digits.

  Have them repeat the problem aloud while pointing to the digits: '72 minus 41 means 1 unit first, then 4 tens.' Use a whiteboard to write the problem vertically as they hop to connect the activity to the column method.

• During the Column Match-Up Game, watch for students who match answers without aligning digits properly in the columns.

  Provide colored pencils and have them trace the digits in the correct columns before matching. Ask peers to verify alignment by reading the problem aloud together before flipping answer cards.

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Methods used in this brief

• Stations Rotation