Subtracting Two-Digit Numbers (No Regrouping)

Active learning works because two-digit subtraction relies on visualizing place value and sequential steps. When students manipulate tens and ones with their hands, it locks the process into memory. Concrete objects turn abstract numbers into something they can control, reducing errors and building confidence.

• Year 2
• Mathematics
• 4 activities
• 20 min–35 min

Learning Objectives

1. Calculate the difference between two 2-digit numbers without regrouping by subtracting tens and then ones.
2. Explain the process of subtracting two 2-digit numbers using place value partitioning.
3. Construct a word problem that requires subtracting two 2-digit numbers without regrouping.
4. Identify the steps involved in subtracting the tens column before the ones column in subtraction problems.

Problem-Based Learning

⏱ 30 min·Pairs

Manipulative Mats: Tens First Subtraction

Provide base-10 blocks and mats marked with tens and ones columns. Students build the starting number, like 48, then remove 20 tens and 5 ones from 25. Record the result and explain steps to a partner. Extend by creating their own problems.

Prepare & details

Explain how to subtract two 2-digit numbers by subtracting the tens first, then the ones.

Facilitation Tip: During Manipulative Mats, remind students to remove tens blocks before ones, modeling the phrase 'tens first, then ones' aloud for the whole group.

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

⏱ 25 min·Small Groups

Pictorial Partition: Drawing Subtractions

Give worksheets with base-10 diagrams. Students draw 48 as four tens and eight ones, cross out two tens and five ones for 25, then count remaining. Discuss 'taking away' versus 'difference' with examples. Swap drawings to solve peers' work.

Prepare & details

Differentiate between 'taking away' and 'finding the difference' in subtraction.

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

⏱ 35 min·Small Groups

Story Station: Problem Creation

In rotations, students write and illustrate a subtraction story without regrouping, such as 53 birds flying away 32. Solve using objects or drawings, then share with group. Teacher circulates to prompt tens-first strategy.

Prepare & details

Construct a story problem that can be solved by subtracting 25 from 48.

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·Pairs

Number Line Relay: Find the Difference

Mark start number on floor number lines. Pairs jump back tens then ones, or find gap between numbers. Record jumps and repeat with varied problems. Whole class debriefs strategies.

Prepare & details

Explain how to subtract two 2-digit numbers by subtracting the tens first, then the ones.

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 by modeling the process slowly with base-10 blocks while narrating each step. Avoid rushing to abstract recording; let students verbalize their actions before writing. Research shows that physical movement paired with speech strengthens numerical reasoning. Always connect the blocks to the written method so students see the link between concrete and symbolic representations.

What to Expect

Successful learning looks like students confidently partitioning numbers into tens and ones, subtracting tens first then ones without regrouping. They explain their steps using base-10 blocks or drawings and justify why this method works. Peer discussions show shared understanding of place value during subtraction.

Watch Out for These Misconceptions

Common Misconception

During Manipulative Mats, watch for students removing ones first even when there aren't enough ones.

What to Teach Instead

Pause the group and ask, 'Can we take away 7 ones from 5 ones without touching the tens? What would happen if we tried?' Guide them to remove tens first, then ones, emphasizing the blocks cannot be broken.

Common Misconception

During Pictorial Partition, some children treat tens and ones as one whole number when drawing.

What to Teach Instead

Model shading exactly 4 tens and 8 ones for the number 48, then ask students to cross out 2 tens and 5 ones. Circle the tens crossed out first and say, 'We always start here.'

Common Misconception

During Story Station, students only create 'taking away' stories and miss 'comparison' stories.

What to Teach Instead

Ask groups to write two stories for 48 - 25: one about taking away and one about finding the difference. Use number lines to show both as backward jumps.

Assessment Ideas

Exit Ticket

After Manipulative Mats, give students a problem like 56 - 23. Ask them to show the subtraction using base-10 blocks and write the answer. Check if they removed tens first, then ones.

Discussion Prompt

During Story Station, listen for students explaining why they subtracted tens first in their story problems. Probe with, 'Why did you remove the tens before the ones in your story?'

Quick Check

During Number Line Relay, observe students solving 74 - 31. Note if they jump back 3 tens first, then 1 one, or if they try to jump back ones first.

Extensions & Scaffolding

• Challenge: Provide subtraction problems with missing digits, like 5_ - 23 = 28. Students use base-10 blocks to find the missing tens digit.
• Scaffolding: Give students a pre-partitioned ten frame with tens and ones shaded. They subtract by crossing out the correct number of tens and ones.
• Deeper: Create a mini-poster showing three subtraction problems solved with base-10 blocks and written steps, explaining why tens are subtracted first.

Key Vocabulary

Tens	The value of a digit in the second position from the right in a number, representing multiples of 10.
Ones	The value of a digit in the first position from the right in a number, representing single units.
Subtract	To take away a number or amount from another number or amount.
Difference	The result of subtracting one number from another; how much one number is greater or less than another.