Using Models for Subtraction within 100

Students need to see subtraction as more than a process when working within 100. Concrete models let them physically act out the decomposition of a ten, which turns an abstract idea into something they can touch and describe. This hands-on work builds confidence before moving to abstract calculations.

• 2nd Grade
• Mathematics
• 4 activities
• 20 min–45 min

Learning Objectives

1. Demonstrate the process of decomposing a ten using base-ten blocks to solve subtraction problems within 100.
2. Create a drawing that accurately represents the decomposition of a ten for subtraction with regrouping.
3. Compare and contrast the steps involved in decomposing a ten for subtraction with composing a ten for addition.
4. Explain the value of using concrete models or drawings before applying abstract subtraction algorithms.
5. Calculate the difference between two-digit numbers within 100, showing work with place value strategies.

Think-Pair-Share

⏱ 20 min·Pairs

Think-Pair-Share: Break Apart or Borrow?

Teacher presents a subtraction problem like 63 - 28. Pairs decide whether decomposing a ten is needed, then each partner models it independently before comparing their drawings to identify any differences.

Prepare & details

Compare the process of decomposing a ten in subtraction to composing a ten in addition.

Facilitation Tip: During Think-Pair-Share, ask students to build the minuend with blocks first, then physically remove the subtrahend while narrating each step aloud to their partner.

Setup: Standard classroom seating; students turn to a neighbor

Materials: Discussion prompt (projected or printed), Optional: recording sheet for pairs

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

Gallery Walk

⏱ 25 min·Small Groups

Gallery Walk: Spot the Error

Post six worked subtraction problems around the room: two correct, two with decomposition errors, and two with correct answers reached by incorrect methods. Students identify and explain the errors in writing.

Prepare & details

Construct a drawing to illustrate how to subtract a two-digit number from another with borrowing.

Facilitation Tip: During the Gallery Walk, have students write a sticky note with one sentence explaining the error they found on each poster before moving to the next problem.

Setup: Wall space or tables arranged around room perimeter

Materials: Large paper/poster boards, Markers, Sticky notes for feedback

• Understand
• Apply
• Analyze
• Create
• Relationship Skills
• Social Awareness

Inquiry Circle

⏱ 30 min·Small Groups

Inquiry Circle: Two Models, Same Problem

Groups solve one subtraction problem using base-ten blocks and then using a drawing. They write one sentence explaining how both models show the same decomposition and arrive at the same answer.

Prepare & details

Evaluate the benefits of using models before moving to abstract algorithms for subtraction.

Facilitation Tip: During the Station Rotation, assign each station a specific subtraction strategy so students explore multiple approaches before choosing their preferred method.

Setup: Groups at tables with access to source materials

Materials: Source material collection, Inquiry cycle worksheet, Question generation protocol, Findings presentation template

• Analyze
• Evaluate
• Create
• Self-Management
• Self-Awareness

Stations Rotation

⏱ 45 min·Small Groups

Stations Rotation: Subtraction Strategy Lab

Three stations feature physical blocks with decomposing, drawn models with circling and crossing out, and number line subtraction. Students solve assigned problems at each station and compare results with peers.

Prepare & details

Compare the process of decomposing a ten in subtraction to composing a ten in addition.

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

Teaching This Topic

Teachers should model the language of decomposition by saying 'I need more ones, so I break a ten into ten ones' while physically acting it out. Avoid rushing to the algorithm; give students time to struggle with the blocks first. Research shows that students who practice explaining their moves with models perform better on subtraction tasks later.

What to Expect

Successful students will clearly show how they break apart a ten-rod when needed, explain why they do it, and record their thinking with accurate drawings or numbers. Partners should be able to follow each step and agree on the solution.

Watch Out for These Misconceptions

Common Misconception

During Think-Pair-Share, watch for students who subtract the smaller digit from the larger regardless of place value.

What to Teach Instead

Have partners build the minuend with blocks first, then physically remove the subtrahend while narrating each step aloud. If a student still flips the digits, ask their partner to point to the blocks being removed and ask, 'Which number are we taking away now?'

Common Misconception

During Collaborative Investigation, watch for students who forget to adjust the tens column after decomposing.

What to Teach Instead

Require students to move the ten-rod to the ones column on their place value mat before starting subtraction. Partners must check and state aloud that the tens column decreased by one before any ones are subtracted.

Common Misconception

During Station Rotation, watch for students who decompose a ten even when not necessary.

What to Teach Instead

Start each problem by asking, 'Do I have enough ones?' Partners predict first, then build the problem with blocks. If a student decomposes unnecessarily, ask, 'Did you check the ones place first? What did you see?'

Assessment Ideas

Exit Ticket

After Think-Pair-Share, give students a problem like 42 - 17. Ask them to draw a picture using base-ten blocks or simple drawings to show their solution, including any decomposition. Collect drawings to check for correct representation of breaking apart a ten.

Quick Check

During Station Rotation, present a problem like 50 - 23. Ask students to hold up fingers to show how many tens they would decompose and how many ones they would get, then state the new number in the ones place. Circulate to listen for accurate explanations.

Discussion Prompt

After Collaborative Investigation, ask students, 'When you add 25 + 37, you make a new ten. When you subtract 42 - 17, you break apart a ten. How are these actions similar, and how are they different?' Listen for discussions about exchanging value between place values and the direction of the action.

Extensions & Scaffolding

• Challenge: Provide problems like 70 - 48 where students must decompose two tens. Ask them to record their process in two different ways (drawings and numbers).
• Scaffolding: Use a place value mat with ten-frames in the ones column so students can visually see when they have enough ones to subtract.
• Deeper: Ask students to create their own subtraction problem within 100 and exchange with a partner to solve, including written explanations of their decomposition steps.

Key Vocabulary

Decompose	To break a number down into smaller parts. In subtraction, we decompose a ten into ten ones when we need more ones to subtract.
Regroup	To exchange a ten for ten ones, or a hundred for ten tens, to make it easier to subtract. This is also called borrowing.
Base-ten blocks	Manipulatives that represent ones, tens, and hundreds. We use rods for tens and units for ones to model subtraction.
Place value	The value of a digit based on its position in a number. We use place value to understand how to decompose and regroup numbers.