Mathematics · 2nd Grade

Active learning ideas

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.

• Common Core State Standards
• CCSS.Math.Content.2.NBT.B.5

• 20–45 min
• Pairs → Whole Class
• 4 activities

Activity 01

• 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.

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.

What to look for

Provide students with a subtraction problem, such as 42 - 17. Ask them to draw a picture using base-ten blocks or simple drawings to show how they solved it, including any decomposition of a ten. Write one sentence explaining their drawing.

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

Activity 02

• 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.

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.

What to look for

Present a problem like 50 - 23. Ask students to hold up fingers to show how many tens they would need to decompose and how many ones they would get. Then, ask them to state the new number they have in the ones place.

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

Activity 03

• 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.

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.

What to look for

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?' Guide them to discuss the concept of exchanging value between place values.

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

Activity 04

• 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.

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

What to look for

Provide students with a subtraction problem, such as 42 - 17. Ask them to draw a picture using base-ten blocks or simple drawings to show how they solved it, including any decomposition of a ten. Write one sentence explaining their drawing.

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

A few notes on teaching this unit

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.

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.

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Watch Out for These Misconceptions

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

  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?'

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

  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.

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

  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?'

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Methods used in this brief

• Think-Pair-Share
• Gallery Walk
• Inquiry Circle
• Stations Rotation