Mathematics · 2nd Grade

Active learning ideas

Using Models for Addition within 100

Active learning works for addition within 100 because students need to physically see and manipulate quantities to understand regrouping. Base-ten blocks and open number lines make abstract concepts visible and allow children to build meaning through touch and movement. These models transform 'carrying the one' from a rote rule into a logical step grounded in place value.

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

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

Activity 01

• Gallery Walk
• 30 min · Pairs

Gallery Walk: Model Museum

Pairs create a poster showing at least two different models for adding two two-digit numbers (base-ten block drawing and open number line). The class walks through the museum and writes sticky notes identifying the strategy used on each poster.

Design a model using base-ten blocks to demonstrate regrouping when adding two-digit numbers.

Facilitation Tip

During the Gallery Walk, have students leave their written explanations on sticky notes next to each model so peers can read and respond to their reasoning.

What to look for

Provide students with two-digit addition problems, such as 37 + 25. Ask them to solve it using base-ten blocks (drawing or physical) and then solve it again using an open number line. Collect their work to check for accurate use of both models.

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

Activity 02

• Think-Pair-Share
• 20 min · Pairs

Think-Pair-Share: Regroup or Not?

Teacher poses a set of addition problems, some requiring composing a ten and some not. Partners predict whether regrouping will be needed before solving, then discuss their reasoning before computing the answer together.

Explain how bundling ten ones into a ten rod simplifies the addition process.

Facilitation Tip

When students pair up for Think-Pair-Share, assign roles: one student solves aloud while the other listens and asks clarifying questions before switching.

What to look for

Present a problem like 48 + 14. Ask students to hold up fingers to show how many tens they would 'carry over' or 'compose' after adding the ones. Then, ask them to draw one jump on an imaginary number line representing adding the tens.

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

Activity 03

• Inquiry Circle
• 35 min · Small Groups

Inquiry Circle: Build It Three Ways

Small groups receive a two-digit addition problem and represent it with physical blocks, a drawing, and a number line. They compare representations and explain which model helped them most and why.

Analyze how an open number line can be used to visualize adding two-digit numbers.

Facilitation Tip

In Build It Three Ways, set a timer for each model so students practice switching representations quickly and deliberately.

What to look for

Pose the question: 'When adding 56 + 38, why is it helpful to think about the ones first? How does this help us find the total sum more easily?' Listen for student explanations that connect to composing a ten and place value.

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

Activity 04

• Stations Rotation
• 45 min · Small Groups

Stations Rotation: Add and Explain

Students rotate through three stations: physical base-ten blocks, drawn models, and open number lines. At each station they solve the same problem and record what the specific model makes visible about the regrouping process.

Design a model using base-ten blocks to demonstrate regrouping when adding two-digit numbers.

Facilitation Tip

At each station during Add and Explain, require students to explain their model to a peer before recording the equation.

What to look for

Provide students with two-digit addition problems, such as 37 + 25. Ask them to solve it using base-ten blocks (drawing or physical) and then solve it again using an open number line. Collect their work to check for accurate use of both models.

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

A few notes on teaching this unit

Teachers should introduce models one at a time, giving students time to explore and name the parts before combining them. Avoid rushing to abstract notation; let students name their own strategies first. Research shows that students who verbalize their process while working with blocks develop stronger place value understanding and fewer calculation errors later.

Successful learning looks like students confidently choosing models to represent two-digit addition, explaining why they regroup, and accurately recording their work. They should connect concrete block arrangements to written notation and justify their jumps on an open number line. Partners should be able to follow each other’s reasoning without prompting.

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Watch Out for These Misconceptions

• During Think-Pair-Share: Regroup or Not?, watch for students who automatically regroup even when the ones sum to less than 10.

  Before students begin, model aloud the habit: 'I see 7 and 2 ones. 7 plus 2 is 9, which is less than 10, so I don’t need to trade. I write 9 in the ones place.' Have students practice this script with partners before solving.

• During Build It Three Ways, watch for students who record the new ten in the wrong column.

  Use a labeled place value mat with a clear tens and ones column. As students narrate their steps aloud, have them point to the mat and say, 'This new ten goes in the tens column because it’s worth 10 ones.' Peer partners check the placement before recording.

• During Gallery Walk: Model Museum, watch for students who confuse the block arrangement with the symbolic sum.

  Have students label their block models with sticky notes showing the total quantity. During the walk, prompt peers to match the written number to the correct arrangement by asking, 'Where do you see the 5 in 57 in this model?'

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Methods used in this brief

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