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.

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

Learning Objectives

1. Design a base-ten block model to demonstrate composing a ten when adding two-digit numbers.
2. Explain how bundling ten ones into a ten rod simplifies the addition process.
3. Calculate the sum of two-digit numbers using an open number line model.
4. Compare the efficiency of using base-ten blocks versus an open number line for adding two-digit numbers.
5. Analyze the relationship between place value and regrouping in addition problems.

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.

Prepare & details

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.

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

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.

Prepare & details

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.

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

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.

Prepare & details

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.

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: 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.

Prepare & details

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.

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 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.

What to Expect

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.

Watch Out for These Misconceptions

Common Misconception

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

What to Teach Instead

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.

Common Misconception

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

What to Teach Instead

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.

Common Misconception

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

What to Teach Instead

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?'

Assessment Ideas

Exit Ticket

After the Gallery Walk, give students two problems like 26 + 47. Ask them to solve one using base-ten blocks (draw or use cut-outs) and one using an open number line. Collect their models and equations to check for accurate use of the models and correct regrouping.

Quick Check

During Add and Explain stations, present a problem like 38 + 25. Ask students to build it with blocks, then hold up fingers to show how many tens they composed after adding the ones. Listen for students who say, 'I had 13 ones, so I made 1 ten and 3 ones.'

Discussion Prompt

After Think-Pair-Share: Regroup or Not?, pose the question: 'Why did you decide to regroup in 45 + 28 but not in 32 + 14?' Listen for answers that mention the total of the ones digits and place value language like 'more than 9 ones' or 'less than 10 ones.'

Extensions & Scaffolding

• Challenge students who finish early to create a real-world word problem using their model and solve it using a different representation.
• For students who struggle, provide a bank of pre-made base-ten block arrangements with the total already written; ask them to match and narrate the quantity.
• Deeper exploration: Invite students to research and present how ancient cultures used similar grouping strategies to add large numbers.

Key Vocabulary

Base-ten blocks	Manipulatives representing ones (units), tens (rods), hundreds (flats), and thousands (cubes) to model numbers and operations.
Composing a ten	The process of combining ten ones to make one ten, often called regrouping or carrying over in addition.
Place value	The value of a digit based on its position within a number (e.g., the '2' in 25 represents 2 tens).
Open number line	A number line without pre-marked numbers, used to visually represent jumps for addition and subtraction.
Regrouping	Exchanging units of one place value for an equivalent number of units in the next higher place value, such as exchanging 10 ones for 1 ten.