Foundations of Mathematical Thinking · 2nd Year

Active learning ideas

Representing Numbers with Base Ten Blocks

Active learning with base ten blocks lets students physically see how numbers break into groups of tens and hundreds. This hands-on work builds a lasting understanding of place value that abstract symbols alone cannot provide.

• NCCA Curriculum Specifications
• NCCA: Primary - Number
• NCCA: Primary - Understanding and recalling facts

• 20–35 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Stations Rotation
• 25 min · Pairs

Pair Build and Trade: Number 56

Partners take turns building 56 using blocks, then exchange 10 units for a ten rod and rebuild. They record the tens and units before and after trading. Switch roles twice.

Can you show the number 34 using base ten blocks?

Facilitation Tip

During Pair Build and Trade, circulate to ensure partners are counting each other’s blocks aloud to reinforce place value vocabulary.

What to look for

Provide students with a number (e.g., 73). Ask them to build the number using base ten blocks and draw their representation, labeling the number of tens and units.

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

Activity 02

• Stations Rotation
• 35 min · Small Groups

Small Group Number Challenges: Up to 199

Groups draw cards with numbers like 89 or 145 and build them collaboratively. One student adds blocks while others count and verify place values. Discuss what happens if they add extra units.

How many tens and units make the number 52?

Facilitation Tip

For Small Group Number Challenges, assign roles so each student handles a different block type to distribute participation.

What to look for

Give students 12 units, 5 tens, and 1 hundred block. Ask them to write the total number represented and then explain how they would exchange blocks to represent the number 100.

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

Activity 03

• Stations Rotation
• 30 min · Whole Class

Whole Class Exchange Relay

Line up students; first builds a number under 100, passes to next who exchanges 10 units for a ten, then to next for hundreds if needed. Class counts aloud at each step.

What happens when you swap 10 unit blocks for one ten block?

Facilitation Tip

In the Whole Class Exchange Relay, model slow, deliberate exchanges so students can watch the process before trying themselves.

What to look for

Pose the question: 'What happens to the value of a number if you swap one ten rod for ten unit blocks?' Facilitate a discussion where students use their base ten blocks to demonstrate and explain their reasoning.

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

Activity 04

• Stations Rotation
• 20 min · Individual

Individual Place Value Mats

Each student gets a mat divided into hundreds, tens, units. They represent 5 teacher-called numbers up to 199, exchanging blocks as needed before showing.

Can you show the number 34 using base ten blocks?

Facilitation Tip

When using Individual Place Value Mats, provide dry-erase markers so students can easily adjust their representations.

What to look for

Provide students with a number (e.g., 73). Ask them to build the number using base ten blocks and draw their representation, labeling the number of tens and units.

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

A few notes on teaching this unit

Teachers should emphasize hands-on exchanges over counting by ones to prevent students from bypassing place value concepts. Avoid rushing through exchanges, as the physical act of breaking and rebuilding numbers builds deep understanding. Research shows that students who manipulate blocks while verbalizing their actions retain place value ideas longer than those who only observe demonstrations.

By the end of these activities, students should confidently use base ten blocks to represent any number up to 199, exchange blocks accurately, and explain why 10 units make a ten rod. They should also articulate how position changes the value of each block.

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Watch Out for These Misconceptions

• During Pair Build and Trade, watch for students who build numbers only with unit cubes, ignoring tens and hundreds.

  Ask partners to count aloud together, reinforcing that 10 unit cubes equal one ten rod. If a student persists, have them recount with a peer before rebuilding using larger blocks.

• During Whole Class Exchange Relay, some students may believe exchanging 10 tens for a hundred changes the total value.

  Have students recount the blocks before and after exchanging to see the total remains the same. Use the class’s shared count to confirm equality.

• During Small Group Number Challenges, students may think a hundreds block represents 100 separate units to count individually.

  Prompt students to decompose the hundreds block into tens and units, then rebuild it to see its compact value. Pair this with visual aids showing the hundreds block as one unit worth 100.

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Methods used in this brief

• Stations Rotation