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.

• 2nd Year
• Foundations of Mathematical Thinking
• 4 activities
• 20 min–35 min

Learning Objectives

1. Demonstrate the value of a digit in numbers up to 199 by representing it with base ten blocks.
2. Explain the process of exchanging 10 unit blocks for 1 ten block, and 10 ten blocks for 1 hundred block.
3. Compare different representations of the same number (e.g., 3 tens and 4 units versus 2 tens and 14 units) using base ten blocks.
4. Calculate the total value of a number constructed with base ten blocks, given the counts of unit, ten, and hundred pieces.

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.

Prepare & details

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.

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

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.

Prepare & details

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.

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

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.

Prepare & details

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.

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

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.

Prepare & details

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.

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 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.

What to Expect

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.

Watch Out for These Misconceptions

Common Misconception

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

What to Teach Instead

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.

Common Misconception

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

What to Teach Instead

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.

Common Misconception

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

What to Teach Instead

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.

Assessment Ideas

Quick Check

After Pair Build and Trade, provide a number like 73. Ask students to build it and draw their representation, labeling the tens and units to check their understanding.

Exit Ticket

After Small Group Number Challenges, give students 12 units, 5 tens, and 1 hundred block. Ask them to write the total number and explain how they would exchange blocks to represent 100.

Discussion Prompt

During Whole Class Exchange Relay, pose the question, 'What happens to the value of a number if you swap one ten rod for ten unit blocks?' Have students use their base ten blocks to demonstrate and explain their reasoning before discussing as a class.

Extensions & Scaffolding

• Challenge early finishers to represent numbers like 199 using the fewest blocks possible, then explain their choices to a peer.
• For struggling students, provide a number line marked with tens and units to guide their block placement.
• During deeper exploration, ask students to create their own word problems that require exchanging blocks to solve.

Key Vocabulary

Unit	A single cube representing the value of one. In base ten, ten units can be grouped to form a ten.
Ten Rod	A rod made of ten unit cubes, representing the value of ten. Ten ten rods can be exchanged for a hundred flat.
Hundred Flat	A flat made of ten ten rods, representing the value of one hundred. It is composed of 100 unit cubes.
Place Value	The value of a digit based on its position within a number. For example, in 34, the '3' represents 3 tens, and the '4' represents 4 units.