Teaching Place Value With Base Ten Blocks

Teaching place value with base ten blocks gives children a hands-on way to understand how numbers are organized. Instead of memorizing that a digit in the tens place represents groups of ten, students can physically build those groups and see how different pieces represent different values.

Place value is a foundation for many later math skills, including addition, subtraction, multiplication, division, rounding, decimals, and working with larger numbers. A strong understanding of place value can therefore make many future math concepts easier.

The central idea students should eventually understand is:

10 ones = 1 ten
10 tens = 1 hundred
10 hundreds = 1 thousand

What Are Base Ten Blocks?

Base ten blocks are manipulatives that represent the structure of our base-ten number system.

The standard pieces include:

Unit Cube

Represents: 1

It is used for the ones place.

Ten Rod

Represents: 10

It is made up of 10 unit cubes and represents one ten.

Hundred Flat

Represents: 100

It contains 10 ten rods and represents one hundred.

Thousand Cube

Represents: 1,000

It contains 10 hundred flats and represents one thousand.

The repeating relationship between the pieces is the most important part:

10 unit cubes → 1 ten rod

10 ten rods → 1 hundred flat

10 hundred flats → 1 thousand cube

Why Use Base Ten Blocks to Teach Place Value?

Place value is an abstract concept. A child may be able to repeat that “the 5 in 50 means five tens” without actually understanding what five tens represents.

Base ten blocks make that idea visible.

For example, place: 5 unit cubes

beside: 5 ten rods

Ask the student whether the two groups have the same value.

The student can see that one represents: 5

while the other represents: 50

This helps demonstrate that the position of a digit changes its value.

Teaching Place Value With Base Ten Blocks

Understanding place value becomes much easier when children can see and touch what each digit represents. Teaching Place Value With Base Ten Blocks gives students a hands-on way to explore ones, tens, and hundreds while building a stronger understanding of how numbers are structured.

Begin With Exploration

Before formally teaching place value, allow students to explore the blocks.

Give them a collection of unit cubes, ten rods, and hundred flats.

Ask questions such as:

• Which piece is smallest?
• Which piece is largest?
• How many small cubes make one rod?
• How many rods make one flat?
• Can you find pieces that represent the same amount?
• What happens when you put 10 small cubes together?

Allow students to touch, count, compare, and arrange the blocks.

This creates an intuitive understanding before introducing mathematical vocabulary.

Introduce Ones

Begin with the smallest unit.

Hold up one cube and explain: “This represents one.”

Give students several cubes and ask them to build:

• 2
• 4
• 6
• 9

Have students count each cube individually.

Then ask: “What place do these cubes represent?”

Introduce the word: ones

Explain that each individual cube represents one unit or one one.

Introduce Tens

Place one ten rod beside 10 individual unit cubes.

Count the cubes together: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10

Then point to the rod.

Explain: “These 10 ones have the same value as one ten.”

Write: 10 ones = 1 ten

This is an important moment. Give students time to physically compare the two representations.

Let Students Make Their Own Tens

Give each student 10 unit cubes.

Ask: “Can you make one group of ten?”

After they count the cubes, let them exchange the 10 cubes for a ten rod.

Repeat the activity several times.

For example:

• 20 ones = 2 tens
• 30 ones = 3 tens
• 40 ones = 4 tens

This builds a connection between counting by ones and counting by tens.

Introduce Hundreds

Once students understand tens, introduce the hundred flat.

Show: 10 ten rods

and: 1 hundred flat

Explain: 10 tens = 1 hundred

Then connect all three levels: 100 ones = 10 tens = 1 hundred

Students should physically count and compare the blocks whenever possible.

Introduce Thousands When Appropriate

For students working with four-digit numbers, introduce the thousand cube.

Show 10 hundred flats and explain: 10 hundreds = 1 thousand

Then build the complete hierarchy:

• 1 one
• 1 ten = 10 ones
• 1 hundred = 10 tens
• 1 thousand = 10 hundreds

This shows students that the same grouping pattern continues as numbers become larger.

Create a Place Value Chart

Place a chart in front of students:

Thousands	Hundreds	Tens	Ones

Give students a number, such as: 3,426

Ask them to build it.

They should use:

• 3 thousand cubes
• 4 hundred flats
• 2 ten rods
• 6 unit cubes

Then place each type of block under its corresponding heading.

This connects the physical blocks to written place value.

Start With Two-Digit Numbers

Do not immediately begin with thousands.

Start with simple numbers such as: 23

Ask students: “How can we build 23?”

They should identify: 2 tens + 3 ones

Then try:

• 41
• 56
• 72
• 89

For every number, ask students to explain what each digit represents.

Move to Three-Digit Numbers

Once students understand tens and ones, introduce hundreds.

For example: 352

Build: 3 hundreds + 5 tens + 2 ones

Then ask: “What does the 3 represent?”

Answer: 300

“What does the 5 represent?”

Answer: 50

“What does the 2 represent?”

Answer: 2

This helps students move beyond simply identifying digits.

Teach the Difference Between a Digit and Its Value

This distinction is extremely important.

Consider: 444

The digit is 4 in all three positions, but the values are different.

The first 4 represents: 400

The second 4 represents: 40

The third 4 represents: 4

Use blocks to physically demonstrate the difference.

Ask: “Do these three 4s have the same value?”

Students should recognize that they do not.

Introduce Expanded Form

After students build a number, translate it into expanded form.

For: 352

the blocks show: 3 hundreds + 5 tens + 2 ones

Write: 352 = 300 + 50 + 2

Repeat with different numbers.

This creates a strong connection:

Physical blocks → Place value → Expanded form

Introduce Standard Form

Reverse the activity.

Tell students: “I have 4 hundreds, 3 tens, and 7 ones. What number did I build?”

Students combine the values: 400 + 30 + 7 = 437

Then write: 437

This gives them practice moving from place-value language to standard notation.

Introduce Word Form

Once students are comfortable with standard and expanded form, introduce word form.

For: 437

students can write: four hundred thirty-seven

Use all three representations together:

• Standard form: 437
• Expanded form: 400 + 30 + 7
• Word form: four hundred thirty-seven

The blocks provide the physical representation behind all three.

Teach Zero as a Placeholder

Zero often causes confusion.

Use: 305

Ask students to build it.

They need:

• 3 hundreds
• 0 tens
• 5 ones

There is no ten rod, but the tens position still exists.

Explain: “Zero tells us that there are no tens in this number.”

Without zero: 305

could incorrectly become: 35

This is why zero is important in place value.

Practice Numbers With Zeros

Give students several examples:

• 204
• 310
• 405
• 507
• 620

Ask them to build each number.

Then ask:

• How many hundreds?
• How many tens?
• How many ones?
• Why is there a zero?
• What would happen if we removed the zero?

This provides repeated practice with placeholder zeros.

Teach Comparing Numbers

Base ten blocks are excellent for teaching greater than and less than.

Build: 42

and: 35

Ask students which number is greater.

Instead of simply looking at the digits, have them compare: 4 tens vs. 3 tens

Because 4 tens are greater than 3 tens: 42 > 35

This teaches students to compare numbers by place value.

Teach Ordering Numbers

Give students three or four numbers.

For example:

• 124
• 142
• 214

Ask them to build each number.

Then arrange them from smallest to largest: 124, 142, 214

Students can compare the blocks at each place-value level.

Start with the hundreds, then tens, then ones when necessary.

Teach “10 More” and “10 Less”

Base ten blocks make this concept very visual.

Build: 36

Then ask: “What happens if we add one ten?”

Students add a ten rod: 36 + 10 = 46

Now remove one ten: 46 − 10 = 36

Practice with numbers such as:

• 25
• 47
• 63
• 81

This reinforces the value of the tens place.

Teach “100 More” and “100 Less”

Once students understand tens, extend the same concept to hundreds.

Build: 326

Add one hundred flat: 426

Therefore: 326 + 100 = 426

Remove one hundred: 426 − 100 = 326

This helps students recognize that moving one place value changes the number by a predictable amount.

Introduce Trading and Regrouping

Trading is one of the most valuable activities with base ten blocks.

Suppose a student has: 13 ones

Place 13 unit cubes in front of them.

Ask: “Can we trade 10 ones for something that has the same value?”

Trade: 10 ones → 1 ten

The student is left with: 1 ten + 3 ones

This represents: 13

This concrete experience prepares students for regrouping in addition and subtraction.

Use Blocks for Addition

Consider: 27 + 16

Build 27: 2 tens + 7 ones

Build 16: 1 ten + 6 ones

Combine: 3 tens + 13 ones

Now trade: 10 ones → 1 ten

The result becomes: 4 tens + 3 ones

Therefore: 27 + 16 = 43

Students can physically see why a new ten is created.

Use Blocks for Subtraction

Consider: 52 − 18

Build: 5 tens + 2 ones

Students need to remove 8 ones, but there are only 2 ones.

Trade: 1 ten → 10 ones

Now there are: 4 tens + 12 ones

Remove: 1 ten + 8 ones

The remaining blocks are: 3 tens + 4 ones

Therefore: 52 − 18 = 34

This makes the traditional borrowing or regrouping process much more meaningful.

Let Students Represent the Same Number in Different Ways

Ask: “Can you build 35 in two different ways?”

One representation is: 3 tens + 5 ones

Another could be: 2 tens + 15 ones

Students can trade one ten for 10 ones.

The total value remains: 35

This teaches that a number can have different physical representations while keeping the same value.

Use “Build It, Draw It, Write It”

This is a useful three-stage activity.

Build It

Students construct the number using blocks.

Draw It

Students draw the blocks on paper.

Write It

Students write the number in standard and expanded form.

For example:

• Build: 4 hundreds + 2 tens + 7 ones
• Draw: corresponding blocks
• Write: 427
• Expanded form: 400 + 20 + 7

This gradually moves students from hands-on learning toward abstract mathematics.

Use a Place Value Mystery Game

Give students clues.

For example:

• “I have 5 hundreds.”
• “I have 2 tens.”
• “I have 8 ones.”

Ask: “What number am I?”

Students build: 528

Then reverse the game.

Build a number and have students create clues for their classmates.

Play “What Changed?”

Build: 246

Then secretly change one block.

For example, replace: 4 tens

with: 5 tens

Ask: “What changed?”

Students should identify: The number increased by 10.

This develops place-value reasoning.

Use Place Value With Money

Money can provide another familiar context.

For example, use pretend money to discuss:

• Ones
• Tens
• Hundreds
• Thousands

A child can see that 5 groups of 10 represent 50.

While money does not exactly match the physical dimensions of base ten blocks, it can help reinforce the idea of grouping quantities.

Encourage Mathematical Language

Ask students to use complete explanations.

Instead of: “It’s 63.”

encourage: “The number is 63 because it has 6 tens and 3 ones.”

For a larger number: “The 7 is worth 700 because it is in the hundreds place.”

This helps children connect mathematical vocabulary to their reasoning.

Use Questions That Encourage Thinking

Good questions include:

• How many ones are in one ten?
• How many tens are in one hundred?
• What is the value of this digit?
• Why is this digit worth more than that one?
• Can you build the same number another way?
• What happens if we add one ten?
• What happens if we remove one hundred?
• Why do we need the zero?
• Which number is greater? How do you know?
• Can you explain your answer using the blocks?

These questions help students develop conceptual understanding.

Common Mistakes to Watch For

Confusing a Digit With Its Value

A child may say the 6 in 64 means 6 instead of 60.

Use the blocks to show six ten rods.

Counting Rods as Ones

Make sure students understand that one rod represents 10, not 1.

Ignoring Zero

Use numbers with missing place values regularly.

Comparing Only the Number of Digits

Explain that a three-digit number is not automatically greater in every comparison without considering the actual values.

Difficulty With Regrouping

Return to the physical trading activity.

Treating Blocks as Objects to Count Rather Than Values

Frequently ask: “How much is this block worth?”

rather than only: “How many blocks are there?”

Move From Concrete to Abstract

Base ten blocks should support understanding rather than become a permanent requirement for every calculation.

A useful progression is:

• Concrete: Physically manipulate blocks.
• Representational: Draw pictures of the blocks.
• Symbolic: Use numerals and place-value charts.
• Abstract: Solve problems mentally or with standard written methods.

If a student becomes confused at the abstract stage, return to the concrete model.

Use a Daily Place Value Warm-Up

A five-minute routine can provide consistent reinforcement.

Write: 4,582

Ask: How many thousands?

4

How many hundreds?

5

How many tens?

8

How many ones?

2

Then ask: What is the value of the 5?

500

What is 10 more?

4,592

What is 100 less?

4,482

This creates repeated exposure without requiring a full lesson every day.

Example 20-Minute Classroom Activity

First 5 Minutes

Review the value of the four types of blocks.

Next 5 Minutes

Call out numbers and have students build them.

Examples:

• 24
• 57
• 103
• 245

Next 5 Minutes

Students write the standard and expanded forms.

Final 5 Minutes

Ask comparison and reasoning questions.

For example: Which is greater, 245 or 254? Why?

This combines hands-on practice with mathematical reasoning.

Example Small-Group Activity

For students who need additional support, use a small group of three or four children.

Give each student a place-value mat and blocks.

Call out: “Build 62.”

Check their models.

Then ask: “Show me 10 more.”

Then: “Show me 10 less.”

Then: “Trade the tens and ones so you represent the same number differently.”

This creates several layers of practice from one number.

Assess Understanding Through Demonstration

A written worksheet does not always show whether a child understands place value.

Ask students to demonstrate: “Build 408.”

Then ask: “Why did you use zero tens?”

Or: “Build 260 in two different ways.”

Or: “Build 350 and then show me 100 more.”

These tasks require students to apply the concept rather than simply recognize an answer.

Final Thoughts

Base ten blocks provide a powerful way to make place value concrete and understandable. They allow children to see, touch, count, compare, combine, and trade quantities, which can make an abstract mathematical system much easier to understand.

Start with the simplest relationships:

1 unit = 1

10 units = 1 ten

10 tens = 1 hundred

10 hundreds = 1 thousand

Then gradually move into building numbers, expanded form, comparing numbers, zeros as placeholders, regrouping, addition, and subtraction.

The strongest approach is to move through three stages:

Build it → Draw it → Write it

Once students can comfortably move between these representations, they are better prepared to understand more advanced mathematical operations and work with numbers independently.