Mathematics · 4th Grade

Active learning ideas

Understanding Place Value: Ten Times Greater

Active learning lets students physically manipulate representations of place value, turning abstract concepts into concrete experiences. When students move and regroup disks or stand in positions, they internalize the multiplicative relationship between places instead of memorizing rules.

• Common Core State Standards
• CCSS.Math.Content.4.NBT.A.1

• 15–30 min
• Pairs → Whole Class
• 3 activities

Activity 01

• Simulation Game
• 20 min · Whole Class

Simulation Game: The Human Place Value Chart

Assign students to be specific digits (0-9) and have them stand in a life-sized place value chart on the floor. When the teacher calls out 'Multiply by 10!', each student must physically shift one chair or spot to the left while a new student fills the ones place with a zero. This helps students visualize the physical movement of digits during multiplication.

Analyze how the value of a digit changes as it moves to the left in a multi-digit number.

Facilitation Tip

During The Human Place Value Chart, remind students that each step left means they trade ten of the previous unit for one of the next.

What to look for

Present students with a number like 333. Ask them to write down the value of each digit. Then, ask: 'How many times greater is the value of the first 3 compared to the second 3?'

• Apply
• Analyze
• Evaluate
• Create
• Social Awareness
• Decision-Making

Activity 02

• Inquiry Circle
• 30 min · Small Groups

Inquiry Circle: The Value Hunt

Give small groups a set of cards with numbers like 50, 500, and 5,000. Students must use base-ten blocks to prove how many of the smaller number 'fit' into the larger number. They then record their findings as '10 times as much' statements to share with the class.

Explain why the number zero is essential for our base ten system to function effectively.

Facilitation Tip

In The Value Hunt, circulate and listen for students using the phrase 'ten times greater' instead of 'just bigger.'

What to look for

Give students a number, for example, 7,052. Ask them to write two sentences explaining why the 7 has a greater value than the 5. Also, ask them to explain the role of the 0 in this number.

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

Activity 03

• Think-Pair-Share
• 15 min · Pairs

Think-Pair-Share: The Zero Hero

Ask students to consider the number 405 and 45. In pairs, students discuss what would happen if the zero disappeared and why that zero is 'holding' a spot that is ten times more valuable than the ones place. Pairs then share their best analogy for why the zero is essential for the system to work.

Compare the value of a digit in the hundreds place to the value of the same digit in the tens place.

Facilitation Tip

For The Zero Hero, pause discussions after each pair shares to ask the class to restate the explanation in their own words.

What to look for

Pose the question: 'If you move the digit 9 one place to the left in the number 90, what happens to its value? How do you know?' Facilitate a class discussion where students use vocabulary like 'ten times greater' and 'place value'.

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

A few notes on teaching this unit

Start with physical models before moving to symbols. Research shows that students who experience the exchange of ten ones for one ten with place value disks develop stronger multiplicative reasoning than those who only see written numbers. Avoid rushing to the abstract; give students time to verbalize the shift from additive to multiplicative thinking.

By the end of these activities, students will confidently state that moving a digit one place to the left multiplies its value by ten. They will use the phrase 'ten times greater' accurately when explaining their reasoning to peers.

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Watch Out for These Misconceptions

• During The Human Place Value Chart, watch for students who say a digit becomes 'ten times bigger' by adding a zero rather than trading ten smaller units for one larger unit.

  Have students physically trade ten one-disks for one ten-disk while saying, 'Ten ones make one ten, so the value is ten times greater.'

• During The Zero Hero, watch for students who think the zero in a number like 7,052 has no value or is 'just a placeholder.'

  Ask students to cover the zero with a finger and read the number aloud to notice the change; then have them use place value disks to show that the zero represents zero tens, confirming its role in maintaining place value.

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Methods used in this brief

• Simulation Game
• Inquiry Circle
• Think-Pair-Share