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.

• 4th Grade
• Mathematics
• 3 activities
• 15 min–30 min

Learning Objectives

1. Compare the value of a digit in a specific place to its value in the adjacent place to its right, identifying the multiplicative factor.
2. Explain the role of the zero as a placeholder in the base-ten system, demonstrating its necessity for place value representation.
3. Calculate the value of a digit in a multi-digit number based on its position.
4. Analyze how moving a digit one place to the left increases its value by a factor of ten.

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.

Prepare & details

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.

Setup: Flexible space for group stations

Materials: Role cards with goals/resources, Game currency or tokens, Round tracker

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

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.

Prepare & details

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.'

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

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.

Prepare & details

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.

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

Teaching This Topic

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.

What to Expect

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.

Watch Out for These Misconceptions

Common Misconception

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.

What to Teach Instead

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.'

Common Misconception

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.'

What to Teach Instead

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.

Assessment Ideas

Quick Check

After The Human Place Value Chart, present students with a number like 333. Ask them to write down the value of each digit and then explain how many times greater the first 3 is compared to the second 3 using the disks to demonstrate.

Exit Ticket

After The Value Hunt, 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, and to describe the role of the 0 in maintaining the place values of the other digits.

Discussion Prompt

During The Zero Hero, 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' to justify their responses.

Extensions & Scaffolding

• Challenge: Provide a three-digit number and ask students to write a number that is ten times greater and explain the change in each digit's value.
• Scaffolding: Give students place value disks and a template with columns labeled 'ones,' 'tens,' and 'hundreds' to physically trade units.
• Deeper exploration: Ask students to compare two numbers of different lengths, like 45 and 450, and explain why the relationship is ten times greater even though one number has an extra digit.

Key Vocabulary

Place Value	The value of a digit based on its position within a number. For example, in the number 345, the digit 4 is in the tens place, representing 40.
Base Ten System	A number system with ten unique digits (0-9) where each digit's value is based on its position, increasing by powers of ten.
Digit	A single symbol used to represent a number. In our base ten system, the digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
Placeholder	A symbol, usually zero, used to indicate an empty place value. It ensures that digits in other places retain their correct value.