Mathematics · Year 3

Active learning ideas

Representing 4-Digit Numbers

Active learning helps students move beyond memorizing place value columns by engaging them in hands-on experiences that reveal the flexible structure of four-digit numbers. When students physically group and regroup materials, they internalize the multiplicative relationships in our base-ten system, making abstract concepts concrete and memorable.

• ACARA Content Descriptions
• AC9M3N01

• 15–45 min
• Pairs → Whole Class
• 3 activities

Activity 01

• Inquiry Circle
• 30 min · Small Groups

Inquiry Circle: The Renaming Challenge

Small groups are given a four-digit number and must find as many ways as possible to rename it using different combinations of thousands, hundreds, tens, and ones. They record their findings on a large sheet of paper to share with the class.

Analyze how the position of a digit changes its value by a factor of ten.

Facilitation Tip

During The Renaming Challenge, circulate and ask guiding questions like, 'How would you explain to a friend why 12 hundreds is the same as 1 thousand and 2 hundreds?' to prompt deeper thinking.

What to look for

Provide students with the number 3,450. Ask them to write two different ways to partition this number (e.g., 3 thousands, 4 hundreds, 5 tens OR 34 hundreds, 5 tens). Then, ask them to explain what the zero in the ones place represents.

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

Activity 02

• Stations Rotation
• 45 min · Small Groups

Stations Rotation: Place Value Proofs

Students move through stations where they use concrete materials like Bundling Sticks or MAB blocks to model a 'renamed' number, such as 14 tens, and then write the standard form on a mini-whiteboard.

Justify why you might choose to partition 1,200 as 12 hundreds instead of 1 thousand and 2 hundreds.

Facilitation Tip

In Place Value Proofs, set a timer for each station to keep the rotation brisk and ensure students stay focused on the task at hand.

What to look for

Present the number 2,100. Ask students: 'Why might a builder prefer to think of 2,100 bricks as 21 hundreds instead of 2 thousands and 1 hundred?' Encourage them to use place value language and examples with concrete materials.

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

Activity 03

• Think-Pair-Share
• 15 min · Pairs

Think-Pair-Share: The Zero Hero

Students consider a number like 3,045 and discuss what happens if the zero is removed or moved to a different place. They share their reasoning with a partner before explaining to the class how the zero acts as a placeholder.

Explain what happens to the value of a number when we place a zero as a placeholder in different positions.

Facilitation Tip

For The Zero Hero, model the expanded notation with exaggerated emphasis on the zero (e.g., 4,056 = 4,000 + 0 + 50 + 6) to highlight its importance.

What to look for

Show students a set of MAB blocks or place value counters representing a four-digit number. Ask them to write the number. Then, ask them to rearrange the blocks to represent the same number using a non-standard partition and write that representation.

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

A few notes on teaching this unit

Start with concrete materials like MAB blocks or place value counters to build a visual and tactile understanding of four-digit numbers. Avoid rushing students into abstract notation before they can explain their partitions aloud. Research shows that students benefit from seeing the same number represented in multiple ways, so plan to revisit key numbers across activities. Encourage students to verbalize their reasoning, as explaining aloud solidifies their understanding.

By the end of these activities, students will confidently rename and partition four-digit numbers in multiple ways. They will articulate how different partitions represent the same quantity and use language like 'hundreds,' 'thousands,' and 'groups of ten' to explain their reasoning. Struggling students will gain clarity through peer discussion and concrete materials.

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Watch Out for These Misconceptions

• During Collaborative Investigation: The Renaming Challenge, watch for students who argue that 12 hundreds is a different value than 1,200 because it 'doesn't fit' the columns.

  Bring students back to the place value mats and physical bundling. Have them group 10 hundreds into a thousand block to see the renaming process. Ask them to explain the total quantity aloud to a partner, reinforcing that the 'name' changes but the value does not.

• During Station Rotation: Place Value Proofs, watch for students who think that the zero in a number like 4,056 means there is 'nothing' there and can be ignored.

  Direct students to the expanded notation station and model writing 4,056 as 4,000 + 0 + 50 + 6. Use place value expanders to show how the zero holds the hundreds place, preventing the digits 5 and 6 from shifting left.

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Methods used in this brief

• Inquiry Circle
• Stations Rotation
• Think-Pair-Share