Mathematics · Year 6

Active learning ideas

Extending Place Value to Millions and Decimals

Students need to physically move digits and build numbers to see how position changes value in large numbers and decimals. Moving from concrete to abstract, students need to shift digits left and right, observe the multiplicative pattern, and articulate the difference between whole and fractional values.

• ACARA Content Descriptions
• AC9M6N01

• 20–45 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Concept Mapping
• 35 min · Small Groups

Manipulative Build: Million and Decimal Towers

Provide base-10 blocks and decimal paper strips. Students build a given number up to millions, then adjust one digit to see value change. In small groups, they create and trade numbers for partners to read aloud and partition.

How does the position of a digit influence its value in a large number?

Facilitation Tip

During Manipulative Build, circulate and ask students to verbalise the place value of each digit they place on the tower before adding the next block.

What to look for

Present students with a number like 7,890,123.456. Ask them to write down the value of the digit '9' and the digit '4' in expanded notation. Then, ask them to write the number in words.

• Understand
• Analyze
• Create
• Self-Awareness
• Self-Management

Activity 02

• Concept Mapping
• 25 min · Pairs

Place Value Chart Race: Digit Shifts

Set up large place value charts from millionths to millions. Pairs race to insert digit cards for target numbers, then shift one digit left or right and calculate the new value. Discuss patterns observed.

Compare the value of a digit in the thousands place versus the thousandths place.

Facilitation Tip

In Place Value Chart Race, have students call out the new value of a shifted digit before recording it to reinforce rapid place-value calculation.

What to look for

Give students two numbers, e.g., 3,456,789 and 3,789,456. Ask them to write one sentence comparing the value of the digit '7' in both numbers. Also, ask them to order the numbers from smallest to largest.

• Understand
• Analyze
• Create
• Self-Awareness
• Self-Management

Activity 03

• Concept Mapping
• 45 min · Whole Class

Decimal Money Shop: Whole Class Simulation

Create a class shop with price tags using dollars and cents to three decimal places. Students take turns as shoppers and cashiers, writing receipts and making change while naming place values aloud.

Explain how place value is crucial for understanding financial transactions.

Facilitation Tip

In Decimal Money Shop, intentionally give a price requiring regrouping across the decimal point to expose gaps in decimal addition.

What to look for

Pose the question: 'Explain why understanding place value to the thousandths is important when discussing a country's national debt versus a personal savings account balance.' Facilitate a class discussion where students share their reasoning.

• Understand
• Analyze
• Create
• Self-Awareness
• Self-Management

Activity 04

• Concept Mapping
• 20 min · Individual

Number Line Compare: Individual Challenges

Students plot pairs of numbers on personal number lines spanning millions and decimals. They label digit places and explain which is larger, focusing on key digit comparisons.

How does the position of a digit influence its value in a large number?

What to look for

Present students with a number like 7,890,123.456. Ask them to write down the value of the digit '9' and the digit '4' in expanded notation. Then, ask them to write the number in words.

• Understand
• Analyze
• Create
• Self-Awareness
• Self-Management

A few notes on teaching this unit

Use the concrete-to-representational-to-abstract sequence: first build with blocks, then draw and label charts, finally write expanded and word forms. Avoid rushing to symbols; students need repeated physical shifts to internalise the 10× change rule. Research shows that students who manipulate digits on charts or with cards develop stronger understanding than those who only write numbers.

Students will confidently name, compare, and partition numbers to millions with three decimal places. They will explain why a digit’s value changes when moved across the decimal point and use place value language to justify their reasoning.

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Watch Out for These Misconceptions

• During Manipulative Build, watch for students who treat each block position as additive rather than multiplicative, stacking identical blocks for millions and thousandths.

  Pause the tower construction and ask students to compare the height or volume of one million block to one unit block, then ask them to predict the size of a hundred-thousand block before building it.

• During Place Value Chart Race, watch for students who shift digits without changing their value, e.g., moving a 4 from thousands to hundreds without dividing by 10.

  Ask students to write the new number after each shift and underline the digit that moved, then ask them to state the place value change in words before continuing the race.

• During Decimal Money Shop, watch for students who add money as if there were no decimal point, e.g., treating $3.45 + $2.60 as 345 + 260.

  Hand students play money and ask them to count out the cents separately, then combine whole dollars and cents to reinforce the role of the decimal as a separator of units and parts.

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Methods used in this brief

• Concept Mapping