Mathematics · Year 5

Active learning ideas

Comparing and Ordering Large Numbers

Active learning works because comparing and ordering large numbers—especially negative numbers—requires spatial and contextual thinking. Students need to move, visualize, and reason, not just memorize rules. Hands-on simulations and role plays make the abstract concrete by placing numbers in real-world situations where their meaning becomes clear.

• ACARA Content Descriptions
• AC9M5N01

• 20–40 min
• Pairs → Whole Class
• 3 activities

Activity 01

• Simulation Game
• 35 min · Small Groups

Simulation Game: The Great Barrier Reef Dive

Students use a vertical number line on the wall to simulate a dive. They start at sea level (0) and move to different depths (negative integers) to 'photograph' sea creatures, then calculate their total distance from the surface after ascending or descending.

Compare two large numbers to determine which is greater, justifying your reasoning.

Facilitation Tip

During The Great Barrier Reef Dive, have students physically stand at positions on a marked floor number line to reinforce the idea that ‘less’ means ‘lower’ on the line.

What to look for

Present students with two large numbers, e.g., 789,456 and 798,456. Ask them to write which number is greater and to explain their reasoning using place value. For example, '798,456 is greater because the digit in the ten thousands place (9) is greater than the digit in the ten thousands place of the other number (8).'

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

Activity 02

• Role Play
• 40 min · Pairs

Role Play: The Classroom Bank

Students manage a simple 'account' where they can earn credits or 'overdraw' their balance to buy classroom rewards. They must record their balance using positive and negative signs, explaining to a 'bank manager' (peer) how they will return to a positive balance.

Order a set of multi-digit numbers from least to greatest.

Facilitation Tip

In The Classroom Bank role play, give each student a transaction slip so they can write and explain their balance change as a negative or positive number.

What to look for

Provide students with a list of five numbers up to one million, such as 1,234,567; 987,654; 1,050,000; 1,100,999; 999,999. Ask them to order these numbers from least to greatest on their ticket and to circle the largest number.

• Apply
• Analyze
• Evaluate
• Social Awareness
• Self-Awareness

Activity 03

• Think-Pair-Share
• 20 min · Pairs

Think-Pair-Share: Temperature Extremes

The teacher provides a list of record temperatures from across Australia and the world. Students think about which is 'colder' (-5 or -15), pair up to plot them on a number line, and share their reasoning for why a 'larger' numeral with a minus sign represents a smaller value.

Analyze real-world situations where ordering large numbers is critical (e.g., population data).

Facilitation Tip

For Temperature Extremes, provide laminated thermometer strips so students can mark and compare temperatures directly on a vertical scale.

What to look for

Pose the question: 'Imagine you are helping to organize a national sporting event. Why would it be important to accurately compare and order the populations of different cities when deciding where to hold events?' Guide students to discuss factors like venue size, audience capacity, and travel logistics.

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

A few notes on teaching this unit

Teach this topic by linking numbers to movement and direction. Avoid starting with rules like ‘the bigger the absolute value, the smaller the number’—this often confuses students. Instead, use a vertical number line first, because sea level, temperature, and altitude are all intuitive contexts. Encourage students to verbalize comparisons aloud so you can catch misconceptions early. Research shows that students who talk through their reasoning develop stronger conceptual understanding than those who only write answers.

By the end of these activities, students should confidently explain why -15 is less than -3 and order numbers like -200, 1500, and -500 correctly. They should use terms like ‘greater than,’ ‘less than,’ and ‘debt’ accurately when describing their reasoning in discussions or written work.

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Watch Out for These Misconceptions

• During The Great Barrier Reef Dive, watch for students who say -10 metres is ‘bigger’ than -5 metres because 10 is bigger than 5.

  Show them the marked floor number line and have them stand at -10 and -5. Ask: ‘Which position is lower?’ Use the thermometer analogy: -10°C is colder than -5°C, so it is less. Reinforce by having them record comparisons like ‘-10 < -5’ next to their dive depths.

• During The Classroom Bank role play, watch for students who believe zero is the smallest possible balance.

  Give each student a $5 starting balance and have them ‘spend’ $7 to reach -$2. Ask: ‘Is -$2 less than $0?’ Use the transaction slips to show that owing $2 is less than having $0. Discuss the difference between ‘owing’ and ‘having’ in simple language.

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Methods used in this brief

• Simulation Game
• Role Play
• Think-Pair-Share