Mathematics · Year 1

Active learning ideas

Representing Numbers to 20

Active learning helps students grasp the concept of representing numbers to 20 by engaging multiple senses and learning styles. When students manipulate objects, draw pictures, and discuss their ideas, they connect abstract numerals to concrete quantities in lasting ways. This hands-on approach builds fluency and confidence with numbers beyond ten.

• ACARA Content Descriptions
• AC9M1N01

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

Activity 01

• Stations Rotation
• 25 min · Pairs

Pairs: Ten Frame Showdown

Pairs receive cards with numbers 11-20 and ten frames. One partner builds the number using counters on the frame; the other draws it and writes the numeral. Partners switch roles, then compare their work to find matches. Discuss why both show the same number.

Design multiple ways to show the number 15 using objects and drawings.

Facilitation Tip

During Ten Frame Showdown, circulate and ask pairs to explain how their arrangement matches the numeral, reinforcing the connection between grouping and notation.

What to look for

Provide students with a collection of 15 counters and a blank ten frame. Ask them to arrange the counters on the ten frame to show 15 and draw their representation. Observe if they correctly group 10 and 5.

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

Activity 02

• Stations Rotation
• 30 min · Small Groups

Small Groups: Representation Relay

Divide class into groups of four. Each student represents a number up to 20 using objects, pictures, numerals, or fingers. Pass to next student who creates a different representation. Groups race to complete five numbers and justify equivalences.

Compare different representations of the same number.

Facilitation Tip

For Representation Relay, assign each small group a specific number to ensure focused practice and quick feedback during the rotation.

What to look for

Show students three different representations of the number 12: a group of 12 loose counters, counters arranged as a full ten frame and 2 more, and a drawing of 12 stars. Ask: 'Which of these shows the same amount as the others? How do you know? Can you draw another way to show 12?'

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

Activity 03

• Stations Rotation
• 40 min · Whole Class

Whole Class: Number Line Gallery

Students create posters showing three ways to represent numbers 10-20. Display around room for a gallery walk. In pairs, visit posters, note similarities, and vote on most creative representation. Debrief as class.

Justify why different representations can still mean the same quantity.

Facilitation Tip

Set clear expectations for the Number Line Gallery by providing examples of varied representations so students understand the range of acceptable responses.

What to look for

Give each student a card with the numeral '17'. Ask them to draw a picture that shows 17 objects and write one sentence explaining why their drawing represents the number 17.

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

Activity 04

• Stations Rotation
• 20 min · Individual

Individual: My Number Journal

Each student picks five numbers to 20 and draws or pastes three representations per page: objects, picture, numeral. Add a sentence justifying one match. Share one page with partner.

Design multiple ways to show the number 15 using objects and drawings.

What to look for

Provide students with a collection of 15 counters and a blank ten frame. Ask them to arrange the counters on the ten frame to show 15 and draw their representation. Observe if they correctly group 10 and 5.

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

A few notes on teaching this unit

Teach this topic by moving from concrete to pictorial to symbolic representations, giving students time to explore each stage. Avoid rushing to numerals before students grasp the quantities they represent. Research shows that students learn best when they build, draw, and discuss their thinking before abstracting it. Use questioning to push their reasoning, asking them to explain why different representations show the same number.

Students will confidently create and compare multiple representations of numbers up to 20 using counters, ten frames, drawings, and numerals. They will justify their choices and recognize that different forms can show the same quantity. Collaboration and discussion will deepen their understanding of number composition.

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Watch Out for These Misconceptions

• During Ten Frame Showdown, watch for students who separate the numeral 15 into 1 and 5 when explaining their arrangement. Redirect them by asking, 'How many counters are in the full ten frame? How many are outside? How does that match the numeral 15?'

  During Ten Frame Showdown, students often see the numeral as separate digits. Have pairs physically place counters on the ten frame to show ten and five, then write the numeral 15 beside it. Ask them to explain how the grouped counters match the written number.

• During Representation Relay, watch for students who assume that different-looking pictures mean different numbers. Redirect them by asking, 'How do you know these all show the same amount?'

  During Representation Relay, provide each group with three different representations of the same number. Ask them to sort the cards and explain why they belong together, using counters to verify equivalence if needed.

• During Number Line Gallery, watch for students who rely only on counting one-by-one to confirm the amount. Redirect them by asking, 'Can you see the number without counting? What other ways can you tell how many there are?'

  During Number Line Gallery, ask students to subitize the quantities in the representations. Provide dot cards or ten frames to help them recognize the numbers instantly, then discuss how these patterns match the numeral.

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Methods used in this brief

• Stations Rotation