Mathematics · Foundation

Active learning ideas

Representing Numbers with Objects and Pictures

Active learning with objects and pictures lets young children connect abstract numbers to concrete experiences, which builds lasting number sense. These hands-on activities move beyond rote counting to develop one-to-one correspondence and cardinality through movement, talk, and repeated exposure.

• ACARA Content Descriptions
• AC9M6N07

• 20–35 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Experiential Learning
• 25 min · Pairs

Matching Game: Numeral to Objects

Lay out numeral cards 1-10 and trays of blocks or counters. In pairs, students select a card, build the matching group, then swap and check each other's work. End with a gallery walk to spot creative representations.

Can you use blocks to make a group that matches this number card?

Facilitation Tip

During Matching Game, circulate and ask each pair to explain their match before moving on.

What to look for

Present students with a collection of 7 counters. Ask: 'How many counters are in this group?' Observe if students count accurately or subitize. Then, provide a numeral card for '7' and ask: 'Can you match the number card to the group?'

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

Activity 02

• Experiential Learning
• 30 min · Small Groups

Picture Interpretation: What Do You See?

Display printed pictures of grouped objects like apples or cars. Students work individually to circle and label the numeral, then discuss in small groups why different arrangements still show the same number. Collect responses on a class chart.

How many different ways can you show the number 5?

Facilitation Tip

While students work on Picture Interpretation, prompt them to point to each item as they count to reinforce one-to-one correspondence.

What to look for

Give each student a small piece of paper. Ask them to draw a picture showing the number 4 in one way, and then write the numeral '4' next to their drawing. Collect as they leave the lesson.

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

Activity 03

• Experiential Learning
• 35 min · Pairs

Build and Draw: My Number Ways

Provide blocks and paper. Students pick a number card 4-7, build it three ways with objects, then draw each. Pairs share one unique way with the class.

What does this picture show , how many objects are there?

Facilitation Tip

For Build and Draw, model drawing quickly and labeling, then invite students to share their different ways with the class.

What to look for

Hold up a picture of 6 apples. Ask: 'What do you see in this picture? How many apples are there?' Encourage students to explain their counting strategy. Ask: 'Can you think of another way to show the number 6 using objects in our classroom?'

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

Activity 04

• Experiential Learning
• 20 min · Whole Class

Scavenger Hunt: Find the Number

Call out a number; students hunt classroom objects to collect that many, place in a hoop, and photograph or draw. Regroup to verify totals together.

Can you use blocks to make a group that matches this number card?

Facilitation Tip

Set a timer for Scavenger Hunt to keep energy high and prevent students from over-searching.

What to look for

Present students with a collection of 7 counters. Ask: 'How many counters are in this group?' Observe if students count accurately or subitize. Then, provide a numeral card for '7' and ask: 'Can you match the number card to the group?'

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

A few notes on teaching this unit

Teach this topic through repeated, varied exposure using hands-on materials and peer discussion. Avoid long whole-group explanations; instead, demonstrate briefly, then step back to observe and question. Research shows that children develop number sense best when they manipulate objects, articulate their thinking, and see multiple representations of the same quantity side by side.

Successful learning looks like students accurately matching numerals to groups, confidently explaining their counts, and creating multiple representations for the same number. You’ll see them using materials flexibly and discussing their thinking with peers.

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Watch Out for These Misconceptions

• During Matching Game, watch for students who match by length or arrangement rather than count.

  Ask students to recount after rearranging the objects into a tight group, then ask if the number changed when they moved them. Have peers demonstrate their counting too.

• During Picture Interpretation, watch for students who count items slowly one by one without noticing patterns.

  Use quick flashcard reveals of familiar pictures and ask, 'How many did you see?' Encourage students to share if they recognized groups of 2 or 5 without counting.

• During Build and Draw, watch for students who only make one type of representation, like only fingers or only circles.

  Provide a tray with varied materials (blocks, beads, sticks) and ask, 'Can you show 5 another way?' Have students explain their choices to peers.

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Methods used in this brief

• Experiential Learning