Mathematics · Year 1

Active learning ideas

Making a Model

Active, hands-on modeling turns abstract symbols into tangible quantities, which is essential for Year 1 learners. When students physically combine or separate objects, they build neural pathways between concrete actions and symbolic math, making addition and subtraction meaningful.

• ACARA Content Descriptions
• AC9M1A02

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

Activity 01

• Hundred Languages
• 25 min · Pairs

Counter Combinations: Addition Models

Give pairs 20 counters and scenario cards like '5 apples plus 3 more'. Students build two groups, join them, and count the total. They draw their model and explain the solution to the class.

Explain how building a model helps you solve a problem.

Facilitation Tip

During Counter Combinations, remind students that any object can represent an item, from counters to buttons, to focus attention on quantity rather than detail.

What to look for

Present students with a simple addition problem, such as 'There are 3 red balls and 2 blue balls. How many balls are there in total?'. Ask students to draw a picture or use counters to model the problem and write down their answer.

• Understand
• Apply
• Create
• Self-Awareness
• Self-Management
• Social Awareness

Activity 02

• Hundred Languages
• 30 min · Small Groups

Block Take-Away: Subtraction Scenes

In small groups, provide blocks and prompts like '8 cars, 3 drive away'. Students represent the start, remove blocks, and record the remainder with drawings. Groups share how the model shows the change.

Design a simple model to show the parts of this problem.

Facilitation Tip

During Block Take-Away, encourage students to narrate their actions aloud to reinforce the connection between physical removal and subtraction.

What to look for

Give each student a card with a subtraction scenario, e.g., 'You had 5 cookies and ate 2. How many are left?'. Ask them to draw a model showing the problem and write one sentence explaining how their drawing helped them find the answer.

• Understand
• Apply
• Create
• Self-Awareness
• Self-Management
• Social Awareness

Activity 03

• Hundred Languages
• 20 min · Individual

Finger Puppets for Sharing

Individuals use fingers or pipe cleaners as puppets for division problems like '6 lollies for 2 friends'. They group puppets equally and note leftovers. Class discusses models on a shared chart.

Compare how your model helps you see the problem differently.

Facilitation Tip

During Finger Puppets for Sharing, ask students to switch roles so they experience both giving and receiving, deepening their understanding of equal groups.

What to look for

After students have created models for a few problems, ask: 'How did using a model help you understand the problem better than just reading the words?' Encourage students to share specific examples from their work.

• Understand
• Apply
• Create
• Self-Awareness
• Self-Management
• Social Awareness

Activity 04

• Hundred Languages
• 35 min · Whole Class

Toy Sort and Model: Whole Class Challenge

Display toys; class suggests a problem like '10 toys minus 4 red ones'. Volunteers build a group model with toys, then students copy in notebooks. Vote on clearest models.

Explain how building a model helps you solve a problem.

Facilitation Tip

During Toy Sort and Model, circulate and ask guiding questions like 'How will you show the change when you take two away?' to prompt strategic thinking.

What to look for

Present students with a simple addition problem, such as 'There are 3 red balls and 2 blue balls. How many balls are there in total?'. Ask students to draw a picture or use counters to model the problem and write down their answer.

• Understand
• Apply
• Create
• Self-Awareness
• Self-Management
• Social Awareness

A few notes on teaching this unit

Teachers should model the process explicitly by thinking aloud as they build a model, emphasizing that the goal is clarity not perfection. Avoid correcting models too quickly; instead, ask students to explain their choices to uncover their reasoning. Research shows that when students justify their models, they develop stronger conceptual understanding and retention.

Successful students will confidently represent problems using simple materials, explain their models using math language, and connect their representations to the correct number sentences. They should also show flexibility by adjusting models when new information is introduced.

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Watch Out for These Misconceptions

• During Counter Combinations, watch for students who insist their counters must look exactly like the items in the problem.

  Prompt students to discuss why different shapes still represent the same quantity, using examples from their own models to show clarity over realism.

• During Block Take-Away, watch for students who believe the model is final and cannot be adjusted.

  Encourage students to rebuild the model with a peer, asking 'What if you had one less to start?' to show how models can change with new information.

• During Toy Sort and Model, watch for students who prefer physical models over drawings, undervaluing sketches.

  Set up a station where students compare a block model to a quick sketch, asking them to identify which better helps them solve the problem when away from the table.

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Methods used in this brief

• Hundred Languages