Mathematics · Year 1 · Problem Solving and Reasoning · Term 4

Making a Model

Creating simple physical or drawn models to represent elements of a problem and find solutions.

• ACARA Content Descriptions
• AC9M1A02

About This Topic

Year 1 students build simple physical or drawn models to represent addition and subtraction problems, aligning with AC9M1A02. They use counters, blocks, fingers, or sketches to show combining groups or removing items in everyday scenarios, such as sharing snacks or packing bags. This practice helps them visualise quantities and operations, moving from concrete to symbolic understanding.

Models support problem solving and reasoning by letting students break down complex situations into parts. They explain how the model reveals solutions, design representations for given problems, and compare models to spot patterns or errors. These skills link to units on number sense and data, building flexibility in mathematical thinking.

Active learning benefits this topic because students manipulate materials to test ideas, adjust for accuracy, and share models in pairs. This hands-on process makes problem solving tangible, encourages peer feedback, and deepens retention through trial and reflection.

Key Questions

1. Explain how building a model helps you solve a problem.
2. Design a simple model to show the parts of this problem.
3. Compare how your model helps you see the problem differently.

Learning Objectives

• Design a physical or drawn model to represent a given addition or subtraction problem.
• Explain how their created model visually represents the parts of a mathematical problem.
• Compare their model to a peer's model, identifying similarities and differences in representation.
• Demonstrate how their model aids in finding the solution to a problem.

Before You Start

Counting and Cardinality

Why: Students need to be able to count objects accurately to build and interpret models of quantities.

Introduction to Addition and Subtraction

Why: Students should have a basic understanding of what addition and subtraction mean conceptually before they can model these operations.

Key Vocabulary

Model	A representation, such as a drawing or a set of objects, used to show how something works or to solve a problem.
Represent	To stand for or symbolize something else, like using blocks to stand for apples in a problem.
Combine	To join together, like putting two groups of objects into one larger group to find a total.
Separate	To take apart or remove, like taking some objects away from a group to find how many are left.

Watch Out for These Misconceptions

Common Misconception

Models must look exactly like the real objects.

What to Teach Instead

Students often think models need precise replicas, but simple shapes or tallies work for math. Pair discussions of varied models show how any clear representation reveals the solution. Hands-on building helps them focus on quantities over appearance.

Common Misconception

Once built, the model cannot change.

What to Teach Instead

Some believe models are fixed, missing the iterative process. Group trials with adjustable blocks demonstrate editing for better fits. Active sharing reveals how tweaks clarify problems, building flexible thinking.

Common Misconception

Drawings are less useful than objects.

What to Teach Instead

Children may undervalue sketches compared to physical items. Comparing both in stations proves drawings capture ideas portably. Collaborative critiques help students see strengths in each, boosting confidence.

Active Learning Ideas

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.

25 min·Pairs

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.

30 min·Small Groups

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.

20 min·Individual

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.

35 min·Whole Class

Real-World Connections

• Construction workers use scale models of buildings to visualize the final structure and plan the building process before laying the first brick.
• Children’s toy sets, like train tracks or dollhouses, are simple models that allow kids to create scenarios and solve problems related to arrangement and play.

Assessment Ideas

Quick Check

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.

Exit Ticket

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.

Discussion Prompt

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.

Frequently Asked Questions

What materials are best for Year 1 model making?

Use everyday items like counters, blocks, buttons, or sticks for physical models, and whiteboard markers for quick drawings. These are accessible, durable, and match AC9M1A02's emphasis on practical representations. Rotate materials weekly to keep engagement high and link to classroom routines.

How does model making support problem solving in Year 1?

Models let students externalise thinking, spotting part-whole relationships in addition or subtraction. They explain solutions via the model, compare methods, and refine ideas. This aligns with unit key questions, fostering reasoning that carries to higher years.

How can active learning enhance model making lessons?

Active approaches like pair building and station rotations let students manipulate, test, and discuss models in real time. Peers challenge inaccuracies, while teacher prompts guide reflections. This builds deeper understanding than worksheets, as hands-on adjustments make abstract math concrete and memorable.

How to assess student models effectively?

Observe explanations of how the model solves the problem, check for accurate part representation, and note comparisons to other methods. Use photos of models in portfolios with student voice recordings. Rubrics focusing on clarity and reasoning provide clear feedback tied to AC9M1A02.