Making a ModelActivities & Teaching Strategies
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.
Learning Objectives
- 1Design a physical or drawn model to represent a given addition or subtraction problem.
- 2Explain how their created model visually represents the parts of a mathematical problem.
- 3Compare their model to a peer's model, identifying similarities and differences in representation.
- 4Demonstrate how their model aids in finding the solution to a problem.
Want a complete lesson plan with these objectives? Generate a Mission →
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.
Prepare & details
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.
Setup: Flexible workspace with access to materials and technology
Materials: Project brief with driving question, Planning template and timeline, Rubric with milestones, Presentation materials
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.
Prepare & details
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.
Setup: Flexible workspace with access to materials and technology
Materials: Project brief with driving question, Planning template and timeline, Rubric with milestones, Presentation materials
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.
Prepare & details
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.
Setup: Flexible workspace with access to materials and technology
Materials: Project brief with driving question, Planning template and timeline, Rubric with milestones, Presentation materials
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.
Prepare & details
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.
Setup: Flexible workspace with access to materials and technology
Materials: Project brief with driving question, Planning template and timeline, Rubric with milestones, Presentation materials
Teaching This Topic
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.
What to Expect
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.
These activities are a starting point. A full mission is the experience.
- Complete facilitation script with teacher dialogue
- Printable student materials, ready for class
- Differentiation strategies for every learner
Watch Out for These Misconceptions
Common MisconceptionDuring Counter Combinations, watch for students who insist their counters must look exactly like the items in the problem.
What to Teach Instead
Prompt students to discuss why different shapes still represent the same quantity, using examples from their own models to show clarity over realism.
Common MisconceptionDuring Block Take-Away, watch for students who believe the model is final and cannot be adjusted.
What to Teach Instead
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.
Common MisconceptionDuring Toy Sort and Model, watch for students who prefer physical models over drawings, undervaluing sketches.
What to Teach Instead
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.
Assessment Ideas
After Counter Combinations, present students with an addition problem and ask them to use counters to model it. Observe whether they combine groups correctly and record their answers to check for accuracy.
After Block Take-Away, give students a subtraction scenario card and ask them to draw a model and write one sentence explaining how the drawing helped them find the answer. Collect these to assess their ability to represent and explain operations.
During Toy Sort and Model, facilitate a whole-class discussion asking, 'How did building the model help you understand the problem better than just reading the words?' Encourage students to reference their specific models during responses to demonstrate connection-making.
Extensions & Scaffolding
- Challenge: Ask students to create a model for a two-step problem, such as 'You have 4 pencils and get 3 more, then give 2 away.' Have them explain their process in pairs.
- Scaffolding: Provide sentence starters for students to use when explaining their models, such as 'I have _____ and then I _____.'
- Deeper: Introduce a story context with larger numbers to explore efficiency, asking students to compare their models to number sentences.
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. |
Suggested Methodologies
Planning templates for Mathematics
5E Model
The 5E Model structures lessons through five phases (Engage, Explore, Explain, Elaborate, and Evaluate), guiding students from curiosity to deep understanding through inquiry-based learning.
Unit PlannerMath Unit
Plan a multi-week math unit with conceptual coherence: from building number sense and procedural fluency to applying skills in context and developing mathematical reasoning across a connected sequence of lessons.
RubricMath Rubric
Build a math rubric that assesses problem-solving, mathematical reasoning, and communication alongside procedural accuracy, giving students feedback on how they think, not just whether they got the right answer.
More in Problem Solving and Reasoning
Using Visuals to Solve Problems
Drawing pictures, diagrams, or using manipulatives to represent and solve word problems.
2 methodologies
Acting Out Problems
Using physical actions or role-play to understand and solve simple word problems.
2 methodologies
Identifying Key Information
Learning to identify and extract important numbers and words needed to solve a problem, and disregard irrelevant information.
2 methodologies