Using Visuals to Solve Problems

Active learning works for this topic because young students need to move from abstract words to concrete images to truly grasp addition and subtraction. When children use their hands and eyes to model problems, they build lasting number sense and reasoning skills that go beyond memorising facts.

• Year 1
• Mathematics
• 4 activities
• 20 min–40 min

Learning Objectives

1. Design a visual representation (drawing, diagram, or manipulative model) for a given addition or subtraction word problem.
2. Explain how a chosen visual representation accurately models the action or relationship described in a word problem.
3. Compare the effectiveness of two different visual representations for solving the same word problem, justifying the choice.
4. Identify the key information and the unknown quantity in a word problem to guide the creation of a visual model.

Problem-Based Learning

⏱ 25 min·Pairs

Pair Sketch Challenge: Animal Adventure

Read a word problem about animals joining or leaving a group. Pairs draw pictures to show starting amounts, changes, and results. They count and label their drawings, then swap with another pair to check the solution.

Prepare & details

Explain how drawing a picture can help solve a math problem.

Facilitation Tip: During Pair Sketch Challenge, remind pairs to take turns listening and drawing so both students contribute equally to the visual solution.

Setup: Groups at tables with access to research materials

Materials: Problem scenario document, KWL chart or inquiry framework, Resource library, Solution presentation template

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management
• Relationship Skills

Problem-Based Learning

⏱ 40 min·Small Groups

Manipulative Stations: Number Stories

Prepare three stations with word problems and tools like counters or ten frames. Small groups model one problem per station, solve it, and sketch their visual. Rotate after 10 minutes and compare solutions.

Prepare & details

Design a visual representation for a given word problem.

Facilitation Tip: At Manipulative Stations, model how to record each step on a small whiteboard before moving to the next station to build metacognitive habits.

Setup: Groups at tables with access to research materials

Materials: Problem scenario document, KWL chart or inquiry framework, Resource library, Solution presentation template

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management
• Relationship Skills

Problem-Based Learning

⏱ 35 min·Whole Class

Visual Strategy Share: Whole Class Gallery

Students solve individual problems using chosen visuals, then display work around the room. The class tours the gallery, votes on clearest representations, and discusses why certain visuals succeed.

Prepare & details

Compare the effectiveness of different visual aids in problem-solving.

Facilitation Tip: During Visual Strategy Share, circulate with a clipboard to jot down which students used ten frames versus drawings so you can group them thoughtfully for the gallery.

Setup: Groups at tables with access to research materials

Materials: Problem scenario document, KWL chart or inquiry framework, Resource library, Solution presentation template

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management
• Relationship Skills

Problem-Based Learning

⏱ 20 min·Individual

Ten Frame Build: Individual Warm-Up

Give problems with numbers to 20. Students use ten frames to represent and solve alone, then pair share to verify accuracy and suggest improvements.

Prepare & details

Explain how drawing a picture can help solve a math problem.

Facilitation Tip: In Ten Frame Build, pause after each build to ask, 'How does this frame show the story?' to reinforce the link between pictures and numbers.

Setup: Groups at tables with access to research materials

Materials: Problem scenario document, KWL chart or inquiry framework, Resource library, Solution presentation template

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management
• Relationship Skills

Teaching This Topic

Teach by modelling your own thinking aloud as you turn a word problem into a drawing or ten frame. Use think-alouds to show how you decide what to draw first, how to group dots, or when to cross out a counter. Keep visuals deliberately simple—circles, dots, or tallies—so students focus on quantity, not art. Avoid correcting every small error; instead, ask guiding questions like, 'What part of the story does this dot show?' to prompt self-correction.

What to Expect

Students confidently choose and use simple drawings, counters, or diagrams to represent word problems and explain their thinking in clear, step-by-step sentences. They compare visuals with peers and adjust their models when needed, showing flexible problem-solving.

Watch Out for These Misconceptions

Common Misconception

During Pair Sketch Challenge, watch for students spending too much time on detailed drawings instead of focusing on quantities and actions.

What to Teach Instead

Set a 30-second timer for the drawing phase and remind students that simple shapes or dots are enough to represent the problem; spend the rest of the time discussing what each mark means.

Common Misconception

During Manipulative Stations, watch for students using the same tool (e.g., counters) for every problem regardless of whether it fits the situation.

What to Teach Instead

Circulate and ask, 'Which tool helps you see the groups best? Why did you pick this one?' to guide students to match tools to problem types like subitising or partitioning.

Common Misconception

During Visual Strategy Share, watch for students assuming their visual is the only correct way to represent a problem.

What to Teach Instead

During the gallery walk, model comparing two different visuals side by side and ask, 'How do both pictures show the same answer? What’s different about them?' to normalise varied but accurate representations.

Assessment Ideas

Quick Check

After Pair Sketch Challenge, collect one drawing per pair and a sentence explaining it. Look for clear representations of quantities and correct operations to identify students ready to move on.

Exit Ticket

After Manipulative Stations, give each student an exit ticket with a subtraction problem and ask them to draw a ten frame or counters to show the problem, then write the answer and one sentence about their strategy.

Discussion Prompt

During Visual Strategy Share, show two different visuals for the same problem (e.g., a drawing of apples and a number line). Ask students to discuss in pairs which visual helps them understand the problem better and why, then share with the class to reveal varied reasoning strategies.

Extensions & Scaffolding

• Challenge: Provide a two-step problem (e.g., 'There were 10 birds. 3 flew away, then 2 more joined. How many now?') and ask students to show it with two different visuals (drawing and ten frame) in one minute.
• Scaffolding: For students struggling with directionality, offer a sentence stem: 'First, I see ___. Then, ___ happens.' to structure their drawings.
• Deeper exploration: Introduce a 'missing part' story (e.g., 'There are 8 fish in the tank. Some are blue, 5 are yellow. How many are blue?') and ask students to create a diagram that shows the unknown part clearly.

Key Vocabulary

Word Problem	A math problem described using words, often telling a short story that requires calculation to solve.
Visual Representation	A picture, drawing, diagram, or physical model used to show the information and action in a math problem.
Manipulatives	Objects that students can touch and move to represent numbers and solve problems, like counters or blocks.
Model	A representation, such as a drawing or a set of objects, that shows how a math problem works.
Part-Part-Whole Diagram	A visual tool with three boxes, showing how two smaller parts combine to make a larger whole, or how a whole can be separated into parts.