Mathematics · 3rd Grade

Active learning ideas

Developing Problem-Solving Strategies

Third graders build confidence when they see strategies as tools they can choose, not rules they must follow. Active learning lets them test these tools in low-stakes situations, so they notice which ones fit different problems before facing high-stakes assessments.

• Common Core State Standards
• Common Core State Standards: CCSS.Math.Practice.MP1 - Make sense of problems and persevere in solving them.
• Common Core State Standards: CCSS.Math.Practice.MP4 - Model with mathematics.
• Common Core State Standards: CCSS.Math.Content.3.OA.D.8 - Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity.

• 20–30 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Think-Pair-Share
• 25 min · Pairs

Think-Pair-Share: Strategy Showcase

Pose a challenging multi-step problem. Students attempt it individually using any strategy they choose, then share their approach with a partner. Pairs present their strategies to the whole class, and the teacher facilitates a discussion about which strategies were most efficient and why.

Evaluate the effectiveness of different problem-solving strategies for a given problem.

Facilitation Tip

During Strategy Showcase, provide sentence stems for students who struggle to verbalize their thinking.

What to look for

Present students with a multi-step word problem. Ask them to choose one strategy (e.g., draw a diagram, make a table) and show their work on a whiteboard or scratch paper. Observe their process and the strategy they select.

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

Activity 02

• Inquiry Circle
• 30 min · Small Groups

Inquiry Circle: Four Strategies, One Problem

Give each group a single word problem and assign each group member a different strategy: draw a diagram, make a table, look for a pattern, or work backward. The group compares solutions and determines which strategy was most efficient for this problem type, then reports their finding to the class.

Design a step-by-step plan to solve a multi-step word problem.

Facilitation Tip

During Collaborative Investigation, assign each group a different strategy so all four are modeled in one lesson.

What to look for

Give students a word problem and two possible strategies. Ask them to write one sentence explaining which strategy they would use and why, based on the problem's details. For example: 'I would use a table because the problem involves comparing quantities over time.'

• Analyze
• Evaluate
• Create
• Self-Management
• Self-Awareness

Activity 03

• Gallery Walk
• 20 min · Pairs

Gallery Walk: Strategy Museum

Post solved problems around the room, each solved using a different strategy. Students rotate with sticky notes and label which strategy was used, then add a note about one strength and one limitation of that approach for the specific problem shown.

Justify the choice of a particular strategy based on the problem's characteristics.

Facilitation Tip

During the Gallery Walk, require each poster to include a problem, a labeled diagram or table, and a written sentence explaining why the strategy fit.

What to look for

Pose a problem that can be solved in multiple ways. Ask students to share their solutions and the strategies they used. Facilitate a discussion: 'Which strategy was easiest for you? Why? Could another strategy have worked? How was it different?'

• Understand
• Apply
• Analyze
• Create
• Relationship Skills
• Social Awareness

Activity 04

• Mystery Object
• 25 min · Pairs

Sorting Activity: Strategy Match

Provide problem cards and strategy name cards. Pairs match each problem with the strategy they think would work best, then explain their reasoning to another pair. After matching, pairs attempt the solution using their chosen strategy to verify the match.

Evaluate the effectiveness of different problem-solving strategies for a given problem.

What to look for

Present students with a multi-step word problem. Ask them to choose one strategy (e.g., draw a diagram, make a table) and show their work on a whiteboard or scratch paper. Observe their process and the strategy they select.

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

A few notes on teaching this unit

Teach strategies one at a time with clear labels and examples, but immediately bring them together so students see they are interchangeable tools. Avoid teaching strategies in isolation; always ask, 'Which tool fits best?' to build metacognition. Research shows that naming and posting the strategies helps students retrieve them in future lessons.

Students will name each strategy, explain when to use it, and show the strategy working on a problem. They will also compare strategies, stating which one fit best and why. Evidence of learning appears in their oral explanations, labeled diagrams, and written justifications during partner and group tasks.

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Watch Out for These Misconceptions

• During Strategy Showcase, watch for students who treat diagrams as simple drawings rather than mathematical models.

  Require students to label every quantity in their diagram and ask peers to read the labels aloud before sharing their solution, reinforcing that diagrams are purposeful mathematical work.

• During Collaborative Investigation, watch for students who believe working backward is only for special trick problems.

  After each group presents, ask, 'Could this problem have been solved by working backward? Why or why not?' Post a sign that names working backward as a first-choice strategy.

• During Gallery Walk, watch for students who apply the same strategy to every problem without evaluating its fit.

  Have students use a checklist on their gallery walk notes to record which strategy they think fits best for each problem and explain their reasoning in one sentence.

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Methods used in this brief

• Think-Pair-Share
• Inquiry Circle
• Gallery Walk
• Mystery Object