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.

• 3rd Grade
• Mathematics
• 4 activities
• 20 min–30 min

Learning Objectives

1. Design a visual representation, such as a diagram or table, to model the steps needed to solve a given word problem.
2. Evaluate the efficiency of different problem-solving strategies, like drawing a diagram versus making a table, for a specific multi-step problem.
3. Justify the selection of a particular problem-solving strategy by explaining how it best fits the structure of a word problem.
4. Solve multi-step word problems by applying a chosen strategy and accurately calculating the final answer.
5. Explain the reasoning process used to arrive at a solution, detailing the steps taken and the strategy employed.

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.

Prepare & details

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.

Setup: Standard classroom seating; students turn to a neighbor

Materials: Discussion prompt (projected or printed), Optional: recording sheet for pairs

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

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.

Prepare & details

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.

Setup: Groups at tables with access to source materials

Materials: Source material collection, Inquiry cycle worksheet, Question generation protocol, Findings presentation template

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

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.

Prepare & details

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.

Setup: Wall space or tables arranged around room perimeter

Materials: Large paper/poster boards, Markers, Sticky notes for feedback

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

Problem-Based Learning

⏱ 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.

Prepare & details

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

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 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.

What to Expect

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.

Watch Out for These Misconceptions

Common Misconception

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

What to Teach Instead

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.

Common Misconception

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

What to Teach Instead

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.

Common Misconception

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

What to Teach Instead

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.

Assessment Ideas

Quick Check

After Strategy Showcase, present a multi-step word problem. Ask students to choose one strategy and show their work on a whiteboard. Circulate and note which strategy they selected and whether they labeled their work appropriately.

Exit Ticket

After Collaborative Investigation, 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.

Discussion Prompt

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

Extensions & Scaffolding

• Challenge: Give students a problem that can be solved by all four strategies and ask them to solve it four different ways, comparing the efficiency of each.
• Scaffolding: Provide partially completed diagrams or tables with key labels and numbers already filled in.
• Deeper exploration: Introduce a fifth strategy, such as acting it out or using manipulatives, and have students invent a label and example for it.

Key Vocabulary

Problem-Solving Strategy	A specific method or plan used to find the solution to a mathematical problem. Examples include drawing a picture, making a table, or working backward.
Diagram	A drawing or sketch that helps visualize the information and relationships within a word problem. It can represent quantities, actions, or sequences.
Table	An organized chart used to record and display information, often showing relationships between different sets of data to reveal patterns or solutions.
Work Backward	A strategy where you start with the final answer or known end result and reverse the steps to find the initial condition or starting value.
Multi-step Word Problem	A word problem that requires more than one mathematical operation or more than one distinct step to find the solution.