Mathematics · 3rd Grade · Foundations of Problem Solving · Weeks 19-27

Developing Problem-Solving Strategies

Exploring and applying various strategies such as drawing diagrams, making tables, and working backward.

About This Topic

Third graders benefit from an explicit toolkit of problem-solving strategies because they are encountering increasingly complex problems that no single approach can handle. The US curriculum at this level expects students to move beyond guess-and-check and apply organized strategies such as drawing a diagram, making a table, looking for a pattern, and working backward. Each strategy is a cognitive tool, and students who know several can select the most efficient one for a given situation.

Teaching these strategies explicitly, with the expectation that students practice each one and evaluate its usefulness, builds mathematical agency. Students who see only one way to solve a problem are more likely to freeze when that approach fails. Exposure to multiple strategies through collaborative tasks gives students a sense that problems are solvable, even when the path forward is not immediately obvious.

Active learning is essential for strategy development because strategies must be practiced, not just described. When students work through a problem in small groups, they naturally use different approaches and can observe and adopt each other strategies. The process of explaining your method to a partner is itself a metacognitive act that strengthens strategic thinking.

Key Questions

1. Evaluate the effectiveness of different problem-solving strategies for a given problem.
2. Design a step-by-step plan to solve a multi-step word problem.
3. Justify the choice of a particular strategy based on the problem's characteristics.

Learning Objectives

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

Before You Start

Addition and Subtraction within 1,000

Why: Students need a strong foundation in basic operations to perform calculations within multi-step problems.

Introduction to Multiplication and Division

Why: Familiarity with multiplication and division concepts is necessary as these operations may be required in more complex word problems.

Representing Data with Simple Graphs and Tables

Why: Prior experience with organizing information in tables or simple graphs supports the use of these strategies for problem-solving.

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.

Watch Out for These Misconceptions

Common Misconception

Students often treat drawing a diagram as a less valid strategy than writing an equation, seeing it as just drawing rather than mathematical work.

What to Teach Instead

Explicitly name diagrams as mathematical models and require students to label all quantities in their diagrams. During partner sharing, highlight how a well-labeled diagram often produces the equation automatically.

Common Misconception

Students may believe that working backward is only for trick problems rather than a general strategy that can be the most efficient first choice.

What to Teach Instead

Choose problems where working backward is clearly the most efficient path and let students discover this during collaborative strategy comparison. Naming and posting the strategy validates it as a legitimate first-choice option.

Common Misconception

Students sometimes apply the same strategy to every problem without evaluating its fit, defaulting to drawing a picture even when a table would be more efficient.

What to Teach Instead

Build the habit of strategy selection through tasks where different strategies are deliberately compared. The four strategies, one problem activity makes this comparison explicit and gives students a reason to evaluate fit.

Active Learning Ideas

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.

25 min·Pairs

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.

30 min·Small Groups

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.

20 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.

25 min·Pairs

Real-World Connections

• City planners use tables and diagrams to organize data about traffic flow and population growth when designing new roads or public transportation routes.
• Bakers often work backward from a desired cake size or number of servings to determine the exact amounts of ingredients needed, adjusting recipes as necessary.
• Retail inventory managers create tables to track stock levels, sales, and reorder points to ensure popular items are always available for customers.

Assessment Ideas

Quick Check

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.

Exit Ticket

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.'

Discussion Prompt

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?'

Frequently Asked Questions

Which problem-solving strategies should third graders know by the end of the year?

At minimum: draw a diagram, make a table, look for a pattern, guess and check with refinement, and work backward. CCSS does not specify a strategy list, but these five appear consistently across third-grade curriculum materials and are developmentally appropriate for the problem types students encounter.

How do I teach problem-solving strategies without making them feel like extra steps?

Connect each strategy to a problem type where it provides a genuine advantage. Students are more motivated to use a strategy when they discover it makes a problem easier, not when they use it because the teacher said to. Comparative tasks where students try two approaches and pick the better one make this concrete.

How does strategy instruction connect to CCSS Mathematical Practice Standards?

Strategy selection is at the heart of MP.1 (Make sense of problems and persevere in solving them) and MP.5 (Use appropriate tools strategically). Teaching students to choose and evaluate strategies explicitly addresses both practices in a way that straightforward computation tasks do not.

How does active learning support problem-solving strategy development?

Strategy development happens through use, not memorization. When students solve problems collaboratively and compare approaches, they see strategies in action and evaluate their effectiveness in real time. The peer discussion that follows a strategy showcase is more instructionally powerful than any textbook explanation of the strategies themselves.