Strengthening Problem-Solving and Critical Thinking in Math

Math is about so much more than just getting the right answer. At its core, math is a thinking subject—one that challenges students to make sense of problems, reason through strategies, and apply what they know to new situations. Developing critical thinking in math begins early, and in elementary classrooms, building these habits sets the stage for long-term success.

Developing strong problem-solvers means giving students space to explore, ask questions, and make decisions. It also means giving them the tools and opportunities to think critically about math—not just what to do, but why it works. Whether during the school year or through a summer math program, incorporating rich thinking tasks into daily instruction helps grow confidence and curiosity alongside skill.

Encouraging Critical Thinking and Problem-Solving as Part of Summer Enrichment

Summer is a valuable time to deepen mathematical thinking, especially through enrichment programs that focus on problem-solving, reasoning, and discovery. Unlike traditional review models that emphasize drill and repetition, summer enrichment can prioritize deeper understanding by engaging students in puzzles, games, and open-ended investigations.

These kinds of experiences challenge students to apply math flexibly and creatively. They promote persistence and strategic thinking—skills that transfer to all areas of learning. Importantly, when students experience success through solving meaningful problems, their confidence grows, and their mindset towards math becomes more positive.

Incorporating critical thinking into a summer math program doesn’t require advanced materials or a complete curriculum shift. It simply takes a focus on meaningful tasks that spark discussion, invite multiple approaches, and allow students to make decisions about their strategies. This focus transforms math from something students do to get it over with into something they do to figure things out.

Using ORIGO Education’s Think Tanks and Other Strategies for Deeper Math Understanding

To help students engage in meaningful problem-solving, ORIGO Education’s Think Tanks offer a ready-made resource designed to stretch student thinking. These tasks include rich, open-ended problems that align with core concepts and are carefully crafted to promote discussion, collaboration, strategic reasoning, and critical thinking in math. Click HERE to download sample cards!

Each Think Tank problem can be used in small groups or whole-class discussions and is structured to support productive struggle. Instead of focusing on speed or rote recall, students work together to explore, reason, and explain. With built-in scaffolding, Think Tanks help students of all ability levels participate meaningfully—making math more inclusive and exciting.

Other Strategies for Promoting Critical Thinking in Math

In addition to ORIGO’s Think Tanks, there are many other ways to foster deeper math thinking in the elementary classroom:

• Number Talks: Use short, focused discussions to explore different strategies for solving mental math problems. Ask students to explain their reasoning and compare approaches.
• Math Journals: Have students write about how they solved a problem or reflect on what strategies they used and why. This helps build metacognition and math vocabulary. ORIGOmath contains Student Journals and Teacher Sourcebooks to help teachers develop students’ mathematical understanding and computation skills. 
• Open-Ended Tasks: Present problems with more than one possible solution or method. For example, “Find three ways to make 100 using addition and subtraction.”
• Math Mysteries: Pose a real-world scenario with a missing piece (like a mystery number) and ask students to solve using clues and logic.
• Puzzle Challenges: Incorporate logic puzzles or pattern games that stretch reasoning skills and encourage persistence.
• Estimation Activities: Use Estimation Jars or “Which is Closer?” number line questions to build number sense and estimation reasoning.
• Collaborative Problem Solving: Pair students to solve challenging tasks, then present their solutions to the class. Emphasize process and explanation over correctness.
• Math Debates: Present a statement like “The largest product you can make with two numbers that add to 20 is 10 × 10,” and have students argue for or against with reasoning.

These strategies, when used regularly, create a culture where math is about thinking, communicating, and exploring—not just memorizing.

Activities That Build Confidence in Applying Math Concepts

Hands-on and engaging math activities build student confidence by showing them that math is not only useful—it’s fun! When students can apply what they know in meaningful ways, they develop a sense of ownership over their learning. Here are ten practical and effective activities you can use to help students build that confidence:

1. Math Scavenger Hunt
   Create a list of math-related items for students to find around the classroom or at home (e.g., something with symmetry, a number pattern, a 3D shape). Let students explain the math behind each item.
2. Shopping with Math
   Set up a pretend store and give students a budget. Let them “shop” using addition, subtraction, multiplication, or division. This builds real-world relevance and fluency.
3. Math Story Problems
   Have students write and solve their own story problems. They can illustrate them and swap with a partner to solve each other’s problems.
4. Roll-a-Problem
   Use dice to generate numbers for custom math problems. For example, roll two dice to create an addition problem or roll three to build a number sentence with parentheses.
5. Fraction Art
   Use paper folding, pattern blocks, or coloring grids to explore fractions in a visual, creative way. Have students explain the math in their artwork.
6. Board Games with a Twist
   Add a math question card element to familiar games (like Connect Four or Jenga). Before making a move, students must solve a math problem.
7. Measurement Olympics
   Set up stations for estimating and measuring (e.g., jump distance, beanbag toss, water volume). Students collect and compare data using charts or graphs.
8. Build It Challenge
   Give students a limited number of blocks or objects and ask them to build a structure that meets specific math criteria (e.g., perimeter, area, shape count).
9. Guess My Number
   One student chooses a number and gives clues based on place value, multiples, or comparison. Others try to guess using logic and reasoning.
10. Math Escape Room
    Create a series of puzzles or math challenges that lead to a final code. Use clues based on operations, patterns, or geometry to keep students engaged and thinking critically.

These activities combine math with fun, creativity, and real-world application—making math feel more like discovery and less like a worksheet.

Making Thinking Visible, All Year Long

When students have regular opportunities to solve problems, explain their reasoning, and explore concepts in meaningful ways, their confidence and competence grow together. Tools like ORIGO’s Think Tanks and strategy-rich activities promote the kind of thinking that sticks. Whether you’re working through a summer math program or planning enrichment throughout the year, emphasizing problem-solving and critical thinking pays off.

By helping students see themselves as capable thinkers and problem-solvers, we give them more than just math skills—we give them the tools to be curious, confident learners for life.

Looking for more ways to enrich your math instruction? Explore ORIGO Education’s resources designed to promote deep understanding and critical thinking at every level.