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Today, I had the pleasure of sitting in a fourth-grade classroom, observing students tackle a series of math problems: 12 ÷ 3, 60 ÷ 3, and 72 ÷ 3. Each time, students shared how they solved the problems in their heads, and I noticed that they used a variety of strategies. For the final problem, 72 ÷ 3, I saw students drawing pictures, using the standard algorithm, counting on their fingers, and even trying out different versions of repeated addition. One student, however, already had the answer written down with no visible work on the page. Curious, the teacher asked how he had come up with the answer so quickly. He confidently explained that he realized 12 + 60 equals 72, so he simply added the results from the previous problems—72 ÷ 3 = 24. As I watched, I saw several lightbulbs go off in the minds of students around him.

This kind of thinking is what we call flexible and efficient mathematical thinking. Flexible thinking allows students to see multiple ways to find a solution, while efficient thinking enables them to choose the quickest method for them. Research shows that students who can decompose and recompose numbers in various ways tend to do better in math.

One of the best ways we foster this flexibility at school is through “number talks.” These are short discussions aimed at helping children explore the many different ways numbers can be manipulated. While we spend a lot of time working on this at school, you can also encourage this flexibility and dialogue at home.

Here are some simple questions you can ask your child while they’re working on math homework:

• How did you think about this problem?
• What was your first step?
• Why did you choose that method?
• Can you think of a different way to solve it?
• What could you change about the problem to make it easier or simpler?

Notice that all of these questions focus on how the problem was solved, not just the final answer. While getting the right answer is important, it’s the process that really encourages flexible thinking.

If deep math conversations during homework don’t sound realistic in your house (trust me, it’s not always easy in mine), try sneaking in math talk during games. Here are some fun ways to make math a part of everyday life:

• Race to 20: Start at zero, and each player adds 1, 2, or 0 to the total on their turn. The first player to reach 20 wins. Discuss the strategy the winner used. This is a perfect car ride game!
• Decomposing Numbers: Give younger children a set number of objects (beans, blocks, paperclips—anything works!) and ask them to see how many ways they can arrange them in three bowls. Then, have them explain their thinking.
• Recipe Adjustments: For older kids, have them adjust a recipe by halving or doubling it. As they work through the fractions, ask them to talk about how they are changing the numbers.

Math is learned through solving problems and talking about how we solve them—more so than through reading or listening alone. If we want to prepare our children for a future that we can’t even imagine yet, we need to foster flexible thinking, persistence, and problem-solving skills. By encouraging these skills at both school and home, we’re setting our children up for success in a world that will demand adaptability and creativity.