Thinking Thursday: Strange Customers

Writing to Learn Math: Problem-solving cares less about whether an answer is right and more about whether a solution makes sense.

Do you want your children to develop the ability to reason creatively and figure out things on their own?

Help kids practice slowing down and taking the time to fully comprehend a math topic or problem-solving situation with these classic tools of learning: Notice. Wonder. Create.

Notice: Look carefully at the details of the numbers, shapes, or patterns you see. What are their attributes? How do they relate to each other? Also notice the details of your own mathematical thinking. How do you respond to a tough problem? Which responses are most helpful? Where did you get confused, or what makes you feel discouraged?

Wonder: Ask the journalist’s questions: who, what, where, when, why, and how? Who might need to know about this topic? Where might we see it in the real world? When would things happen this way? What other way might they happen? Why? What if we changed the situation? How might we change it? What would happen then? How might we figure it out?

Create: Create a description, summary, or explanation of what you learned. Make your own related math puzzle, problem, art, poetry, story, game, etc. Or create something totally unrelated, whatever idea may have sparked in your mind.

Math journaling may seem to focus on this third tool, creation. But even with artistic design prompts, we need the first two tools because they lay a solid groundwork to support the child’s imagination.

How To Use a Problem-Solving Prompt

When children face a tough math problem, their attitude can make all the difference — not so much their “I hate homework!” attitude, but their mathematical worldview. Does your child see math as answer-getting or as problem-solving?

Answer-getting asks “What is the answer?”, decides whether it is right, then forgets it and goes on to the next question. Problem-solving cares less about whether an answer is right and more about whether a solution makes sense.

Students who care about problem-solving want to explore the web of interrelated ideas they discovered along the way: How can they recognize this type of problem? Can this one help them figure out others?

What could they do if they had never seen a problem like this one before? How would they reason it out?

Why does the formula work? Where did it come from, and how is it related to basic principles?

What is the easiest or most efficient way to manipulate the numbers? Does this help the problem-solver see more of the patterns and connections within our number system?

Is there another way to approach the problem? How many ways can they think of? Which do they like best, and why?

Journaling Prompt 143: Strange Customers

Mr. Tam sold apples at the Farmer’s Market. One morning, each customer bought half of Mr. Tam’s apples plus one more, until the seventh customer bought the last two apples. How many apples did Mr. Tam have at the start of the day?