“Ivan Moscovich’s Grasshopper” is an excerpt from Task Cards Book #5, available as a digital printable activity guide at my bookstore. Read more about my playful math books here.
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: See. Wonder. Create.
See: 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 an Experiment Prompt
Many people know it’s important for students to do hands-on experiments in science. But did you know the same is true for mathematics? People learn math by playing with ideas.
A math journal can be like a science lab book. Not the pre-digested, fill-in-the-blank lab books that some curricula provide. But the real lab books scientists write to keep track of their data, and what they’ve tried so far, and what went wrong, and what finally worked. Children may draw pictures of their investigations, write explanations, or play with equations.
When students find a solution to their prompt question, that’s when the fun begins. The point of a math experiment is to change something in the problem and explore how that changes the answer. For older students, the bonus challenge of a math puzzle is to generalize the solution: Can they discover a method that works for any starting conditions?
Besides these prompts, let students pose research topics of their own. What do they wonder? What questions can they ask? Can they expand one of the previous activity prompts into a more general investigation?
Any math topic or prompt offers an overwhelming variety of paths for exploration. Pick your rabbit hole, dive in, and discover the crazy Wonderland of mathematics.
Be patient with math experiments. Allow plenty of time for students to be scientists, doing their own research. Work for a while and then let the investigation rest. Come back to it later to see if they can discover anything new.
Journaling Prompt #252
Ivan Moscovich’s Grasshopper
The grasshopper starts at point 0 on a number line. It makes jumps of 1, 2, 3, …, each jump one unit longer than the previous. Is it possible for the hopper to land on a specific number N after exactly N jumps?
N = 1 works, of course. Can you find any others?
Denise Gaskins' Let's Play Math 