Thinking Thursday: Painting Blocks

Writing to Learn Math: At its heart, geometry is all about seeing connections and relationships.

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 Geometry Prompt

At its heart, geometry is all about seeing connections and relationships. How can students break shapes apart, put them together, move them around the page, turn them, or distort them? Which properties change, and which stay the same?

Every activity has the potential to spawn hundreds of variations. Alter something in the prompt to make a fresh investigation. Tweak the size, shape, or other properties of interest. What new things can your children see in the math? What questions can they ask?

For older students, use algebra to put some teeth in the relationships they see. Give the points names. Identify the line segments. Can your students write any equations about them? Which distances are equal to other distances, or areas equal to other areas? How can they know for sure? When they add new points, lines, or circles to the diagram, what new connections do they find?

Journaling Prompt 269: Painting Blocks 3

You have a cubic block of wood that is painted all over. Then you cut it into smaller cubes.

How many cubes will you make?

How many sides of each smaller cube will have paint? Will you have any cubes with no paint at all?

If you put all the cubes into a bag and pulled out one at random, what is the probability it would have paint on three sides? What other questions can you ask?