Thinking Thursday: Perimeter Puzzle 1

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 61: Perimeter Puzzle 1

A rectangle has a perimeter of _____ grid units. [Choose any number.] What might the area be? How many different rectangles can you find with that perimeter? What if the sides don’t have to be whole unit lengths?

 

Extra challenge: Perimeter values less than 4 units force the use of at least one fraction or decimal side length.