Math in Our World: Puzzle Path

Uncolored tiles with patterns drawn on them ready to be painted.
Colored tiles are arranged in a 2 by 4 array. The colors make shapes that cover parts of each tile. A dark line around the edge of some shapes snakes across the tiles. The shapes include squares, triangles, quadrilaterals, and hexagons.

You can make all kinds of designs with squares. This puzzle is made of square tiles. Each tile is divided into fractional parts. The goal is to create a line from one side of the board to another, kind of like a snake! It can be tricky to do sometimes. You may need to try a few different ways before you get a path that works.

  1. What do you notice? What do you wonder?
  2. Use pictures, models, or numbers to describe this puzzle.
  3. What mathematical questions can you ask about this situation? Answer all the questions you can!

Choose a color. Find all of the tiles with that color. Identify the fraction of each tile that is your chosen color.

  • Show your work to someone else, and explain your thinking. Did they understand?
  • Ask if they have any other questions you can answer!

Make your own connected squares design. Cut out squares from paper. Fold each square in half twice to make fourths. Draw lines to divide each square into fractional parts. Make sure each line begins and ends where a fold mark meets the edge.

Color the parts on your squares, then make an array with the squares. Using a dark pen or marker, connect some of the lines on your squares to make a path across all of the tiles. Try rearranging your squares to make a new path.