Puzzles and Riddles

Learning Goals:

  • Solve problems requiring the estimation and calculation of areas of rectangles
  • Multiply and divide whole numbers using a variety of tools and strategies
  • Determine the missing numbers in equations

The Challenge:

The goal of an area maze puzzle is to use what you know about the area of rectangles, multiplication, and division, to find unknown areas or dimensions (labelled with a question mark.) How could you use what you know in the puzzles below to find the mystery area of the blue rectangle?

REMINDER: The area of a rectangle can be found by multiplying the length x the width.

(These puzzles are not drawn to scale, so measuring side lengths with a ruler won’t help you solve them!)

Three rectangles connected to form a rotated capital L shape. The largest, yellow rectangle has a labelled area of 40 square cm and a labelled length of 8 cm (connected to the side of the blue rectangle by an unknown width.) The smallest green rectangle has a labelled area of 8 square cm and a labelled width of 2 cm (connected to the bottom of the blue rectangle by an unknown length.) The blue rectangle is connected to the right side of the yellow rectangle and the top of the green rectangle. None of its side lengths are labelled, and its area is labelled with a question mark.

Four rectangles connected to form a larger rectangle. A green rectangle in the upper left corner has a labelled area of 20 square cm and shares its right side with the red rectangle and its bottom side with the yellow square (all side lengths unlabelled.) To its right is a red rectangle in the upper right corner with a labelled area of 30 square cm. It shares its left side with the green rectangle, and its bottom side with the blue rectangle (all side lengths unlabelled.) The yellow square in the bottom left corner has a labelled area of 16 square cm and shares its top side with the green rectangle and its right side with the blue rectangle. Its left hand side is labelled 4 cm long. The blue rectangle in the bottom right corner has an unknown area labelled by a question mark and shares its left side with the yellow square and its top side with the red rectangle (all side lengths unlabelled.)

A square and a rectangle connected to form a capital L shape. The blue square sits on top of the left side of the red rectangle, and has an unknown area, labelled with a question mark. Its top side is labelled with a length of 4 cm. The largest, red rectangle is on the bottom and has a labelled area of 28 square cm. The combined left hand side length of both shapes is labelled as 8 cm long, and the portion of the red rectangle's top side that sticks out past the blue rectangle is labelled as 3 cm long.

Questions and Prompts to Support your Child:

  • What have you tried so far? What could we try together?
  • What missing dimensions do we need to calculate the area of the blue rectangle?
  • If you feel stuck, it might help to start by looking for known dimensions – if we know that this 8 cm2 rectangle has a width of 2 cm, what would the width need to be? How does this newfound dimension help us get closer to finding our mystery area?

Extensions & Adaptations:

  • If calculations are feeling too tricky, grab a calculator!
  • This might be our first time experiencing a known area as a means to figure out a missing dimension – remember that division is a way to “undo” multiplication!
  • Try creating your own area puzzles by sketching some connected rectangles, labelling all of the lengths and widths, calculating the areas, then erasing all but a few so someone can solve it. How much information do you need to leave so it’s still possible to solve? How much information is too much and would make it too easy?
  • Check out areamaze.com for many more puzzles – including some more challenging options!

Adapted from Areamaze.com