Puzzles and Riddles

Learning Goals:

  • Multiply and divide using a variety of mental strategies
  • Determine the missing numbers in equations
  • Develop and apply reasoning skills to make and test math predictions

The Puzzle:

The goal of a Stay the Same Puzzle is to figure out the starting number for each puzzle that, after going through all four steps, will end up staying the same. In the example below, the solution is 3, because 3+5=8, then 8รท2=4, then 4-3=1, and finally 1×3=3.

A solved example of a "Stay the Same Puzzle" consisting of a large square outline containing a starting point in the top left corner, and four arrows labelled with math operations, leading back to the starting point. The first arrow is labelled +5, the second arrow is labelled /2, the third arrow is labelled -3, and the fourth arrow is labelled x3. In between each arrow, an equation has been included to explain how to solve these puzzles: After the first arrow is 3+5=8, then after the second arrow is 8/2=4, then after the third arrow is 4-3=1, then after the fourth arrow is 1x3=3.

Try these other Stay the Same Puzzles:

Remember that if you end up with a final number different than the one you started with, choose a different starting number and try again!

A "Stay the Same Puzzle" consisting of a large square outline containing a starting point in the top left corner, and four arrows labelled with math operations, leading back to the starting point. The first arrow is labelled +15, the second arrow is labelled /4, the third arrow is labelled -4, and the fourth arrow is labelled x5.

A "Stay the Same Puzzle" consisting of a large square outline containing a starting point in the top left corner, and four arrows labelled with math operations, leading back to the starting point. The first arrow is labelled x2, the second arrow is labelled +2 the third arrow is labelled /10, and the fourth arrow is labelled +3.

Questions and Prompts to Support your Child:

  • What strategies did you use to choose and adjust your starting numbers?
  • What have you tried so far? What could we try together?
  • What mental math strategies are you using to walk through these calculations?

Extensions & Adaptations:

  • If struggling with calculations, grab a calculator to double check each step
  • More Stay the Same Puzzles are available here!
  • Try to create your own Stay the Same Puzzles by taking a starting number through three steps, and figuring out what the fourth step will need to be to get back to the starting number. Once you have your steps figured out, erase your starting number and challenge someone to try figuring it out!

Source: Don Steward Blog