Puzzles and Riddles

Learning Goals:

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

The Challenge:

The goal of a yohaku puzzle is to find four numbers that will fit in the boxes, so that each row and column multiplies to the corresponding products at the right and bottom.

A two-by-two yohaku puzzle where numbers need to multiply to the products 60 and 32 (at the bottom), as well as 48 and 40 (down the right side.)

A two-by-two yohaku puzzle where numbers need to multiply to the products 72 and 60 (at the bottom), as well as 120 and 36 (down the right side.)

A two-by-two yohaku puzzle where numbers need to multiply to the products 144 and 80 (at the bottom), as well as 120 and 96 (down the right side.)

Questions and Prompts to Support your Child:

  • What have you tried so far? What could we try together?
  • If that combination of numbers didn’t work out, what could you try instead?
  • If you feel stuck, try thinking about a blank as a number that could multiply to BOTH the product to the right of it and the product below it? (For example, what number could be a factor to multiply to 48, but ALSO be a factor that multiplies to 60?)

Extensions & Adaptations:

  • Do any of these puzzles have more than one possible solution? How can you prove it?
  • Try creating your own yohaku puzzle by starting with four numbers in the boxes, multiplying to get the products to the right and below, then erasing the original numbers
  • For an extra challenge, check back next week for some three by three yohaku puzzles!

Source: Yohaku.ca