Puzzles and Riddles

Learning Goals:

  • Develop an understanding of equality between expressions
  • Develop and apply reasoning skills to make and test math predictions
  • Communicate mathematical thinking orally and visually

The Challenge:

A set of ten cards, each showing one of the digits from 0 to 9, is divided up between five envelopes so that there are two cards in each envelope.

A series of numbers from 0 to 9.

The sum of the two numbers inside it is written on each envelope: 7, 8, 13, 14, and 3.

A graphic of envelopes with the following numbers written on them: 7, 8, 13, 14, and 3.

Can you figure out which combination of cards should be in each envelope, so that they will each add to these sums?

Questions and Prompts to Support your Child:

  • Which envelope did you start with? Why did you choose that total first?
  • Which envelopes do you think have the most possible combinations of cards? Which do you think have the least?
  • (Once a solution has been found) – Do you think there are any other possible solutions? Why or why not?

Extensions & Adaptations:

  • If you’re feeling stuck, get a head start by noticing that the “14” envelope could contain the 8 & 6 cards OR the 9 & 5 cards – pick one combination and go from there!
  • Once you have found one possible combination of cards in envelopes, take some time to try to find the other one

Source: NRICH Math