Problem Solving. Guess, Iterate

When tackling a problem that we can’t immediately see how to solve, it is useful to play around with the given information to see if it gives us any suggestions. It can sometimes be helpful to not down the things we already know and which areas of mathematics they relate to.

Rice Example

Emma bought a bag of rice at the supermarket and is curious about how many grains it has inside. Can you help her?


Clearly there is no single answer of this question, but we can suggest strategies that she could use.
Here are some ideas:

  • Count every single grain
    • Doesn’t seem efficient unless the bag is very small.
  • Weight a single grain, weight the total amount of rice, then divide the first number from the second.
    • This would give an accurate answer, but a single grain of rice is very light and so typical scales may not accurately measure it (of course you could use 10 grains of rice, say and then divide your final answer by 10).
  • Use scales to identify how many grains of rice are in a gram, then multiply that number of grains by the weight (in grams) of the bag.
  • Measure the volume of a single grain of rice, measure the total volume of the bag, then divide the first number from the second
    • This relies on the fact that the rice will tesselate within the bag. Does this seem a reasonable assumption.

24 Questions of Increasing Difficulty

Solutions to Question Set

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