Losing Your Marbles

The names of the marbles in this exercise might be different from the names used at your school. The investigation asks students to look at the names used for marbles in your school.
Students could begin the activity by using the information in speech bubbles to work out marble exchange rates. Some students may need to organise this information into a table. However, when you are sure that they have understood the exchange rate information, you could encourage them to use algebraic notation to prepare them for later work in algebra. For example, “b” could represent boulders, “q” could represent queenies, and so on.
The exchange rates are:
2b = 1q
2g = 6c
2q = 10m (This can be simplified to 1q = 5m.)
3b = 15c (This can be simplified to 1b = 5c.)
Students have the exchange rate for cat’s-eyes and boulders (15 cat’s-eyes equal three boulders), so question 1 is quite straightforward: 1b = 5c so 2b = 10c. (Both sides of the exchange rate have been multiplied by two, so the rate remains the same.)
Students don’t have the exchange information for the swaps in the remaining questions, so they have to go through several steps to calculate the swaps. For example, for question 2:
4b = m. They know that 2b = 1q and 2q = 10m, so by doubling both sides of the first exchange rate, they have 4b = 2q = 10m.
See also Answers and Teachers’ Notes: Algebra, Figure It Out, Levels 2–3, page 27.

Answers to Activity

1. 10 cat’s-eyes
2. 10 milkies
3. 3 queenies (10 galaxies = 30 cat’s-eyes = 6 boulders = 3 queenies)
4. a. 4 boulders (1 kingie = 2 queenies = 4 boulders)
b. 20 cat’s eyes (1 kingie = 2 queenies = 4 boulders = 20 cat’s eyes)
c. 10 milkies (1 kingie = 2 queenies = 10 milkies)
Investigation
Answers will vary.