Number nibbles

Students can use counters to experiment to find the correct solutions. Getting students to work in cooperative groups will help those students who have reading difficulties.

The activity focuses on finding unknowns. The clues could be described using algebraic symbols, but this is not the purpose at this level. (For example, “There are three more red stones than green” could be written as g + 3 = r.)

Encourage students to prioritise the clues in order of significance. For instance, in recipe 4, the clue “There are six blue stones” defines a key part of the solution from which the other clues develop.

The progression below illustrates a possible path for solving recipe 3.

• There are 25 stones in total. [Student draws 25 circles on paper.]
• At least half the stones are blue. [Blue could occupy 13 or more circles.]
• There are twice as many blue stones as red stones. [There must be an even number of blue stones, so the possibilities are 14 blue and 7 red (21 in total) or 16 blue and 8 red (24 in total).]
• There are the same number of yellow stones as there are green stones. [Only the 14 blue and 7 red possibilities will work, so there are 2 yellow and 2 green stones as well.]

With recipe 6, restrict students to a maximum of 24 stones. This may curb their inclination to use large numbers, making the equipment difficult to use.

Students will need to realise that it is easier to create these problems than solve them!

1.

2 blue, 4 green, and 7 red

2.

Answers will vary. For example, 12 green, 4 blue, and 4 red

3.

14 blue, 7 red, 2 yellow, and 2 green

4.

6 blue, 5 red, and 3 green

5.

Answers will vary. For example, 6 yellow, 2 blue, and 4 red

6.

Answers will vary.