Flying Feet

This activity allows students to explore the way the factors of a number relate to a context.
Encourage the students to form a mental picture of each of the children described on the page as they cross the 48 paving stones. You could encourage them to make a diagram of the first 12 stones and then act out or draw the way each child crosses those stones. This would give them a good feel for the problem.
Emphasise the fact that each stride takes the same amount of time, regardless of how long the stride is. This is vital in understanding the problem.

Their answers to question 1a will give you an indication of whether or not the students have grasped the idea, while question 1b leads them to connect the factors of 48 with the strides taken. Make sure that this connection is understood. A simple chart form of recording may help to show this:

In questions 2 and 3, the students may find it helpful to draw a diagram showing the stones numbered from 1 to 48. Check that the students have numbered the stone closest to the pool as number 48.
Extend the question by introducing a fifth person who has a stride that uses a factor of 48 not yet mentioned. Ask the students what this stride might be. (It would be either 6 or 8 because 6 x 8 = 48.) This question would confirm which students have made the connection between the context and the factors of 48 because it completes the set of factors of 48.
As a further extension, have the students make up a similar problem using all the factors of 60.

Answers to Activity

1. a. Eru: 12 strides, Matiu: 16 strides, Api: 24 strides, Myra: 48 strides
b. Eru: 48 ÷ 4 = 12, 4 x 12 = 48
Matiu: 48 ÷ 3 = 16, 3 x 16 = 48
Api: 48 ÷ 2 = 24, 2 x 24 = 48
Myra: 48 ÷ 1 = 48, 1 x 48 = 48
2. a. Api
b. Matiu
3. Matiu: step 12, Api: step 24, Myra: step 36