Lights Out

The tent lights problem on page 12 demonstrates the concept of equivalent fractions. This concept is critical to students’ understanding of decimals and percentages.
Discussing the meaning of fractions is vitally important. For example, 27 of the 36 tents are lit up at 9.30 p.m. As a fraction, this is 27/36, the denominator (bottom number) giving the number of members in the set, and the numerator (top number) giving how many of those members have been identified.
Note that 27/36 can be simplified as follows:

as 9/12 by grouping in threes, so

Students need to reverse this process to answer question 3. The 36 tents must be grouped into six equal subsets. One of those subsets shows the lighted tents:

One-sixth of 36 is 6.

Activity Two

In this activity, students are asked to interpret and draw graphs to show the relationship between time and the fraction of tents lit up. Each point on the graph can be represented as an ordered pair. For example, (9, 5/6) means 5/6 of the tents are lit at 9 p.m. Using a corner of a sheet of paper is a good way to confirm the position of ordered pairs on a number plane:

The completed graph for Monday night is shown in the answers.

Answers to Activities

Activity One

1. a. 27/36 (3/4)
b. 24/36 (2/3)
c. 18/36 (1/2)
d. 12/36 (1/3)
2. 9/36 (1/4)
3. 6
Activity Two
1. 10/12 (5/6)
2.

3. Graph a: Tuesday
Graph b: Thursday (concert)
Graph c: Wednesday