Discover Mathematics P4: Term 2, Unit 11, Lessons 1–5
GoalRead and make line plots whose number line is marked in halves, quarters or eighths, and use them to solve problems.
New words
line plot · a number line with a dot above it for each piece of datadata · facts or measurements that we collectequal steps · the distance between marks on the number line is always the same
Explanation
A line plot shows data on a number line. We put one dot above the number line for every measurement. When the measurements are fractions, we mark the number line in equal steps of halves, quarters or eighths. For quarters the marks are 0, 1/4, 2/4 (= 1/2), 3/4 and 1. A tall stack of dots shows the measurement that happens most often. To answer questions, count dots and use fractions with the same denominator. If 4 ribbons are 3/4 m long, their total length is 4 × 3/4 = 12/4 = 3 m. To find the whole total, multiply each length by its number of dots and add. To find the difference between the longest and the shortest, subtract.
Worked examples
Ten ribbons were measured in metres. The plot shows 2 ribbons of 1/4 m, 3 of 1/2 m, 4 of 3/4 m and 1 of 1 m. How many ribbons are longer than 1/2 m? 4 + 1 = 5 ribbons. What is the difference between the longest and the shortest? 1 − 1/4 = 3/4 m.
Eight bottles hold different amounts of water, measured in litres in eighths. The plot shows 1 bottle with 1/8 L, 3 with 2/8 L, 2 with 3/8 L and 2 with 4/8 L. Total water: 1/8 + 6/8 + 6/8 + 8/8 = 21/8 L = 2 5/8 L. (3 × 2/8 = 6/8, 2 × 3/8 = 6/8, 2 × 4/8 = 8/8.)
Make a line plot from a list. Eight children walked these distances in km: 1/2, 1/4, 1/2, 3/4, 1/4, 1/2, 1, 3/4. Count each distance: 1/4 appears 2 times, 1/2 appears 3 times, 3/4 appears 2 times and 1 appears 1 time. 2 + 3 + 2 + 1 = 8 dots, one for each child.
Class activity
Measure and plot. Cut 10 paper strips of different lengths, each a whole number of quarters of a metre if you can, or measure ten objects at home in quarters of a metre. Write the lengths as fractions, make a tally, and draw a line plot with equal steps from 0 to 1 1/2 on your page. Which length happens most?
Practice
1
Nine ropes were measured in metres. How many ropes are 1/2 m long, and how many are longer than 1 m?
3 ropes are 1/2 m. Longer than 1 m: 1 + 3 = 4 ropes (1 1/2 m and 2 m).
2
What is the total length of all nine ropes in the plot above?
3 × 1/2 = 1 1/2 m; 2 × 1 = 2 m; 1 × 1 1/2 = 1 1/2 m; 3 × 2 = 6 m. Total: 1 1/2 + 2 + 1 1/2 + 6 = 11 m.
3
A line plot has marks 0, 1/4, 1/2, 3/4 and 1. How many equal steps are there between 0 and 1?
4 steps, each of 1/4.
4
The data are 1/2, 3/4, 1/2, 1/4. How many dots go above 1/2?
2 dots, because 1/2 appears twice.
5
Why must the steps on the number line of a line plot be equal?
If the steps were not equal, the dots would sit at the wrong distances and we could not compare the measurements fairly.
