Week 6 · Time, scales and measurement problems · 3 lessons
2
Scales and line plots of measurements
Discover Mathematics P4: Term 1, Unit 3, Lessons 5–9
GoalRead the scale of a graph and make and read line plots of measurements.
New words
scale · the equal steps of numbers along a graph; each step may be 1, 5, 10…line plot · a number line with a mark above each measurement we collectedkey · tells what one mark stands for
Explanation
A graph has a scale, which tells how much each step is worth. If the scale counts in tens, a bar that ends at the third line is 30. Always read the numbers on the side before you read a bar. A line plot is good for measurements. We measure many things with the same ruler and put one dot above the number line for each thing. The key says what one dot means. A line plot of 10 leaves shows how many leaves are 8 cm, 9 cm, 10 cm, 11 cm and 12 cm long. The tallest stack shows the most common length. To find the total length, multiply each length by the number of dots, then add: 8 + 18 + 40 + 22 + 12 = 100 cm. The difference between the longest and shortest leaf is 12 − 8 = 4 cm.
Worked examples
Mariam measures 10 leaves. The plot shows 1 leaf of 8 cm, 2 of 9 cm, 4 of 10 cm, 2 of 11 cm and 1 of 12 cm. The most common length is 10 cm. There are 1 + 2 + 4 + 2 + 1 = 10 dots, one for each leaf.
A library graph has a scale that counts in tens. The bars show books borrowed: Sunday 30, Monday 50, Tuesday 20 and Wednesday 40. Together: 30 + 50 + 20 + 40 = 140 books. Monday is 50 − 20 = 30 books more than Tuesday.
Length (cm)
8
9
10
11
12
Leaves
1
2
4
2
1
Total (cm)
8
18
40
22
12
The total length of the 10 leaves in the first plot: 8 × 1 + 9 × 2 + 10 × 4 + 11 × 2 + 12 × 1 = 8 + 18 + 40 + 22 + 12 = 100 cm. The table shows each product.
Class activity
Measure and plot. Collect 10 spoons, pencils or leaves. Measure each to the nearest cm. Make a line plot with a title, a number line and a key. Tell a friend the most common length, the shortest and longest, and the total length of all of them.
Practice
1
How many leaves are 10 cm long in the plot above, and how many leaves are shorter than 10 cm?
4 leaves are 10 cm. Shorter than 10 cm: 1 + 2 = 3 leaves.
2
A graph has a scale that counts in fives. A bar ends at the 4th line. What number is it?
4 × 5 = 20.
3
Pencil lengths in cm: 12, 13, 13, 14, 14, 14, 15. How many dots go above 14 and what is the total length?
