Discover Mathematics P5: Term 2, Unit 10, Lessons 9–11
GoalTurn a table of real data into points on a coordinate plane, choosing a sensible scale.
New words
data · facts or measurements collected, such as heights or pricesscale · the number each grid square stands for on an axisaxis label · the words and unit that say what an axis shows
Explanation
Real data can be graphed in four steps. First, read the table and write each row as an ordered pair (first number, second number). Second, choose a scale: if the values are 10, 20, 30 and 40, let each square on the vertical axis stand for 10, so that the numbers fit on the paper. Third, plot each point: go across to the first number, then up to the second. Fourth, give the graph labels that say what each axis shows, with its unit, for example “hours” and “kilometres”. If the quantity changes all the time, such as distance while cycling, you may join the points with line segments. The points of a steady rate, such as 10 km every hour, line up on a straight line.
Table→Scale→Plot→Label
Worked examples
Karim cycles at a steady speed. After 1, 2, 3 and 4 hours he has gone 10, 20, 30 and 40 km. The pairs are (1, 10), (2, 20), (3, 30), (4, 40). Each square up stands for 10 km. The points make a straight line because he goes 10 km every hour.
A plant is measured every week: 2, 3, 5, 6 and 8 cm in weeks 1 to 5. The pairs (1, 2), (2, 3), (3, 5), (4, 6), (5, 8) do not make a straight line, because the plant did not grow the same amount each week.
Salma saves 5, 10, 15 and 20 LE in weeks 1 to 4. The largest value is 20, so a scale of 5 LE per square needs only 4 squares. A scale of 1 LE per square would need 20 squares and would not fit.
Class activity
Our class data. Collect real data, for example each child’s height in cm or the number of books in each school bag. Write it in a table with two columns, choose a scale, and graph it on squared paper. Add the axis labels and a title. Ask three questions that someone could answer by reading your graph.
Practice
1
Marina’s savings: 5, 10, 15 and 20 LE after weeks 1 to 4. Write the ordered pairs and say how much she will have after week 5 if she keeps saving the same amount.
(1, 5), (2, 10), (3, 15), (4, 20). She saves 5 LE a week, so after week 5 she has 25 LE.
2
A tuk-tuk goes 40, 80 and 120 km in 1, 2 and 3 hours. Write the ordered pairs and find the speed.
(1, 40), (2, 80), (3, 120). The speed is 40 km per hour.
3
The values to graph are 20, 40, 60, 80 and 100. Choose a good scale for the vertical axis and say how many squares you need.
Let each square stand for 20. You need 5 squares.
4
The graph shows a puppy’s weight in kg in weeks 1 to 5. In which weeks did the weight stay the same?
Weeks 3 and 4: the weight stayed at 4 kg.
5
In the cycling story the point (3, 30) is on the graph. What does it tell us?
