Practice 1
Using the graph, how many votes did mystery and space receive altogether?
Answer and teaching response
16 · Add the category counts 6 and 10, not the numbers of scale intervals.
Read the scale before comparing bars
Convert graph intervals into quantities before comparing categories or finding a total.
Get the student and teacher materialsPrepare the group
Learning goal: A learner can read a bar graph with a scale of two, calculate a comparison and explain the meaning of an interval.
You will need: Pencil and paper. The book-choice counts below are invented classroom data for practising graph interpretation.
Start with this question
The graph shows 6 mystery votes, 10 space votes and 14 nature votes. How many more learners chose nature than mystery?
8 learners. The bars differ by four scale intervals, and each interval represents two votes: 14 − 6 = 8.
- Read the category labels and the vertical-axis label before comparing the bars. Each count is a number of votes, with one vote per learner in this example.
- Check the labelled ticks: 0, 2, 4 and so on. Equal spaces represent equal differences of two votes, not one vote.
- Read the top of each bar against that scale. Mystery reaches 6 and nature reaches 14, so subtract 6 from 14.
- Check using the drawing: four intervals separate the bar heights, and 4 × 2 = 8 votes. Keep the unit in the final comparison.
Run the 15-minute workshop
- 3 minutes. Cover the bar tops and ask learners what the labels and scale alone tell them.
- 4 minutes. Read each bar and check the nature–mystery comparison using both numbers and intervals.
- 5 minutes. Use the same graph for the practice. Have learners name the relevant categories before calculating.
- 3 minutes. Complete the independent scale check and explain why counting intervals alone is insufficient.
A useful error to discuss
A learner might say: The nature bar is four boxes taller, so it has four more votes.
A box or interval has a meaning supplied by the scale. Here each interval counts two votes. Four intervals therefore represent eight votes.
Practise, then check independently
Use the first three tasks for guided practice. Try the final task without help. Record a drawing or equation as well as the answer.
Practice 2
How many more votes did nature receive than space?
Answer and teaching response
4 · Nature has 14 votes and space has 10.
Practice 3
How many votes are represented by all three bars?
Answer and teaching response
30 · Six plus ten plus fourteen accounts for every category.
Independent check
A different graph uses a scale of 5 votes per interval. A bar reaches 4 intervals above zero. How many votes does it represent?
Answer and teaching response
20 · Multiply the four intervals by five votes per interval.
Transfer the idea
If the same 14 nature votes are redrawn using one vote per interval, does the number of votes change?
Discuss a possible response
No. The data remain 14 votes. The bar now spans fourteen intervals instead of seven; the scale changes the representation, not the count.
Choose the next teaching step
Look for:
- Reads the axis scale before reporting a value.
- Separates the number of intervals from the number of votes.
If the idea is not secure: Write the counting sequence beside the ticks and trace horizontally from the bar top.
If the learner is ready: Redraw the data using a scale of one and explain why totals and comparisons stay the same.
Materials for your group
Student pages and teacher answers are separate. Download an HTML file to keep or use your browser to print or save as PDF.