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Fraction Classroom · 2.3.0 · Teacher answers & responses

Read the scale before comparing bars

Convert graph intervals into quantities before comparing categories or finding a total.

Illustrative class votes. The vertical scale starts at zero and increases by two votes per equal interval.02468101214VotesMysterySpaceNature
Illustrative class votes. The vertical scale starts at zero and increases by two votes per equal interval.

Build the idea

model. The graph shows 6 mystery votes, 10 space votes and 14 nature votes. How many more learners chose nature than mystery?

  1. 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.
  2. Check the labelled ticks: 0, 2, 4 and so on. Equal spaces represent equal differences of two votes, not one vote.
  3. Read the top of each bar against that scale. Mystery reaches 6 and nature reaches 14, so subtract 6 from 14.
  4. Check using the drawing: four intervals separate the bar heights, and 4 × 2 = 8 votes. Keep the unit in the final comparison.

Worked example: 8 learners. The bars differ by four scale intervals, and each interval represents two votes: 14 − 6 = 8.

Practise and explain

Try p1–p3 with a partner. Use a drawing and label your units. Try e1 independently before comparing responses.

p1. Using the graph, how many votes did mystery and space receive altogether?

Answer: 16

Teacher response: Add the category counts 6 and 10, not the numbers of scale intervals.

p2. How many more votes did nature receive than space?

Answer: 4

Teacher response: Nature has 14 votes and space has 10.

p3. How many votes are represented by all three bars?

Answer: 30

Teacher response: Six plus ten plus fourteen accounts for every category.

e1. 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: 20

Look for:

  • Reads the axis scale before reporting a value.
  • Separates the number of intervals from the number of votes.

Teacher response: Multiply the four intervals by five votes per interval.

Transfer the idea

transfer. If the same 14 nature votes are redrawn using one vote per interval, does the number of votes change?

Answer: No. The data remain 14 votes. The bar now spans fourteen intervals instead of seven; the scale changes the representation, not the count.

Run the 15-minute workshop

teach-1. 3 minutes: Cover the bar tops and ask learners what the labels and scale alone tell them.

teach-2. 4 minutes: Read each bar and check the nature–mystery comparison using both numbers and intervals.

teach-3. 5 minutes: Use the same graph for the practice. Have learners name the relevant categories before calculating.

teach-4. 3 minutes: Complete the independent scale check and explain why counting intervals alone is insufficient.

Respond to the learner

misconception. The nature bar is four boxes taller, so it has four more votes.

Teacher response: A box or interval has a meaning supplied by the scale. Here each interval counts two votes. Four intervals therefore represent eight votes.

support. Write the counting sequence beside the ticks and trace horizontally from the bar top.

extend. Redraw the data using a scale of one and explain why totals and comparisons stay the same.

Teaching notes