Comparative displays | Year 6

01 / LEARN

Understand the idea.

Compare like with like

Read the title, key and both axes before comparing bars. Here the horizontal labels give books finished, while each frequency counts students. A bar of height $4$ above $1$ book means four students each finished one book.

Check the group totals and use the same scale. Each class here contains ten students. If group sizes differ, counts can still be compared, but a larger count alone does not establish a larger fraction of the group.

Grouped column graph. At zero, one, two and three books the Class A frequencies are 2, 4, 3, 1; Class B frequencies are 1, 2, 4, 3. Both classes have ten students.

Practice data: books finished during one week by ten students in each class
Books finished	Class A frequency	Class B frequency
0	2	1
1	4	2
2	3	4
3	1	3

Describe a comparison with evidence

Match the comparison to the wording. Exactly two books uses only the two-book row. At least two books includes two and every larger value in the data, so combine the frequencies for two and three books.

Support a conclusion with both counts and totals: seven of ten Class B students finished at least two books, compared with four of ten in Class A. This describes the recorded week; it does not explain why the classes differ.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Compare a single value

Using the supplied table, how many more Class B students than Class A students finished exactly three books?

Practice data: books finished during one week by ten students in each class
Books finished	Class A frequency	Class B frequency
0	2	1
1	4	2
2	3	4
3	1	3

Worked solution

1
Select the three-book row.
$\begin{aligned} Class B: & 3 students \\ Class A: & 1 student \end{aligned}$
Exactly three books excludes every other row of the table.
2
Subtract the two frequencies.
$3 - 1 = 2$
How many more asks for the difference between the student counts.
3
State which class has the larger count.
Class B has two more students who finished exactly three books.

Answer

2 more students.

EXAMPLE 02

Combine categories

Using the table, compare the numbers who finished at least two books.

Practice data: books finished during one week by ten students in each class
Books finished	Class A frequency	Class B frequency
0	2	1
1	4	2
2	3	4
3	1	3

Worked solution

1
Choose the rows that count.
$2 books or 3 books$
At least two includes two itself and every larger number listed.
2
Combine Class A's frequencies.
$3 + 1 = 4 students$
The two groups of students occupy different rows, so add their counts.
3
Combine Class B's frequencies.
$4 + 3 = 7 students$
These are the Class B counts for the same two book totals.
4
Compare using the equal class sizes.
$\begin{aligned} Class A: & \frac{4}{10} \\ Class B: & \frac{7}{10} \\ 7 - 4 & = 3 \end{aligned}$
Class B has seven of ten students compared with four of ten in Class A, a difference of three students.

Answer

Class B: 7 of 10; Class A: 4 of 10.

03 / YOUR TURN

Try it yourself.

Check your understanding

In the supplied data, which class has more students who finished no books?

Show answer & reasoning

Class A.

Use the zero-book row, because no books means exactly zero. It records $2$ students in Class A and $1$ in Class B, so Class A has more.

Keep practising

6 worksheet questions · 11 marks

Open worksheet Worked solutions

Read the questions online

Using the table, how many Class A students finished exactly one book?
1 mark
Practice data: books finished during one week by ten students in each class
Books finished Class A frequency Class B frequency
0 2 1
1 4 2
2 3 4
3 1 3
Using the table, how many students are recorded in Class B?
2 marks
Practice data: books finished during one week by ten students in each class
Books finished Class A frequency Class B frequency
0 2 1
1 4 2
2 3 4
3 1 3
How many students across both classes finished exactly two books?
2 marks
Practice data: books finished during one week by ten students in each class
Books finished Class A frequency Class B frequency
0 2 1
1 4 2
2 3 4
3 1 3
Compare the numbers who finished zero or one book.
2 marks
Practice data: books finished during one week by ten students in each class
Books finished Class A frequency Class B frequency
0 2 1
1 4 2
2 3 4
3 1 3
A different school compares 8 students out of 10 with 12 students out of 30. Why is comparing 8 and 12 alone unfair?
2 marks
Write a true comparison about the two classes using a number from the table.
2 marks
Practice data: books finished during one week by ten students in each class
Books finished Class A frequency Class B frequency
0 2 1
1 4 2
2 3 4
3 1 3

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

Using the table, how many Class A students finished exactly one book?
1 mark
Practice data: books finished during one week by ten students in each class
Books finished Class A frequency Class B frequency
0 2 1
1 4 2
2 3 4
3 1 3
Read Class A at the value 1 book.
4 students.
Using the table, how many students are recorded in Class B?
2 marks
Practice data: books finished during one week by ten students in each class
Books finished Class A frequency Class B frequency
0 2 1
1 4 2
2 3 4
3 1 3
Add the frequencies: $1 + 2 + 4 + 3 = 10$ .
10 students.
How many students across both classes finished exactly two books?
2 marks
Practice data: books finished during one week by ten students in each class
Books finished Class A frequency Class B frequency
0 2 1
1 4 2
2 3 4
3 1 3
Class A has 3 and Class B has 4.
$3 + 4 = 7$ .
7 students.
Compare the numbers who finished zero or one book.
2 marks
Practice data: books finished during one week by ten students in each class
Books finished Class A frequency Class B frequency
0 2 1
1 4 2
2 3 4
3 1 3
Class A: $2 + 4 = 6$ .
Class B: $1 + 2 = 3$ .
Class A: 6; Class B: 3.
A different school compares 8 students out of 10 with 12 students out of 30. Why is comparing 8 and 12 alone unfair?
2 marks
Twelve is a larger count, but it comes from three times as many students.
Compare parts of equally sized groups or proportions before deciding.
The groups have different sizes.
Write a true comparison about the two classes using a number from the table.
2 marks
Practice data: books finished during one week by ten students in each class
Books finished Class A frequency Class B frequency
0 2 1
1 4 2
2 3 4
3 1 3
State the group names and the feature.
Use matching frequencies or combined categories. Other supported comparisons are valid.
For example, 7 of 10 Class B students finished at least two books, compared with 4 of 10 in Class A.

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Curriculum reference & lesson scope

Australian Curriculum v9.0; SA Mathematics Curriculum 2026

Variable types; comparative displays; mode/range/shape; media claims; investigations.

Official curriculum source ↗

In this lesson

Understand the idea.

Compare like with like

Describe a comparison with evidence

See the method in action.

Compare a single value

Select the three-book row.

Subtract the two frequencies.

State which class has the larger count.

Combine categories

Choose the rows that count.

Combine Class A's frequencies.

Combine Class B's frequencies.

Compare using the equal class sizes.

Try it yourself.

Check your understanding

Keep practising