IGNITE maths practice: from a diagram to an equation

Quick Answer

To turn a diagram into an equation, label what the picture shows, relate the labelled parts in one sentence, then solve the equation that sentence gives. This page from Braintree Coaching Australia has eight original diagram problems, each worked in those three steps. It is written for Year 6 children in South Australia preparing for Year 7 IGNITE entry. It is our own practice for the mathematical reasoning part and is not a copy of, or a claim to match, any school's or ACER's paper. It is free and prints on one or two pages in black and white.

Who is this practice for, and which test does my school use?

This set suits a Year 6 child in South Australia who is preparing for IGNITE entry to Year 7 and can already solve a one-step equation. Younger children can try the balance scales first.

Schools publish different information about the assessment (all checked 15 October 2026):

• Glenunga International High School calls it the ACER Ignite Assessment. Children sit in Year 6 for Year 7 entry. See Glenunga's IGNITE page.
• The Heights School calls it the ACER Ignite assessment. Children sit in Year 6 for Year 7 entry. See The Heights' IGNITE page.
• Aberfoyle Park High School describes a Year 7 to 10 specialist program and does not name the assessment or the entry year on its IGNITE page. ACER's participating schools list places it under "Ignite Program".

Both of the school pages that name the components list Mathematical Reasoning with Reading Comprehension, Abstract Reasoning and Written Expression. Our IGNITE exam format guide explains the four parts. Neither school page links a sample paper, so we cannot say what a real maths item looks like, and this page does not try to copy one.

How do I get from a picture to an equation?

Use the same three steps every time.

1. Label. Give each unknown number a letter and write every known number on the picture. Mark any sides or parts that are equal, even if only one of them is labelled.
2. Relate. Say in one sentence how the labelled parts are connected: "the two pans are equal", "all the units add to 84", "the angles make 180°". Then write that sentence as an equation.
3. Solve. Work the equation backwards one operation at a time, then put the answer back into the picture to check.

Worked model. A balance is level with a bag of mass b and a 20 g weight on the left, and a 50 g weight on the right.

1. Step 1, label. The bag is b grams. The left pan holds b and 20. The right pan holds 50.
2. Step 2, relate. The scale is level, so the pans are equal: b + 20 = 50.
3. Step 3, solve. 50 − 20 = 30, so b = 30 g. Check: 30 + 20 = 50.

The questions

Work on paper with a pencil. The diagrams are not drawn to scale, so read every length and angle from its label. Each diagram has a text description underneath, so a child can also solve a problem from the words alone.

Problem 1: Balance scale: one bag and a weight

Diagram description: A balance scale sits level. The left pan holds one bag of unknown mass, labelled b, and a 35 g weight. The right pan holds one 100 g weight.

What is the mass of the bag, in grams?

• A. 35 g
• B. 65 g
• C. 100 g
• D. 135 g

Problem 2: Balance scale: three equal blocks and a weight

Diagram description: A balance scale sits level. The left pan holds three identical blocks, each of unknown mass n, and a 10 g weight. The right pan holds one 100 g weight.

What is the mass of one block, in grams?

• A. 10 g
• B. 30 g
• C. 90 g
• D. 110 g

Problem 3: Rectangle with a perimeter and one labelled side

Diagram description: A rectangle has its top side labelled 12 cm and its left side labelled w. The other two sides are not labelled. A note beside the rectangle says the perimeter is 40 cm.

What is w, in centimetres?

• A. 16 cm
• B. 28 cm
• C. 8 cm
• D. 52 cm

Problem 4: Rectangle split in two, with a total area

Diagram description: A rectangle is split by a vertical line into a left part 6 cm wide and a right part 4 cm wide. Its height is labelled h. A note says the total area is 80 cm².

What is h, in centimetres?

• A. 8 cm
• B. 10 cm
• C. 70 cm
• D. 90 cm

Problem 5: Strip diagram: sharing in the ratio of units

Diagram description: One long strip, labelled 84 stickers in total, is cut into 7 equal units. The first 3 units are labelled Mia. The last 4 units are labelled Tom.

How many stickers does Tom have?

• A. 12
• B. 28
• C. 36
• D. 48

Problem 6: Strip diagram: two strips and a difference

Diagram description: Two strips sit one above the other. Sam's strip is 4 equal units long. Ana's strip is 7 equal units long, so it is 3 units longer. A bracket marks the extra 3 units as 24 marbles.

How many marbles does Ana have?

• A. 56
• B. 32
• C. 31
• D. 168

Problem 7: Angles on a straight line

Diagram description: A straight line has two rays leaving a point on it, making three angles that together fill the line. From left to right the angles are 40°, 65° and a. The angle a is not labelled with a number.

What is angle a, in degrees?

• A. 105°
• B. 115°
• C. 140°
• D. 75°

Problem 8: Angles at a point

Diagram description: Three angles meet at one point and fill the whole turn. One is a right angle, marked with a small square, and it is 90°. One is 150°. The third is labelled x.

What is angle x, in degrees?

• A. 240°
• B. 60°
• C. 120°
• D. 210°

Answers and worked steps

Check one problem at a time and look at the steps, not only the letter. The answers are 1 B, 2 B, 3 C, 4 A, 5 D, 6 A, 7 D, 8 C.

Problem 1: B, 65 g

1. Step 1, label. The bag is b grams. The left pan holds b and 35. The right pan holds 100. The scale is level, so the two pans have the same mass.
2. Step 2, relate. Left pan equals right pan: b + 35 = 100.
3. Step 3, solve. 100 − 35 = 65, so b = 65 g. Check: 65 + 35 = 100.

Tempting wrong answers: 135 g adds every number shown. 35 g reads the weight on the pan as the answer.

Problem 2: B, 30 g

1. Step 1, label. Each block is n grams, and all three are the same. The left pan holds 3 blocks and 10 g. The right pan holds 100 g.
2. Step 2, relate. Left pan equals right pan: 3 × n + 10 = 100.
3. Step 3, solve. 100 − 10 = 90, so 3 × n = 90 and n = 30 g. Check: 3 × 30 + 10 = 100.

Tempting wrong answers: 90 g stops before dividing by 3. 110 g adds the 10 g instead of taking it away.

Problem 3: C, 8 cm

1. Step 1, label. A rectangle has two sides of 12 cm and two sides of w, even though only one of each is labelled. The perimeter is the distance all the way round: 40 cm.
2. Step 2, relate. Two 12s and two ws make 40: 12 + w + 12 + w = 40, or 24 + 2 × w = 40.
3. Step 3, solve. 40 − 24 = 16, so 2 × w = 16 and w = 8 cm. Check: 12 + 8 + 12 + 8 = 40.

Tempting wrong answers: 28 cm counts only one 12 cm side. 16 cm stops before halving. 52 cm adds the perimeter to a side.

Problem 4: A, 8 cm

1. Step 1, label. The two parts share one height, h. Together the widths are 6 + 4 = 10 cm. The total area is 80 cm².
2. Step 2, relate. Area is width times height, so 10 × h = 80.
3. Step 3, solve. 80 ÷ 10 = 8, so h = 8 cm. Check: 10 × 8 = 80.

Tempting wrong answers: 10 cm is the combined width, not the height. 70 cm subtracts and 90 cm adds, but area is found by multiplying.

Problem 5: D, 48

1. Step 1, label. Each equal unit is u stickers. The whole strip is 7 units and holds 84. Tom has 4 of the 7 units.
2. Step 2, relate. Seven units make 84: 7 × u = 84. Tom has 4 × u.
3. Step 3, solve. 84 ÷ 7 = 12, so u = 12 and Tom has 4 × 12 = 48 stickers. Check: Mia 3 × 12 = 36, and 36 + 48 = 84.

Tempting wrong answers: 36 is Mia's share. 12 is one unit. 28 divides by 3 instead of 7.

Problem 6: A, 56

1. Step 1, label. Each equal unit is u marbles. Sam has 4 units and Ana has 7 units, so Ana has 3 units more. Those 3 units are 24 marbles.
2. Step 2, relate. The difference gives the unit: 3 × u = 24. Ana has 7 × u.
3. Step 3, solve. 24 ÷ 3 = 8, so u = 8 and Ana has 7 × 8 = 56 marbles. Check: Sam has 4 × 8 = 32 and 56 − 32 = 24.

Tempting wrong answers: 32 is Sam's number. 31 adds 24 to 7. 168 multiplies 24 by 7 without finding one unit first.

Problem 7: D, 75°

1. Step 1, label. The three angles fill a straight line, so they add up to 180°. The known angles are 40° and 65°. The unknown is a.
2. Step 2, relate. Angles on a straight line total 180°: 40 + 65 + a = 180.
3. Step 3, solve. 40 + 65 = 105 and 180 − 105 = 75, so a = 75°. Check: 40 + 65 + 75 = 180.

Tempting wrong answers: 105° is the two known angles added and not taken from 180°. 115° and 140° take away only one of the known angles.

Problem 8: C, 120°

1. Step 1, label. Angles at a point make a full turn, which is 360°. The known angles are 90° and 150°. The unknown is x.
2. Step 2, relate. The three angles total 360°: 90 + 150 + x = 360.
3. Step 3, solve. 90 + 150 = 240 and 360 − 240 = 120, so x = 120°. Check: 90 + 150 + 120 = 360.

Tempting wrong answers: 240° is the two known angles added. 60° subtracts one from the other, and 210° takes only 150° from 360°.

What goes wrong with diagrams?

The wrong options in this set come from three errors.

• Adding every number shown. The numbers are on the picture, so the child adds them. Ask first: what is the picture saying about how they connect?
• Missing an unlabelled equal side. In Problem 3, only one 12 cm side and one w side are labelled. Children who count only those get the wrong perimeter. Say "a rectangle has two of each".
• Reading lengths off the drawing. A side that looks twice as long is not twice as long. The labels are the data, and the picture is only a guide.

Transfer task: draw the diagram for an equation

Here is an equation: 4 × m + 15 = 63. On paper, draw a balance scale or a strip diagram that this equation could come from, label it, and write one sentence that says what it shows. Then solve it.

Self-check: a good answer has four equal blocks marked m and a 15 g weight on one pan, balanced against 63 g on the other, or a strip of four equal units plus a 15 unit that totals 63. Taking away 15 gives 48, and 48 ÷ 4 gives m = 12.

Where are the official samples?

We have not found an official sample paper with diagram-to-equation items, and neither school page links a sample. Glenunga's page directs families to its IGNITE team for information. For what each school publishes, start with the pages linked above, and see ACER's HAST information for the testing body.

What should we do after this set?

• Try the mathematical reasoning item in our IGNITE sample questions.
• For the full range of material, read what kinds of IGNITE practice your child actually needs.
• Read the IGNITE exam format guide for the four parts.
• If you want a structured program, see the IGNITE course and check which year level its packs list before you buy.

Sources and review

Official sources (checked 2026-10-15): Glenunga International High School and The Heights School IGNITE pages, linked above, for the assessment name and Year 6 sitting for Year 7 entry; Aberfoyle Park High School's page and ACER's participating schools list for its program description. No source was found that describes diagram-to-equation items, so no resemblance is claimed.

Where the problems came from: all eight problems, diagrams and worked steps are original Braintree Coaching Australia material written for this page. None is taken from an official or third-party paper.

Author: James Rush, content writer, Braintree Coaching Australia.

Answer check: each problem was worked by the author using the three steps above. A second solve without the key, run on 2026-10-15 by an automated review pass and not by a teacher, gave the same answer for all eight problems, including from the text descriptions alone. A named teacher review has not yet been recorded for this set. If you find an error, please tell us.

Last updated: 2026-10-15.