AQA GCSE Mathematics Paper 1 (Foundation), June 2025: Question 3

Pictograms: Working Out Values from a Missing Key

Foundation Tier • Statistics & Number • 3 Marks

What this question tests

Interpreting a pictogram when the key is not explicitly provided.
Recognising fractional parts of symbols (circles divided into quarters).
Setting up a two-step proportional calculation: finding the value of one symbol (or fractional section) and scaling up to find an unknown category.

Question Breakdown & Method

Information given: 48 street names end in "Close". Find the number ending in "Avenue".

📐 Step-by-Step Calculation

Step 1: Determine the value of one whole circle or one quarter

Looking at the row for Close:

There are 2 full circles.
Each circle is split into 4 equal quarters, meaning there are 2 × 4 = 8 quarters in total.
These represent 48 street names.

Value of 1 whole circle = 48 ÷ 2 = 24
Value of 1 quarter ( ¼ ) = 24 ÷ 4 = 6 (or 48 ÷ 8 = 6 )

Step 2: Calculate the number of street names for Avenue

Looking at the row for Avenue:

There is 1 whole circle and 1 quarter of a circle ( 1¼ symbols or 5 quarters ).

Method A (Adding parts): 24 + 6 = 30
Method B (Using quarters): 5 × 6 = 30
Method C (Fraction of circle): 24 × 1.25 = 30

✅ Correct Answer & Mark Breakdown

M1: For calculating the value of a key element:
• 48 ÷ 8 = 6 (one quarter), OR
• 48 ÷ 2 = 24 (one full circle)
(Also implied by finding 72 for Road)

M1dep: Dependent on the first M1. A fully correct method to calculate Avenue:
• their 24 + their 6 , OR
• their 6 × 5 , OR
• their 24 × 5/4

A1: Correct answer of 30.

💡 Key Knowledge

Pictogram parts: Lines inside shapes divide them into equal fractional portions. Here, cross-hairs split each circle into quarters (¼).
Finding the unit value: Always find the value of either one whole symbol or one smallest division first.
Reconstructing the key: Even if not asked, sketching out a key on your paper (e.g. ◯ = 24, quarter = 6) prevents simple counting mistakes.

🧠 Exam Technique & Examiner Commentary

Check your diagram for working: Examiners actively check annotations directly on the pictogram! Writing numbers like 24 or 6 next to the circles can earn you method marks even if your final answer is wrong.
Misreading the row: Special credit was awarded if candidates accidentally used the wrong row but did the correct process:
- SC2 (2 marks): If 48 was treated as Road (giving 1 circle = 16, quarter = 4 → Avenue = 20).
- SC1 (1 mark): If 48 was treated as Lane (giving 1 circle = 48, quarter = 12 → Avenue = 60).
Show full lines of working: Never just write down mental arithmetic. Writing 48 ÷ 2 = 24 guarantees the first mark.

❌ Common Errors

Assuming 1 circle = 1 item: Overlooking that pictograms scale values up, or assuming each quarter is 1.
Misidentifying fractions: Assuming the partial circle is a half ( ½ ) instead of a quarter ( ¼ ). Always look closely at the angle (90° = one quarter).
Row mix-up: Pairing the value 48 with "Road" (3 circles) or "Lane" (1 circle) instead of "Close" (2 circles). Read the question prompt carefully!