You will learn
- Read a picture graph key.
- Use a scale where one picture means 2.
- Count symbols to find values.
- Draw a picture graph from a table.
Version 0.2 · expanded edition · expert review pending Standards alignment: pending verification. Written in the style of common primary school assessments. No exam result is promised.
Student lesson
- Read the key first.
- Count the symbols.
- Multiply by the key.
- Draw a picture graph from a table.
Words to know
A graph that uses pictures.
Tells what each picture stands for.
The value of one symbol.
A picture used to show data.
1. Discover: sports club
Many children join the sports club, so drawing one picture for each child takes too much space. Can one picture stand for more than one child?
2. Understand: scaled picture graphs
In a scaled picture graph, one symbol stands for more than one. The key tells us how many. Suppose each ● stands for 2 children.
- Football: 4 symbols → 4 × 2 = 8.
- Netball: 3 symbols → 3 × 2 = 6.
- Swimming: 5 symbols → 5 × 2 = 10.
- Running: 2 symbols → 2 × 2 = 4.
To draw a graph: divide each count by the scale. 8 ÷ 2 = 4 symbols.
Idea 1: The key
Key: 1 symbol = 2. Three symbols show 3 × 2 = 6. Five symbols show 10.
Idea 2: Other scales
Key: 1 symbol = 5. Four symbols show 4 × 5 = 20.
Idea 3: Draw
12 children with key 1 symbol = 2 need 12 ÷ 2 = 6 symbols.
Why read the key first? Without it we cannot tell what a symbol means.
3. Worked examples
Example 1 (I show you): ×2
Key: 1 symbol = 2. Three symbols?
- 3 × 2.
Answer: 6
Example 2 (We do it together): ×5
Key: 1 symbol = 5. Four symbols?
- 4 × 5.
Answer: 20
Example 3 (You try): Draw
12 children, key 1 symbol = 2. How many symbols?
Show the steps and answer
- 12 ÷ 2.
Answer: 6
Did you know?
A half symbol shows half of the key value.
Why this matters
Scaled graphs show big numbers with few pictures.
4. Explore: draw it
You need paper and a pencil.
- Use the key: one symbol = 2 children.
- Football 8 → draw 4 symbols.
- Draw swimming 10 and running 4.
- Check each by multiplying.
Think about it: what did you notice?
4, 5 and 2 symbols.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- The key says ___.
- I count ___ symbols.
- ___ × ___ = ___.
- I need ___ symbols.
Guided practice
Question 1. Key: 1 symbol = 2. Four symbols?
8.
Question 2. Key: 1 symbol = 2. Six children: how many symbols?
3.
Question 3. Swimming has 5 symbols. How many children?
10.
Independent practice
Level 1: Start
- 1 symbol = 2: 3 symbols
- 1 symbol = 2: 5 symbols
- 1 symbol = 2: 12 children, symbols?
- 1 symbol = 5: 4 symbols
- Why read the key first?
Level 2: Grow
- Key 1 symbol = 2. Eight symbols
- Key 1 symbol = 5. Six symbols
- Key 1 symbol = 2. 18 children need how many symbols?
Level 3: Stretch
- Key 1 symbol = 10. 45 children need how many symbols?
- Key 1 symbol = 2. Row A has 7 symbols and row B has 3. Total?
- Ali reads 4 symbols with key 5 as 4. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
In a graph, one symbol means 5 books. A class has 6 symbols. How many books?
Show a sample answer
30 books.
Another one. Draw a picture graph with 1 symbol = 2 for cats 8, dogs 12 and birds 6.
Show a sample answer
cats 4 symbols, dogs 6 symbols, birds 3 symbols
7. Common mistakes
Fix: Multiply by the scale.
Fix: Multiply by the key.
Fix: A half symbol is half the key.
8. Lesson summary and revision card
- I can read a picture graph key.
- I can use a scale of 2 or 5.
- I can count symbols to find values.
- I can draw a picture graph from a table.
9. Check and master
Answer all 14 questions. You will see feedback after each one.
Your result appears here after you answer every question.
10. Key takeaways
- Always read the key.
- Symbols × scale = value.
- Divide to draw.
11. Next lesson
Next lesson: Scaled bar graphs. Keep going with the next idea in this course.
Exam practice
These questions are written in the style of common school and international primary assessments. Try them on your own, without looking back. Then check your answers in the marking guide. The marks are shown in brackets.
- Key: 1 symbol = 2. Four symbols show how many? [2 marks]
- Key: 1 symbol = 2. How many symbols for 10 children? [2 marks]
- Key: 1 symbol = 5. Four symbols show how many? [2 marks]
- What does the key tell us? [1 mark]
- Ben says six symbols with key 5 show 6. Is he right? Explain. [3 marks]
Total: 10 marks.
Marking guide and model answers
- 4 × 2 [1] = 8 [1]
- 10 ÷ 2 [1] = 5 [1]
- 4 × 5 [1] = 20 [1]
- What each symbol means [1]
- No [1]. Each symbol is 5 [1]. 6 × 5 = 30 [1].
Score guide: 9 to 10 = secure. 6 to 8 = nearly there, revise the parts you missed. Under 6 = work through the lesson again with a grown-up.
Printable worksheet
- 1 symbol = 2: 3 symbols
- 1 symbol = 2: 5 symbols
- 1 symbol = 2: 12 children, symbols
- 1 symbol = 5: 4 symbols
- What should we read first?
- Key: 1 symbol = 2. Four symbols show ___.
- Key: 1 symbol = 2. Ten children need ___ symbols.
- Key: 1 symbol = 5. Four symbols show ___.
- The key tells us what each ___ means.
- One symbol means 5 books. Six symbols show ___.
Homework
Draw a picture graph for the number of siblings, cousins and friends you have. Use a key.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 1 symbol = 2: 3 symbols | 6 | 2 |
| 1 symbol = 2: 5 symbols | 10 | 2 |
| 1 symbol = 2: 12 children, symbols | 6 | 2 |
| 1 symbol = 5: 4 symbols | 20 | 2 |
| What should we read first? | the key | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 6; 2 10; 3 6; 4 20; 5 the key.
Quiz answers: 1 A, 2 B, 3 C, 4 A, 5 B, 6 A, 7 B, 8 C, 9 A, 10 B, 11 C, 12 A, Challenge 1 C, Challenge 2 C.
Extra worksheet answers (items 6 onward): 6 8; 7 5; 8 20; 9 symbol; 10 30 books.
Independent practice answers. Level 1: 1 6; 2 10; 3 6 symbols; 4 20; 5 because the key tells us what each symbol means. Level 2: 1 16; 2 30; 3 9. Level 3: 1 4 and a half; 2 20; 3 Use the key. 4 × 5 = 20..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Read a picture graph key | Shows this with help from an adult or a picture | Does this independently and explains how they know | Explains it clearly and uses it in a new situation |
| O2 Use a scale where one picture means 2 | Shows this with help from an adult or a picture | Does this independently and explains how they know | Explains it clearly and uses it in a new situation |
| O3 Count symbols to find values | Shows this with help from an adult or a picture | Does this independently and explains how they know | Explains it clearly and uses it in a new situation |
| O4 Draw a picture graph from a table | Shows this with help from an adult or a picture | Does this independently and explains how they know | Explains it clearly and uses it in a new situation |
Proposed Courseversity thresholds for this page: Bronze = at least 8 of 12 core questions correct; Silver = all 12; Gold = all 12 plus both challenge questions. A badge is never a full record of progress.
If a learner struggles
- Find the misconception: Counting each symbol as 1 without reading the key. Multiply by the scale.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Practise skip counting by 2s and 5s.
- Guided practice: work through one example together and let the learner try the next one.
- Reassess: use the quiz again or the worksheet.
- Move on when the learner shows Silver-level evidence independently.
For parents and guardians
In this lesson your child reads and draws picture graphs with a scale. You do not need to be good at mathematics to help.
- Draw a family picture graph with a key.
- Ask: what does one symbol mean?
- Skip count together.
- Ask “how do you know?” after each answer, and listen.
- Praise effort, not only right answers. Mistakes are how we learn.
- Ten to fifteen minutes a day is better than one long session.
Teacher package
1–5. Objectives, prerequisites, materials, preparation, duration
Lesson objectives. Learners will: read a picture graph key; use a scale where one picture means 2; count symbols to find values; draw a picture graph from a table.
Prerequisite knowledge. Lesson 2 and skip counting by 2 and 5.
Materials. Counters (stones, seeds or bottle tops), paper, pencils, board or chalkboard. Low-resource options: use stones, seeds, sticks, bottle tops or drawings in the sand or on the board instead of printed materials.
Preparation. Gather the counters and draw the example pictures on the board before the lesson.
Suggested duration. 45–60 minutes. It can be split into two shorter sessions.
6–9. Teaching procedure, explanation notes, guided and independent activities
Introduction (5 min). Start with the Discover situation and let learners suggest ideas before you teach.
Explanation (10 min). Teach the Understand section with real objects first, then pictures, then symbols and words.
Guided activity (10 min). You need paper and a pencil. Learners follow the Explore steps in pairs.
Independent activity (10 min). Learners complete the independent practice and the worksheet.
Assessment and reflection (5 min). Ask each learner to say one thing they learned and how they know it.
Key questions. What does one symbol mean? How many symbols? What is the total?
Teacher explanation notes. Use the concrete, pictorial, abstract order: real objects first, then pictures, then symbols and words. Return to real objects whenever a learner needs support.
10–12. Differentiation, formative assessment, common misconceptions
Support. Use real objects and work with a partner; say each step aloud together. Extension. Ask learners to make up their own example and explain it to a partner.
Formative assessment. Listen to learner explanations, ask “how do you know?”, and check the independent work.
Misconceptions. Counting each symbol as 1 without reading the key. Multiply by the scale.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 10-mark exam practice scheme, the 10-mark scheme and all answers are in the answer sections above. Re-check every answer and the marking scheme before publication.
16–19. Remediation, enrichment, homework, teacher reflection
Remediation. Practise skip counting by 2s and 5s. Enrichment. Invite learners to find or create three more examples at home or in the classroom and explain them. Homework. See above.
Teacher reflection. After teaching, record: which concepts learners understood; which misconceptions occurred; which activities worked; which learners need more practice; and what to improve next time.
Sources and standards
Alignment is pending verification and no external endorsement is claimed. Reference starting points named in the Courseversity standard: Common Core State Standards for Mathematics, Cambridge Primary and the IB Primary Years Programme. Specific standard codes will be added once checked against the official documents.
Research used to shape this lesson. Common Core 3.MD.B.3 (scaled picture graphs); Cambridge Primary Mathematics Stage 3 (pictograms). These sources informed the lesson; no official alignment is claimed.