You will learn
- Read exact values.
- Find totals and differences.
- Find a fraction of the total.
- Answer questions from a graph.
Version 0.2 · expanded edition · built from cited public sources Content is based on the official frameworks and sources listed under Sources and standards. No official endorsement is claimed. Written in the style of common primary school assessments. No exam result is promised.
Student lesson
- Read exact values from the graph.
- Find totals and differences.
- Write part of the total as a fraction.
- Answer questions using the graph.
Words to know
Explain what data shows.
How much more or less.
All added.
A part out of the whole.
1. Discover: reading a graph
The pet graph shows 100 pupils: dogs 40, cats 30, birds 10, fish 20. What fraction like dogs?
2. Understand: interpreting
- Dogs minus cats: 40 − 30 = 10.
- Dogs and cats together: 70, so 70 of 100 pupils.
- Fraction who like dogs: 40/100 = 2/5.
- Birds are 10/100 = 1/10 of the pupils.
Idea 1: Fractions
Pets: dogs 40, cats 30, fish 20, birds 10, total 100. Cats are 30/100 = 3/10. Dogs are 40/100 = 2/5.
Idea 2: Totals
Dogs + fish = 40 + 20 = 60. Cats − birds = 30 − 10 = 20.
Idea 3: Combined
Birds + fish = 30, which is 30/100 = 3/10. The total is 100.
Why out of 100? The total is the whole.
3. Worked examples
Example 1 (I show you): Fraction
Cats 30 out of 100
- 30/100 simplified.
Answer: 3/10
Example 2 (We do it together): Total
Dogs 40 + fish 20
- 40 + 20.
Answer: 60
Example 3 (You try): Difference
Cats 30 − birds 10
Show the steps and answer
- 30 − 10.
Answer: 20
Did you know?
A fraction of a graph is part ÷ total.
Why this matters
Reading graphs is how we make decisions from data.
4. Explore: ask the graph
You need a bar graph.
- Find the biggest and smallest bars.
- Find a difference.
- Find a total.
- Write a fraction of the total.
Think about it: what did you notice?
40/100 = 2/5.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- The value for ___ is ___.
- The total is ___.
- The fraction is ___/___ = ___.
- The difference is ___.
Guided practice
Question 1. Fraction who like dogs?
2/5.
Question 2. Dogs and cats together?
70.
Question 3. Birds as a fraction?
1/10.
Independent practice
Level 1: Start
- Cats as a fraction of 100
- Dogs + fish
- Cats − birds
- Birds + fish as a fraction
- Total
Level 2: Grow
- Pets (dogs 40, cats 30, fish 20, birds 10): dogs − cats
- Cats + birds
- Fish as a fraction of all pets
Level 3: Stretch
- Dogs + cats + birds
- Pets that are not fish, as a fraction
- Ana says dogs are 4/10 of the pets, so there are 4 dogs. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
Out of 100 pupils, 20 like fish. What fraction is that?
Show a sample answer
1/5.
Another one. Write two sentences comparing dogs and cats on the pets graph.
Show a sample answer
Dogs (40) are 10 more than cats (30). Dogs are 2/5 of all pets and cats are 3/10.
7. Common mistakes
Fix: Follow the label to the bar.
Fix: Total all bars for the whole.
Fix: Divide top and bottom by the greatest common factor.
8. Lesson summary and revision card
- I can read exact values.
- I can find totals and differences.
- I can find a fraction of the total.
- I can answer questions from a graph.
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
- Read exact values.
- Add and subtract.
- Use fractions.
11. Next lesson
Next lesson: Comparing datasets. 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.
- Pets graph: dogs 40, cats 30, fish 20, birds 10. What fraction of the pets are cats? [2 marks]
- Find dogs + fish. [2 marks]
- Find cats − birds. [2 marks]
- What fraction of the pets are birds + fish? [2 marks]
- Ben says the total is 90. Is he right? Explain. [3 marks]
Total: 11 marks.
Marking guide and model answers
- 30/100 [1]; 3/10 [1]
- 40 + 20 [1]; 60 [1]
- 30 − 10 [1]; 20 [1]
- 10 + 20 = 30 [1]; 3/10 [1]
- No [1]. 40 + 30 + 20 + 10 [1]. It is 100 [1].
Score guide: 10 to 11 = secure. 7 to 9 = nearly there, revise the parts you missed. Under 7 = work through the lesson again with a grown-up.
Printable worksheet
- Cats as a fraction
- Dogs + fish
- Cats − birds
- Birds + fish as a fraction
- Total
- Pets: dogs 40, cats 30, fish 20, birds 10. Dogs as a fraction of 100:
- Dogs + cats:
- Cats − birds:
- Birds as a fraction:
- Fish as a fraction:
Homework
Write four questions about a graph and answer them.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| Cats as a fraction | 3/10 | 2 |
| Dogs + fish | 60 | 2 |
| Cats − birds | 20 | 2 |
| Birds + fish as a fraction | 3/10 | 2 |
| Total | 100 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 3/10; 2 60; 3 20; 4 3/10; 5 100.
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 2/5; 7 70; 8 20; 9 1/10; 10 1/5.
Independent practice answers. Level 1: 1 30/100 = 3/10; 2 60; 3 20; 4 30/100 = 3/10; 5 100. Level 2: 1 10; 2 40; 3 1/5. Level 3: 1 80; 2 80/100 = 4/5; 3 4/10 of 100 pets is 40 dogs, not 4..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Read exact 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 |
| O2 Find totals and differences | 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 Find a fraction of the total | 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 Answer questions from a graph | 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 |
Courseversity badge thresholds (overall quiz score): Gold = 90–100%; Silver = 80–89.9%; Bronze = 70–79.9%. A badge is never a full record of progress.
If a learner struggles
- Find the misconception: Reading the wrong bar. Follow the label to the bar.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Read graph values.
- 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 interprets graphs, finds totals and writes fractions of the total. You do not need to be good at mathematics to help.
- Look at graphs in news and ask questions.
- Ask: what is the total?
- Turn parts into fractions.
- 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 exact values; find totals and differences; find a fraction of the total; answer questions from a graph.
Prerequisite knowledge. Lessons 1 to 3.
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 a bar graph. 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 is the whole? What fraction is this part?
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. Reading the wrong bar. Follow the label to the bar.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 11-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. Read graph values. 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
This lesson is based on the sources below, and no official 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. Where a standard code is named, it points to the official framework.
Official standards for this topic area. Common Core State Standards for Mathematics (official site): Grade 4 » Measurement & Data. These pages list the standards that cover this topic area; read them alongside the lesson.
Research used to shape this lesson. Common Core 4.MD.B.4 and 4.NF.B.3; Cambridge Primary Mathematics Stage 4 and 5 (interpreting graphs). These sources informed the lesson.