You will learn
- Read the highest and lowest bars.
- Find totals from a graph.
- Find differences between bars.
- Answer questions about a graph.
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
- Find the highest and lowest bars.
- Add bars to find totals.
- Subtract bars to find differences.
- Answer questions about a graph.
Words to know
Explain what data shows.
How much more or less.
The greatest amount.
The smallest amount.
1. Discover: what does it say?
A graph shows books read on four days: 10, 15, 5 and 20. What can we find out just by looking at it?
2. Understand: interpreting graphs
To interpret a graph, read the values and ask questions.
- Most books: Thursday, 20. Fewest: Wednesday, 5.
- Difference between Thursday and Wednesday: 20 − 5 = 15.
- Total: 10 + 15 + 5 + 20 = 50.
- Tuesday and Thursday together: 15 + 20 = 35.
Read the title, labels and scale before answering.
Idea 1: Most and fewest
Books: Monday 10, Tuesday 15, Wednesday 5, Thursday 20. Most on Thursday, fewest on Wednesday.
Idea 2: Total
10 + 15 + 5 + 20 = 50 books. Tuesday plus Thursday: 15 + 20 = 35.
Idea 3: Difference
Thursday minus Wednesday: 20 − 5 = 15.
Why interpret? Graphs are only useful if we can explain what they show.
3. Worked examples
Example 1 (I show you): Most
Which day had the most?
- Tallest bar.
Answer: Thursday
Example 2 (We do it together): Total
Total for four days?
- 10 + 15 + 5 + 20.
Answer: 50
Example 3 (You try): Difference
Thursday minus Wednesday?
Show the steps and answer
- 20 − 5.
Answer: 15
Did you know?
Interpret means explain what something shows.
Why this matters
Reading graphs is a life skill.
4. Explore: ask the graph
You need a bar graph.
- Read the title.
- Find the highest and lowest bars.
- Find the total.
- Find one difference.
Think about it: what did you notice?
Total 50; difference 15.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- The most is on ___.
- The fewest is on ___.
- The total is ___.
- ___ is ___ more than ___.
Guided practice
Question 1. Most books were read on?
Thursday.
Question 2. Fewest on?
Wednesday.
Question 3. Total for four days?
50.
Independent practice
Level 1: Start
- Thursday minus Wednesday
- Tuesday plus Thursday
- Total of 10, 15, 5, 20
- Monday minus Wednesday
- Which day had 15?
Level 2: Grow
- Which day had 5 books?
- Monday plus Tuesday
- Total for the four days
Level 3: Stretch
- Tuesday minus Wednesday
- Which days had more than 12 books?
- Ana says Thursday had the fewest because it is the tallest bar. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
Tuesday 15 books and Monday 10. How many more on Tuesday?
Show a sample answer
5 more.
Another one. Write two sentences about the books graph.
Show a sample answer
for example Thursday had the most books with 20. Wednesday had the fewest with 5.
7. Common mistakes
Fix: Follow the label down to the bar.
Fix: The tallest bar is the most.
Fix: Add every bar.
8. Lesson summary and revision card
- I can read the highest and lowest bars.
- I can find totals from a graph.
- I can find differences between bars.
- I can answer questions about 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 title and scale first.
- Add for totals.
- Subtract for differences.
11. Next lesson
Next lesson: Comparing data. 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.
- On which day were the most books? [1 mark]
- On which day were the fewest books? [1 mark]
- Find Thursday minus Wednesday. [2 marks]
- Find the total for the four days. [2 marks]
- Kofi says Tuesday plus Thursday is 30. Is he right? Explain. [3 marks]
Total: 9 marks.
Marking guide and model answers
- Thursday [1]
- Wednesday [1]
- 20 − 5 [1] = 15 [1]
- 10 + 15 + 5 + 20 [1] = 50 [1]
- No [1]. 15 + 20 [1] = 35 [1].
Score guide: 8 to 9 = secure. 6 to 7 = nearly there, revise the parts you missed. Under 6 = work through the lesson again with a grown-up.
Printable worksheet
- Thursday minus Wednesday
- Tuesday plus Thursday
- Total of 10, 15, 5, 20
- Monday minus Wednesday
- Day with 15 books
- Books: Mon 10, Tue 15, Wed 5, Thu 20. Most on ___.
- Fewest on ___.
- Thursday minus Wednesday =
- Total for four days =
- Tuesday plus Thursday =
Homework
Find a graph in a newspaper and write three questions about it.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| Thursday minus Wednesday | 15 | 2 |
| Tuesday plus Thursday | 35 | 2 |
| Total of 10, 15, 5, 20 | 50 | 2 |
| Monday minus Wednesday | 5 | 2 |
| Day with 15 books | Tuesday | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 15; 2 35; 3 50; 4 5; 5 Tuesday.
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 Thursday; 7 Wednesday; 8 15; 9 50; 10 35.
Independent practice answers. Level 1: 1 15; 2 35; 3 50; 4 5; 5 Tuesday. Level 2: 1 Wednesday; 2 25; 3 50. Level 3: 1 10; 2 Tuesday and Thursday; 3 The tallest bar shows the most..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Read the highest and lowest bars | 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 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 |
| O3 Find differences between bars | 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 about 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 |
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: Reading the wrong bar. Follow the label down to the bar.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Practise adding and subtracting 2-digit numbers.
- 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 answers questions about graphs. You do not need to be good at mathematics to help.
- Find a graph in a newspaper and discuss it.
- Ask: which is the most? the fewest?
- Make up questions about a graph.
- 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 the highest and lowest bars; find totals from a graph; find differences between bars; answer questions about a graph.
Prerequisite knowledge. Lesson 4.
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. Which bar? What is its value? Do I add or subtract?
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 down to the bar.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 9-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 adding and subtracting 2-digit numbers. 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 (solve problems using graphs); Cambridge Primary Mathematics Stage 3 (reading charts). These sources informed the lesson; no official alignment is claimed.