You will learn
- Find the most and least.
- Find the total of all bars.
- Find how many more or fewer.
- Explain what the graph shows.
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 most and the least.
- Add the bars to find the total.
- Subtract to find how many more or fewer.
- Say what the graph shows.
Words to know
The biggest number.
The smallest number.
All added together.
How many more or fewer.
1. Discover: what does the graph say?
Look at the fruit graph: mango 6, orange 4, banana 8, pawpaw 2. What can you say about the class?
2. Understand: reading graphs
First read the title and labels. Then answer questions.
- Most: banana (8). Least: pawpaw (2).
- Total: 6 + 4 + 8 + 2 = 20 children.
- Mango and orange together: 6 + 4 = 10.
- How many fewer chose pawpaw than orange: 4 − 2 = 2.
Idea 1: Most and least
In the fruit graph the most popular is banana (8) and the least popular is pawpaw (2). The difference is 8 − 2 = 6.
Idea 2: Total
Add all the bars: 6 + 8 + 4 + 2 = 20 children.
Idea 3: More or fewer
How many fewer chose pawpaw than orange? 4 − 2 = 2.
Why add all the bars? The total tells how many children were asked.
3. Worked examples
Example 1 (I show you): Least
Which fruit is the least popular?
- Find the shortest bar.
Answer: Pawpaw
Example 2 (We do it together): Total
How many children altogether?
- 6 + 8 + 4 + 2.
Answer: 20
Example 3 (You try): Fewer
How many fewer chose pawpaw than orange?
Show the steps and answer
- 4 − 2.
Answer: 2
Did you know?
The graph shows mango 6, banana 8, orange 4 and pawpaw 2.
Why this matters
Reading a graph tells us what people like and how many.
4. Explore: question time
You need the fruit graph.
- Find the most popular fruit.
- Find the total.
- Find mango and orange together.
- Ask your own question for a partner.
Think about it: what did you notice?
Banana is most; total 20; mango + orange = 10.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- The most popular is ___.
- The least popular is ___.
- The total is ___.
- ___ is ___ more than ___.
Guided practice
Question 1. Most popular?
Banana (8).
Question 2. Total children?
6 + 4 + 8 + 2 = 20.
Question 3. Mango + orange?
10.
Independent practice
Level 1: Start
- Least popular fruit
- Total number of children
- How many fewer chose pawpaw than orange?
- Difference between most and least
- Mango + banana
Level 2: Grow
- How many chose orange?
- How many more chose mango than orange?
- Orange + pawpaw = ___.
Level 3: Stretch
- How many children did not choose mango?
- Mango + pawpaw = ___. Is this the same as banana?
- Ana says the most votes is the shortest bar. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
How many children chose banana or pawpaw?
Show a sample answer
10.
Another one. Write two sentences about the fruit graph.
Show a sample answer
For example: Banana is the most popular with 8 votes. Pawpaw is the least with 2.
7. Common mistakes
Fix: Total means all the bars.
Fix: The tallest bar is the most.
Fix: Add every bar.
8. Lesson summary and revision card
- I can find the most and least.
- I can find the total of all bars.
- I can find how many more or fewer.
- I can explain what the graph shows.
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 the title and labels.
- Most, least, total.
- Difference by subtracting.
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.
- Which fruit is the most popular? [1 mark]
- How many children chose mango and orange? [2 marks]
- How many fewer chose pawpaw than banana? [2 marks]
- How many children were asked altogether? [2 marks]
- Ali says mango is the least popular. Is he right? Explain. [3 marks]
Total: 10 marks.
Marking guide and model answers
- Banana [1]
- 6 + 4 [1] = 10 [1]
- 8 − 2 [1] = 6 [1]
- 6 + 8 + 4 + 2 [1] = 20 [1]
- No [1]. Pawpaw has the fewest votes [1]. It has 2, mango has 6 [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
- Least popular fruit
- Total children
- Fewer for pawpaw than orange
- Difference most and least
- Mango + banana
- Which is the most popular fruit?
- Which is the least popular?
- Total number of children?
- Mango + orange = ___.
- Difference between most and least?
Homework
Make up three questions about the fruit graph and answer them.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| Least popular fruit | pawpaw | 2 |
| Total children | 20 | 2 |
| Fewer for pawpaw than orange | 2 | 2 |
| Difference most and least | 6 | 2 |
| Mango + banana | 14 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 pawpaw; 2 20; 3 2; 4 6; 5 14.
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 banana; 7 pawpaw; 8 20; 9 10; 10 6.
Independent practice answers. Level 1: 1 pawpaw; 2 20; 3 2; 4 6; 5 14. Level 2: 1 4; 2 2; 3 6. Level 3: 1 14; 2 8; yes; 3 The tallest bar shows the most..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Find the most and least | 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 the total of all 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 |
| O3 Find how many more or fewer | 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 Explain what the graph shows | 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: Adding only two bars when asked for the total. Total means all the bars.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Use counters for each bar to answer the questions.
- 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 graphs to find the most, the least, the total and the differences. You do not need to be good at mathematics to help.
- Look at charts in newspapers or shops together.
- Ask: which is the most? the least?
- Practise adding the bars.
- 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: find the most and least; find the total of all bars; find how many more or fewer; explain what the graph shows.
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 the fruit 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 is the most? Which is the least? 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. Adding only two bars when asked for the total. Total means all the bars.
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. Use counters for each bar to answer the questions. 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 2.MD.D.10 and 3.MD.B.3 (interpret graphs); Cambridge Primary Mathematics Stage 2 (data). These sources informed the lesson; no official alignment is claimed.