You will learn
- Read the scale on a bar graph.
- Read a bar between two scale lines.
- Draw bars for given data.
- Give a graph a title and labels.
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 the scale on a bar graph.
- A bar can end between two scale lines.
- Draw bars for given data.
- Give a graph a title and labels.
Words to know
A graph that uses bars.
The numbers up the side.
The line with labels.
The name of the graph.
1. Discover: books read
Four pupils read many books in a week. Numbers like 10, 15 and 20 are large. How can a bar graph with a scale show them neatly?
2. Understand: scaled bar graphs
A bar graph uses bars. The scale shows the value of each step up the side, for example 0, 5, 10, 15, 20.
- Monday bar reaches 10.
- Tuesday bar reaches 15, halfway between 10 and 20.
- Wednesday bar reaches 5.
- Thursday bar reaches 20.
When drawing, give the graph a title, label both axes and keep bars the same width.
Idea 1: Scale
The scale is the numbers up the side. A bar that reaches the 10 line shows 10. A bar at the 5 line shows 5.
Idea 2: Between lines
A bar halfway between 10 and 20 is 15. Halfway between 20 and 30 is 25.
Idea 3: Title and labels
A graph needs a title and labels so that readers know what it shows.
Why halfway? Not every bar ends on a line.
3. Worked examples
Example 1 (I show you): Halfway
Halfway between 20 and 30?
- (20 + 30) ÷ 2.
Answer: 25
Example 2 (We do it together): Scale
0, 5, 10, 15, next?
- Step of 5.
Answer: 20
Example 3 (You try): Title
What goes at the top of a graph?
Show the steps and answer
- It names the graph.
Answer: title
Did you know?
The scale of a bar graph can go up in 2s, 5s, 10s or 100s.
Why this matters
The scale tells us how to read every bar.
4. Explore: read the bars
You need squared paper and a pencil.
- Draw an axis with scale 0, 5, 10, 15, 20.
- Draw bars for 10, 15, 5 and 20.
- Label each bar.
- Give the graph a title.
Think about it: what did you notice?
Bars are different heights but the same width.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- The scale goes up in ___.
- The bar reaches ___.
- It is halfway between ___ and ___.
- The title is ___.
Guided practice
Question 1. A bar halfway between 10 and 20?
15.
Question 2. The bar for Thursday is at?
20.
Question 3. What does the scale show?
The value of each step.
Independent practice
Level 1: Start
- Bar at the 10 line
- Bar halfway between 0 and 10
- Bar halfway between 20 and 30
- Scale of 0, 5, 10: next number?
- What goes at the top of a graph?
Level 2: Grow
- A bar at the 15 line
- A bar halfway between 10 and 20
- Scale 0, 2, 4, 6. Next number?
Level 3: Stretch
- Scale 0, 20, 40, 60. A bar halfway between 20 and 40
- Bars read 25 and 40. The difference?
- Ben says a bar halfway between 20 and 30 is 50. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
A bar reaches the line marked 25. How many books?
Show a sample answer
25 books.
Another one. Draw a bar graph with scale 0 to 20 in steps of 5 for cats 10, dogs 15 and birds 5. Give it a title.
Show a sample answer
bars at 10, 15 and 5 with a title such as Pets in our class
7. Common mistakes
Fix: Look straight across from the top.
Fix: Check the scale.
Fix: Every graph needs a title.
8. Lesson summary and revision card
- I can read the scale on a bar graph.
- I can read a bar between two lines.
- I can draw bars for given data.
- I can give a graph a title and labels.
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 scale.
- Bars have equal width.
- Add a title and labels.
11. Next lesson
Next lesson: Reading and interpreting 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.
- A bar halfway between 10 and 20. What is its value? [1 mark]
- A bar halfway between 20 and 30. What is its value? [1 mark]
- Scale 0, 5, 10, 15. What comes next? [1 mark]
- What should a graph have at the top? [1 mark]
- Ali says the scale shows the title. Is he right? Explain. [3 marks]
Total: 7 marks.
Marking guide and model answers
- 15 [1]
- 25 [1]
- 20 [1]
- A title [1]
- No [1]. The scale shows the numbers [1]. The title names the graph [1].
Score guide: 6 to 7 = secure. 5 to 5 = nearly there, revise the parts you missed. Under 5 = work through the lesson again with a grown-up.
Printable worksheet
- Bar at the 10 line
- Halfway between 0 and 10
- Halfway between 20 and 30
- Scale 0, 5, 10: next
- Name at top of a graph
- The scale shows the value of each ___.
- Halfway between 10 and 20 is ___.
- A bar at the 5 line shows ___.
- Scale 0, 5, 10, 15, next: ___
- Halfway between 20 and 30 is ___.
Homework
Draw a bar graph of five numbers with a scale of 5.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| Bar at the 10 line | 10 | 2 |
| Halfway between 0 and 10 | 5 | 2 |
| Halfway between 20 and 30 | 25 | 2 |
| Scale 0, 5, 10: next | 15 | 2 |
| Name at top of a graph | title | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 10; 2 5; 3 25; 4 15; 5 title.
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 step; 7 15; 8 5; 9 20; 10 25.
Independent practice answers. Level 1: 1 10; 2 5; 3 25; 4 15; 5 the title. Level 2: 1 15; 2 15; 3 8. Level 3: 1 30; 2 15; 3 He added. Halfway is 25..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Read the scale on a bar 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 |
| O2 Read a bar between two scale lines | 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 Draw bars for given data | 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 Give a graph a title and labels | 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 bar at the wrong line. Look straight across from the top.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Practise counting in 5s and 10s up a number line.
- 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 bar graphs with a scale. You do not need to be good at mathematics to help.
- Draw a bar graph from your family’s data.
- Ask: what is the scale?
- Use squared paper.
- 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 scale on a bar graph; read a bar between two scale lines; draw bars for given data; give a graph a title and labels.
Prerequisite knowledge. Lessons 2 and 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 squared 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 is the scale? Where does the bar end? What is the value?
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 bar at the wrong line. Look straight across from the top.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 7-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 counting in 5s and 10s up a number line. 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 3 » 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 3.MD.B.3 (scaled bar graphs); Cambridge Primary Mathematics Stage 3 (bar charts). These sources informed the lesson.