You will learn
- Choose a scale.
- Draw bars accurately.
- Read exact values.
- Compare bars.
Version 0.1 · published for early use · expert review pending Standards alignment: pending verification. Not yet reviewed against the Courseversity scorecard.
Student lesson
Words to know
Numbers up the axis.
A labelled line.
Graph of bars.
Step in the scale.
1. Discover: shop sales
A shop sells 20, 35, 15 and 40 loaves Monday to Thursday. What scale would you use?
2. Understand: bar graphs
- The biggest value is 40, so a scale of 0 to 40 in steps of 5 or 10 fits.
- Draw equal-width bars, label both axes and add a title.
- Tuesday minus Wednesday: 35 − 15 = 20.
- Total: 20 + 35 + 15 + 40 = 110.
3. Explore: draw
You need squared paper.
- Choose a scale.
- Draw the bars.
- Label axes.
- Add a title.
Think about it: what did you notice?
A bar graph.
4. Practise
Guided practice
Question 1. Total sales?
110.
Question 2. Tuesday minus Wednesday?
20.
Question 3. Scale for 40?
0 to 40 in fives.
Independent practice
- Thursday minus Monday
- Total
- Highest day
- Lowest day
- Tuesday + Wednesday
Answers are in the answer key below. Try first, then check.
5. Apply: everyday mathematics
Why must a bar graph start at 0?
Show a sample answer
So bar heights compare fairly.
6. Common mistake
Fix: Start at 0.
7. Check and master
Answer all questions. You will see feedback after each one.
Your result appears here after you answer every question.
8. Key takeaways
- Choose a scale.
- Equal bars.
- Label and title.
9. Next lesson
Next lesson: Line graphs. Keep going with the next idea in this course.
Printable worksheet
- Thursday minus Monday
- Total
- Highest day
- Lowest day
- Tuesday + Wednesday
Homework
Draw a bar graph of five numbers with a scale of 10.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| Thursday minus Monday | 20 | 2 |
| Total | 110 | 2 |
| Highest day | Thursday | 2 |
| Lowest day | Wednesday | 2 |
| Tuesday + Wednesday | 50 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 20; 2 110; 3 Thursday; 4 Wednesday; 5 50.
Quiz answers: 1 A, 2 B, 3 C, 4 A, 5 B, challenge C.
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Choose a scale | 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 Draw bars accurately | 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 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 |
| O4 Compare 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 |
Proposed Courseversity thresholds for this page: Bronze = at least 3 of 5 core questions correct; Silver = all 5; Gold = all 5 plus the challenge. A badge is never a full record of progress.
If a learner struggles
- Find the misconception: Starting the scale above 0. Start at 0.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Bar graphs with scale 5.
- 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.
Teacher package
1–5. Objectives, prerequisites, materials, preparation, duration
Lesson objectives. Learners will: choose a scale; draw bars accurately; read exact values; compare bars.
Prerequisite knowledge. Lesson 2.
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. 35–45 minutes.
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. 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.
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. Starting the scale above 0. Start at 0.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 10-mark scheme and all answers are in the answer key above. Re-check every answer and the marking scheme before publication.
16–19. Remediation, enrichment, homework, teacher reflection
Remediation. Bar graphs with scale 5. 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.