You will learn
- Put data on a number line.
- Use × marks for each data value.
- Read the most common value.
- Find the range.
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
- A line plot shows data on a number line.
- Put one × above the value for each data point.
- The most common value has the most × marks.
- Range = greatest − least.
Words to know
Marks above a number line.
Greatest minus least.
Value that appears most.
One measurement.
1. Discover: pencil lengths
Eight pencils measure 5, 6, 6, 7, 7, 7, 8 and 9 cm. How could you show them on one line?
2. Understand: line plots
A line plot puts a × above the number line for each value.
- 5: one ×. 6: two. 7: three. 8: one. 9: one.
- Most common length: 7 cm.
- Range = 9 − 5 = 4 cm.
- Total pencils: 1 + 2 + 3 + 1 + 1 = 8.
Idea 1: Reading
Pencil lengths: 5 cm ×1, 6 cm ×2, 7 cm ×3, 8 cm ×1, 9 cm ×1. The most common length is 7 cm. There are 1 + 2 + 3 + 1 + 1 = 8 pencils.
Idea 2: Range
Range = 9 − 5 = 4 cm. Range of 3, 5, 9 is 9 − 3 = 6.
Idea 3: Longer than
Pencils longer than 7 cm: 1 + 1 = 2. The least length is 5 cm.
Why a line plot? We can see how data spreads.
3. Worked examples
Example 1 (I show you): Count
7 cm pencils (×3)
- Count the × marks.
Answer: 3
Example 2 (We do it together): Range
3, 5, 9
- 9 − 3.
Answer: 6
Example 3 (You try): Total
1 + 2 + 3 + 1 + 1
Show the steps and answer
- Add the × marks.
Answer: 8
Did you know?
Each × stands for exactly one measurement.
Why this matters
Line plots show the shape of data on a number line.
4. Explore: plot
You need a ruler and pencils.
- Measure 8 objects.
- Draw a number line.
- Mark × for each.
- Find the range.
Think about it: what did you notice?
Range = greatest − least.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- The most common value is ___.
- There are ___ data values.
- The range is ___ − ___ = ___.
- The least value is ___.
Guided practice
Question 1. Most common length?
7 cm.
Question 2. Range?
4 cm.
Question 3. How many pencils?
8.
Independent practice
Level 1: Start
- Count of 7 cm pencils
- Count of 5 cm pencils
- Range of 3, 5, 9
- Total of 1+2+3+1+1
- Least length
Level 2: Grow
- Range of 1, 1, 2, 4
- Most common value in 6, 6, 6, 9
- A plot has 2 × at 2 and 1 × at 3. How many data values?
Level 3: Stretch
- Range of 12, 15, 15, 18, 20
- Most common value in 12, 15, 15, 18, 20
- Ana says the range of 5, 5, 5 is 5. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
Lengths are 5, 6, 6, 7, 7, 7, 8, 9. How many are longer than 7?
Show a sample answer
2.
Another one. Describe how to make a line plot for 2, 3, 3, 5, 5, 5.
Show a sample answer
Draw a number line from 2 to 5. Put 1 × above 2, 2 × above 3, none above 4 and 3 × above 5.
7. Common mistakes
Fix: Mark every value.
Fix: Range = greatest − least.
Fix: One × for each data value.
8. Lesson summary and revision card
- I can put data on a number line.
- I can use × marks.
- I can read the most common value.
- I can find the range.
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
- × for each value.
- Range = max − min.
- Most common = tallest stack.
11. Next lesson
Next lesson: 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.
- Pencil lengths: 5 cm ×1, 6 cm ×2, 7 cm ×3, 8 cm ×1, 9 cm ×1. How many 7 cm pencils? [1 mark]
- Using the same pencils, how many 5 cm pencils? [1 mark]
- Find the range of 3, 5, 9. [2 marks]
- How many pencils are there in all (5 cm ×1, 6 cm ×2, 7 cm ×3, 8 cm ×1, 9 cm ×1)? [2 marks]
- Kofi says the range of the pencils (5 to 9 cm) is 9 cm. Is he right? Explain. [3 marks]
Total: 9 marks.
Marking guide and model answers
- 3 [1]
- 1 [1]
- 9 − 3 [1]; 6 [1]
- 1 + 2 + 3 + 1 + 1 [1]; 8 [1]
- No [1]. Range = greatest − least = 9 − 5 [1]. It is 4 cm [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
- Count of 7 cm pencils
- Count of 5 cm pencils
- Range of 3, 5, 9
- Total × marks
- Least length
- Pencils: 5 cm ×1, 6 cm ×2, 7 cm ×3, 8 cm ×1, 9 cm ×1. The most common length is
- The range is
- How many pencils?
- Range of 3, 5, 9:
- Pencils longer than 7 cm:
Homework
Measure the lengths of ten leaves and make a line plot.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| Count of 7 cm pencils | 3 | 2 |
| Count of 5 cm pencils | 1 | 2 |
| Range of 3, 5, 9 | 6 | 2 |
| Total × marks | 8 | 2 |
| Least length | 5 cm | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 3; 2 1; 3 6; 4 8; 5 5 cm.
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 7 cm; 7 4 cm; 8 8; 9 6; 10 2.
Independent practice answers. Level 1: 1 3; 2 1; 3 6; 4 8; 5 5 cm. Level 2: 1 3; 2 6; 3 3. Level 3: 1 8; 2 15; 3 Range = greatest − least = 5 − 5 = 0..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Put data on a number line | 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 Use × marks for each data value | 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 the most common value | 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 Find the range | 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: Leaving a value out. Mark every value.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Plot five whole 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 makes and reads line plots and finds the range. You do not need to be good at mathematics to help.
- Measure shoes or leaves and make a line plot.
- Ask: which value is most common?
- Find the biggest and smallest.
- 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: put data on a number line; use × marks for each data value; read the most common value; find the range.
Prerequisite knowledge. Lessons 1 and 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. 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 ruler and pencils. 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 does each × stand for? What is the range?
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. Leaving a value out. Mark every value.
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. Plot five whole 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 4.MD.B.4 (line plots); Cambridge Primary Mathematics Stage 4 (data representation). These sources informed the lesson; no official alignment is claimed.