You will learn
- Say when to use a line graph.
- Plot points and join them.
- Read values and trends.
- Find rises and falls.
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
- A line graph shows change over time.
- Plot points in time order and join them.
- A rise is an increase; a fall is a decrease.
- Find the biggest rise by subtracting.
Words to know
Shows change over time.
The pattern of change.
Increase.
Decrease.
1. Discover: temperature
The temperature is 22, 26, 31, 33 and 28 degrees at 6 a.m., 9 a.m., 12, 3 p.m. and 6 p.m. What graph shows change over a day?
2. Understand: line graphs
- A line graph plots points and joins them in order of time.
- 6 a.m. to 12: rise of 31 − 22 = 9°.
- Greatest rise: 6 a.m. to 9 a.m. is 4; 9 to 12 is 5; 12 to 3 is 2.
- 3 p.m. to 6 p.m.: fall of 33 − 28 = 5°.
Idea 1: Read
The temperature is 22, 26, 31, 33 and 28 degrees at 6 a.m., 9 a.m., 12, 3 p.m. and 6 p.m. At 9 a.m. it is 26.
Idea 2: Rise and fall
9 a.m. to 12: 31 − 26 = 5. 3 p.m. to 6 p.m.: 33 − 28 = 5 fall.
Idea 3: Biggest rise
6 to 9 is 4, 9 to 12 is 5, 12 to 3 is 2, so the biggest is 5.
Why a line? The line shows how things change.
3. Worked examples
Example 1 (I show you): Read
Temperature at 9 a.m.
- Second point.
Answer: 26
Example 2 (We do it together): Rise
9 a.m. to 12
- 31 − 26.
Answer: 5
Example 3 (You try): Fall
3 p.m. to 6 p.m.
Show the steps and answer
- 33 − 28.
Answer: 5
Did you know?
Steeper lines mean faster change.
Why this matters
Line graphs show trends in weather, growth and sales.
4. Explore: plot
You need squared paper.
- Plot each point.
- Join in order.
- Find the highest point.
- Find the biggest rise.
Think about it: what did you notice?
Highest 33 at 3 p.m.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- At ___ the value is ___.
- From ___ to ___ it rises / falls by ___.
- The biggest rise is ___.
- The trend is ___.
Guided practice
Question 1. Highest temperature?
33.
Question 2. Rise 6 a.m. to 12?
9.
Question 3. Fall 3 p.m. to 6 p.m.?
5.
Independent practice
Level 1: Start
- Temperature at 9 a.m.
- Rise 9 a.m. to 12
- Fall 3 p.m. to 6 p.m.
- Biggest rise between readings
- Why use a line graph?
Level 2: Grow
- Rise from 22 to 26
- Fall from 33 to 28
- Temperature at 12 (22, 26, 31, 33, 28)
Level 3: Stretch
- Rise from 6 a.m. (22) to 3 p.m. (33)
- Between which readings does the temperature fall?
- Ben says points can be joined in any order. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
Temperature at noon is 31 and at 3 p.m. is 33. What is the change?
Show a sample answer
Rise of 2.
Another one. At noon the temperature is 31 and at 3 p.m. it is 33. What is the change?
Show a sample answer
A rise of 2
7. Common mistakes
Fix: Plot in time order.
Fix: Plot in time order.
Fix: Rise goes up; fall goes down.
8. Lesson summary and revision card
- I can say when to use a line graph.
- I can plot and join points.
- I can read values and trends.
- I can find rises and falls.
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
- Points in time order.
- Read rises and falls.
- Trend.
11. Next lesson
Next lesson: Line plots. 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.
- Temperatures at 6 a.m., 9 a.m., 12, 3 p.m. and 6 p.m. are 22, 26, 31, 33 and 28. What is the temperature at 9 a.m.? [1 mark]
- Find the rise from 9 a.m. (26) to 12 (31). [2 marks]
- Find the fall from 3 p.m. (33) to 6 p.m. (28). [2 marks]
- Find the biggest rise between readings (22, 26, 31, 33). [3 marks]
- Ali says 33 is the lowest temperature. Is he right? Explain. [3 marks]
Total: 11 marks.
Marking guide and model answers
- 26 [1]
- 31 − 26 [1]; 5 [1]
- 33 − 28 [1]; 5 [1]
- 6 to 9 is 4, 9 to 12 is 5, 12 to 3 is 2 [1]; compare [1]; 5 [1]
- No [1]. 33 is the highest point [1]. The lowest is 22 [1].
Score guide: 10 to 11 = secure. 7 to 9 = nearly there, revise the parts you missed. Under 7 = work through the lesson again with a grown-up.
Printable worksheet
- Temperature at 9 a.m.
- Rise 9 a.m. to 12
- Fall 3 p.m. to 6 p.m.
- Highest temperature
- Graph for change over time
- The highest temperature is…
- Rise from 6 a.m. to noon:
- Fall from 3 p.m. to 6 p.m.:
- Line graphs show…
- Biggest rise between readings:
Homework
Record the temperature at four times today and draw a line graph.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| Temperature at 9 a.m. | 26 | 2 |
| Rise 9 a.m. to 12 | 5 | 2 |
| Fall 3 p.m. to 6 p.m. | 5 | 2 |
| Highest temperature | 33 | 2 |
| Graph for change over time | line graph | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 26; 2 5; 3 5; 4 33; 5 line graph.
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 33; 7 9; 8 5; 9 change over time; 10 5.
Independent practice answers. Level 1: 1 26; 2 5; 3 5; 4 5 (from 9 a.m. to 12); 5 to show change over time. Level 2: 1 4; 2 5; 3 31. Level 3: 1 11; 2 3 p.m. to 6 p.m.; 3 Join them in time order..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Say when to use a line 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 Plot points and join them | 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 values and trends | 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 rises and falls | 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: Joining points out of order. Plot in time order.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Bar graphs.
- 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 line graphs. You do not need to be good at mathematics to help.
- Record the temperature each hour.
- Ask: is it rising or falling?
- Plot your height over the years.
- 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: say when to use a line graph; plot points and join them; read values and trends; find rises and falls.
Prerequisite knowledge. Lesson 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. 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 changed? When was the biggest rise?
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. Joining points out of order. Plot in time order.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 11-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. Bar graphs. 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 5 » 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 5.G.A.2 and 5.MD.B.2; Cambridge Primary Mathematics Stage 5 (line graphs). These sources informed the lesson.