You will learn
- Read and plan a measurement problem.
- Add, subtract, multiply or divide measures.
- Change units when needed.
- Write the answer with its unit.
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 and plan the problem.
- Use add, subtract, multiply or divide.
- Change units when needed.
- Write the answer with its unit.
Words to know
What we measure in.
All added together.
The distance around.
Change from one unit to another.
1. Discover: cloth, rice and water
A rope is 3 m 50 cm long. A tailor cuts off 1 m 20 cm. How much rope is left?
2. Understand: measurement problems
Read the problem, find the unit, decide the operation, and write the unit in your answer.
- 3 m 50 cm − 1 m 20 cm = 2 m 30 cm (350 − 120 = 230 cm).
- 3 bags of 2 kg 500 g: 3 × 2,500 g = 7,500 g = 7 kg 500 g.
- 12 L in jugs of 2 L: 12 ÷ 2 = 6 jugs.
- Field 40 m by 25 m: perimeter = 2 × (40 + 25) = 130 m.
- 3 bottles of 500 ml: 1,500 ml = 1 L 500 ml.
Idea 1: Subtract
A rope of 3 m 50 cm has 1 m 20 cm cut off. 350 cm − 120 cm = 230 cm = 2 m 30 cm.
Idea 2: Multiply
3 bags of 2 kg 500 g: 3 × 2,500 g = 7,500 g = 7 kg 500 g.
Idea 3: Divide
12 L in 2 L jugs: 12 ÷ 2 = 6 jugs. A field 40 m by 25 m has perimeter 130 m.
Why write the unit? The number alone does not say what we measured.
3. Worked examples
Example 1 (I show you): Rope
3 m 50 cm minus 1 m 20 cm.
- 350 − 120.
Answer: 2 m 30 cm
Example 2 (We do it together): Bags
3 bags of 2 kg 500 g.
- 3 × 2,500 g.
Answer: 7 kg 500 g
Example 3 (You try): Fence
Field 40 m by 25 m.
Show the steps and answer
- 2 × 40 + 2 × 25.
Answer: 130 m
Did you know?
Measurement problems often need two steps and a change of unit.
Why this matters
We use these steps to buy, build and cook.
4. Explore: problem time
You need paper and a pencil.
- Read the rope problem.
- Change to cm and subtract.
- Change back to m and cm.
- Write the answer.
Think about it: what did you notice?
2 m 30 cm.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- I change ___ to ___.
- Step 1 is ___.
- Step 2 is ___.
- The answer is ___ with the unit ___.
Guided practice
Question 1. 350 cm − 120 cm?
230 cm.
Question 2. 12 L in 2 L jugs?
6 jugs.
Question 3. Field 40 m by 25 m, perimeter?
130 m.
Independent practice
Level 1: Start
- Rope 3 m 50 cm minus 1 m 20 cm
- 3 bags of 2 kg 500 g
- 12 L in 2 L jugs
- Field 40 m by 25 m: perimeter
- 3 bottles of 500 ml
Level 2: Grow
- 5 m − 2 m 30 cm
- 6 packets of 250 g
- 15 L in 3 L jugs
Level 3: Stretch
- Field 50 m by 30 m: perimeter
- 2 L − 650 ml
- Ali adds 3 m 50 cm and 1 m 80 cm and gets 4 m 130 cm. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
A field is 40 m long and 25 m wide. How long is the fence around it?
Show a sample answer
130 m.
Another one. A baker uses 3 bags of 2 kg 500 g flour. Find the total mass.
Show a sample answer
7 kg 500 g
7. Common mistakes
Fix: Write the unit with the number.
Fix: Change to the same unit first.
Fix: Rewrite 130 cm as 1 m 30 cm.
8. Lesson summary and revision card
- I can read and plan a measurement problem.
- I can add, subtract, multiply and divide measures.
- I can change units.
- I can write the answer with its unit.
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
- Same unit first.
- Choose the operation.
- Write the unit.
11. Next lesson
Next lesson: Reading analogue clocks. 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 rope is 3 m 50 cm. 1 m 20 cm is cut off. How much is left? [3 marks]
- 3 bags each have mass 2 kg 500 g. What is the total? [3 marks]
- 12 L is poured into 2 L jugs. How many jugs? [2 marks]
- A field is 40 m by 25 m. How much fence is needed? [2 marks]
- Kofi says 3 bottles of 500 ml hold 1,500 L. Is he right? Explain. [3 marks]
Total: 13 marks.
Marking guide and model answers
- 350 − 120 [1] = 230 cm [1] = 2 m 30 cm [1]
- 3 × 2,500 g [1] = 7,500 g [1] = 7 kg 500 g [1]
- 12 ÷ 2 [1] = 6 jugs [1]
- 2 × 40 + 2 × 25 [1] = 130 m [1]
- No [1]. 3 × 500 = 1,500 ml [1] = 1 L 500 ml [1].
Score guide: 12 to 13 = secure. 8 to 11 = nearly there, revise the parts you missed. Under 8 = work through the lesson again with a grown-up.
Printable worksheet
- 3 m 50 cm − 1 m 20 cm
- 3 × 2 kg 500 g
- 12 L ÷ 2 L
- Perimeter of 40 m by 25 m
- 3 × 500 ml
- Rope 3 m 50 cm minus 1 m 20 cm =
- 3 bags of 2 kg 500 g =
- 12 L in 2 L jugs needs ___ jugs.
- Field 40 m by 25 m: perimeter =
- 3 bottles of 500 ml hold ___.
Homework
Write a measurement problem about a market and solve it.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 3 m 50 cm − 1 m 20 cm | 2 m 30 cm | 2 |
| 3 × 2 kg 500 g | 7 kg 500 g | 2 |
| 12 L ÷ 2 L | 6 | 2 |
| Perimeter of 40 m by 25 m | 130 m | 2 |
| 3 × 500 ml | 1 L 500 ml | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 2 m 30 cm; 2 7 kg 500 g; 3 6; 4 130 m; 5 1 L 500 ml.
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 2 m 30 cm; 7 7 kg 500 g; 8 6; 9 130 m; 10 1 L 500 ml.
Independent practice answers. Level 1: 1 2 m 30 cm; 2 7 kg 500 g; 3 6 jugs; 4 130 m; 5 1 L 500 ml. Level 2: 1 2 m 70 cm; 2 1 kg 500 g; 3 5 jugs. Level 3: 1 160 m; 2 1 L 350 ml; 3 130 cm = 1 m 30 cm, so the answer is 5 m 30 cm..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Read and plan a measurement problem | 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 Add, subtract, multiply or divide measures | 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 Change units when needed | 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 Write the answer with its unit | 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: Forgetting the unit. Write the unit with the number.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Draw a bar for each step.
- 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 solves word problems with lengths, masses and capacities. You do not need to be good at mathematics to help.
- Cook together and measure the ingredients.
- Ask: do the units match?
- Plan the steps before calculating.
- 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 and plan a measurement problem; add, subtract, multiply or divide measures; change units when needed; write the answer with its unit.
Prerequisite knowledge. Lessons 1 to 7.
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 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 units? What are the steps? Is the answer reasonable?
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. Forgetting the unit. Write the unit with the number.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 13-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. Draw a bar for each step. 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.A.2 and 4.MD.A.2; Cambridge Primary Mathematics Stage 3 (measurement problems). These sources informed the lesson.