You will learn
- Choose a plan.
- Convert units first.
- Solve multistep problems.
- Check reasonableness.
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
- Choose a plan before calculating.
- Convert units first.
- Break the problem into steps.
- Check the answer makes sense.
Words to know
More than one step.
Change units.
Container size.
Makes sense.
1. Discover: a water tank
A tank is 40 by 25 by 20 cm. A jug holds 2 L. How many jugs to fill it?
2. Understand: measurement problems
- Volume: 40 × 25 × 20 = 20,000 cm³ = 20 L.
- 20 L ÷ 2 L = 10 jugs.
- A 6 m by 4 m floor, tiles 50 cm by 50 cm: floor 24 m²; tile 0.25 m²; 24 ÷ 0.25 = 96 tiles.
Idea 1: Tiles
Tiles of 0.25 m² for 24 m²: 24 ÷ 0.25 = 96. Floor 6 by 4: 24 m².
Idea 2: Capacity
5,000 cm³ = 5 L. Jugs of 2.5 L for 20 L: 20 ÷ 2.5 = 8.
Idea 3: Units
A 50 cm square: 0.5 m × 0.5 m = 0.25 m².
Why convert first? All measures must use the same unit.
3. Worked examples
Example 1 (I show you): Tiles
24 m² with 0.25 m² tiles
- 24 ÷ 0.25.
Answer: 96
Example 2 (We do it together): Capacity
5,000 cm³
- ÷ 1,000.
Answer: 5 L
Example 3 (You try): Area
50 cm square in m²
Show the steps and answer
- 0.5 × 0.5.
Answer: 0.25 m²
Did you know?
Mixed units must be converted before multiplying.
Why this matters
Measurement problems appear in building, cooking and science.
4. Explore: solve
You need paper.
- Find the volume.
- Convert to litres.
- Divide by 2 L.
- Check.
Think about it: what did you notice?
10 jugs.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- First I convert ___.
- Then I ___.
- The answer is ___.
- It is reasonable because ___.
Guided practice
Question 1. Volume of the tank?
20,000 cm³.
Question 2. In litres?
20 L.
Question 3. Jugs of 2 L?
10.
Independent practice
Level 1: Start
- Tiles needed: floor 24 m², tile 0.25 m²
- Litres in 5,000 cm³
- Jugs of 2.5 L for 20 L
- Floor 6 by 4 in m²
- Area of a 50 cm square in m²
Level 2: Grow
- 10 L in cm³
- Tiles of 0.5 m² for 6 m²
- Jugs of 2 L for 14 L
Level 3: Stretch
- Tank 50 × 40 × 30 cm in litres
- Carpet for a 6 m by 4.5 m room
- Ben says 20 L needs 50 jugs of 2.5 L. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
A tank holds 20 L. A jug holds 2 L. How many jugs fill it?
Show a sample answer
10.
Another one. A path 12 m by 2 m is covered with 0.5 m² tiles. How many tiles?
Show a sample answer
24 ÷ 0.5 = 48
7. Common mistakes
Fix: Same unit before dividing.
Fix: Convert first.
Fix: Total ÷ size of each.
8. Lesson summary and revision card
- I can choose a plan.
- I can convert units first.
- I can solve multistep problems.
- I can check reasonableness.
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 units first.
- Plan the steps.
- Check sense.
11. Next lesson
Next lesson: Collecting numerical data. 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 floor of 24 m² uses 0.25 m² tiles. How many tiles? [3 marks]
- How many litres are in 5,000 cm³? [2 marks]
- How many 2.5 L jugs fill 20 L? [2 marks]
- Find the area of a 6 m by 4 m floor. [2 marks]
- Ali says a 50 cm square has area 2,500 m². Is he right? Explain. [3 marks]
Total: 12 marks.
Marking guide and model answers
- 24 ÷ 0.25 [1]; 4 tiles per m² [1]; 96 [1]
- 1,000 cm³ = 1 L [1]; 5 L [1]
- 20 ÷ 2.5 [1]; 8 [1]
- 6 × 4 [1]; 24 m² [1]
- No [1]. 50 cm = 0.5 m [1]. 0.5 × 0.5 = 0.25 m² [1].
Score guide: 11 to 12 = secure. 8 to 10 = nearly there, revise the parts you missed. Under 8 = work through the lesson again with a grown-up.
Printable worksheet
- Tiles for 24 m², tile 0.25 m²
- Litres in 5,000 cm³
- Jugs of 2.5 L for 20 L
- Floor 6 by 4 in m²
- 50 cm square in m²
- A 40 × 25 × 20 cm tank holds…
- Jugs of 2 L to fill 20 L:
- Tiles of 0.25 m² for 24 m²:
- 5,000 cm³ =
- A 50 cm square has area…
Homework
Solve two measurement problems from your kitchen.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| Tiles for 24 m², tile 0.25 m² | 96 | 2 |
| Litres in 5,000 cm³ | 5 | 2 |
| Jugs of 2.5 L for 20 L | 8 | 2 |
| Floor 6 by 4 in m² | 24 | 2 |
| 50 cm square in m² | 0.25 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 96; 2 5; 3 8; 4 24; 5 0.25.
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 20 L; 7 10; 8 96; 9 5 L; 10 0.25 m².
Independent practice answers. Level 1: 1 96; 2 5 L; 3 8; 4 24 m²; 5 0.25 m². Level 2: 1 10,000 cm³; 2 12; 3 7. Level 3: 1 60 L; 2 27 m²; 3 20 ÷ 2.5 = 8 jugs..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Choose a plan | 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 Convert units first | 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 Solve multistep problems | 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 Check reasonableness | 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: Not converting units first. Same unit before dividing.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: One-step conversions.
- 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 multistep measurement problems. You do not need to be good at mathematics to help.
- Plan a tiling or painting job.
- Ask: which units do we use?
- Check answers by estimating.
- 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: choose a plan; convert units first; solve multistep problems; check reasonableness.
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. 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 steps? Does it make sense?
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. Not converting units first. Same unit before dividing.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 12-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. One-step conversions. 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.MD.A.1 and 5.MD.C.5; Cambridge Primary Mathematics Stage 5 and 6 (measurement problems). These sources informed the lesson.