You will learn
- Solve money problems.
- Solve measurement problems.
- Compare times and distances.
- 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
- Read the problem and find what is asked.
- Choose add, subtract, multiply or divide.
- Line up decimal points.
- Check the answer makes sense.
Words to know
Number with a point.
All added.
Money back.
How much more.
1. Discover: in real life
Three books cost 2.75 each. You pay 10. How much change? Two runners took 12.8 s and 13.25 s. What is the difference?
2. Understand: decimals in life
- 3 × 2.75 = 8.25; 10 − 8.25 = 1.75.
- 13.25 − 12.8 = 0.45 s.
- A 5 m board cut into 0.8 m pieces gives 5 ÷ 0.8 = 6.25, so 6 full pieces.
Idea 1: Money
4 × 1.25 = 5.00. 20 − 13.45 = 6.55 change.
Idea 2: Total
2.5 + 3.75 + 1.2 = 7.45.
Idea 3: Pieces
Pieces of 0.8 m from 5 m: 5 ÷ 0.8 = 6.25, so 6 full pieces. 100 ÷ 8 = 12.5.
Why 6, not 6.25? Only whole pieces count.
3. Worked examples
Example 1 (I show you): Multiply
4 × 1.25
- 4 × 125 = 500.
Answer: 5
Example 2 (We do it together): Change
20 − 13.45
- 20.00 − 13.45.
Answer: 6.55
Example 3 (You try): Pieces
5 m cut in 0.8 m pieces
Show the steps and answer
- 5 ÷ 0.8 = 6.25.
Answer: 6 full pieces
Did you know?
Real problems often need us to round a decimal answer to a whole.
Why this matters
Decimals are in every shop, race and recipe.
4. Explore: solve
You need paper.
- Multiply 3 × 2.75.
- Subtract from 10.
- Find the difference in times.
- Check.
Think about it: what did you notice?
1.75; 0.45.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- I need to find ___.
- I will ___.
- The answer is ___.
- It makes sense because ___.
Guided practice
Question 1. 3 × 2.75?
8.25.
Question 2. 10 − 8.25?
1.75.
Question 3. 13.25 − 12.8?
0.45.
Independent practice
Level 1: Start
- 4 × 1.25
- 20 − 13.45
- Full 0.8 m pieces from 5 m
- 2.5 + 3.75 + 1.2
- 100 ÷ 8
Level 2: Grow
- 3 × 1.5
- 10 − 7.8
- 6.4 ÷ 4
Level 3: Stretch
- 2 × 3.45 + 1.2
- 50 − 3 × 12.75
- Ana says 2.2 m makes 4.4 pieces of 0.5 m. How many full pieces?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
Runner A takes 12.8 s, runner B 13.25 s. How much longer for B?
Show a sample answer
0.45 s.
Another one. Ben buys 3 notebooks at 2.75 each and pays 10. How much change?
Show a sample answer
3 × 2.75 = 8.25 and 10 − 8.25 = 1.75
7. Common mistakes
Fix: Align the points.
Fix: Think about what the question asks.
Fix: Line up before adding.
8. Lesson summary and revision card
- I can solve money problems.
- I can solve measurement problems.
- I can compare times and distances.
- 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
- Choose the operation.
- Align points.
- Interpret the answer.
11. Next lesson
Next lesson: Meaning of percent. 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.
- Find 4 × 1.25. [2 marks]
- Find the change from 20 for 13.45. [2 marks]
- How many full 0.8 m pieces come from 5 m? [3 marks]
- Find 2.5 + 3.75 + 1.2. [3 marks]
- Ali says 100 ÷ 8 = 1.25. Is he right? Explain. [3 marks]
Total: 13 marks.
Marking guide and model answers
- 4 × 125 = 500 [1]; 5.00 [1]
- 20.00 − 13.45 [1]; 6.55 [1]
- 5 ÷ 0.8 = 6.25 [1]; only whole pieces count [1]; 6 [1]
- Line up decimal points [1]; add [1]; 7.45 [1]
- No [1]. 8 × 1.25 = 10, not 100 [1]. The answer is 12.5 [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
- 4 × 1.25
- 20 − 13.45
- Full 0.8 m pieces from 5 m
- 2.5 + 3.75 + 1.2
- 100 ÷ 8
- 3 × 2.75 =
- 10 − 8.25 =
- 13.25 − 12.8 =
- 4 × 1.25 =
- 2.5 + 3.75 + 1.2 =
Homework
Write a decimal shopping problem and solve it.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 4 × 1.25 | 5 | 2 |
| 20 − 13.45 | 6.55 | 2 |
| Full 0.8 m pieces from 5 m | 6 | 2 |
| 2.5 + 3.75 + 1.2 | 7.45 | 2 |
| 100 ÷ 8 | 12.5 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 5; 2 6.55; 3 6; 4 7.45; 5 12.5.
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 8.25; 7 1.75; 8 0.45; 9 5; 10 7.45.
Independent practice answers. Level 1: 1 5; 2 6.55; 3 6 pieces; 4 7.45; 5 12.5. Level 2: 1 4.5; 2 2.2; 3 1.6. Level 3: 1 8.1; 2 11.75; 3 4 full pieces, because only whole pieces count..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Solve money 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 |
| O2 Solve measurement 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 |
| O3 Compare times and distances | 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: Ignoring the point when subtracting. Align the points.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Decimals in money.
- 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 uses decimals in money and measurement problems. You do not need to be good at mathematics to help.
- Work out change when shopping.
- Ask: what operation does this need?
- Estimate before you calculate.
- 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: solve money problems; solve measurement problems; compare times and distances; check reasonableness.
Prerequisite knowledge. Lessons 5 to 8.
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 is asked? Does the answer 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. Ignoring the point when subtracting. Align the points.
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. Decimals in money. 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 » Number & Operations—Fractions; Grade 5 » Number & Operations in Base Ten. These pages list the standards that cover this topic area; read them alongside the lesson.
Research used to shape this lesson. Common Core 5.NBT.B.7; Cambridge Primary Mathematics Stage 5 (decimal problems). These sources informed the lesson.