You will learn
- See repeated addition.
- Multiply numerator by the whole.
- Simplify.
- Use area/array models.
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
- Multiplying by a whole number is repeated addition.
- Multiply the numerator by the whole number.
- Keep the denominator.
- Simplify and write as a mixed number.
Words to know
Answer.
0, 1, 2, 3 …
Adding equal groups.
Top number.
1. Discover: 3 bags
Each bag holds 2/5 kg of rice. How much in 3 bags?
2. Understand: fraction × whole
- 3 × 2/5 = 2/5 + 2/5 + 2/5 = 6/5 = 1 1/5.
- 4 × 3/8 = 12/8 = 1 1/2.
- 6 × 1/3 = 6/3 = 2.
- 5 × 2/3 = 10/3 = 3 1/3.
Idea 1: Repeated addition
2 × 3/4 = 3/4 + 3/4 = 6/4 = 1 1/2.
Idea 2: Numerator only
5 × 1/2 = 5/2 = 2 1/2. 4 × 2/3 = 8/3 = 2 2/3.
Idea 3: Simplify
6 × 5/6 = 30/6 = 5. 3 × 3/10 = 9/10.
Why keep the denominator? The size of the pieces does not change; only how many pieces.
3. Worked examples
Example 1 (I show you): Multiply
2 × 3/4
- 2 × 3 = 6.
Answer: 1 1/2
Example 2 (We do it together): Multiply
4 × 2/3
- 4 × 2 = 8.
Answer: 2 2/3
Example 3 (You try): Multiply
6 × 5/6
Show the steps and answer
- 30/6.
Answer: 5
Did you know?
A whole number times a fraction can give a whole number.
Why this matters
Multiplying fractions by wholes is used in scaling recipes.
4. Explore: multiply
You need paper.
- Write 2/5 three times.
- Add.
- Multiply 3 × 2.
- Simplify.
Think about it: what did you notice?
6/5 = 1 1/5.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- I add ___ copies of ___.
- The numerator becomes ___.
- The denominator stays ___.
- As a mixed number it is ___.
Guided practice
Question 1. 3 × 2/5?
1 1/5.
Question 2. 4 × 3/8?
1 1/2.
Question 3. 6 × 1/3?
2.
Independent practice
Level 1: Start
- 2 × 3/4
- 5 × 1/2
- 4 × 2/3
- 6 × 5/6
- 3 × 3/10
Level 2: Grow
- 3 × 1/5
- 4 × 3/5
- 5 × 2/5
Level 3: Stretch
- 9 × 2/3
- 7 × 3/8
- Ben says 4 × 1/4 = 4/16. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
3 bags hold 2/5 kg each. Total?
Show a sample answer
1 1/5 kg.
Another one. Each glass holds 3/4 L. How much do 5 glasses hold?
Show a sample answer
5 × 3/4 = 15/4 = 3 3/4 L
7. Common mistakes
Fix: Keep the denominator.
Fix: Keep the denominator.
Fix: Change improper fractions to mixed numbers.
8. Lesson summary and revision card
- I can see repeated addition.
- I can multiply the numerator by the whole number.
- I can simplify.
- I can use models.
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
- Repeated addition.
- Multiply the numerator.
- Simplify.
11. Next lesson
Next lesson: Multiplying fractions. 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 2 × 3/4. [3 marks]
- Find 5 × 1/2. [3 marks]
- Find 4 × 2/3. [3 marks]
- Find 6 × 5/6. [2 marks]
- Ali says 3 × 3/10 = 9/30. Is he right? Explain. [3 marks]
Total: 14 marks.
Marking guide and model answers
- 2 × 3 = 6 so 6/4 [1]; simplify [1]; 1 1/2 [1]
- 5 × 1 = 5 [1]; 5/2 [1]; 2 1/2 [1]
- 4 × 2 = 8 [1]; 8/3 [1]; 2 2/3 [1]
- 30/6 [1]; 5 [1]
- No [1]. Only the numerator is multiplied [1]. The answer is 9/10 [1].
Score guide: 12 to 14 = secure. 9 to 11 = nearly there, revise the parts you missed. Under 9 = work through the lesson again with a grown-up.
Printable worksheet
- 2 × 3/4
- 5 × 1/2
- 4 × 2/3
- 6 × 5/6
- 3 × 3/10
- 3 × 2/5 =
- 4 × 3/8 =
- 6 × 1/3 =
- 5 × 2/3 =
- 2 × 3/4 =
Homework
Multiply six whole numbers by fractions.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 2 × 3/4 | 1 1/2 | 2 |
| 5 × 1/2 | 2 1/2 | 2 |
| 4 × 2/3 | 2 2/3 | 2 |
| 6 × 5/6 | 5 | 2 |
| 3 × 3/10 | 9/10 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 1 1/2; 2 2 1/2; 3 2 2/3; 4 5; 5 9/10.
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 1 1/5; 7 1 1/2; 8 2; 9 3 1/3; 10 1 1/2.
Independent practice answers. Level 1: 1 1 1/2; 2 2 1/2; 3 2 2/3; 4 5; 5 9/10. Level 2: 1 3/5; 2 2 2/5; 3 2. Level 3: 1 6; 2 2 5/8; 3 Only the numerator is multiplied: 4/4 = 1..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 See repeated addition | 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 Multiply numerator by the whole | 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 Simplify | 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 Use area/array models | 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: Multiplying the denominator too. Keep the denominator.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Repeated addition of fractions.
- 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 multiplies fractions by whole numbers. You do not need to be good at mathematics to help.
- Double or triple a recipe with fractions.
- Ask: how many copies of the fraction?
- Use fraction strips.
- 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: see repeated addition; multiply numerator by the whole; simplify; use area/array models.
Prerequisite knowledge. Lessons 3 to 5.
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. How many copies? What is the new numerator?
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. Multiplying the denominator too. Keep the denominator.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 14-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. Repeated addition of fractions. 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.NF.B.4 and 5.NF.B.4a; Cambridge Primary Mathematics Stage 5 (fractions times wholes). These sources informed the lesson; no official alignment is claimed.