You will learn
- Use factoring.
- Use compensation.
- Use halving and doubling.
- Choose a strategy.
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
- Break a factor into easier parts.
- Use compensation: round, then adjust.
- Halve one factor and double the other.
- Choose the easiest strategy.
Words to know
Adjust then fix.
Halve one factor, double the other.
Number multiplied.
A plan.
1. Discover: quick products
How can you find 25 × 36 in your head?
2. Understand: mental strategies
- 25 × 36 = 25 × 4 × 9 = 100 × 9 = 900.
- 99 × 7 = 100 × 7 − 7 = 693.
- 15 × 18 = 10 × 18 + 5 × 18 = 180 + 90 = 270.
- 48 × 5 = half of 480 = 240.
Idea 1: Factoring
25 × 24 = 25 × 4 × 6 = 100 × 6 = 600. 15 × 14 = 150 + 60 = 210.
Idea 2: Compensation
98 × 6 = 100 × 6 − 2 × 6 = 600 − 12 = 588.
Idea 3: Halve and double
64 × 5 = 640 ÷ 2 = 320. 50 × 18 = 100 × 9 = 900.
Why many ways? A good strategy makes the numbers friendly.
3. Worked examples
Example 1 (I show you): Factor
25 × 24
- 24 = 4 × 6.
Answer: 600
Example 2 (We do it together): Compensate
98 × 6
- 100 × 6 − 2 × 6.
Answer: 588
Example 3 (You try): Halve and double
50 × 18
Show the steps and answer
- 100 × 9.
Answer: 900
Did you know?
25 × 4 = 100 is one of the most useful mental facts.
Why this matters
Mental strategies are quick in exams and in daily life.
4. Explore: think
No tools.
- Do 25 × 36 as 25 × 4 × 9.
- Do 99 × 7.
- Do 48 × 5.
- Explain your strategy.
Think about it: what did you notice?
900; 693; 240.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- I change ___ into ___.
- Then I calculate ___.
- I adjust by ___.
- The answer is ___.
Guided practice
Question 1. 25 × 36?
900.
Question 2. 99 × 7?
693.
Question 3. 48 × 5?
240.
Independent practice
Level 1: Start
- 25 × 24
- 98 × 6
- 15 × 14
- 64 × 5
- 50 × 18
Level 2: Grow
- 25 × 12
- 98 × 5
- 16 × 5
Level 3: Stretch
- 25 × 28
- 99 × 13
- Ben says 98 × 6 = 600 − 2 = 598. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
A trader sells 99 bags at 7 each. Total?
Show a sample answer
693.
Another one. Tickets cost 99 each. What do 8 tickets cost?
Show a sample answer
8 × 100 − 8 = 792
7. Common mistakes
Fix: If you used 100, take away the extra.
Fix: Fix the difference times the other factor.
Fix: Halve one and double the other.
8. Lesson summary and revision card
- I can use factoring.
- I can use compensation.
- I can use halving and doubling.
- I can choose a strategy.
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
- Make friendly numbers.
- Adjust afterwards.
- Factor to use 100.
11. Next lesson
Next lesson: Order of operations. 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 25 × 24 using factoring. [2 marks]
- Find 98 × 6 using compensation. [2 marks]
- Find 15 × 14. [2 marks]
- Find 64 × 5 by halving. [2 marks]
- Ali says 99 × 7 = 700 − 1 = 699. Is he right? Explain. [3 marks]
Total: 11 marks.
Marking guide and model answers
- 25 × 4 = 100 [1]; 100 × 6 = 600 [1]
- 600 − 12 [1]; 588 [1]
- 150 + 60 [1]; 210 [1]
- 640 ÷ 2 [1]; 320 [1]
- No [1]. He must subtract 7 [1]. 693 [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
- 25 × 24
- 98 × 6
- 15 × 14
- 64 × 5
- 50 × 18
- 25 × 36 =
- 99 × 7 =
- 48 × 5 =
- 25 × 24 =
- 15 × 14 =
Homework
Do five mental products and check.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 25 × 24 | 600 | 2 |
| 98 × 6 | 588 | 2 |
| 15 × 14 | 210 | 2 |
| 64 × 5 | 320 | 2 |
| 50 × 18 | 900 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 600; 2 588; 3 210; 4 320; 5 900.
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): 6 900; 7 693; 8 240; 9 600; 10 210.
Independent practice answers. Level 1: 1 600; 2 588; 3 210; 4 320; 5 900. Level 2: 1 300; 2 490; 3 80. Level 3: 1 700; 2 1,287; 3 He must subtract 2 × 6 = 12, so 588..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Use factoring | 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 Use compensation | 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 Use halving and doubling | 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 Choose a strategy | 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 to undo the adjustment. If you used 100, take away the extra.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Practise ×10 and ×5.
- 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 learns mental multiplication strategies. You do not need to be good at mathematics to help.
- Try quick tricks when shopping.
- Ask: is there an easier way?
- Practise 25 × 4 = 100.
- 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: use factoring; use compensation; use halving and doubling; choose a strategy.
Prerequisite knowledge. Lessons 1 to 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). No tools. 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. Can I make the numbers friendlier? What do I adjust?
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 to undo the adjustment. If you used 100, take away the extra.
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. Practise ×10 and ×5. 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 » Operations & Algebraic Thinking; 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.5; Cambridge Primary Mathematics Stage 5 (mental strategies). These sources informed the lesson.