You will learn
- Recall facts up to 12 × 12.
- Use patterns and doubling.
- Use known facts to find new ones.
- Solve quick fact problems.
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
- Know facts up to 12 × 12.
- Use doubles and patterns.
- Use a known fact to find a new one.
- Division facts come from multiplication facts.
Words to know
A number being multiplied.
The answer to multiplication.
Times 2.
Related multiplication and division facts.
1. Discover: fact fluency
You know 5 × 8 = 40. How could you use it to find 6 × 8?
2. Understand: facts
Use what you know.
- 6 × 8 = 5 × 8 + 8 = 40 + 8 = 48.
- 7 × 8 = 56; 9 × 6 = 54; 12 × 4 = 48.
- Doubling: 8 × 8 = double 4 × 8 = double 32 = 64.
- Fact family: 7 × 8 = 56, 8 × 7 = 56, 56 ÷ 7 = 8, 56 ÷ 8 = 7.
Idea 1: Known facts
7 × 8 = 56. 9 × 6 = 54. 11 × 6 = 66.
Idea 2: Doubling
12 × 4 = double 6 × 4 = double 24 = 48.
Idea 3: Fact family
9 × 8 = 72, so 72 ÷ 9 = 8.
Why learn facts? They make bigger problems quicker.
3. Worked examples
Example 1 (I show you): Fact
7 × 8
- Think 7 × 8 = 56.
Answer: 56
Example 2 (We do it together): Doubling
12 × 4
- 6 × 4 = 24, then double.
Answer: 48
Example 3 (You try): Divide
72 ÷ 9
Show the steps and answer
- 9 × 8 = 72.
Answer: 8
Did you know?
There are only a few facts to learn once you know the pattern.
Why this matters
Strong facts make multiplication and division fast.
4. Explore: fact grid
You need paper.
- Write 5 × 8.
- Add one more 8 to get 6 × 8.
- Double 4 × 8 to get 8 × 8.
- Write the fact family.
Think about it: what did you notice?
40, 48, 64.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- I know ___ × ___ = ___.
- I can double ___ to get ___.
- The fact family is ___.
- The answer is ___.
Guided practice
Question 1. 6 × 8?
48.
Question 2. 8 × 8?
64.
Question 3. 56 ÷ 7?
8.
Independent practice
Level 1: Start
- 7 × 8
- 9 × 6
- 12 × 4
- 11 × 6
- 72 ÷ 9
Level 2: Grow
- 8 × 9
- 7 × 6
- 56 ÷ 8
Level 3: Stretch
- 12 × 9
- 132 ÷ 11
- Kofi says 7 × 8 = 54. Check with 7 × 7 = 49.
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
A box holds 12 eggs. How many in 4 boxes?
Show a sample answer
48.
Another one. A box holds 12 eggs. How many eggs are in 9 boxes?
Show a sample answer
12 × 9 = 108 eggs
7. Common mistakes
Fix: Use a known fact and adjust.
Fix: Use a known fact and add one more group.
Fix: Use the fact family.
8. Lesson summary and revision card
- I can recall facts up to 12 × 12.
- I can use doubling.
- I can use known facts.
- I can solve quick fact problems.
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
- Use known facts.
- Doubling helps.
- Fact families link multiply and divide.
11. Next lesson
Next lesson: Multiplication properties. 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 7 × 8. [1 mark]
- Find 9 × 6. [1 mark]
- Find 12 × 4 using doubles. [2 marks]
- Find 72 ÷ 9 using a fact family. [2 marks]
- Ali says 11 × 6 = 60. Is he right? Explain. [3 marks]
Total: 9 marks.
Marking guide and model answers
- 56 [1]
- 54 [1]
- 6 × 4 = 24 [1]; double = 48 [1]
- 9 × 8 = 72 [1]; 8 [1]
- No [1]. 10 × 6 + 6 [1]. It is 66 [1].
Score guide: 8 to 9 = secure. 6 to 7 = nearly there, revise the parts you missed. Under 6 = work through the lesson again with a grown-up.
Printable worksheet
- 7 × 8
- 9 × 6
- 12 × 4
- 11 × 6
- 72 ÷ 9
- 7 × 8 =
- 9 × 6 =
- 12 × 4 =
- 11 × 6 =
- 72 ÷ 9 =
Homework
Practise your times tables to 12 for ten minutes each day.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 7 × 8 | 56 | 2 |
| 9 × 6 | 54 | 2 |
| 12 × 4 | 48 | 2 |
| 11 × 6 | 66 | 2 |
| 72 ÷ 9 | 8 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 56; 2 54; 3 48; 4 66; 5 8.
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 56; 7 54; 8 48; 9 66; 10 8.
Independent practice answers. Level 1: 1 56; 2 54; 3 48; 4 66; 5 8. Level 2: 1 72; 2 42; 3 7. Level 3: 1 108; 2 12; 3 49 + 7 = 56, so 7 × 8 = 56..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Recall facts up to 12 × 12 | 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 patterns 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 |
| O3 Use known facts to find new ones | 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 Solve quick fact 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 |
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: Mixing 7 × 8 with 6 × 8. Use a known fact and adjust.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Practise skip counting.
- 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 recalls multiplication and division facts up to 12 × 12. You do not need to be good at mathematics to help.
- Practise one fact a day.
- Ask for the fact family.
- Play fact games in the car.
- 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: recall facts up to 12 × 12; use patterns and doubling; use known facts to find new ones; solve quick fact problems.
Prerequisite knowledge. Grade 3 times tables.
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. Which fact do I know? Can I double it?
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. Mixing 7 × 8 with 6 × 8. Use a known fact and adjust.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 9-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 skip counting. 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 3.OA.C.7 and 4.OA.A.1 (fluency with facts); Cambridge Primary Mathematics Stage 4 (multiplication tables). These sources informed the lesson; no official alignment is claimed.