You will learn
- Review fractions and decimals.
- Review percent and ratio.
- Review algebra and integers.
- Review geometry and data.
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
- Fractions: use a common denominator.
- Integers: use a number line.
- Equations: use inverse operations.
- Percent, area and mean: know the key rules.
Words to know
Quick, accurate recall.
Positive, negative or zero.
Two equal sides.
Rule with letters.
1. Discover: looking ahead
What skills will you use in secondary school mathematics?
2. Understand: readiness review
- Fractions: 2/3 + 1/6 = 5/6.
- Integers: −3 + 5 = 2.
- Equations: 3x = 12, so x = 4.
- Percent: 25% of 80 = 20; area of a 6 by 4 rectangle = 24; mean of 2, 4, 6 is 4.
Idea 1: Number
2/3 + 1/6 = 4/6 + 1/6 = 5/6. −3 + 5 = 2. 25% of 80 = 20.
Idea 2: Algebra
3x = 12, so x = 12 ÷ 3 = 4.
Idea 3: Geometry and data
Area of 6 by 4 = 24. Mean of 2, 4, 6 = 12 ÷ 3 = 4.
Why review? Secondary maths builds on every one of these.
3. Worked examples
Example 1 (I show you): Fractions
2/3 + 1/6
- 4/6 + 1/6.
Answer: 5/6
Example 2 (We do it together): Equation
3x = 12
- Divide by 3.
Answer: x = 4
Example 3 (You try): Area
6 by 4
Show the steps and answer
- 6 × 4.
Answer: 24
Did you know?
Secondary school maths is built on exactly the skills reviewed here.
Why this matters
Fluency now makes secondary maths much easier.
4. Explore: review
You need paper.
- Pick a topic.
- Do a quick question.
- Check.
- Note weak areas.
Think about it: what did you notice?
All topics.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- I use ___ to solve this.
- First ___, then ___.
- The answer is ___.
- I check by ___.
Guided practice
Question 1. 2/3 + 1/6?
5/6.
Question 2. −3 + 5?
2.
Question 3. 3x = 12?
x = 4.
Independent practice
Level 1: Start
- 2/3 + 1/6
- −3 + 5
- 3x = 12
- 25% of 80
- Area of 6 by 4
Level 2: Grow
- 3/4 − 1/2
- −2 + 7
- 4x = 20
Level 3: Stretch
- 10% of 70
- Share 40 in the ratio 2 : 3. Larger share
- Ben says the area of a 6 by 4 rectangle is 20. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
Which skills do you want to practise more?
Show a sample answer
Choose from fractions, algebra, ratio, geometry, data.
Another one. Write one thing you find easy and one you want to practise from this review.
Show a sample answer
Personal answer
7. Common mistakes
Fix: Practise them.
Fix: Show every step.
Fix: Perimeter adds; area multiplies.
8. Lesson summary and revision card
- I can review fractions and decimals.
- I can review percent and ratio.
- I can review algebra and integers.
- I can review geometry and data.
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
- Know your basics.
- Practise weak areas.
- Explain your thinking.
11. Next lesson
You have finished Grade 6 Mathematics. Well done!
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.
- Work out 2/3 + 1/6. [3 marks]
- Work out −3 + 5. [2 marks]
- Solve 3x = 12. [2 marks]
- Find 25% of 80. [2 marks]
- Ali says the area of a 6 by 4 rectangle is 20. Is he right? Explain. [3 marks]
Total: 12 marks.
Marking guide and model answers
- Common denominator 6: 4/6 + 1/6 [1]; add the numerators [1]; 5/6 [1]
- Start at −3 and move right 5 [1]; 2 [1]
- Divide both sides by 3 [1]; x = 4 [1]
- 25% is a quarter [1]; 20 [1]
- No [1]. 20 is the perimeter [1]. Area = 6 × 4 = 24 [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
- 2/3 + 1/6
- −3 + 5
- 3x = 12
- 25% of 80
- Area of 6 by 4
- 2/3 + 1/6
- −3 + 5
- 3x = 12
- 25% of 80
- Area of 6 by 4
Homework
Write a list of three topics to practise before secondary school.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 2/3 + 1/6 | 5/6 | 2 |
| −3 + 5 | 2 | 2 |
| 3x = 12 | 4 | 2 |
| 25% of 80 | 20 | 2 |
| Area of 6 by 4 | 24 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 5/6; 2 2; 3 4; 4 20; 5 24.
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 5/6; 7 2; 8 x = 4; 9 20; 10 24.
Independent practice answers. Level 1: 1 5/6; 2 2; 3 x = 4; 4 20; 5 24. Level 2: 1 1/4; 2 5; 3 x = 5. Level 3: 1 7; 2 24; 3 20 is the perimeter. Area = 6 × 4 = 24..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Review fractions and decimals | 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 Review percent and ratio | 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 Review algebra and integers | 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 Review geometry and data | 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: Skipping topics you find hard. Practise them.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Earlier grades.
- 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 reviews the key skills for secondary mathematics. You do not need to be good at mathematics to help.
- Celebrate how far your child has come.
- Ask them to teach you one idea.
- Practise a little every day.
- 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: review fractions and decimals; review percent and ratio; review algebra and integers; review geometry and data.
Prerequisite knowledge. Grade 6 units.
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 skills are strong? Which need practice?
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. Skipping topics you find hard. Practise them.
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. Earlier grades. 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): Standards for Mathematical Practice. These pages list the standards that cover this topic area; read them alongside the lesson.
Research used to shape this lesson. Common Core Grade 6 review and Grade 7 readiness; Cambridge Primary Mathematics Stage 6 (review). These sources informed the lesson.