Learning objectives
- Recognise, explain, and apply “Integers”.
- Recognise, explain, and apply “Fractions”.
- Recognise, explain, and apply “Decimals”.
- Recognise, explain, and apply “Percentages”.
- Recognise, explain, and apply “Ratio and proportion”.
IGCSE Year 10 / Mathematics / Curriculum
Number
Number: structured theory, worked examples, answered practice, and a mastery checklist for IGCSE Year 10.
CHAPTER PLAN
Learn, practise, and check your progress
Follow the steps in order or jump directly to the part you need.
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completed
Estimated active study time
209 minutes
1. Understand
Objectives, key ideas, and structured theory.
Open →2. Follow the method
Worked examples that explain every step.
Open →3. Practise
Graded tasks with hints and answer guidance.
Open →4. Consolidate
Assignments from core work to challenge.
Open →5. Check
A timed, marked test with solution guidance.
Open →
Progress is stored only in this browser and does not require AI credits.
Key ideas and checks
- I can convert safely between number forms.
- I can explain why the chosen operation is appropriate.
- Every solution or explanation for “Number” should include a method, justification, and final check.
Unit
Core theory
The essential chapter ideas in a clear sequence before practice.
Represent before calculating
Write the number in a useful form, check sign and place value, and only then choose the operation. A clear representation reduces mechanical errors.
Equivalent forms
Fractions, decimals, percentages, ratios, and powers can describe the same quantity. Changing form is a solving tool, not a separate trick.
Reasonableness check
Estimate before and after the exact calculation. The sign, order of magnitude, and unit must agree with the problem context.
Integers
Use a suitable representation, state the rule, and keep every numerical or algebraic step equivalent. Finish with estimation, an inverse operation, or substitution as a check.
Fractions
Use a suitable representation, state the rule, and keep every numerical or algebraic step equivalent. Finish with estimation, an inverse operation, or substitution as a check.
Decimals
Use a suitable representation, state the rule, and keep every numerical or algebraic step equivalent. Finish with estimation, an inverse operation, or substitution as a check.
Percentages
Use a suitable representation, state the rule, and keep every numerical or algebraic step equivalent. Finish with estimation, an inverse operation, or substitution as a check.
Ratio and proportion
Use a suitable representation, state the rule, and keep every numerical or algebraic step equivalent. Finish with estimation, an inverse operation, or substitution as a check.
Mathematics
Worked examples
Follow the method step by step and check why every step is valid.
Worked number example
Calculate and simplify 5/15 + 3/15.
- 1The denominators are equal, so add the numerators.
- 2Write (5 + 3)/15.
- 3Simplify by a common factor and check that the value is reasonable.
8/15
Reasoning example
Before calculating, explain the key idea from “Integers” and which conditions must be checked.
- 1Define the idea in one clear sentence.
- 2Connect it to a representation, law, or formula.
- 3State a restriction, unit, or final check that makes the solution valid.
The answer should show not only which rule is used for “Integers”, but also why it is valid here.
Number
Practice with answers
Eight graded tasks from core fluency to exam-style application. Work independently before opening a hint or answer.
Core fluency4 minutes
Calculate 8 + 2 × 10 and justify the order of operations.
Hint
Multiplication precedes addition.
Answer guide
8 + 2 · 10 = 28.
Core fluency5 minutes
Find 4/16 of 64.
Hint
Multiply by the fraction and simplify first.
Answer guide
4/16 · 64 = 16.
Application6 minutes
Increase 420 by 35%.
Hint
Use multiplier 1 + 35/100.
Answer guide
420 · 1.35 = 567.0.
Application7 minutes
Divide 72 in the ratio 3:3.
Hint
There are 6 ratio parts.
Answer guide
72 : 6 = 12; 36 and 36.
Reasoning8 minutes
Compare 6/11 and 5/30 using a common denominator or decimals.
Hint
Use cross-products.
Answer guide
6 · 30 = 180, 5 · 11 = 55; 6/11 > 5/30.
Reasoning9 minutes
Write 1800000 in standard form.
Hint
The first factor must be at least 1 and less than 10.
Answer guide
1800000 = 1.8 × 10^6.
Exam style10 minutes
Estimate 490 ÷ 39.6, then calculate to one decimal place.
Hint
Round to compatible numbers before calculating exactly.
Answer guide
Estimate ≈ 500 ÷ 40 = 12.5. Exact ≈ 12.4.
Exam style12 minutes
Test the claim 8² + 6² = 14² and explain.
Hint
Calculate both sides separately.
Answer guide
64 + 36 = 100, while 14² = 196; false.
Common mistakes
- Dropping brackets or using the wrong order of operations.
- Converting a fraction or percentage without checking equivalence.
- Answering without an estimate, unit, or sign check.
Mastery check
- I can convert safely between number forms.
- I can explain why the chosen operation is appropriate.
- I check the result with estimation or an inverse operation.
Number
Chapter homework
Six distinct assignments from core fluency to challenge, each with an estimated time, hint, and answer guide.
Core8 minutes
Homework 1: Calculate 4 + 3 × 7 and justify the order of operations.
Hint
Multiplication precedes addition.
Answer guide
4 + 3 · 7 = 25.
Core10 minutes
Homework 2: Find 7/35 of 175.
Hint
Multiply by the fraction and simplify first.
Answer guide
7/35 · 175 = 35.
Stretch12 minutes
Homework 3: Increase 60 by 15%.
Hint
Use multiplier 1 + 15/100.
Answer guide
60 · 1.15 = 69.0.
Stretch15 minutes
Homework 4: Divide 120 in the ratio 6:4.
Hint
There are 10 ratio parts.
Answer guide
120 : 10 = 12; 72 and 48.
Challenge18 minutes
Homework 5: Compare 9/15 and 6/54 using a common denominator or decimals.
Hint
Use cross-products.
Answer guide
9 · 54 = 486, 6 · 15 = 90; 9/15 > 6/54.
Challenge20 minutes
Homework 6: Write 1500000 in standard form.
Hint
The first factor must be at least 1 and less than 10.
Answer guide
1500000 = 1.5 × 10^6.
50 minutes / 40 marks
Full chapter test
A timed, full-mark self-assessment with model-answer guidance.
Start the timer when ready, work without notes, show every step, and open model answers only after finishing.
1. Calculate 9 + 3 × 12 and justify the order of operations.
2 marksAnswer guide
9 + 3 · 12 = 45.
2. Find 5/25 of 125.
3 marksAnswer guide
5/25 · 125 = 25.
3. Increase 160 by 40%.
3 marksAnswer guide
160 · 1.40 = 224.0.
4. Divide 96 in the ratio 4:4.
4 marksAnswer guide
96 : 8 = 12; 48 and 48.
5. Compare 7/13 and 6/42 using a common denominator or decimals.
4 marksAnswer guide
7 · 42 = 294, 6 · 13 = 78; 7/13 > 6/42.
6. Write 900000 in standard form.
4 marksAnswer guide
900000 = 0.9 × 10^6.
7. Estimate 588 ÷ 49.5, then calculate to one decimal place.
5 marksAnswer guide
Estimate ≈ 600 ÷ 50 = 12.0. Exact ≈ 11.9.
8. Test the claim 9² + 2² = 11² and explain.
5 marksAnswer guide
81 + 4 = 85, while 11² = 121; false.
9. Create and solve a two-step exam-style problem about “Bounds introduction” using 5, 4, and 20.
5 marksAnswer guide
A valid response uses the data in two justified steps and includes an independent check; for example 5 × 4 = 20, then 20 + 9 = 29.
10. Write a revision rule for “Money problems”, one example, and one counterexample.
5 marksAnswer guide
Full response: an accurate rule for “Money problems”, a numerical example that satisfies it, and an explained counterexample.
Unit
Official sources and verification
Curriculum reference sources. Always confirm the teaching sequence with the school and tutor.
Mathematics
Start from the board specification and work topic by topic before full papers.
What this chapter covers
The structure follows the official textbook layout and is used to organise study.
Integers
Fractions
Decimals
Percentages
Ratio and proportion
Indices
Standard form
Estimation
Bounds introduction
Money problems
Percentage increase/decrease
Where to focus
The areas that usually create mistakes or need extra revision.
I can convert safely between number forms.
I can explain why the chosen operation is appropriate.
I check the result with estimation or an inverse operation.
Sources, daily material, and resources
Where to start: textbook, daily material, PDFs, videos, and worked examples.
Start from the official textbook or specification referenced on the subject page.
Use the notes and examples as support, not as a replacement for the official syllabus.
Check the current syllabus version before exam preparation.
Practice by subtopic
Targeted practice before full tests so coverage is clear.
Calculate 8 + 2 × 10 and justify the order of operations.
Find 4/16 of 64.
Increase 420 by 35%.
Divide 72 in the ratio 3:3.
Compare 6/11 and 5/30 using a common denominator or decimals.
Write 1800000 in standard form.
Estimate 490 ÷ 39.6, then calculate to one decimal place.
Test the claim 8² + 6² = 14² and explain.
Mocks and progress checks
How to measure progress in this chapter and when it enters a cumulative mock.
Start with untimed practice by subtopic.
Move to a short timed checkpoint only after completing the mastery checklist.
Record each error with the correct method and revisit it after 48 hours.
Next step
What to do after finishing the chapter and how it connects to the next unit.
Complete the practice without support.
Explain the core method aloud in under two minutes.
Continue to the next chapter or request targeted tutor support.
Note: for the official examinable syllabus of each school year, always confirm with the school, tutor, and current Ministry/IEP announcements.