Цели обучения
- 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.
Ключевые идеи и проверки
- 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.
Раздел
Основная теория
Ключевые идеи главы в понятной последовательности перед практикой.
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
Разобранные примеры
Следуйте методу шаг за шагом и проверяйте обоснование каждого шага.
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
Практика с ответами
Восемь заданий от базовых навыков до экзаменационного уровня. Сначала решите самостоятельно.
Базовый навык4 минут
Calculate 8 + 2 × 10 and justify the order of operations.
Подсказка
Multiplication precedes addition.
Ответ
8 + 2 · 10 = 28.
Базовый навык5 минут
Find 4/16 of 64.
Подсказка
Multiply by the fraction and simplify first.
Ответ
4/16 · 64 = 16.
Применение6 минут
Increase 420 by 35%.
Подсказка
Use multiplier 1 + 35/100.
Ответ
420 · 1.35 = 567.0.
Применение7 минут
Divide 72 in the ratio 3:3.
Подсказка
There are 6 ratio parts.
Ответ
72 : 6 = 12; 36 and 36.
Обоснование8 минут
Compare 6/11 and 5/30 using a common denominator or decimals.
Подсказка
Use cross-products.
Ответ
6 · 30 = 180, 5 · 11 = 55; 6/11 > 5/30.
Обоснование9 минут
Write 1800000 in standard form.
Подсказка
The first factor must be at least 1 and less than 10.
Ответ
1800000 = 1.8 × 10^6.
Экзаменационный10 минут
Estimate 490 ÷ 39.6, then calculate to one decimal place.
Подсказка
Round to compatible numbers before calculating exactly.
Ответ
Estimate ≈ 500 ÷ 40 = 12.5. Exact ≈ 12.4.
Экзаменационный12 минут
Test the claim 8² + 6² = 14² and explain.
Подсказка
Calculate both sides separately.
Ответ
64 + 36 = 100, while 14² = 196; false.
Частые ошибки
- 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.
Проверка понимания
- 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
Домашняя работа по главе
Шесть разных заданий от базового уровня до сложного с временем, подсказками и ответами.
Базовый8 минут
Homework 1: Calculate 4 + 3 × 7 and justify the order of operations.
Подсказка
Multiplication precedes addition.
Ответ
4 + 3 · 7 = 25.
Базовый10 минут
Homework 2: Find 7/35 of 175.
Подсказка
Multiply by the fraction and simplify first.
Ответ
7/35 · 175 = 35.
Углубленный12 минут
Homework 3: Increase 60 by 15%.
Подсказка
Use multiplier 1 + 15/100.
Ответ
60 · 1.15 = 69.0.
Углубленный15 минут
Homework 4: Divide 120 in the ratio 6:4.
Подсказка
There are 10 ratio parts.
Ответ
120 : 10 = 12; 72 and 48.
Сложный18 минут
Homework 5: Compare 9/15 and 6/54 using a common denominator or decimals.
Подсказка
Use cross-products.
Ответ
9 · 54 = 486, 6 · 15 = 90; 9/15 > 6/54.
Сложный20 минут
Homework 6: Write 1500000 in standard form.
Подсказка
The first factor must be at least 1 and less than 10.
Ответ
1500000 = 1.5 × 10^6.
50 минут / 40 баллов
Полный тест по главе
Полный тест с таймером, баллами и образцами ответов.
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 балловОтвет
9 + 3 · 12 = 45.
2. Find 5/25 of 125.
3 балловОтвет
5/25 · 125 = 25.
3. Increase 160 by 40%.
3 балловОтвет
160 · 1.40 = 224.0.
4. Divide 96 in the ratio 4:4.
4 балловОтвет
96 : 8 = 12; 48 and 48.
5. Compare 7/13 and 6/42 using a common denominator or decimals.
4 балловОтвет
7 · 42 = 294, 6 · 13 = 78; 7/13 > 6/42.
6. Write 900000 in standard form.
4 балловОтвет
900000 = 0.9 × 10^6.
7. Estimate 588 ÷ 49.5, then calculate to one decimal place.
5 балловОтвет
Estimate ≈ 600 ÷ 50 = 12.0. Exact ≈ 11.9.
8. Test the claim 9² + 2² = 11² and explain.
5 балловОтвет
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 балловОтвет
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 балловОтвет
Full response: an accurate rule for “Money problems”, a numerical example that satisfies it, and an explained counterexample.
Раздел
Официальные источники
Источники программы; порядок тем уточняйте в школе и у преподавателя.
Mathematics
IGCSE Year 10: структурированный маршрут по математике и физике с главами, практикой и следующими шагами.
Что покрывает глава
Структура следует учебнику и помогает организовать изучение темы.
Integers
Fractions
Decimals
Percentages
Ratio and proportion
Indices
Standard form
Estimation
Bounds introduction
Money problems
Percentage increase/decrease
Где сфокусироваться
Темы, где чаще возникают ошибки или нужна дополнительная практика.
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.
Источники, ежедневные материалы и ресурсы
С чего начать: учебник, daily material, PDFs, videos и 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.
Практика по подтемам
Целевая практика перед full tests, чтобы coverage было понятным.
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 и проверка прогресса
Как измерять прогресс по главе и когда включать ее в общий 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.
Следующий шаг
Что делать после главы и как она связана со следующим разделом.
Complete the practice without support.
Explain the core method aloud in under two minutes.
Continue to the next chapter or request targeted tutor support.
Примечание: официальную экзаменационную программу каждого года всегда уточняйте в школе, у преподавателя и по текущим официальным источникам.