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KS3 Year 8 / Mathematics / Curriculum

Number

Number: structured theory, worked examples, answered practice, and a mastery checklist for KS3 Year 8.

Цели обучения

Recognise, explain, and apply “Negative number calculations”.
Recognise, explain, and apply “Powers and roots introduction”.
Recognise, explain, and apply “Prime factorisation”.
Recognise, explain, and apply “HCF and LCM”.
Recognise, explain, and apply “Fractions and mixed numbers”.

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.

01

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.

02

Equivalent forms

Fractions, decimals, percentages, ratios, and powers can describe the same quantity. Changing form is a solving tool, not a separate trick.

03

Reasonableness check

Estimate before and after the exact calculation. The sign, order of magnitude, and unit must agree with the problem context.

04

Negative number calculations

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.

05

Powers and roots introduction

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.

06

Prime factorisation

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.

07

HCF and LCM

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.

08

Fractions and mixed numbers

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 2/10 + 5/10.

1The denominators are equal, so add the numerators.
2Write (2 + 5)/10.
3Simplify by a common factor and check that the value is reasonable.

7/10

Reasoning example

Before calculating, explain the key idea from “Negative number calculations” 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 “Negative number calculations”, 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 + 4 × 12 and justify the order of operations.

Подсказка

Multiplication precedes addition.

Ответ

8 + 4 · 12 = 56.

Базовый навык5 минут

Find 4/24 of 144.

Подсказка

Multiply by the fraction and simplify first.

Ответ

4/24 · 144 = 24.

Применение6 минут

Increase 210 by 35%.

Подсказка

Use multiplier 1 + 35/100.

Ответ

210 · 1.35 = 283.5.

Применение7 минут

Divide 96 in the ratio 3:5.

Подсказка

There are 8 ratio parts.

Ответ

96 : 8 = 12; 36 and 60.

Обоснование8 минут

Compare 6/8 and 2/12 using a common denominator or decimals.

Подсказка

Use cross-products.

Ответ

6 · 12 = 72, 2 · 8 = 16; 6/8 > 2/12.

Обоснование9 минут

Write 3600000 in standard form.

Подсказка

The first factor must be at least 1 and less than 10.

Ответ

3600000 = 3.6 × 10^6.

Экзаменационный10 минут

Estimate 490 ÷ 59.400000000000006, then calculate to one decimal place.

Подсказка

Round to compatible numbers before calculating exactly.

Ответ

Estimate ≈ 500 ÷ 60 = 8.3. Exact ≈ 8.2.

Экзаменационный12 минут

Test the claim 8² + 3² = 11² and explain.

Подсказка

Calculate both sides separately.

Ответ

64 + 9 = 73, while 11² = 121; 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 + 5 × 9 and justify the order of operations.

Подсказка

Multiplication precedes addition.

Ответ

4 + 5 · 9 = 49.

Базовый10 минут

Homework 2: Find 7/14 of 28.

Подсказка

Multiply by the fraction and simplify first.

Ответ

7/14 · 28 = 14.

Углубленный12 минут

Homework 3: Increase 120 by 15%.

Подсказка

Use multiplier 1 + 15/100.

Ответ

120 · 1.15 = 138.0.

Углубленный15 минут

Homework 4: Divide 144 in the ratio 6:6.

Подсказка

There are 12 ratio parts.

Ответ

144 : 12 = 12; 72 and 72.

Сложный18 минут

Homework 5: Compare 9/12 and 3/27 using a common denominator or decimals.

Подсказка

Use cross-products.

Ответ

9 · 27 = 243, 3 · 12 = 36; 9/12 > 3/27.

Сложный20 минут

Homework 6: Write 2500000 in standard form.

Подсказка

The first factor must be at least 1 and less than 10.

Ответ

2500000 = 2.5 × 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 + 5 × 14 and justify the order of operations.

2 баллов

Ответ

9 + 5 · 14 = 79.

2. Find 5/10 of 20.

3 баллов

Ответ

5/10 · 20 = 10.

3. Increase 320 by 40%.

3 баллов

Ответ

320 · 1.40 = 448.0.

4. Divide 120 in the ratio 4:6.

4 баллов

Ответ

120 : 10 = 12; 48 and 72.

5. Compare 7/10 and 3/21 using a common denominator or decimals.

4 баллов

Ответ

7 · 21 = 147, 3 · 10 = 30; 7/10 > 3/21.

6. Write 1500000 in standard form.

4 баллов

Ответ

1500000 = 1.5 × 10^6.

7. Estimate 588 ÷ 19.8, then calculate to one decimal place.

5 баллов

Ответ

Estimate ≈ 600 ÷ 20 = 30.0. Exact ≈ 29.7.

8. Test the claim 9² + 4² = 13² and explain.

5 баллов

Ответ

81 + 16 = 97, while 13² = 169; false.

9. Create and solve a two-step exam-style problem about “Best buys” using 5, 6, and 30.

5 баллов

Ответ

A valid response uses the data in two justified steps and includes an independent check; for example 5 × 6 = 30, then 30 + 11 = 41.

10. Write a revision rule for “Rates”, one example, and one counterexample.

5 баллов

Ответ

Full response: an accurate rule for “Rates”, a numerical example that satisfies it, and an explained counterexample.

Раздел

Официальные источники

Источники программы; порядок тем уточняйте в школе и у преподавателя.

UK Department for Education - MathematicsOfficial national curriculum progression and attainment guidance.

Mathematics

KS3 Year 8: структурированный маршрут по математике и физике с главами, практикой и следующими шагами.

Назад к предмету

Что покрывает глава

Структура следует учебнику и помогает организовать изучение темы.

Negative number calculations

Powers and roots introduction

Prime factorisation

HCF and LCM

Fractions and mixed numbers

Percentage increase/decrease

Reverse percentage introduction

Ratio problems

Best buys

Rates

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 + 4 × 12 and justify the order of operations.

Find 4/24 of 144.

Increase 210 by 35%.

Divide 96 in the ratio 3:5.

Compare 6/8 and 2/12 using a common denominator or decimals.

Write 3600000 in standard form.

Estimate 490 ÷ 59.400000000000006, then calculate to one decimal place.

Test the claim 8² + 3² = 11² 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.