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KS3 Year 7 / Mathematics / Curriculum

Number

Number: structured theory, worked examples, answered practice, and a mastery checklist for KS3 Year 7.

Цели обучения

Recognise, explain, and apply “Integers and place value”.
Recognise, explain, and apply “Four operations”.
Recognise, explain, and apply “Order of operations”.
Recognise, explain, and apply “Negative numbers introduction”.
Recognise, explain, and apply “Rounding and estimation”.

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

Integers and place value

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

Four operations

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

Order of operations

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

Negative numbers 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.

08

Rounding and estimation

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 3/18 + 6/18.

1The denominators are equal, so add the numerators.
2Write (3 + 6)/18.
3Simplify by a common factor and check that the value is reasonable.

1/2

Reasoning example

Before calculating, explain the key idea from “Integers and place value” 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 and place value”, 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 5 + 5 × 10 and justify the order of operations.

Подсказка

Multiplication precedes addition.

Ответ

5 + 5 · 10 = 55.

Базовый навык5 минут

Find 8/16 of 32.

Подсказка

Multiply by the fraction and simplify first.

Ответ

8/16 · 32 = 16.

Применение6 минут

Increase 160 by 20%.

Подсказка

Use multiplier 1 + 20/100.

Ответ

160 · 1.20 = 192.0.

Применение7 минут

Divide 156 in the ratio 7:6.

Подсказка

There are 13 ratio parts.

Ответ

156 : 13 = 12; 84 and 72.

Обоснование8 минут

Compare 3/6 and 3/9 using a common denominator or decimals.

Подсказка

Use cross-products.

Ответ

3 · 9 = 27, 3 · 6 = 18; 3/6 > 3/9.

Обоснование9 минут

Write 3000000 in standard form.

Подсказка

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

Ответ

3000000 = 3.0 × 10^6.

Экзаменационный10 минут

Estimate 882 ÷ 19.8, then calculate to one decimal place.

Подсказка

Round to compatible numbers before calculating exactly.

Ответ

Estimate ≈ 900 ÷ 20 = 45.0. Exact ≈ 44.5.

Экзаменационный12 минут

Test the claim 5² + 4² = 9² and explain.

Подсказка

Calculate both sides separately.

Ответ

25 + 16 = 41, while 9² = 81; 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 8 + 6 × 14 and justify the order of operations.

Подсказка

Multiplication precedes addition.

Ответ

8 + 6 · 14 = 92.

Базовый10 минут

Homework 2: Find 4/12 of 36.

Подсказка

Multiply by the fraction and simplify first.

Ответ

4/12 · 36 = 12.

Углубленный12 минут

Homework 3: Increase 350 by 35%.

Подсказка

Use multiplier 1 + 35/100.

Ответ

350 · 1.35 = 472.5.

Углубленный15 минут

Homework 4: Divide 60 in the ratio 3:2.

Подсказка

There are 5 ratio parts.

Ответ

60 : 5 = 12; 36 and 24.

Сложный18 минут

Homework 5: Compare 6/10 and 4/24 using a common denominator or decimals.

Подсказка

Use cross-products.

Ответ

6 · 24 = 144, 4 · 10 = 40; 6/10 > 4/24.

Сложный20 минут

Homework 6: Write 5400000 in standard form.

Подсказка

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

Ответ

5400000 = 5.4 × 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 6 + 6 × 12 and justify the order of operations.

2 баллов

Ответ

6 + 6 · 12 = 78.

2. Find 9/27 of 81.

3 баллов

Ответ

9/27 · 81 = 27.

3. Increase 250 by 25%.

3 баллов

Ответ

250 · 1.25 = 312.5.

4. Divide 120 in the ratio 8:2.

4 баллов

Ответ

120 : 10 = 12; 96 and 24.

5. Compare 4/8 and 4/16 using a common denominator or decimals.

4 баллов

Ответ

4 · 16 = 64, 4 · 8 = 32; 4/8 > 4/16.

6. Write 4200000 in standard form.

4 баллов

Ответ

4200000 = 4.2 × 10^6.

7. Estimate 294 ÷ 29.700000000000003, then calculate to one decimal place.

5 баллов

Ответ

Estimate ≈ 300 ÷ 30 = 10.0. Exact ≈ 9.9.

8. Test the claim 6² + 5² = 11² and explain.

5 баллов

Ответ

36 + 25 = 61, while 11² = 121; false.

9. Create and solve a two-step exam-style problem about “Fractions” using 9, 2, and 18.

5 баллов

Ответ

A valid response uses the data in two justified steps and includes an independent check; for example 9 × 2 = 18, then 18 + 11 = 29.

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

5 баллов

Ответ

Full response: an accurate rule for “Equivalent fractions”, 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 7: 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.

Integers and place value

Four operations

Order of operations

Negative numbers introduction

Rounding and estimation

Factors and multiples

Prime numbers

HCF and LCM introduction

Fractions

Equivalent fractions

Adding and subtracting fractions

Multiplying and dividing fractions in simple cases

Decimals

Percentages

Fraction/decimal/percentage conversions

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 5 + 5 × 10 and justify the order of operations.

Find 8/16 of 32.

Increase 160 by 20%.

Divide 156 in the ratio 7:6.

Compare 3/6 and 3/9 using a common denominator or decimals.

Write 3000000 in standard form.

Estimate 882 ÷ 19.8, then calculate to one decimal place.

Test the claim 5² + 4² = 9² 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.