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KS3 Year 7 / Mathematics / Curriculum

Ratio, proportion and rates

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

Цели обучения

Recognise, explain, and apply “Simplifying ratios”.
Recognise, explain, and apply “Sharing in a ratio”.
Recognise, explain, and apply “Direct proportion in tables”.
Recognise, explain, and apply “Unitary method”.
Recognise, explain, and apply “Simple scale problems”.

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 “Ratio, proportion and rates” 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

Simplifying ratios

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

Sharing in a ratio

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

Direct proportion in tables

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

Unitary method

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

Simple scale problems

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 5/35 + 7/35.

1The denominators are equal, so add the numerators.
2Write (5 + 7)/35.
3Simplify by a common factor and check that the value is reasonable.

12/35

Reasoning example

Before calculating, explain the key idea from “Simplifying ratios” 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 “Simplifying ratios”, but also why it is valid here.

Ratio, proportion and rates

Практика с ответами

Восемь заданий от базовых навыков до экзаменационного уровня. Сначала решите самостоятельно.

Базовый навык4 минут

Calculate 6 + 6 × 12 and justify the order of operations.

Подсказка

Multiplication precedes addition.

Ответ

6 + 6 · 12 = 78.

Базовый навык5 минут

Find 9/27 of 81.

Подсказка

Multiply by the fraction and simplify first.

Ответ

9/27 · 81 = 27.

Применение6 минут

Increase 250 by 25%.

Подсказка

Use multiplier 1 + 25/100.

Ответ

250 · 1.25 = 312.5.

Применение7 минут

Divide 120 in the ratio 8:2.

Подсказка

There are 10 ratio parts.

Ответ

120 : 10 = 12; 96 and 24.

Обоснование8 минут

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

Подсказка

Use cross-products.

Ответ

4 · 16 = 64, 4 · 8 = 32; 4/8 > 4/16.

Обоснование9 минут

Write 4200000 in standard form.

Подсказка

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

Ответ

4200000 = 4.2 × 10^6.

Экзаменационный10 минут

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

Подсказка

Round to compatible numbers before calculating exactly.

Ответ

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

Экзаменационный12 минут

Test the claim 6² + 5² = 11² and explain.

Подсказка

Calculate both sides separately.

Ответ

36 + 25 = 61, 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.

Ratio, proportion and rates

Домашняя работа по главе

Шесть разных заданий от базового уровня до сложного с временем, подсказками и ответами.

Базовый8 минут

Homework 1: Calculate 9 + 2 × 11 and justify the order of operations.

Подсказка

Multiplication precedes addition.

Ответ

9 + 2 · 11 = 31.

Базовый10 минут

Homework 2: Find 5/20 of 80.

Подсказка

Multiply by the fraction and simplify first.

Ответ

5/20 · 80 = 20.

Углубленный12 минут

Homework 3: Increase 480 by 40%.

Подсказка

Use multiplier 1 + 40/100.

Ответ

480 · 1.40 = 672.0.

Углубленный15 минут

Homework 4: Divide 84 in the ratio 4:3.

Подсказка

There are 7 ratio parts.

Ответ

84 : 7 = 12; 48 and 36.

Сложный18 минут

Homework 5: Compare 7/12 and 5/35 using a common denominator or decimals.

Подсказка

Use cross-products.

Ответ

7 · 35 = 245, 5 · 12 = 60; 7/12 > 5/35.

Сложный20 минут

Homework 6: Write 600000 in standard form.

Подсказка

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

Ответ

600000 = 0.6 × 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 7 + 2 × 9 and justify the order of operations.

2 баллов

Ответ

7 + 2 · 9 = 25.

2. Find 3/12 of 48.

3 баллов

Ответ

3/12 · 48 = 12.

3. Increase 360 by 30%.

3 баллов

Ответ

360 · 1.30 = 468.0.

4. Divide 144 in the ratio 9:3.

4 баллов

Ответ

144 : 12 = 12; 108 and 36.

5. Compare 5/10 and 5/25 using a common denominator or decimals.

4 баллов

Ответ

5 · 25 = 125, 5 · 10 = 50; 5/10 > 5/25.

6. Write 1600000 in standard form.

4 баллов

Ответ

1600000 = 1.6 × 10^6.

7. Estimate 392 ÷ 39.6, then calculate to one decimal place.

5 баллов

Ответ

Estimate ≈ 400 ÷ 40 = 10.0. Exact ≈ 9.9.

8. Test the claim 7² + 6² = 13² and explain.

5 баллов

Ответ

49 + 36 = 85, while 13² = 169; false.

9. Create and solve a two-step exam-style problem about “Unitary method” using 3, 3, and 9.

5 баллов

Ответ

A valid response uses the data in two justified steps and includes an independent check; for example 3 × 3 = 9, then 9 + 6 = 15.

10. Write a revision rule for “Simple scale problems”, one example, and one counterexample.

5 баллов

Ответ

Full response: an accurate rule for “Simple scale problems”, 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.

Simplifying ratios

Sharing in a ratio

Direct proportion in tables

Unitary method

Simple scale problems

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 6 + 6 × 12 and justify the order of operations.

Find 9/27 of 81.

Increase 250 by 25%.

Divide 120 in the ratio 8:2.

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

Write 4200000 in standard form.

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

Test the claim 6² + 5² = 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.