Year 1 / Mathematics / Geometry and data

Patterns and simple data

Patterns and simple data: structured theory, worked examples, answered practice, and a mastery checklist for Year 1.

Цели обучения

Recognise, explain, and apply “repeating patterns”.
Recognise, explain, and apply “sorting”.
Recognise, explain, and apply “pictograms”.

Ключевые идеи и проверки

I choose an appropriate statistic.
I calculate and interpret probabilities.
Every solution or explanation for “Patterns and simple data” should include a method, justification, and final check.

Раздел

Основная теория

Ключевые идеи главы в понятной последовательности перед практикой.

Data and population

Before calculating, identify what each value measures, the population, and whether the sample is representative.

Statistic with interpretation

Mean, median, range, and probability answer different questions. Give the value together with a contextual interpretation.

Scale and probability check

A graph needs a valid scale and a probability must lie from 0 to 1. These checks immediately expose inconsistent answers.

repeating patterns

State what each value measures, organise it in a table or graph, then choose the appropriate statistic. Finish with estimation, an inverse operation, or substitution as a check.

sorting

State what each value measures, organise it in a table or graph, then choose the appropriate statistic. Finish with estimation, an inverse operation, or substitution as a check.

pictograms

State what each value measures, organise it in a table or graph, then choose the appropriate statistic. 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 data example

For the data 3, 7, 10, 9, 6, find the mean and range.

1Sum = 35 and count = 5.
2Mean = 35/5.
3Range = maximum - minimum.

Mean 7.0, range 7.

Thinking and explanation example

Explain “repeating patterns” in your own words and use a picture, objects, a table, or a simple measurement to support it.

1State what is known and what is being found.
2Choose one clear representation.
3Explain what it shows and check that the answer is sensible.

A complete explanation connects the correct idea, a clear representation, and a sensible check.

Patterns and simple data

Практика с ответами

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

Базовый навык3 минут

Calculate 9 + 6 and show two representations connected with “repeating patterns”.

Подсказка

Use a number line, place value, or objects.

Ответ

9 + 6 = 15. Valid representations include number-line jumps and grouped objects.

Базовый навык4 минут

3 equal groups contain 5 objects each. Find the total and write an addition and multiplication statement.

Подсказка

Add 5 a total of 3 times.

Ответ

5 + 5 + 5 = 3 · 5 = 15.

Применение4 минут

Continue 8, 13, 18, ... for three more terms and explain the rule.

Подсказка

Check how much each term increases.

Ответ

23, 28, 33; +5.

Применение5 минут

A rectangle has sides 4 cm and 2 cm. Find its perimeter and explain why four sides are counted.

Подсказка

Opposite sides are equal.

Ответ

Perimeter = 4 + 2 + 4 + 2 = 12 cm.

Обоснование5 минут

Out of 28 objects, 7 are shaded. What fraction is shaded and how does it simplify?

Подсказка

Put shaded objects over the total.

Ответ

7/28 = 1/4.

Обоснование6 минут

The measurements are 3, 6, 3, and 6. Find the greatest, least, and range.

Подсказка

Range = greatest value minus least value.

Ответ

Greatest 6, least 3, range 3.

Экзаменационный7 минут

Anna has 18 cards, gives away 6, then shares the rest into 2 equal groups. How many are in each group?

Подсказка

Subtract first, then divide.

Ответ

18 - 6 = 12; (12) : 2 = 6.

Экзаменационный8 минут

A learner says 9 + 5 = 15. Find the error, correct it, and check the correction.

Подсказка

Check with a number line or inverse subtraction.

Ответ

9 + 5 = 14; 14 - 5 = 9.

Частые ошибки

Using the mean when outliers distort the result.
Using the wrong denominator in a probability.
Drawing a graph without title, units, or consistent scale.

Проверка понимания

I choose an appropriate statistic.
I calculate and interpret probabilities.
I check sample and graph quality.

Patterns and simple data

Домашняя работа по главе

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

Базовый5 минут

Homework 1: Calculate 5 + 2 and show two representations connected with “repeating patterns”.

Подсказка

Use a number line, place value, or objects.

Ответ

5 + 2 = 7. Valid representations include number-line jumps and grouped objects.

Базовый6 минут

Homework 2: 4 equal groups contain 8 objects each. Find the total and write an addition and multiplication statement.

Подсказка

Add 8 a total of 4 times.

Ответ

8 + 8 + 8 + 8 = 4 · 8 = 32.

Углубленный7 минут

Homework 3: Continue 4, 10, 16, ... for three more terms and explain the rule.

Подсказка

Check how much each term increases.

Ответ

22, 28, 34; +6.

Углубленный8 минут

Homework 4: A rectangle has sides 7 cm and 3 cm. Find its perimeter and explain why four sides are counted.

Подсказка

Opposite sides are equal.

Ответ

Perimeter = 7 + 3 + 7 + 3 = 20 cm.

Сложный10 минут

Homework 5: Out of 15 objects, 3 are shaded. What fraction is shaded and how does it simplify?

Подсказка

Put shaded objects over the total.

Ответ

3/15 = 1/5.

Сложный12 минут

Homework 6: The measurements are 6, 2, 6, and 2. Find the greatest, least, and range.

Подсказка

Range = greatest value minus least value.

Ответ

Greatest 6, least 2, range 4.

35 минут / 30 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 3 + 2 and show two representations connected with “repeating patterns”.

2 баллов

Ответ

3 + 2 = 5. Valid representations include number-line jumps and grouped objects.

2. 4 equal groups contain 6 objects each. Find the total and write an addition and multiplication statement.

3 баллов

Ответ

6 + 6 + 6 + 6 = 4 · 6 = 24.

3. Continue 9, 15, 21, ... for three more terms and explain the rule.

3 баллов

Ответ

27, 33, 39; +6.

4. A rectangle has sides 5 cm and 3 cm. Find its perimeter and explain why four sides are counted.

4 баллов

Ответ

Perimeter = 5 + 3 + 5 + 3 = 16 cm.

5. Out of 40 objects, 8 are shaded. What fraction is shaded and how does it simplify?

4 баллов

Ответ

8/40 = 1/5.

6. The measurements are 4, 2, 4, and 2. Find the greatest, least, and range.

4 баллов

Ответ

Greatest 4, least 2, range 2.

7. Anna has 28 cards, gives away 7, then shares the rest into 3 equal groups. How many are in each group?

5 баллов

Ответ

28 - 7 = 21; (21) : 3 = 7.

8. A learner says 3 + 6 = 10. Find the error, correct it, and check the correction.

5 баллов

Ответ

3 + 6 = 9; 9 - 6 = 3.

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

Year 1: 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.

repeating patterns

sorting

pictograms

Где сфокусироваться

Темы, где чаще возникают ошибки или нужна дополнительная практика.

I choose an appropriate statistic.

I calculate and interpret probabilities.

I check sample and graph quality.

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.