UK K12 GCSE/A-Level: Year 2 KS1 Mathematics - Fractions, Halves, Thirds, Quarters

Learning Objectives

By the end of this topic, students will be able to: - Identify and name fractions of a whole, including halves, thirds, and quarters. - Recognize and create equivalent fractions. - Compare and order fractions. - Use fractions to describe parts of a shape or a quantity. - Apply their understanding of fractions in real-world contexts.

Core Concepts

Fractions are a way to show part of a whole. A fraction is made up of two parts: the numerator (the top number) and the denominator (the bottom number). The numerator tells us how many equal parts we have, and the denominator tells us how many parts the whole is divided into.

For example, if we have a pizza that is divided into 4 equal parts, and we eat 2 of them, we can write this as a fraction: 2/4. This means we have 2 out of 4 equal parts of the pizza.

Halves

A half is a fraction that has a numerator of 1 and a denominator that is twice the numerator. For example, 1/2, 2/4, and 3/6 are all halves.

Thirds

A third is a fraction that has a numerator of 1 and a denominator that is three times the numerator. For example, 1/3, 2/6, and 3/9 are all thirds.

Quarters

A quarter is a fraction that has a numerator of 1 and a denominator that is four times the numerator. For example, 1/4, 2/8, and 3/12 are all quarters.

Worked Examples

Example 1

Tom has a toy box that is divided into 6 equal parts. He gives 2 of them to his friend. What fraction of the toy box does Tom have left?

Answer: Tom has 4 out of 6 equal parts of the toy box left. This can be written as the fraction 4/6.

Example 2

A bookshelf has 12 books on it, and 3 of them are red. What fraction of the books on the bookshelf are red?

Answer: There are 3 red books out of 12 books on the bookshelf. This can be written as the fraction 3/12.

Common Misconceptions

• Students may think that a fraction is always a part of a whole, but it can also be a part of a shape or a quantity.
• Students may struggle to recognize equivalent fractions, such as 2/4 and 1/2.
• Students may have difficulty comparing and ordering fractions, such as 1/2 and 2/4.

Exam Tips

• Make sure to simplify fractions before comparing or ordering them.
• Use visual aids, such as diagrams or number lines, to help you understand and compare fractions.
• Practice, practice, practice! The more you practice, the more confident you will become with fractions.

MCQs

MCQ 1 [F]

What is the fraction of the pizza that is eaten if it is divided into 4 equal parts and 2 parts are eaten?

A) 1/2 B) 2/4 C) 3/4 D) 4/4

Correct answer: B) 2/4 Why the distractors fail: A) 1/2 is a half, but it is not the correct answer. C) 3/4 is more than half, but it is not the correct answer. D) 4/4 is the whole pizza, not the fraction that is eaten.

MCQ 2 [H]

What is the equivalent fraction of 2/4?

A) 1/2 B) 2/6 C) 3/6 D) 4/8

Correct answer: A) 1/2 Why the distractors fail: B) 2/6 is not equivalent to 2/4. C) 3/6 is not equivalent to 2/4. D) 4/8 is not equivalent to 2/4.

MCQ 3 [F]

A bookshelf has 12 books on it, and 3 of them are red. What fraction of the books on the bookshelf are red?

A) 1/4 B) 2/4 C) 3/12 D) 4/12

Correct answer: C) 3/12 Why the distractors fail: A) 1/4 is not the correct answer. B) 2/4 is not the correct answer. D) 4/12 is the whole bookshelf, not the fraction of red books.

MCQ 4 [H]

A shape is divided into 6 equal parts, and 4 of them are colored. What fraction of the shape is colored?

A) 2/6 B) 3/6 C) 4/6 D) 5/6

Correct answer: C) 4/6 Why the distractors fail: A) 2/6 is not the correct answer. B) 3/6 is not the correct answer. D) 5/6 is more than half, but it is not the correct answer.

MCQ 5 [F]

A toy box is divided into 4 equal parts, and 2 of them are filled with toys. What fraction of the toy box is filled with toys?

A) 1/2 B) 2/4 C) 3/4 D) 4/4

Correct answer: B) 2/4 Why the distractors fail: A) 1/2 is a half, but it is not the correct answer. C) 3/4 is more than half, but it is not the correct answer. D) 4/4 is the whole toy box, not the fraction that is filled with toys.

Short-answer questions

Question 1

A bookshelf has 12 books on it, and 4 of them are fiction. What fraction of the books on the bookshelf are fiction?

Answer: There are 4 fiction books out of 12 books on the bookshelf. This can be written as the fraction 4/12.

Question 2

A shape is divided into 8 equal parts, and 3 of them are colored. What fraction of the shape is colored?

Answer: There are 3 colored parts out of 8 parts of the shape. This can be written as the fraction 3/8.

Question 3

A toy box is divided into 6 equal parts, and 2 of them are filled with toys. What fraction of the toy box is filled with toys?

Answer: There are 2 toy-filled parts out of 6 parts of the toy box. This can be written as the fraction 2/6.