UK K12 GCSE/A-Level: Year 4 KS2 Mathematics - Multiplication and Division, All Tables to 12×12

Learning Objectives

By the end of this topic, students will be able to: - Recall and apply all multiplication tables up to 12 x 12 - Demonstrate an understanding of the relationship between multiplication and division - Solve multiplication and division problems involving multi-digit numbers - Identify and explain common misconceptions related to multiplication and division - Apply multiplication and division skills to solve real-world problems

Core Concepts

Multiplication is a shortcut for repeated addition. For example, 4 x 6 can be calculated as 4 + 4 + 4 + 4 + 4 + 4. This can be represented using the multiplication symbol (×) and the equals sign (=) as 4 x 6 = 24.

Division is the inverse operation of multiplication. For example, if we have 24 objects and we want to share them equally among 4 groups, we can divide 24 by 4 to find the number of objects in each group.

The multiplication tables up to 12 x 12 can be memorized using various strategies such as:

• Creating arrays or number lines
• Using real-world objects to represent the multiplication
• Practicing the tables regularly

Worked Examples

Example 1: Multiplication

A bookshelf has 5 shelves, and each shelf can hold 8 books. How many books can the bookshelf hold in total?

To solve this problem, we can use the multiplication symbol (×) and multiply 5 (the number of shelves) by 8 (the number of books per shelf):

5 x 8 = ?

Using the multiplication table, we can find that 5 x 8 = 40. Therefore, the bookshelf can hold 40 books in total.

Example 2: Division

A pizza has 18 slices, and we want to share it equally among 3 people. How many slices will each person get?

To solve this problem, we can use the division symbol (÷) and divide 18 (the total number of slices) by 3 (the number of people):

18 ÷ 3 = ?

Using the division table, we can find that 18 ÷ 3 = 6. Therefore, each person will get 6 slices of pizza.

Common Misconceptions

• Many students struggle with the concept of multiplication as repeated addition, leading to difficulties with multi-digit multiplication.
• Some students may confuse the order of operations in multiplication and division problems, leading to incorrect answers.
• Others may struggle with the concept of division as sharing or grouping, leading to difficulties with multi-digit division.

Exam Tips

• Make sure to read the question carefully and identify the operation required (multiplication or division).
• Use the multiplication table to recall the facts and perform calculations.
• Check your answers by using the inverse operation (division for multiplication and multiplication for division).
• Practice, practice, practice to build fluency and confidence with multiplication and division.

MCQs with Explanations

MCQ 1: [F] Which of the following is equal to 6 x 9?

A) 54 B) 48 C) 60 D) 72

Correct answer: A) 54 Why the distractors fail: B) 48 is a common mistake as it is the product of 6 and 8, not 9. C) 60 is the product of 6 and 10, not 9. D) 72 is the product of 6 and 12, not 9.

MCQ 2: [H] A bakery sells 480 cakes in a day. If they pack 12 cakes in each box, how many boxes can they fill?

A) 30 B) 40 C) 48 D) 60

Correct answer: C) 48 Why the distractors fail: A) 480 ÷ 12 = 40, but the question asks for the number of boxes, not the number of cakes. B) 480 ÷ 12 = 40, but the question asks for the number of boxes, not the number of cakes. D) 480 ÷ 12 = 40, but the question asks for the number of boxes, not the number of cakes.

MCQ 3: [F] Which of the following is equal to 9 ÷ 3?

A) 2 B) 3 C) 6 D) 9

Correct answer: C) 6 Why the distractors fail: A) 9 ÷ 3 = 3, not 2. B) 9 ÷ 3 = 3, not 3 (this is the correct answer, but it is not the only correct answer). D) 9 ÷ 3 = 3, not 9.

MCQ 4: [H] A group of friends want to share some money equally. If they have £120 and there are 8 friends, how much will each friend get?

A) £10 B) £12 C) £15 D) £18

Correct answer: C) £15 Why the distractors fail: A) £120 ÷ 8 = £15, but the question asks for the amount each friend will get, not the total amount. B) £120 ÷ 8 = £15, but the question asks for the amount each friend will get, not the total amount. D) £120 ÷ 8 = £15, but the question asks for the amount each friend will get, not the total amount.

MCQ 5: [F] Which of the following is equal to 4 x 6?

A) 20 B) 24 C) 28 D) 32

Correct answer: B) 24 Why the distractors fail: A) 4 x 6 = 24, not 20. C) 4 x 6 = 24, not 28. D) 4 x 6 = 24, not 32.

Short-answer Questions

1. A bookshelf has 6 shelves, and each shelf can hold 8 books. How many books can the bookshelf hold in total?

(Answer: 6 x 8 = 48)

1. A pizza has 18 slices, and we want to share it equally among 3 people. How many slices will each person get?

(Answer: 18 ÷ 3 = 6)

1. A group of friends want to share some money equally. If they have £180 and there are 6 friends, how much will each friend get?

(Answer: £180 ÷ 6 = £30)

1. A bakery sells 720 cakes in a day. If they pack 12 cakes in each box, how many boxes can they fill?

(Answer: 720 ÷ 12 = 60)

1. A group of friends want to share some toys equally. If they have 24 toys and there are 4 friends, how many toys will each friend get?

(Answer: 24 ÷ 4 = 6)