UK K12 GCSE/A-Level: Year 3 KS2 Mathematics - Multiplication and Division, 3 4 8 Times Tables

Learning Objectives

Year 3 Mathematics: Multiplication and Division of 3, 4, and 8 Times Tables

By the end of this topic, students will be able to: - Recall and apply the multiplication and division facts for 3, 4, and 8 times tables. - Demonstrate an understanding of the relationship between multiplication and division. - Use mental calculation strategies to solve multiplication and division problems. - Apply multiplication and division to solve real-world problems.

Core Concepts

Understanding Multiplication and Division

Multiplication is a shortcut for repeated addition. For example, 3 x 4 means 3 groups of 4, which is the same as 4 + 4 + 4. Division is the inverse operation of multiplication, finding how many groups of a certain size can be made from a given number. For example, 12 ÷ 4 means how many groups of 4 can be made from 12.

Multiplication Facts for 3, 4, and 8 Times Tables

The 3 times table is multiples of 3, where each number is 3 multiplied by a different number (e.g., 3 x 1 = 3, 3 x 2 = 6, 3 x 3 = 9). The 4 times table is multiples of 4, where each number is 4 multiplied by a different number (e.g., 4 x 1 = 4, 4 x 2 = 8, 4 x 3 = 12). The 8 times table is multiples of 8, where each number is 8 multiplied by a different number (e.g., 8 x 1 = 8, 8 x 2 = 16, 8 x 3 = 24).

Worked Examples

Multiplication and Division in Real-World Situations

Imagine you have 12 pencils and you want to put them into boxes of 4. How many boxes can you make? (12 ÷ 4 = 3) Now, if you want to know how many pencils you have in total if you have 3 boxes of 4 pencils each, you can multiply 3 x 4 = 12.

Mental Calculation Strategies

To calculate 4 x 8, you can use the fact that 4 x 10 = 40 and then subtract 8 (i.e., 40 - 8 = 32). This strategy helps to reduce the calculation to a more manageable one.

Common Misconceptions

Confusing Multiplication and Division

Some students may confuse multiplication and division, thinking that they are the same operation. However, multiplication is a shortcut for repeated addition, while division is the inverse operation of multiplication, finding how many groups of a certain size can be made from a given number.

Not Using Mental Calculation Strategies

Students may not use mental calculation strategies to solve multiplication and division problems, relying instead on counting or using a calculator. However, mental calculation strategies can help to make calculations more efficient and accurate.

Exam Tips

Practicing Multiplication and Division Facts

To perform well in exams, students should practice recalling multiplication and division facts for 3, 4, and 8 times tables. This can be done through mental calculation exercises, worksheets, or online resources.

Using Mental Calculation Strategies

Students should also practice using mental calculation strategies to solve multiplication and division problems. This can help to reduce the calculation to a more manageable one and make it easier to arrive at the correct answer.

MCQs with Explanations

[F] Multiplication Facts for 3 Times Table

What is 3 x 6? A) 10 B) 12 C) 15 D) 18

Correct answer: B) 12

Why the distractors fail: - A) 10 is the result of 3 x 5, not 3 x 6. - C) 15 is the result of 3 x 5, not 3 x 6. - D) 18 is the result of 3 x 6, but the question asks for the product of 3 and 6, not the sum.

[H] Division Facts for 4 Times Table

What is 24 ÷ 4? A) 5 B) 6 C) 8 D) 10

Correct answer: B) 6

Why the distractors fail: - A) 5 is the result of 20 ÷ 4, not 24 ÷ 4. - C) 8 is the result of 32 ÷ 4, not 24 ÷ 4. - D) 10 is the result of 40 ÷ 4, not 24 ÷ 4.

[F] Multiplication Facts for 8 Times Table

What is 8 x 3? A) 20 B) 24 C) 28 D) 30

Correct answer: B) 24

Why the distractors fail: - A) 20 is the result of 8 x 2, not 8 x 3. - C) 28 is the result of 8 x 4, not 8 x 3. - D) 30 is the result of 8 x 5, not 8 x 3.

[H] Division Facts for 8 Times Table

What is 48 ÷ 8? A) 5 B) 6 C) 7 D) 8

Correct answer: B) 6

Why the distractors fail: - A) 5 is the result of 40 ÷ 8, not 48 ÷ 8. - C) 7 is the result of 56 ÷ 8, not 48 ÷ 8. - D) 8 is the result of 64 ÷ 8, not 48 ÷ 8.

[F] Multiplication and Division Relationship

What is 12 ÷ 4? A) 3 B) 4 C) 6 D) 9

Correct answer: A) 3

Why the distractors fail: - B) 4 is the result of 12 ÷ 3, not 12 ÷ 4. - C) 6 is the result of 12 ÷ 2, not 12 ÷ 4. - D) 9 is the result of 12 ÷ 1, not 12 ÷ 4.

[H] Mental Calculation Strategy

What is 6 x 9? A) 50 B) 54 C) 56 D) 60

Correct answer: B) 54

Why the distractors fail: - A) 50 is the result of 6 x 8, not 6 x 9. - C) 56 is the result of 6 x 10, not 6 x 9. - D) 60 is the result of 6 x 10, not 6 x 9.

Short-answer Questions

1. Explain the relationship between multiplication and division.

Multiplication is a shortcut for repeated addition, while division is the inverse operation of multiplication, finding how many groups of a certain size can be made from a given number.

2. Describe a mental calculation strategy for solving 4 x 8.

One strategy is to use the fact that 4 x 10 = 40 and then subtract 8 (i.e., 40 - 8 = 32).

3. What is the product of 3 and 6?

The product of 3 and 6 is 18.

4. Explain how to use the 4 times table to find the product of 4 and 9.

To find the product of 4 and 9, we can use the fact that 4 x 10 = 40 and then multiply 9 by 4 (i.e., 40 x 9 = 360).

5. Describe a real-world situation where division is used.

Division is used when sharing a certain number of items among a group of people. For example, if we have 12 pencils and we want to share them equally among 4 people, we can divide 12 by 4 to find out how many pencils each person will get (i.e., 12 ÷ 4 = 3).