Multiplication and division (T3 W10)
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Multiplication is essentially repeated addition, while division is the process of distributing a number into equal parts. For example, 4 × 3 can be visualized as adding 4 three times (4 + 4 + 4 = 12). Conversely, 12 ÷ 4 asks how many groups of 4 can be made from 12, which equals 3. Visual models such as arrays or number lines can help students grasp these concepts more concretely.
Let's consider the multiplication problem 6 × 5. To solve this, we can create an array with 6 rows and 5 columns. Counting all the squares gives us 30. Therefore, 6 × 5 = 30. This visual representation helps in understanding how multiplication works as grouping.
For the division problem 20 ÷ 4, we can think of it as distributing 20 items into 4 equal groups. If we divide 20 into 4 groups, each group will contain 5 items. Thus, 20 ÷ 4 = 5. Using counters or drawing circles can further illustrate this division process.
Now, let's practice multiplication together. Calculate 7 × 4 using an array model. Draw 7 rows with 4 dots in each row. Count the total number of dots. Discuss how this visual helps in understanding the multiplication process.
Next, let's work on a division problem: 30 ÷ 6. Use counters or draw circles to represent 30 items. Distribute them into 6 equal groups. How many items are in each group? Share your findings with the class and explain your reasoning.
Now it's your turn! Solve the following problems on your own: 1) 8 × 3, 2) 45 ÷ 5, 3) 12 × 6, 4) 36 ÷ 4. Show your working clearly, and be prepared to explain your methods to a partner.
Answer: 63
9 multiplied by 7 equals 63, which can be calculated as 9 + 9 + 9 + 9 + 9 + 9 + 9.
Answer: 8
48 divided by 6 equals 8, meaning there are 8 groups of 6 in 48.
Answer: 60
5 multiplied by 12 equals 60, which can be understood as adding 5 twelve times.
Answer: 25
100 divided by 4 equals 25, indicating that 100 can be split into 4 equal groups of 25.
Answer: 5
15 divided by 3 equals 5, as there are 5 groups of 3 in 15.
Answer: 56
7 multiplied by 8 equals 56, which can be calculated as 7 + 7 + 7 + 7 + 7 + 7 + 7 + 7.
Answer: 99
11 multiplied by 9 equals 99, which can be verified through repeated addition.
Answer: 9
72 divided by 8 equals 9, meaning there are 9 groups of 8 in 72.