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Multiplication

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visibility 6update 10 hours agobookmarkshare

In this topic you will

Add and represent equal groups to model multiplication.
Explain multiplication as repeated addition and as an array model.
Build and use the 1, 2, 5, and 10 times tables.

Key Words

array
equal groups
multiply, times
multiplication table, times table
repeated addition

Show Definitions

array: An arrangement of objects in rows and columns used to represent multiplication clearly and visually.
equal groups: Sets that contain the same number of items, used to model multiplication situations.
multiply, times: To find the total number of items in equal groups by combining them efficiently using multiplication.
multiplication table, times table: A chart that shows the products of numbers when they are multiplied together.
repeated addition: Adding the same number several times to find a total, which is another way to understand multiplication.

Equal groups and arrays

When things come in equal groups, we can multiply to find out how many. Arrays help you to see equal groups, like on a muffin tray.

A muffin tray showing an array of muffin cases

❓ EXERCISES

Exercise $1.6$

1. Write the repeated addition and multiplication number sentences.

Number line showing jumps of $+10$ from $0$ to $70$

👀 Show answer

$10+10+10+10+10+10+10=70$

$7\times 10=70$

2. Show this repeated addition number sentence on the number line.

$2+2+2+2+2+2+2+2=16$

Write the multiplication number sentence.

Number line from $0$ to $20$ for showing jumps of $2$ to reach $16$

👀 Show answer

$8\times 2=16$

3. Write the missing number sentences.

Table with columns Repeated addition and Multiplication, with some number sentences missing

👀 Show answer

Missing multiplication:

$5\times 5=25$

$5\times 10=50$

$5\times 2=10$

Missing repeated addition:

$2+2+2+2=8$

$5+5+5=15$

$10+10=20$

4. Write a multiplication sentence for each array.

Two arrays: four equal groups of beans and a chocolate bar arranged in rows and columns

👀 Show answer

Beans:$5\times 5=25$

Chocolate:$2\times 6=12$

5. Draw an array to show that $2\times 8=16$.

$Blank box for drawing an array to show $2\times 8=16$$

👀 Show answer

Draw an array with $2$ rows of $8$ (or $8$ columns of $2$) to make $16$ counters in total.

6. Write the multiplication table for $1$, to $1\times 10=10$.

$Multiplication table for the $1$ times table with boxes to fill from $1\times 1$ to $1\times 10$$

👀 Show answer

$1\times 1=1$

$1\times 2=2$

$1\times 3=3$

$1\times 4=4$

$1\times 5=5$

$1\times 6=6$

$1\times 7=7$

$1\times 8=8$

$1\times 9=9$

$1\times 10=10$

Think like a Mathematician

Task: Write the multiplication table for $0$.

Method:

Write the number sentences from $0\times 0$ up to $0\times 10$.
Calculate each product.
Look for patterns in the answers.

Follow-up Questions:

1. How is this the same as any other multiplication table?

2. How is it different? Write your ideas down clearly.

👀 show answer

Multiplication table for $0$:

$0\times 0=0$

$0\times 1=0$

$0\times 2=0$

$0\times 3=0$

$0\times 4=0$

$0\times 5=0$

$0\times 6=0$

$0\times 7=0$

$0\times 8=0$

$0\times 9=0$

$0\times 10=0$
1: It is the same because it uses the same structure as any times table: you keep the first number fixed and multiply it by $0$, $1$, $2$, …, $10$, writing each result as a multiplication sentence.
2: It is different because every answer is $0$. In other times tables, the answers change and often grow, but when one factor is $0$, the product is always $0$. This shows the rule: $0\times n=0$ for any number $n$.

❓ EXERCISES

7. Write the missing double, addition and multiplication sentences.

Table with columns Double, Addition, and Multiplication, with some sentences missing

👀 Show answer

Row $1$: double $5$ is $10$, $5+5=10$, $5\times 2=10$

Row $2$: double $2$ is $4$, $2+2=4$, $2\times 2=4$

Row $3$: double $10$ is $20$, $10+10=20$, $10\times 2=20$

8. Use the counting stick to help you find the correct answers.

Count in twos from zero. What is the $5$th number you say? ________

Count in fives from zero. What is the $7$th number you say? ________

Count in tens from $0$. What is the $2$nd number you say? ________

Count in twos from $0$. What is the $8$th number you say? ________

👀 Show answer

$5$th number counting in twos from zero: $8$

$7$th number counting in fives from zero: $30$

$2$nd number counting in tens from $0$: $10$

$8$th number counting in twos from $0$: $14$

9. Marcus likes to count in twos, fives and tens from zero.

When he says $20$, what could he be counting in?

Write some multiplication facts to explain your answer.

Blank answer box for explaining what counting pattern could make $20$ and giving multiplication facts

👀 Show answer

He could be counting in twos, fives, or tens, because $20$ is a multiple of $2$, $5$, and $10$.

$10\times 2=20$ (counting in twos)

$4\times 5=20$ (counting in fives)

$2\times 10=20$ (counting in tens)

10. Work with a partner. Take it in turns to ask each other multiplication or division questions. Check the answers together.

👀 Show answer

Example questions you could ask:

$2\times 6=$$12$

$5\times 4=$$20$

$10\times 3=$$30$

$20\div 5=$$4$

$16\div 2=$$8$

What we've learned

We learned how to represent multiplication using equal groups and arrays.
We understood multiplication as repeated addition, such as $5+5+5+5=4\times 5$.
We practiced writing multiplication number sentences from number lines and counting patterns.
We explored doubles and connected them to multiplication facts like $2\times n$.
We built and used the $1$, $2$, $5$, and $10$ times tables.
We discovered that multiplying any number by $0$ always gives $0$, following the rule $0\times n=0$.

Multiplication

In this topic you will

Key Words

Equal groups and arrays

❓ EXERCISES

Think like a Mathematician

❓ EXERCISES

What we've learned

Related Past Papers

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