Multiplication
Multiplication as repeated addition
Multiplication as repeated addition is a way to help students understand what multiplication means. It’s like adding the same number over and over again.
Here’s how you can explain it:
1. Start with Addition:
– Let’s say you have 3 apples. If you get 3 more apples, how many apples do you have? You add them: 3 + 3 = 6.
– If you get 3 more apples again, you add once more: 6 + 3 = 9.
– You’re adding 3 apples each time.
2. Introducing Multiplication:
– Instead of adding 3 apples three times (3 + 3 + 3), you can just multiply: 3 × 3.
– Multiplication is just a quicker way to do this. It means you have 3 groups of 3 apples.
3. Examples:
– If you have 2 groups of 5 pencils, instead of adding 5 + 5, you multiply: 2 × 5 = 10.
– This means you have 10 pencils in total.
Summary:
Multiplication is a faster way to add the same number many times. When you multiply, you’re just doing repeated addition!
Example-
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What is a Number Line?
A number line is a straight line with numbers on it, usually starting from 0 and going up. We can use this line to help us add, subtract, and even multiply.
Multiplication on a Number Line
Multiplication on a number line is like taking steps along the line. Each step is the same size, and the number of steps you take depends on what you’re multiplying.
Example: Multiplying 3 × 4
Let’s see how 3 × 4 works on a number line.
1. Start at 0:
– Imagine you’re standing at 0 on the number line.
2. Step Size:
– Since we’re multiplying by 4, each step you take will be 4 numbers long.
3. Number of Steps:
– You need to take 3 steps because we’re multiplying by 3.
4. Take the Steps:
– First step: Move from 0 to 4.
– Second step: Move from 4 to 8.
– Third step:Move from 8 to 12.
You’ve taken 3 steps of 4 each, and you’ve landed on 12!
Conclusion
So, 3 × 4 = 12, and you can see that on the number line by counting 3 jumps of 4.
Here’s how it looks on a number line
Each arrow shows a jump of 4, and after 3 jumps, you land on 12.
Example:
Let’s try another one: 2 × 5
– Start at 0.
– Make 2 jumps of 5 (from 0 to 5, then from 5 to 10).
– You land on 10, so 2 × 5 = 10.
Summary
Multiplying on a number line is like taking equal jumps. The number of jumps is the first number, and how far each jump goes is the second number. By following these jumps, you can see how multiplication works!
Properties of multiplication
1. Order Property (Commutative Property)
What It Means:
– The order in which you multiply two numbers doesn’t change the answer.
Example:
– 3 × 4 = 12
– 4 × 3 = 12
Explanation:
– Imagine you have 3 baskets, and each basket has 4 apples. If you count all the apples, you’ll get 12.
– Now, imagine you have 4 baskets with 3 apples each. If you count all those apples, you still get 12.
– So, 3 × 4 is the same as 4 × 3. The order doesn’t matter—you get the same answer!
2. Multiplicative Property of 0
What It Means:
– Any number multiplied by 0 is always 0.
Example:
– 5 × 0 = 0
– 0 × 8 = 0
Explanation:
– If you have 5 groups with 0 items in each group, you don’t have anything. No matter how many groups you have, if there’s nothing in each group, you have 0 altogether.
– So, whenever you multiply a number by 0, the answer is always 0.
3. Multiplicative Property of 1 (Identity Property of Multiplication)
What It Means:
– Any number multiplied by 1 stays the same.
Example:
– 6 × 1 = 6
– 1 × 9 = 9
Explanation:
– Imagine you have 6 apples. If you make just 1 group of those 6 apples, you still have 6 apples.
– So, when you multiply any number by 1, it doesn’t change—it stays the same!
Summary :
– Order Property: You can switch the order of the numbers you’re multiplying, and the answer will be the same.
– Multiplicative Property of 0: Any number times 0 is always 0.
– Multiplicative Property of 1: Any number times 1 stays the same.
These properties make it easier to understand and solve multiplication problems!
Multiplication tables
| Multiplication table of 2 | ||
|---|---|---|
|
|
1 two is 2 |
2 x 1 = 2 |
|
|
2 twos are 4 |
2 x 2 = 4 |
|
|
3 twos are 6 |
2 x 3 = 6 |
|
|
4 twos are 8 |
2 x 4 = 8 |
|
|
5 twos are 10 |
2 x 5 = 10 |
|
|
6 twos are 12 |
2 x 6 = 12 |
|
|
7 twos are 14 |
2 x 7 = 14 |
|
|
8 twos are 16 |
2 x 8 = 16 |
|
|
9 twos are 18 |
2 x 9 = 18 |
|
|
10 twos are 20 |
2 x 10 = 20 |
| Multiplication table of 3 | ||
|---|---|---|
|
|
1 three is 3 |
3 x 1 = 3 |
|
|
2 threes are 6 |
3 x 2 = 6 |
|
|
3 threes are 9 |
3 x 3 = 9 |
|
|
4 threes are 12 |
3 x 4 = 12 |
|
|
5 threes are 15 |
3 x 5 = 15 |
|
|
6 threes are 18 |
3 x 6 = 18 |
|
|
7 threes are 21 |
3 x 7 = 21 |
|
|
8 threes are 24 |
3 x 8 = 24 |
|
|
9 threes are 27 |
3 x 9 = 27 |
|
|
10 threes are 30 |
3 x 10 = 30 |
