seegongsik
Grade 3 (age 8-9)

grade 3 Multiplication

Multiplication is a short way to write adding the same number again and again. If there are 3 rows of apples with 4 in each row, 4 + 4 + 4 = 12, which we write as 3 × 4 = 12. Swapping the order of the two factors does not change the product, and a bigger problem like 23 × 4 is easier if you multiply 20 × 4 and 3 × 4 and then add. Change the rows and the number in each row of the dot array, and follow how a two-digit number is split by place value and multiplied.

Adding the Same Number

🍎 What Is Multiplication?
①3 rows of apples with 4 in each row is 4 added 3 times: 4 + 4 + 4 = 12
②We write that sum as 3 × 4 = 12 and read it three times four equals twelve
③The more times you add the same number, the more a multiplication sentence saves you

Multiplication as an Array

3
4
💡 Order Does Not Matter
①3 rows of 4 is 3 × 4 = 12, and 4 rows of 3 is 4 × 3 = 12
②Turn the dot array on its side and the rows and columns trade places, but the number of dots stays the same
③So you can swap the two factors without changing the product; this is the commutative property of multiplication

Multiplying by Place Value

23
4
✏️ Splitting by Place Value
①23 is 20 plus 3, so 23 × 4 is the same as 20 × 4 plus 3 × 4
②20 × 4 = 80 is just 2 × 4 = 8 with a zero on the end
③Add 3 × 4 = 12 to 80 and you get 23 × 4 = 92
④If the ones digit of the two-digit factor is 0, its ones product is 0 too, so the tens product is the whole answer

Summary

What Multiplication Means
3 × 4 = 4 + 4 + 4 = 12
Adding the same number several times can be written as multiplication
Commutative Property
A × B = B × A
Swapping the order of the factors gives the same product
Splitting by Place Value
23 × 4 = (20 × 4) + (3 × 4)
Multiply the tens and the ones separately, then add
🎯 Summary
①Multiplication is a short way to write repeated addition of the same number
②Swapping the two factors does not change the product
③For a two-digit number, multiply the tens and the ones separately, then add
④Any number times 0 is 0, and any number times 1 stays the same
⑤Knowing your multiplication facts makes bigger multiplication faster too

Examples and Unit Test

Example 1
Multiply 23 × 4 by splitting it by place value.
1
Split 23 into 20 and 3: 23 × 4 = (20 × 4) + (3 × 4).
2
20 × 4 = 80 and 3 × 4 = 12, so 80 + 12 = 92.
▸ 92
Finding the tens product, 80, and the ones product, 12, separately makes the work easier.
Example 2
6 × 3 = 18. Use this to find 3 × 6.
1
Swapping the two factors does not change the product.
2
So 3 × 6 = 6 × 3 = 18.
▸ 18
3 groups of 6 and 6 groups of 3 both make 18.
Unit Test
What is 34 × 2?
①64
②68
③74
④38
▸ ② 68
1
Split 34 into 30 and 4: (30 × 2) + (4 × 2).
2
30 × 2 = 60 and 4 × 2 = 8, so 60 + 8 = 68.
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Three-Digit Addition & Subtraction
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Division Basics

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