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Grade 3 (age 8-9)

Multiplication

Multiplication

Multiplication is a short way to write repeated addition. 3 rows of 4 apples make 4 + 4 + 4 = 12, so 3 × 4 = 12. The order does not change the answer, and a big product like 23 × 4 splits into 20 × 4 and 3 × 4. Slide the rows and columns to see the array, then split a two-digit number by place value.

Multiplication = Repeated Addition
🍎 What is Multiplication?
①3 rows of apples, 4 per row
②3+3+3+3? No! 4+4+4 = 12, so 3 × 4 = 12
③Repeated addition can be written as multiplication!
Multiplication as Arrays
3
4
💡 Commutative Law
①3 × 4 = 12 and 4 × 3 = 12
②Swapping rows and columns gives the same total!
③This is the commutative law
Two-digit × One-digit Decomposition
23
4
✏️ Decompose to Calculate
①Big multiplication: split by place values
②23 × 4 = (20 × 4) + (3 × 4) = 80 + 12 = 92
③Multiply ones, multiply tens, then add!
Summary
Meaning of Multiplication
3 × 4 = 4 + 4 + 4 = 12
Repeated addition written as multiplication
Commutative Law
A × B = B × A
Order does not change result
Decomposition
23 × 4 = (20 × 4) + (3 × 4)
Multiply by place values then sum
🎯 Key Points
①Memorize times tables = easy multiplication
②Order does not matter (commutative)
③Big multiplication: decompose by place
④Multiply by 0 → always 0
⑤Multiply by 1 → same number
Examples and Unit Test
Example 1
Calculate 23 × 4 by decomposing into place values.
1
Split 23 into 20 and 3: (20 × 4) + (3 × 4).
2
20 × 4 = 80, 3 × 4 = 12. 80 + 12 = 92.
▸ 92
Two-digit multiplication splits into tens and ones, multiplies each, then adds.
Example 2
Given 6 × 3 = 18, use it to find 3 × 6.
1
Multiplication gives the same answer when the order is swapped (commutative law).
2
So 3 × 6 = 6 × 3 = 18.
▸ 18
3 × 6 and 6 × 3 give the same answer; this is the commutative law of multiplication.
Unit Test
What is the value of 34 × 2?
①64
②68
③74
④38
▸ ② 68
1
Split 34 into 30 and 4: (30 × 2) + (4 × 2).
2
60 + 8 = 68.
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Division