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N.4 Multiply 3 by numbers up to 12

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What is multiplication?

Multiplication is a mathematical operation that combines equal groups to find a total amount. When we multiply, we are adding the same number repeatedly.

Examples:
  • 3 × 4 means three groups of four: 4 + 4 + 4 = 12
  • 3 × 5 means three groups of five: 5 + 5 + 5 = 15
  • 3 × 6 means three groups of six: 6 + 6 + 6 = 18
Note

The numbers being multiplied are called factors. The answer is called the product. In 3 × 4 = 12, 3 and 4 are factors, and 12 is the product.

Understanding the pattern of multiplying by 3

When multiplying by 3, each product increases by 3. This creates a predictable pattern that can help you memorize the multiplication facts.

Pattern Example:
  • 3 × 1 = 3
  • 3 × 2 = 6 (3 more than 3)
  • 3 × 3 = 9 (3 more than 6)
  • 3 × 4 = 12 (3 more than 9)
  • This pattern continues through 3 × 12 = 36
Note

All products when multiplying by 3 are multiples of 3. You can check if a number is a multiple of 3 by adding its digits. If the sum is divisible by 3, the original number is too. Example: 12 → 1+2=3, and 3 is divisible by 3.

Multiplication facts for 3 up to 12

These are the basic multiplication facts you should practice and memorize. Knowing these facts helps solve more complex math problems quickly and accurately.

Multiplication Table for 3:
  • 3 × 0 = 0
  • 3 × 1 = 3
  • 3 × 2 = 6
  • 3 × 3 = 9
  • 3 × 4 = 12
  • 3 × 5 = 15
  • 3 × 6 = 18
  • 3 × 7 = 21
  • 3 × 8 = 24
  • 3 × 9 = 27
  • 3 × 10 = 30
  • 3 × 11 = 33
  • 3 × 12 = 36
Note

Notice that when multiplying 3 by an even number, the product is even. When multiplying 3 by an odd number, the product is odd. This pattern is true for all multiplication facts.

Using multiplication facts in real situations

Multiplication facts help solve everyday problems. When you encounter equal groups in real life, you can use multiplication to find the total quickly instead of adding repeatedly.

Real-World Examples:
  • If 3 friends each have 8 stickers, how many stickers are there total? (3 × 8 = 24 stickers)
  • There are 3 boxes with 7 crayons in each box. How many crayons are there? (3 × 7 = 21 crayons)
  • A tricycle has 3 wheels. How many wheels do 4 tricycles have? (3 × 4 = 12 wheels)
  • You practice piano for 3 days each week. How many days do you practice in 11 weeks? (3 × 11 = 33 days)
Note

In word problems, phrases like "each has," "in each," "per," or "for every" often indicate multiplication. Look for situations with equal groups.

Strategies for remembering multiplication facts

Several strategies can help you learn and remember multiplication facts. Different strategies work for different people, so try several to find what works best for you.

Memory Strategies:
  • Skip Counting: Count by 3s: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36
  • Doubling Then Adding: For 3 × 7, think: double 7 is 14, then add 7 more to get 21
  • Related Facts: If you know 3 × 6 = 18, then you know 6 × 3 = 18
  • Visual Grouping: Draw 3 groups with dots in each group to visualize the product
  • Rhymes and Songs: Create rhymes like "3 times 8 is 24, shut the door and say no more!"
Note

Regular practice is the most effective way to memorize multiplication facts. Try practicing for a few minutes each day rather than for a long time once a week.