Multiplication:

Multiplication is a mathematical operation that involves adding a number to itself several times. For example, it means adding 3 four times (3 + 3 + 3 + 3). Fluently multiplying within 100 means quickly and accurately multiplying numbers where the product is 100 or less, using strategies that help solve these problems efficiently.

Strategies for Multiplying Within 100:

1. Using Known Multiplication Facts: memorize multiplication tables to recall answers quickly.
2. Skip Counting: Repeat the count by a number to reach the product (e.g., for 3×4, count "3, 6, 9, 12").
3. Using the Distributive Property: Break down larger problems into smaller parts (e.g., 6×8 as $+6\times 3$).
4. Commutative Property of Multiplication: Recognize that the order of factors doesn’t matter ($4\times 3$).
5. Using Arrays: Visualizes multiplication by arranging objects in rows and columns.

Example 1:

Simple Multiplication Using Skip Counting. Find the product of 4×5.

Solution Using Skip Counting:

• Count by 4 five times: 4, 8, 12, 16, 20.
• Final solution: 4×5=20

Example 2:

Using the Distributive Property: Find 6×8 by breaking it down.

Solution Using Distributive Property:

• Break down 8 as 5 + 3.
• Rewrite 6×8 as 6×(5+3).
• Use the distributive property: $+6\times 3$.
  • 6×5=30.
  • 6×3=18.
• Add the two results: 30 + 18 = 48.

Final solution: 30+18=48.

Example 3:

Memorizing a One-Digit Product: What is 9×7?

Solution using memorization:

• Recall from memory or previous practice that 9×7=63.
• Final solution: $63$.

Example 4:

2-Digit by 1-Digit Multiplication Using Standard Algorithm Calculate 9×23.

Solution:

• Write the numbers vertically and multiply each place separately:23× 9
• Multiply the ones place:
  • 9×3=27. Write down 7 in the one's place and carry over 2 to the tens.
• Multiply the tens place:
  • 9×2=18.
  • Add the carried-over 2: 18 + 2 = 20.
• Write the final product:

Final solution: $9\times \; 23\; =\; 207.$

Example 4:

Multiplying two 2-digit numbers: calculate 13×15.

Solution Using the Distributive Property:

• Break down both numbers:
  • 13=10+3 and
  • $15=10+5$.
• Apply the distributive property:
  • $13\times 15=(10+3)\times (10+5)$.
  • Distribute each term:
    • 10×10=100
    • 10×5=50
    • 3×10=30
    • 3×5=15
• Add the products together:
  • 100+50+30+15=195

Final solution: 13×15=195.

Why it matters:

Multiplication within 100 is a foundational skill that helps students understand patterns and relationships in numbers. It builds fluency for solving real-world problems like calculating quantities, costs, or areas. Mastering this skill prepares students for more advanced topics, including division, fractions, and algebra.

By practicing multiplication, you'll be able to solve real-world problems quickly!

Let’s practice and evaluate your work together by multiplication.