1/15
00:00

D.1 Recognize multiplication patterns with increasing place value

Loading questions...

What are multiplication patterns?

Multiplication patterns are predictable relationships between numbers that help us understand how multiplication works when numbers increase or decrease. Recognizing these patterns helps students multiply larger numbers efficiently and understand place value relationships.

Examples:
  • 3 × 4 = 12
  • 30 × 4 = 120
  • 300 × 4 = 1,200
Note

Each time you multiply a number by 10, 100, or 1,000, the product increases by one or more place values — moving one, two, or three places to the left.

How does place value affect multiplication?

In multiplication, place value determines the size or magnitude of each digit in a number. When you multiply by powers of 10, each digit shifts one place to the left for every zero added, increasing the product by a factor of ten.

Examples:
  • 7 × 10 = 70 (the 7 moves one place to the left)
  • 7 × 100 = 700 (the 7 moves two places to the left)
  • 7 × 1,000 = 7,000 (the 7 moves three places to the left)
Note

The number of zeros in the factor of 10 tells you how many places to move each digit to the left in the product.

Recognizing patterns in multiplication tables

Multiplication tables show repeating patterns that continue as numbers grow. Understanding these helps predict products and connect multiplication facts to larger numbers.

Examples:
  • 2 × 3 = 6 → 20 × 3 = 60 → 200 × 3 = 600
  • 5 × 6 = 30 → 50 × 6 = 300 → 500 × 6 = 3,000
Note

When one factor increases by a power of 10, the product also increases by the same power of 10. This pattern helps build fluency in multiplying larger numbers.

Applying multiplication patterns to solve problems

Using multiplication patterns allows students to solve problems mentally and check for reasonableness. By noticing how place value shifts, students can estimate and calculate efficiently.

Examples:
  • If 4 × 6 = 24, then 40 × 6 = 240 and 400 × 6 = 2,400.
  • If 8 × 7 = 56, then 80 × 7 = 560.
  • If 9 × 5 = 45, then 900 × 5 = 4,500.
Note

Always relate the new problem to a basic fact you already know. Use place value reasoning to adjust your answer correctly.

Thinking mathematically about patterns

Understanding multiplication patterns helps you think critically about numbers and their relationships. Patterns are the foundation for algebraic thinking, preparing you to analyze relationships between numbers and variables.

Examples:
  • When you multiply by 10, each product is 10 times greater than before.
  • When both factors increase by 10, the product increases by 100 times.
  • Recognizing patterns helps identify errors and understand how numbers grow.
Note

Mathematical patterns show how multiplication connects to place value and algebra. Understanding these patterns builds confidence for higher-level math concepts.