Factor Pairs

Factor pairs are two numbers that you can multiply together to get another number.

Example: Finding Factor Pairs

Example with 12:

• To find factor pairs of 12, think about which numbers you can multiply together to get 12.
  • 1×12=12
  • 2×6=12
  • 3×4=12
• So, the factor pairs of 12 are:
  • (1, 12)
  • (2, 6)
  • (3, 4)

Visualizing Factor Pairs:

• You can think of factor pairs as making a rectangle with an area of 12 squares. Each pair shows the dimensions of the rectangle.
  • 1×12: One row of 12 squares.
  • 2×6: Two rows of 6 squares.
  • 3×4: Three rows of 4 squares.

Commutativity

Commutativity means that you can swap the numbers you’re adding or multiplying, and the result will be the same. This works for addition and multiplication.

Example: Commutativity of Addition

Example with 3 and 5:

• 3+5=8
• 5+3=8
• It doesn't matter if you add 3 to 5 or 5 to 3; you get the same answer.

Example: Commutativity of Multiplication

Example with 4 and 2:

• 4×2=8
• 2×4=8
• It doesn't matter if you multiply 4 by 2 or 2 by 4; you get the same answer.

Visualizing Commutativity

Addition Example:

Imagine you have 3 red apples and 5 green apples.

• If you count the red apples first: 3 (red) + 5 (green) = 8 (total apples)
• If you count the green apples first: 5 (green) + 3 (red) = 8 (total apples)
• You still have 8 apples either way.

Multiplication Example:

Imagine you have 4 rows of 2 stars each, or 2 rows of 4 stars each.

• 4×2:

* * 

* * 

* * 

* * 

= 8 stars

• 2×4:

 

* * * * 

* * * * 

= 8 stars

• You still have 8 stars either way.

Summary

1. Factor Pairs:
   • Two numbers you multiply to get another number.
   • Example: Factor pairs of 12 are (1, 12), (2, 6), and (3, 4).
2. Commutativity:
   • You can swap numbers in addition or multiplication, and the result stays the same.
   • Example: 3+5=8 and 5+3=8 (Addition); 4×2=8and 2×4=8 (Multiplication).

By using simple language and visual examples, children can easily grasp these fundamental math concepts.