MathIsimple
Lesson 5-2

Addition Properties

Explore the commutative and associative properties of addition through hands-on activities

CommutativeAssociativeVisual LearningHands-on
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Two Important Properties

Learn how numbers can be rearranged and grouped in addition

Commutative Property

a + b = b + a

The order of addends doesn't change the sum. You can add numbers in any order and get the same answer.

Examples:

3 + 5 = 5 + 3 (both equal 8)
2 + 7 = 7 + 2 (both equal 9)
4 + 6 = 6 + 4 (both equal 10)

Associative Property

(a + b) + c = a + (b + c)

The way you group addends doesn't change the sum. You can add numbers in different groups and get the same answer.

Examples:

(2 + 3) + 4 = 2 + (3 + 4) (both equal 9)
(1 + 5) + 2 = 1 + (5 + 2) (both equal 8)
(3 + 4) + 6 = 3 + (4 + 6) (both equal 13)

Interactive Practice

Practice the properties through hands-on activities

Block Building Challenge

Use virtual blocks to demonstrate the commutative property.

Activity: Rearrange blocks to show that 3 + 5 = 5 + 3

Grouping Game

Practice the associative property by grouping numbers differently.

Activity: Show that (2 + 3) + 4 = 2 + (3 + 4) using visual grouping

Property Detective

Identify which property is being used in different equations.

Activity: Match equations to their properties and explain why they work

Example Library

See step-by-step demonstrations of addition properties

Commutative Property: Block Building

Problem:

Show that 3 + 5 = 5 + 3 using blocks

Solution:

Both arrangements give the same total: 8 blocks

Steps:

  1. 1Arrange 3 blue blocks + 5 red blocks = 8 total
  2. 2Rearrange to 5 red blocks + 3 blue blocks = 8 total
  3. 3Notice both arrangements have the same total
  4. 4This shows 3 + 5 = 5 + 3

Visual:

3 blue + 5 red = 5 red + 3 blue = 8 blocks total

Associative Property: Grouping Blocks

Problem:

Show that (2 + 3) + 4 = 2 + (3 + 4) using blocks

Solution:

Both groupings give the same total: 9 blocks

Steps:

  1. 1First way: (2 + 3) + 4 = 5 + 4 = 9
  2. 2Second way: 2 + (3 + 4) = 2 + 7 = 9
  3. 3Both ways give the same answer: 9
  4. 4This shows (2 + 3) + 4 = 2 + (3 + 4)

Visual:

(2 + 3) + 4 = 2 + (3 + 4) = 9 blocks total

Commutative Property: Real Objects

Problem:

Use toys to show that 4 + 6 = 6 + 4

Solution:

4 cars + 6 trucks = 6 trucks + 4 cars = 10 vehicles

Steps:

  1. 1Count 4 cars and 6 trucks: 4 + 6 = 10
  2. 2Rearrange to 6 trucks and 4 cars: 6 + 4 = 10
  3. 3Both arrangements have 10 vehicles
  4. 4This shows 4 + 6 = 6 + 4

Visual:

4 cars + 6 trucks = 6 trucks + 4 cars = 10 vehicles

Associative Property: Making 10

Problem:

Use the associative property to make addition easier

Solution:

Group numbers that make 10 first

Steps:

  1. 1Problem: 7 + 3 + 2
  2. 2Group (7 + 3) + 2 = 10 + 2 = 12
  3. 3Or group 7 + (3 + 2) = 7 + 5 = 12
  4. 4Both ways give the same answer: 12

Visual:

(7 + 3) + 2 = 7 + (3 + 2) = 12

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