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# Addition Properties

### Review of the Identity, Commutative, and Associative Properties of Addition

Question | Answer |
---|---|

7 + 0 = 0 | Identity |

0 + 5 = 5 | Identity |

a + 0 = a | Identity |

3 + 0 = 3 | Identity |

12 + 0 = 12 | Identity |

0 + 9 = 9 | Identity |

0 + 15 = 15 | Identity |

0 + a = a | Identity |

11 + 0 = 11 | Identity |

8 + 0 = 8 | Identity |

4 + 5 = 5 + 4 | Commutative |

2 + 1 = 1 + 2 | Commutative |

a + b = b + a | Commutative |

16 + 4 = 4 + 16 | Commutative |

9 + 2 = 2 + 9 | Commutative |

3 + 6 = 6 + 3 | Commutative |

b + a = a + b | Commutative |

red + blue = blue + red | Commutative |

yellow + nothing else = yellow | Identity |

me + no one = me | Identity |

purple + orange = orange + purple | Commutative |

six + three = three + six | Commutative |

twelve + zero = twelve | Identity |

ten + two = two + ten | Commutative |

(6 + 5) + 2 = 6 + (5 + 2) | Associative |

To have the ability to travel around, or commute, in a math sentence | Commutative |

To have the ability to change groupings, or associations, with other numbers in a math sentence | Associative |

To have the ability to maintain the same number, or identity, when added to zero in a math sentence | Identity |

A property that says you can keep a number's identity when it is added to zero | Identity |

A rule in math that allows you to write the same number as the answer when you add that number to zero | Identity |

A rule in math that lets you regroup numbers in any order when you are adding | Associative |

A property that says you can group addends in any way and still get the same sum | Associative |

A rule in math that lets you move the numbers around in any order when working with an addition problem | Commutative |

A property that says you can rearrange numbers in an addition sentence in any order and the results will still be the same | Commutative |

5 + (8 + 2) = (5 + 8) + 2 | Associative |

7 + (10 + 20) = (7 + 10) + 20 | Associative |

(3 + 11) + 6 = 3 + (11 + 6) | Associative |

(3 + 4) + 3 = 3 + (4 + 3) | Associative |

9 + (15 + 2) = (9 + 15) + 2 | Associative |

a + (b + c) = (a + b) + c | Associative |

red + (blue + yellow) = (red + blue) + yellow | Associative |

(one + two) + five = one + (two + five) | Associative |

chair + stool = stool + chair | Commutatuve |

chair + (table + lamp) = (chair + table) + lamp | Associative |

16 + (7 + 5) = (16 + 7) + 5 | Associative |

a + o = a | Identity |

a + b = b + c | Commutative |

(a + b) + c = a + (b + c) | Associative |

a + 0 = a | Identity |

a + b = b + c | Commutative |

(a + b) + c = a + (b + c) | Associative |

States that the sum of zero and any number or variable is the number or variable itself | Identity |

When zero is added to any real number the number remains unchanged, i.e. it does not looses its identity | Identity |

Tells us that with addition we can group numbers in any way we want and still get the same answer | Associative |

When three or more numbers are added, the sum is the same regardless of the grouping of the addends | Associative |

The sum of any number and zero is the original number | Identity |

When two numbers are added, the sum is the same regardless of the order of the addends | Commutative |

A property of real numbers which states that the sum of two terms is unaffected by the order in which the terms are added | Commutative |

This property means that addends can be added in any order and the sum is always the | Commutative |

An addition property that says changing the order of addends does not change the sum, for example, if a and b are two real numbers, then a + b = b + a | Commutative |

It does not matter if you put your left shoe on and then your right, or your right shoe on and then your left. The result is exactly the same. Either way, you go from a state of not wearing shoes, to a state of wearing shoes. | Commutative |

In addition, this is when two items give the same result regardless of order they appear. | Commutative |

Q + P = P + Q | Commutative |

You are paying for an item that costs $6. Regardless of whether you hand the cashier $1 first and then $5 OR you hand her $5 first and then $1, the amount you handed her is the same, $6. This demonstrates which property? | Commutative |

You have 2 apples. Your friend gives you zero apples. Therefore, the total number of apples you have remains the same, 2 apples. This demonstrates which property? | Identity |

y + z = z + y | Commutative |

When adding zero to any number, the quantity does not change. | Identity |

Zero becomes the same as whatever number is added to it. | Identity |

Rearranging the grouping parentheses in an addition sentence will not change its total value. | Associative |

In making a cake, you can mix the eggs and the sugar together first and then add the oil OR you can mix the oil and sugar together first and then add the eggs and the result will be the same either way. This demonstrates which math property? | Associative |

y + (z + n) = (y + z) + n | Associative |

(Q + P) + S = Q + (P + S) | Associative |

This property of addition simply says that the way in which you group three or more numbers when adding them up does not affect the sum | Associative |

Created by:
OhanaTribe