Mathematics
Grade 3
15 min
Solve using properties of addition
Solve using properties of addition
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1
Introduction & Learning Objectives
Learning Objectives
Identify the Commutative, Associative, and Identity properties of addition.
Explain that changing the order of addends does not change the sum (Commutative Property).
Explain that changing the grouping of addends does not change the sum (Associative Property).
By the end of of this lesson, students will be able to apply the Identity Property by showing that any number plus zero equals that same number.
Solve addition problems with three or more numbers by reordering or regrouping addends to make the calculation easier.
Use the properties of addition to find missing numbers in an equation.
Have you ever noticed that counting your red blocks and then your blue blocks gives you the same total as counting the blue ones first? Let's find out why! 🤔
Toda...
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Key Concepts & Vocabulary
TermDefinitionExample
AddendAny of the numbers that are being added together.In the problem 5 + 3 = 8, the numbers 5 and 3 are the addends.
SumThe total or the answer you get when you add numbers together.In the problem 5 + 3 = 8, the number 8 is the sum.
Commutative Property (Order Property)This rule says you can add numbers in any order, and the sum will stay the same.4 + 6 is the same as 6 + 4. Both equal 10.
Associative Property (Grouping Property)This rule says you can group addends in different ways using parentheses, and the sum will stay the same. Parentheses tell you which numbers to add first.(2 + 3) + 5 is the same as 2 + (3 + 5). Both equal 10.
Identity Property (Zero Property)This rule says that the sum of any number and zero is that same number.9 + 0 = 9. The number 9 keeps...
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Core Formulas
Commutative Property of Addition
a + b = b + a
Use this rule to switch the order of numbers to put 'friendly numbers' (like pairs that make 10) next to each other.
Associative Property of Addition
(a + b) + c = a + (b + c)
Use this rule to change which numbers you add first. The parentheses show you which group to add first to make the problem simpler.
Identity Property of Addition
a + 0 = a
Use this rule when you see a zero in an addition problem. You know the answer is just the other number.
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Challenging
Four friends have sticker collections: Amy has 47, Ben has 32, Carla has 18, and David has 19. To find the total number of stickers for all four friends, which two friends' collections should you add together first to make the problem easiest?
A.Amy and David (47 + 19)
B.Ben and Carla (32 + 18)
C.Amy and Ben (47 + 32)
D.Carla and David (18 + 19)
Challenging
If `X + Y = Z`, then which of the following must also be true because of the Commutative Property?
A.Y + X = Z
B.Z - Y = X
C.X + Y + 0 = Z
D.(X + Y) + 1 = Z + 1
Challenging
A student is asked to solve `135 + 29 + 0`. They say, "I can't solve this because there's a zero." What property of addition could you explain to help them realize the problem is simpler than it looks?
A.The Commutative Property, because you can change the order.
B.The Associative Property, because you can group the big numbers.
C.The Distributive Property, because you can break the numbers apart.
D.The Identity Property, because adding zero doesn't change the number.
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