How are - 11 + 9 and 9 + (- 11) related?
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Transcript of How are - 11 + 9 and 9 + (- 11) related?
How are -11 + 9 and 9 + (-11) related?
In this lesson you will learn to demonstrate the commutative property of addition by using a
number line.
Let’s ReviewLet’s Review
What’s an integer?Integers include positive and negative
whole numbers as well as 0. ...-3, -2, -1, 0, 1, 2, 3 ...
Non-Examples: -5.2 0.28 -9.9 4
Let’s ReviewLet’s Review
Positive NumbersNegative Numbers
Increasing in Value
Decreasing in Value
What’s a number line?
Let’s ReviewLet’s Review
What’s addition?Addition is the process of joining two groups.
7 + 11 = 18
addend addend sum
Let’s ReviewA Common Mistake
Re-ordering the addends in an addition problem without re-ordering the signs.
+9-11+
9 11-
Commutative Property
Let’s ReviewA Common Mistake
+9-11+9 11-
=-
Re-ordering the addends in an addition problem without re-ordering the signs.
Let’s ReviewA Common Mistake
+9-11+
9-11( )( )
Re-ordering the addends in an addition problem without re-ordering the signs.
Let’s ReviewA Common Mistake
+9-11=+9 -11( )( )
Commutative Property
Re-ordering the addends in an addition problem without re-ordering the signs.
Let’s ReviewCore Lesson
62
8
6 2
8
6 + 2
2 + 6Commutative Property
Let’s ReviewCore Lesson
-4 -3
-4 + (-3)
-3 + (-4)
-7
-4-3
-7
Commutative Property
Let’s ReviewCore Lesson9-11
9 + (-11)
-11 + 9
-2-11
9
-2
Commutative Property
In this lesson you learned to demonstrate the commutative property of addition by using a
number line.
Let’s ReviewGuided Practice
14 + (-9)
-9 + 14
Show that 14 + (-9) is equal to -9 + 14.
Let’s ReviewGuided Practice
-6 + (-8)
-8 + (-6)
Demonstrate that -6 + (-8) has the same value as -8 + (-6).
Let’s ReviewExtension Activities
Use Cuisenaire rods to represent integers 1-10. Model addition problems that show the commutative property by laying the rods on a number line.These rods represent 8 + (-5) and -5 + 8.
Both sums are positive 3!
Let’s ReviewExtension Activities
The commutative property of addition is sometimes called the order property.Use the commutative property to rearrange these addition expressions so you can add them mentally. (Hint: Try to make sets of ten.)A) -15 + 28 + (-5)B) -99 + 17 + 3 + (-1)C) 74 + 12 + (-4) + 5
Let’s ReviewExtension Activities
Partner Game:First partner writes an integer addition problem for the second partner.
The first partner solves the original problem on her own paper. The second partner switches addends using the commutative property and solves the equivalent problem on his paper.
Both partners compare their answers.
Let’s ReviewQuick Quiz
Which expression has the same value as -13 + 7?A) 7 + (-13)B) 13 + (-7)C) -13 + (-7)D) -7 + 13
Which expression has the same sum as -9 and -2?A) 2 + 9B) 2 + (-9)C) 9 + 2D) -9 + (-2