note to the presenter
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Note to the Presenter. Print the notes of the power point (File – Print – select print notes) to have as you present the slide show. There are detailed notes for the presenter that go with each slide. Investigating Properties of Real Numbers. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Note to the Presenter](https://reader033.vdocuments.site/reader033/viewer/2022051316/568157f3550346895dc571ae/html5/thumbnails/1.jpg)
Note to the Presenter
Print the notes of the power point (File – Print – select print notes) to have as you present the slide show. There are detailed notes for the presenter that go with each slide.
![Page 2: Note to the Presenter](https://reader033.vdocuments.site/reader033/viewer/2022051316/568157f3550346895dc571ae/html5/thumbnails/2.jpg)
Investigating Properties of Real
NumbersCommutative, Associative, Identity Properties
of Addition and Multiplication
Distributive Property of Multiplication over Addition
Additive and Multiplicative Inverse Properties
Multiplicative Property of Zero
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Changes in the SOL
• The properties are now taught in the following order:
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Commutative Property of Addition
Does the order in which we add two quantities matter?
That is, does a+b = b+a ?
Let’s use Cuisinaire Rods to investigate the property.
Is 3+5 the same as 5+3?
They are the same because both have a length of 8 units.
3+5 = 8 5+3 = 8
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Commutative Property of Multiplication
Does the order in which we multiply two quantities matter?
That is, does a x b = b x a ?
Let’s use counters to investigate the property.
Is 6x2 the same as 2x6?
They are the same because both equal 12.
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Commutative Property of Multiplication
We can also use grid paper to investigate.
Cut out a rectangle with 2 rows and 6 columns and another with 6 rows and 2 columns.
They have the same area of 12 square units.
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Associative Property of Addition
Does the way in which we group quantities when adding matter?
That is, does a+(b+c) = (a+b)+c ?
Let’s use Cuisinaire Rods to investigate the property.
Is 2+(3+5) the same as (2+3)+5?
They are the same because both have a length of 10 units.
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Associative Property of Multiplication
Does the way in which we group quantities when multiplying matter?
That is, does a(bc) = (ab)c ?
Let’s use counters to investigate the property.
Are 3x(2x6) and (3x2)x6 the same?
They are both equivalent to 36.
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Distributive Property of Multiplication over
AdditionDoes the product of a number and a
sum equal the sum of the individual products?
That is, does a(b+c) = ab+ac ?
Let’s use counters to investigate the property.
Are 2(3+5) and 2x3+2x5 the same?
They are both equivalent to 16.
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Identity Properties For Addition and Multiplication
Adding or Multiplying a number by an identity number retains the “identity” or original value of that number
What number can we add to 5 and not change its value?
Zero
0+5 = 5 and 5+0 = 5
What number can we multiply by 6 and not change its value?
One
1x6 = 6 (one group of six) and 6x1 = 6 (six groups of one)
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Multiplicative Property of Zero
What happens when you multiply by zero?
The result is zero.
a x 0 = 0 and 0 x a = 0
Discuss how 0x6 (zero groups of six) and
6x0 (six groups of zero) both result in 0.
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Inverse Property for Multiplication
The inverse property of multiplication tells us that two numbers are inverses if their product is one (the multiplicative identity).
That is, a×1a
=1 orab
×ba
=1
Let’s use pattern blocks to show and 1
4×4 =1
2
3×
32
=1
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Inverse Property for Multiplication
Lay out 4 unit pieces.
1
4×4 =1
One-forth of four gives one unit piece.
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Inverse Property for Multiplication
Lay out three half pieces
Two-thirds of three-halves gives two halves which is equivalent to one unit piece
2
3×
32
=1
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Inverse Property for Multiplication
3 groups of what will equal 1?
Make 3 groups
Take a unit piece and divide it into three pieces. Put one piece in each group.
3×? =1
Thus 3×13
=1
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Discussion
• What did you learn from this session?
• How would you apply this to your classroom?
• What is still unclear?
• Comments and/or concerns?