Download Presentation
## Note to the Presenter

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -

**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**Commutative, Associative, Identity Properties of Addition and Multiplication Distributive Property of Multiplication over Addition Additive and Multiplicative Inverse Properties Multiplicative Property of Zero**Changes in the SOL**• The properties are now taught in the following order:**Commutative Property of Addition**3+5 = 8 5+3 = 8 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.**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.**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.**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.**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.**Distributive Property of Multiplication over Addition**Does 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.**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)**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.**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, Let’s use pattern blocks to show and**Inverse Property for Multiplication**Lay out 4 unit pieces. One-forth of four gives one unit piece.**Inverse Property for Multiplication**Lay out three half pieces Two-thirds of three-halves gives two halves which is equivalent to one unit piece**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.**Discussion**• What did you learn from this session? • How would you apply this to your classroom? • What is still unclear? • Comments and/or concerns?