Activity: Identifying Properties of Real Numbers

Format: Small group or Large Group

Objectives: Participants will identify properties of real numbers.

Related 2009 SOL(s): 7.16 The student will apply the following properties of operations with real numbers: a) the commutative and associative properties for addition and

multiplication; b) the distributive property; c) the additive and multiplicative identity properties; d) the additive and multiplicative inverse properties; and e) the multiplicative property of zero.

Materials: A set of the activity cards (Note that you will need multiples of the operation cards and variable cards) A recording sheet for each participant

Time Required: 90 minutes

Directions: 1. Seventh grade is now about reviewing the properties that are now taught in the grades 3 through 6.

2. Have three participants stand in front of the group with the cards 3, +, and 5 and have the other participants record on the left hand side of the recording sheet 3+5 then have the participants holding the 3 and 5 cards switch places to show the commutative aspect. Have the seated participants record on the right hand side 5+3. Emphasize around what card (operation) the participants are moving.

3. Next, have the five participants stand in front of the group holding cards to make the expression 2 + 3+ 4 , and have the other participants record this expression on the left hand side of the recording sheet. Which participants could move in order to demonstrate the commutative property of addition? Is there another possibility? (Show 2 + 3+ 4 = 2 + 4 + 3 and 2 + 3+ 4 = 3+ 2 + 4 )

4. Include examples that involve variables and other operations as distracters. Possible examples could include: c + 5 = 5 + c a + b = b + a 2x + 5 = 5 + 2x 2i3+ 4 = 4 + 2i3 2 3+ 4( ) = 2 4 + 3( ) 2 + 3( ) + 4 + 5( ) = 4 + 5( ) + 2 + 3( ) a b + c( ) = a c + b( )

5. Repeat the activity for the Commutative property for multiplication, the Associative properties for addition and multiplication, and the Distributive property of multiplication over addition, having the participants record on a new chart for each property.

6. Possible examples could include: Commutative property for multiplication (use whichever multiplication symbol you prefer in your examples) 6 × 5 = 5 × 6 7i2 = 2i7 5y = yi5 (Discuss the understood multiplication symbol on the left) 2i3i4 = 2i4i3 ab = ba 2z + 5 = zi2 + 5

2i 3+ 4( ) = 3+ 4( )i2

2 3i4( ) = 2 4i3( ) 6 + 7( ) 4 + 5( ) = 4 + 5( ) 6 + 7( ) xzy = xyz Associative property for addition 2 + 7 + 5( ) = 2 + 7( ) + 5 2 + 3+ 4 = 2 + 3+ 4( ) (Has the order in which we add changed?) 2a + 3( ) + 8 = 2a + 3+ 8( ) 4x + 2x + 9( ) = 4x + 2x( ) + 9 9 2 + 3+ 8( )( ) + 7 = 9 2 + 3( ) + 8( ) + 7 Associative property for multiplication

2 7i5( ) = 2i7( )5

2i3i4 = 2 3i4( ) (Has the order in which we multiply changed?)

2ai3( )8 = 2a 3i8( )

4x 2xi9( ) = 4xi2x( )9

9 − 2 3i8( )( ) + 7 = 9 − 2i3( )8( ) + 7 Distributive property of multiplication over addition 2 c + 3( ) = 2c + 6 2 1+ 4( ) = 2 + 8 3 a + 2b( ) = 3a + 6b a x + y + 4( ) = ax + ay + 4a 3+ 4( )2 = 6 + 8 3x 1+ 2y( ) = 3x + 6xy b + c( )a = ab + ac

7. Note: it is important to emphasize the entire name of the property when working with students because they often try to misapply properties to other situations. For example with the distributive property, students try and apply to exponents and make the incorrect statement of 2 + 3( )2 = 22 + 32 . There is no distributive property of exponents over addition!

8. Discussion – How would you use this activity with students? How would you assess students’ ability to identify properties?

Closing and Debriefing:

Possible questions to ask: • What did you learn from this session? • How would you apply this to your classroom? • What is still unclear? • Comments and/or concerns?

Reflection for Presenter: (Please reflect on and complete the questions below immediately after delivering the session) What specific examples of learning did you note? What specific errors and/or misconceptions still need to be corrected? Summarize the workshop evaluations.

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