reciprocal Multiplicative Property Atctbtc Multiplicative Identity Multiplicative Property =bta Commutative Reflexive Property Identity b=c Atb

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1 Properties of s Reflexive Property ll # 's equal mselves If same nvmber equals C # anor y and nor # Z n Yandz aretm Property Substitution If for bc b Transitive Property dditive a Second Identity Inverse can you same as equal to that # O itself minus Zero 'l times of Inverse Zero Property equal times zero reciprocal reciprocal tb bt matter to 00 i k times doesn't one it zero Multiplicative Property Commutative plus t Multiplicative Identity n anor as t0 Multiplicative same ny dditive tctbtc b order you zero at L equals I ofit add or multiply replace first

2 ssociative Property ( at b) + C atlbtc )

3 ) 2) How many fires would re be in 5 years? Lesson 13 Properties of Numbers Objectives I can recognize properties of equality and identity I can recognize Commutative and ssociate Properties CCSS SSE1b SSE2 MP2 MP3 Example 1 Evaluate Using Properties Evaluate ( 4) t 3 ( 15 't 5 Name property used in each step Sub Multiplicative It 3 ( 1) inverse 14 Multiplicative + } sins 4 4 ( 4) + 3 (32) identity +3 ( 1) Guided Practice 1 Evaluate Using Properties Name property used in each step dditive inverse a Sub dditive identity dditive inverse multiplicative multiplicative dditive identity inverse property of zero

4 25 Real World Example 2 pply Properties of Numbers Trail Name Miles Bent Tree 425 Knob Hill 650 Meadowrun 900 ] Pinehurst 775 Melanie made a lt of trail lengths to find total miles she rode Find total miles Melanie rode her horse ( ) (650+9) commgtihu associative Guided Practice 2 pply Properties of Numbers 2750M Rafael buying furnhings for h first apartment He buys a couch for $300 lamps for $3050 a rug for $2550 and a table for $50 Find total cost of se items Example 3 Use Multiplication Properties Evaluate using properties of s Name property used in each step Guided Practice 3 Use Multiplication Properties Evaluate each expression using properties of s Name property used in each step a 4 (25) ( g 7) 10 ( 56 ) 560 )4 ( 2940 ) t Sub communard associative commutative 5 b 5 y Commutative Hub zs@ubl25z Sub $2

5 Lesson 14 The Dtributive Property Objectives I can use Dtributive Property to evaluate expressions I can use Dtributive Property to simplify expressions CCSS SSE1a SSE2 MP1 MP8 Real World Example 1 Dtribute Over ddition (UPS Check Strategy) John walks 5 days a week He walks at a fast rate for 7 minutes and cools down for 2 minutes Use Dtributive Property to write and evaluate an expression that determines total of minutes John walks ~ 5 7 ( + 2) Guided Practice 1 Dtribute Over ddition (UPS Check Strategy) group of 3 adults an 11year old and 2 children under 10 years old are going to a University of South Florida Bulls baseball game Write and evaluate an expression to determine cost of tickets for group 35T 3 n (1+2) Example 2 Mental Math Use Dtributive Property to rewrite Then evaluate Guided Practice 2 Mental Math Use Dtributive Property to rewrite each expression Then evaluate 24 ( 1* ) + 2C 8D a 304(15) x 304 ( 10+5 )

6 6a2 44#tk ) Example 3 lgebraic Expressions Rewrite each expression using Dtributive Property Then a 12(y + 3) 12g v Guided Practice 3 lgebraic Expressions Rewrite each expression using Dtributive Property Then simplify a a (8 + 4n)2 16 t 8h an 6(r + 3g t) her 18g + let M c (2 5q)(3) 6 +15g Example 4 Combine Like Terms a Simplify 17a + 21a 38 a Simplify Guided Practice 4 Combine Like Terms Simplify each expression If not possible write simplified a Simplified 4b2+6b + 5a +4

7 ' Lesson 15 Equations Objectives I can solve equations with one variable I can solve equations with two variables CCSS CED1 REI3 MP3 Example 1 Use a Replacement Set Find solution set of equation 4a if replacement set { } a z No! a4 Yes! No! 4( 2) C 4) Solve {3 4C 6) No a 3 NO! y( g) +yzz ) 1723 zz±z Standardized Test Example 2 pply Order of Operations 3+4 ( 82 ) 344 ( 6) 3+24 } B 27 C 33 D 42 Guided Practice 2 pply Order of Operations Solve % 81 ( 3) O F 3 G 6 H 142 J Example 3 Solutions of Equations Solve each equation a 4+(9+7) th8 4tl6 h8 n4 4h ( 14 )4n 9 Guided Practice 3 Solutions of Equations a Nosowsim 22 1 m ZM MZZ

8 Kc 32kt 45 32k TO No solution Example 4 Identities Solve 7t3k 7 kt7 (5+2) +3k 3k True Guided Practice 4 Identities Solve each equation a 2 d t (85) c Zd K R bbcmu?c C Example 5 Equations Involving Two Variables Dalila pays $16 per month for a gym membership In addition she pays $2 per Pilates class Write and solve an equation to find total amount Dalila spent th month if she took 12 Pilates classes Guided Practice 5 Equations Involving Two Variables melia drives an average of 65 miles per hour Write and solve an equation to find time it will take her to drive 36 miles g 13g ( B 65T It Zd NO 42 C solution 12 ) B B@ t