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Learning Objective: We&will&add&and&subtract...

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Name: ___________________________________ Math 7.2, Period _____________ Mr. Rogove Date: _______________ Alg1M1L3: Adding and Subtracting Polynomials 1 Learning Objective: We will add and subtract polynomials. (Alg1M1L3) Activating Prior Knowledge: We know how to combine like terms with monomials 4! ! 5! 3! ! + !! ! + 12! 3! ! ! ! + 2! ! ! ! 12! ! ! ! ! ! ! ! Concept Development: We need to use the commutative property when adding polynomials to group like terms together. Example: 5! ! + 3 + (! ! 6) We need to use the distributive property when subtracting polynomials to distribute the negative. Example: 13! ! 2! ! (2! ! + 6! ! ) We can add or subtract vertically or horizontally. Example: 5! ! 3! + 12 + (3! ! 12! 1)
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Page 1: Learning Objective: We&will&add&and&subtract ...mrrogove2016.weebly.com/uploads/4/3/0/0/43009773/alg1m1l...Name:&_____& & Math7.2,Period_____& Mr.Rogove& & Date:_____& 1& Alg1M1L3:&Adding&and&Subtracting&Polynomials&

Name:&___________________________________& & Math&7.2,&Period&_____________&Mr.&Rogove& & Date:&_______________&

Alg1M1L3:&Adding&and&Subtracting&Polynomials&1&

Learning Objective:&We&will&add&and&subtract&polynomials.&(Alg1M1L3)&&Activating Prior Knowledge: We&know&how&to&combine&like&terms&with&monomials&&

4!! − 5! − 3!! + !!! + 12!&&&&&&&&

&3!!!! + 2!!!! − 12!!!! − !!!!&

&&Concept Development: We&need&to&use&the&commutative&property&when&adding&polynomials&to&group&like&terms&together.&&Example:))5!! + 3 + (!! − 6)&&&&&&We&need&to&use&the&distributive&property&when&subtracting&polynomials&to&distribute&the&negative.&&Example:&13!! − 2!! − (2!! + 6!!)&&&&&&We&can&add&or&subtract&vertically&or&horizontally.&&Example:&&5!! − 3! + 12 + (3!! − 12! − 1)&&&&&&

Page 2: Learning Objective: We&will&add&and&subtract ...mrrogove2016.weebly.com/uploads/4/3/0/0/43009773/alg1m1l...Name:&_____& & Math7.2,Period_____& Mr.Rogove& & Date:_____& 1& Alg1M1L3:&Adding&and&Subtracting&Polynomials&

Name:&___________________________________& & Math&7.2,&Period&_____________&Mr.&Rogove& & Date:&_______________&

Alg1M1L3:&Adding&and&Subtracting&Polynomials&2&

Guided Practice: Steps&for&Adding&Polynomials&1.&Use&the&commutative&property&to&group&like&terms.&&2.&Combine&like&terms&and&restate&the&polynomial&in&standard&form.&&&

6!! + 5! + 2 + −4!! + 3! − 7 &&&&&&&

5!! − 2! + 3 + !! + ! + 2 &

3!! − 2! + 4!! − 14 + (5! + 6 − 5!!)&&&&&&&&

−2!! + 3! − 7!! − 4 + (2!! + 8!! − 6 + 10!!)&

&Steps&for&Subtracting&Polynomials&1.&Use&the&distributive&property&to&distribute&the&negative&sign.&2.&Use&the&commutative&property&to&group&the&like&terms.&&3.&Combine&like&terms&and&restate&the&polynomial&in&standard&form.&&4.&Or,&line&up&vertically&and&subtract.&&&

5!! + 4! + 3 − 2!! − 6! + 8 &&&&&&&

3!!!! + !!!! − 4!!!! −&&!!!!!!!!!!!!!!!!!!!!!!!!(−3!!!! + 2!!!! − 6!!!!)&

!! − 7! − 2!! − 4 − (3!! − 8! + 4!!)&&&&&&&&&

−3! + 4!! + 9 − 7!! − (−6!! + 2 − !!)&

Page 3: Learning Objective: We&will&add&and&subtract ...mrrogove2016.weebly.com/uploads/4/3/0/0/43009773/alg1m1l...Name:&_____& & Math7.2,Period_____& Mr.Rogove& & Date:_____& 1& Alg1M1L3:&Adding&and&Subtracting&Polynomials&

Name:&___________________________________& & Math&7.2,&Period&_____________&Mr.&Rogove& & Date:&_______________&

Alg1M1L3:&Adding&and&Subtracting&Polynomials&3&

&Independent Practice: In&square&inches&the&area&of&the&square&is&4!! − 2! − 6&and&the&area&of&the&triangle&is&2!! + 4! − 5.&&What&polynomial&represents&the&shaded&region?&&&&&&&&&&&&&&&&&&&&

The&area&of&the&shaded&triangle&is&5!! + 3! − 4.&What&is&the&area&of&the&entire&figure?&&

Amelie&subtracted&a&quantity&from&the&polynomial&3!! + 8! − 16&and&produced&the&expression&(! + 2)(! − 2).&&What&quantity&did&Amelie&subtract?&&&&&&&&&&&&&&&&&&

Ash&thinks&that&the&sum&of&&5!!!! + 6! + 7!!and&8! + 4!!!! + 2!!&is&9!!!! + 8! + 15!.&Explain&Ash’s&error&and&find&the&correct&sum.&&

Page 4: Learning Objective: We&will&add&and&subtract ...mrrogove2016.weebly.com/uploads/4/3/0/0/43009773/alg1m1l...Name:&_____& & Math7.2,Period_____& Mr.Rogove& & Date:_____& 1& Alg1M1L3:&Adding&and&Subtracting&Polynomials&

Name:&___________________________________& & Math&7.2,&Period&_____________&Mr.&Rogove& & Date:&_______________&

Alg1M1L3:&Adding&and&Subtracting&Polynomials&4&

&Closure: How&many&terms&will&the&polynomial&have&when&all&simplification&is&done?&&Simplify.&&&

(31!!!! − 2!! + 12!!! − 21!!!!)− (11!! + 10!!!! − !!!! − 12!!!)&&&&&&&&&&Notes: In&ENY,&this&translates&to&lesson&8&of&Alg&1,&module&1.&Try&to&combine&with&lesson&2.&&&&HW:&Problem&Set&from&Alg&1&Mod&1&Lesson&8:&Q1&and&Q4&only??&&&&&&&&


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