Lesson  Title:  Introduction  to  Pythagorean  Theorem    Grade  and  Subject:   8th  Grade  Mathematics        

1.    Overview,  Background  &  Rationale  For  Lesson  Plan    Overview  Abstract   This  lesson  introduces  the  concept  of  Pythagorean  Theorem.  Student  will  

examine  the  proof  and  algebraic  reasoning  behind  the  Pythagorean  Theorem.  The  Pythagorean  theorem  is  a  geometry  topic  that  is  taught  as  part  of  an  overall  goal  to  increase  students’  fluency  in  Mathematics  and  aiding  them  in  understanding  the  world  in  which  they  live.  This  specific  class  has  students  who  are  considered  struggling  readers  and  a  few  students  are  performing  below  grade  level.  The  lesson  will  be  taught  using  a  Promethean  board  flipchart,  a  corresponding  booklet  with  student  notes  and  a  brief  assessment  to  close  the  lesson.    

Background,  Culture  and  Context  

                     I  teach  predominantly  African-­‐‑American  students  who  are  growing  up  in  an  urban  environment.  The  culture  within  the  class  has  been  designed  to  have  a  balance  between  rewards  and  consequences.  I  am  seeking  to  teach  students  a  method  to  find  the  missing  side  of  a  right  tringle  using  a  theorem  that  was  proven  many  years  ago.  In  order  to  do  this  I  have  to  make  the  lesson  interesting  and  engaging.  I’ve  chosen  to  incorporate  a  picture  book  to  introduce  Unit  3.  According  to  Zimmerman  (2012),  “What’s  Your  Angle  Pythagoras?’  would  be  considered  a  Tier  1  Fundamental  Math  Picture  book  because  it  is  directly  content  related.  We  are  currently  behind  on  the  pacing  calendar  by  about  three  weeks  so  to  save  time  the  lesson  will  be  loosely  based  on  the  text  and  the  book  will  be  available  for  the  students  to  read  on  their  own  during  homeroom,  tutorial,  and  lunch.  The  lesson  plan  is  for  a  60minute  class  period  and  can  be  the  foundation  for  a  2-­‐‑  3  day  exploration  of  the  Pythagorean  Theorem.        

Reference        Zimmerman,  Alycia.  (2012,  November  14).  Teaching  Math  With  Picture  Books,  Part  1.  Retrieved  from  http://www.scholastic.com/teachers/top-­‐‑teaching/2012/11/teaching-­‐‑math-­‐‑picture-­‐‑books-­‐‑part-­‐‑1    

Rationale    

Builders  use  the  Pythagorean  Theorem  to  help  keep  right  angles  and  build  houses,  decks,  buildings,  and  to  put  windows,  doors  and  floors  in.  The  theorem  has  practical  applications  that  students  can  apply  this  too  real  life  situations  once  the  basics  are  understood.    The  students  respond  positively  to  rhythmically  engaging  songs  and  activities  Therefore  I  have  chosen  to  introduce  this  lesson  with  a  rap.    The  lesson  elicits  prior  knowledge  of  equations,  triangles  and  exponents.  King  MS  students  like  a  good  narrative  or  story  line,  which  is  why  I  kept  young  Pythagoras,  from  the  text,    a  common  theme  throughout  the  lesson.  Coming  up  to  the  board  and  working  together  in  pairs  are  also  activities  that  appeal  to  middle  school  students.  Students  also  have  an  opportunity  to  be  exposed  to  proofs,  checking  math  calculations  and  forming  generalizations.    

2.  Lesson  Plan  Learning  Outcomes  And  Procedure  

 Essential  Question(s)  /  Central  Focus  

 

}   What  is  the  relationship  among  the  lengths  of  the  sides  of  a  right  triangle?    

}   How  can  the  Pythagorean  Theorem  be  used  to  solve  problems?    }   How  can  I  use  the  Pythagorean  Theorem  to  find  the  length  of  the  

hypotenuse  of  a  right  triangle?    }   How  do  I  use  the  Pythagorean  Theorem  to  find  the  length  of  the  legs  of  a  

right  triangle?    Learning  Objective(s)  

At  the  end  of  this  lesson,  students  should  know  and  be  able  to  explain  the  attributes  of  a  right  triangle.    They  should  be  able  to  apply  their  new  found  knowledge  of  the  Pythagorean  Theorem  to  a  real  life  scenario  in  order  to  correctly  answer  3  out  of  4  (75%)  questions  on  the  final  assessment  and  attempt  the  challenge  problem.    

 

CCGPS  or  GPS  Standard(s)  

MCC8.G.7  Apply  the  Pythagorean  Theorem  to  determine  unknown  side  lengths  in  right  triangles  in  real-­‐‑world  and  mathematical  problems  in  two  and  three  dimensions.    

Instructional  Strategies  &  Learning  Tasks  that  Support  Diverse  Student  Needs   Introduc-­‐‑  

tion  to  Lesson      10  minutes  

I  plan  to  capture  the  student’s  attention  using  a  picture  from  the  book  for  the  Do  Now.  I  will  also  use  a  rap  to  engage  the  students  in  the  activity.  In  the  text  the  picture  shows  an  image  of  a  Pythagorean  Theorem  proof.  The  students  will  get  a  chance  to  examine  the  image,  talk  with  a  partner  and  write  down  their  ideas.  They  would  look  for  patterns  and  make  observations.  After  hearing  student’s  observations  I  would  play  the  YouTube  video  of  the  Pythagorean  Theorem  rap.  It  will  engage  the  students  as  well  as  introduce  key  vocabulary  terms  that  the  student’s  will  need  to  understand  the  lesson.  The  image  allows  students  to  observe  the  characteristics  of  a  right  triangle  without  being  told  directly.      

       Pythagorean  Theorem  Rap  -­‐‑  https://youtu.be/nbopLhP4kpo?t=40s      

Body  of  Lesson  

Students  will  be  led  through  the  flipchart  by  the  teacher  and  follow  along  by  completing  the  guided  notes  in  the  interactive  booklet.    

1.   Students  will  have  a  review  of  radicals,  exponents  and  square  root.  2.   Student  will  label  the  parts  of  a  right  triangle  and  highlight  the  

hypotenuse  with  a  marker.    3.   Students  will  write  the  vocabulary  words  such  as  hypotenuse,  right  

triangle,  legs  and  Pythagorean  Theorem  4.   Students  will  be  introduced  to  the  Pythagorean  Theorem  and  write  

down  the  algebraic  formula.    5.   Students  will  identify  the  hypotenuse  on  right  triangles  with  different  

orientations.  

 6.   Student  will  work  through  two  examples  of  solving  triangles  for  the  

missing  side.  One  example  would  involve  finding  the  hypotenuse  and  the  other  example  will  involve  finding  a  leg  of  the  right  triangle.  

 Each  step  was  chosen  based  on  common  steps  and  misconceptions  made  by  students.  Students  tend  to  have  difficulty  correctly  labeling  the  hypotenuse  which  may  affect  their  use  of  the  formula.  Students  also  think  that  the  hypotenuse  is  always  the  missing  side  resulting  in  errors  when  substituting  values  into  the  equation.  I  chose  to  use  an  interactive  booklet  and  guided  notes  so  students  could  focus  more  on  what  is  being  said  rather  than  trying  to  record  everything  from  the  flipchart.  Also  I’ve  highlighted  notes  that  should  be  written  using  a  pink  glow.  This  way  students  know  if  it  glows  it  is  something  they  should  know.  I  have  provided  support  for  students  who  struggle  in  Mathematic  by  reviewing  key  radical  concepts  before  beginning  the  lesson.  This  will  help  reactivate  prior  knowledge.    The  lesson  will  consist  of  primarily  teacher  student  interaction  because  the  topic  is  new.  However,  students  are  given  opportunities  to  collaborate  with  a  partner  during  the  Do  Now  activity,  the  class  examples  and  the  final  challenge  problem.  I  will  use  call  and  response  techniques  such  as  “Class  Class!”  ,  “Yes,  Yes!”  to  get  student’s  attention  when  necessary.  The  closing  activity  (formal  assessment)  will  be  an  individual  activity  but  will  be  reviewed  together  as  the  closure  of  the  lesson.  Language  supports  for  academic  language  will  be  in  the  rap  introduction,  throughout  the  flipchart  and  in  the  constructive  response  section  of  the  final  challenge.    

Closure   Students  will  summarize  and  share  what  they  have  learned  by  answering  a  four  question  quiz  and  helping  Pythagoras,  from  the  text  find  a  direct  route  to  Crete  from  his  home.  Students  will  have  to  explain  how  they  found  the  distance  using  their  vocabulary  words.  Students  will  receive  a  homework  assignment  due  the  following  day  based  on  the  lesson  as  well  as  an  extension  question.    

Learning  Supports:  Differentiation,  Modification(s)and    Accommoda-­‐‑tion(s)  

•   Provided  guided  notes  to  students.  Many  are  struggling  readers  and  writers.  Guided  notes  relieve  the  stress  of  having  to  record  perfect  notes  while  still  keeping  the  students  engaged.  

•   Have  students  repeat  given  directions.  Students  that  have  issues  focusing  tend  to  miss  initial  directions.  This  just  helps  the  students  stay  on  task.    

•   Extra  visual  and  verbal  cues  and  prompts  having  important  information  highlighted  on  the  flipchart,  scaffolds  students  to  discern  important  information  during  the  note  taking  process.  

•   Take  a  longer  time  to  go  through  the  lesson  in  order  to  maximize  understanding.  This  will  eliminate  the  challenge  question  but  will  provide  the  students  with  a  stronger  content  knowledge  foundation.    

Formal  and  Informal  Assessment  

Formal  Assessment:  The  formal  assessment  is  the  four  question  task  that  students  are  required  to  turn  in  during  the  closure  of  the  lesson.  The  formal  assessment  consists  of  the  fundamental  concepts  of  the  Pythagorean  theorem  and  can  indicate  clearly  what  a  student  may  be  struggling  with.  The  information  from  the  assessment  can  be  incorporated  into  the  Do  Now  off  the  next  lesson  to  increase  understanding.  The  final  challenge  requires  students  to  use  their  knowledge  in  a  real  world  situation.    

 

                 

 https://www.brainingcamp.com/content/pythagorean-­‐‑theorem/questions.php  (Questions  1-­‐‑4)      Informal  Assessment:  Throughout  the  lesson  I  will  request  a  show  of  hands  to  identify  whether  or  not  students  are  struggling.  This  allows  me  to  provide  immediate  changes,  repetition  or  clarification.      

3.  Resources  

Academ

ic  Language  

Language  Functions  

•   Justify the use of the Pythagorean Theorem to solve for the missing side of a right triangle.

•   Argue whether a triangle is a right triangle using the Pythagorean Theorem and the three given sides

•   Define the hypotenuse based on the characteristics of a right triangle. Vocabulary   The  students  will  demonstrate  their  understanding  of  the  vocabulary  by  

labeling  a  right  triangle,  using  correct  terminology  when  contributing  to  class  discussions  and  by  writing  using  clear  and  complete  sentences  in  the  constructive  response  portion  of  the  Final  Challenge.  

•   Pythagorean  Theorem  •   Square  •   Square  root  •   Legs  of  a  triangle    •   Hypotenuse  •   Inverse  Operations    

 Syntax  or  Discourse  

Students  will  identify  the  Pythagorean  theorem  algebraic  formula  as  an  equation  that  can  be  solved  for  the  unknown  using  integer  properties  and  inverse  operations.  Students  will  be  able  to  create  and  identify  right  triangles  by  the  right  angle  symbol.  Symbols  such  as  the  radical  should  be  used  appropriately  as  the  inverse  operation  for  a  number  or  variable  that  has  been  squared.  

Materials   •   Calculators  •   iPads  •   Promethean  Board    •   Formal  Assessment  Worksheet  •   Homework  Worksheet    •   Interactive  Booklet    •   2  markers  per  student    

Technology   Calculators  were  used  in  the  closure  of  the  lesson  to  calculate  the  square  root  of  numbers  that  are  not  perfect  squares.  The  promethean  board  was  used  as  an  interactive  tool  for  students  to  participate  in  class  discussions  during  the  review  of  the  formal  assessment  as  well  as  an  engagement  tool  for  students  to  view  the  Pythagorean  Theorem  rap.  iPads  can  be  integrated  into  this  lesson  for  the  formal  assessment  to  be  done  online.      

                 

Lesson  Flipchart  –  Pythagorean  Theorem  

 

 

INTERACTIVE  STUDENT  BOOKLET      

   

   

     

 

Formal  Assessment      

                                         

                                                                     

 

Final  Challenge                                                                                        

   

 

Name: ___________________________

Date: ________________ Period: _____

Pythagorean Theorem Homework

1.   In each of the following problems, highlight the hypotenuse and find the value of x.

a.  

x =

________ b.

x = ________

2.   Is triangle ABC a right triangle? Justify your reasoning.

34  

30  

x  

5  

15  

x  

Show  your  work.  

 

 

A  

C  

B  

9   12  

18