Introduc)on  Students  will    represent    fi/hs,  quarters,  thirds  and  halves  on  a  number  line.      Resources  •  Frac;on  umbrellas    •  Skipping  rope  •  Number  line  floor  mat  •  Half  and  quarter  game.  •  Frac;on  equivalence  cards  -­‐  1/2,  1/3,  1/4,  1/5    •  Colour  a  frac;on  game:  1/2  1/3  1/4  1/5  

       Time  /  Classroom  Organisa3on    Each  ac;vity  process  may  be  introduced  in  a  whole  group  or  small  group  as  a  20  minute  hands-­‐on  focused  teaching  and  learning  event.  Repeat  these    experiences  a  number  of  ;mes  to  allow  students  to  prac;ce  and  consolidate  these  concepts.      Australian  Curriculum-­‐Year  Three  ACMNA058  Model  and  represent  unit  frac;ons  including  ½,  ¼,  1/3,    1/5  and  their  mul;ples  to  a  complete  whole.  Proficiency  Strand:    Understanding  –  represen;ng  unit  frac;ons          

               Ac-vity  Process-­‐  Loca-ng  frac-ons  on  a  number  line    

1.  Hold up a skipping rope, and peg the 0 umbrella on one end and 2 umbrella on the other end

2.  Using umbrellas (one, 1, and a pictorial representation), ask three students to locate where 1 would be on the number line. Ask each student to explain why they would place 1 in this position, for example: I know that 1 is half way between 0 and 2, so put the number one umbrella in the middle.

3.  Check the position of the umbrellas by folding the

skipping rope in half to determine where 1 would be located. Place the number one in this position. Hook the equivalent fractions on to this umbrella.

4.  Give each student a fraction umbrella ½, ¼, ¾, to place on the line. Ask each student to explain why they chose this position for their fraction. Ask students to hook fractions that are the same onto the equivalent fraction.

   

 

Word  Wall:  frac-ons,  quarter,  half,  third,  fi>h,  number  line,  fold,  posi-on,  ‘I  know  that….’,  locate,  half,  halves,  ‘count  up  in  …’,  part,  whole

               Ac-vity  Process-­‐Halves  game    1.  Lay  the  number  line  mat  out  to  the  side..  

 Give  each  student  a  Half  Game  Board,      half  circles  and  2  post-­‐it  notes,  and  a  12      sided  dice.    

 2.   Each  student  takes  a  turn  to  roll  the  12    

 sided  dice  and  places  the  rolled  number      of  halves  onto  the  game  board.    

           Encourage  students  to  change  colour                each  ;me  they  complete  a  ‘whole’  circle.    3.  Ask  each  student  to  write  how  many  halves    

 they  have  in  words  (7  halves),  and  then  using      a  frac;on  numeral  (7/2)  .    Write  this  onto  one      of  the  s;cky  notes.  

     4.  Refer  to  the  number  line.    Say:  This  number  line  starts  

with  ‘0’  and  counts  up  in  halves.  Explain  that  you  are  going  to  find  where  on  the  number  line  each  student’s  number  belongs.    Ask:  Does  anyone  have  1  half?      Place  this  on  the  number  line.      Ask:  Does  anyone  have  2  halves?  Place  this  on  the      number  line.    Con;nue  this  way  un;l  each  of  the  student’s  frac;on  post-­‐it  notes  are  placed  on  the  number  line.      

 5.  Go  back  to  the  game  boards.  Ask  students  

   to  count  up  how  many  “whole”  circles  and      how  many  “half”  circles  they  have.    Write      this  on  the  page,  and    then  on  a  post-­‐it.    

 

3.3.6  

Assessment  Observe  students  as  they  place    the  frac;on  umbrellas  on  the  number  line.    Note  their  explana;ons  for  placement  of  the  frac;ons.    • What  is  the  whole?    Say:  Here  is  one  third  of  the    chocolate  bar.  Draw  the  whole  chocolate  bar.    Source:  First  steps  in  Mathema;cs  –  Number  –  Understand  Frac;onal  Numbers  ,  2007.  Rigby:  Port  Melbourne.  p  120.  Achievement  Standard:  model  and  represent  unit  frac;ons    Background  Reading  “The  idea  that  things  can  be  par--oned  or  split  into  parts  of  equal  size  underpins  the  frac-on  concept.  ....  Students  need  extensive  experience  in  spliTng  a  diverse  range  of  discrete  and  con-nuous  wholes  into  equal-­‐size  parts.  Collec-ons  (discrete  quan--es)  can  be  shared  into  equal  parts  by  dealing  out  or  distribu-ng,  while  objects  can  be  shared  into  equal  parts  by  cuTng,  folding,  drawing,  pouring  and  weighing.  ...Students  should  become  flexible  in  par--oning  and  develop  the  following  ideas.  Equal  parts  need  not  look  alike,  but  they  must  have  the  same  size  or  amount  of  the  relevant  quan-ty.  When  spliTng  a  whole  into  equal  parts,  the  whole  should  be  completely  used  up.  Regardless  of  how  we  par--on,  the  whole  remains  the  same  amount.  The  more  shares  something  is  split  into,  the  smaller  each  share  is”.    Source:  First  steps  in  Mathema;cs  –  Number  –  Understand  Frac;onal  Numbers  ,  2007.  Rigby:  Port  Melbourne.  p  104.    Year  three  NAPLAN  Numeracy  test  links  •  Frac;ons    Links  to  Related  MAGs  2.1.7  –  Frac;ons  –Area  and  Linear  2.3.6  –  Frac;ons  -­‐  Collec;ons  3.2.7–  Frac;ons  1  

Adapted for use in the Cairns Diocese with the permission of the Catholic Education Office Toowoomba

6.  Place  these  post-­‐it  notes  with  whole  and      halves    on  the  number  line.  Discuss  how  2      halves  is  the  same  as  1  whole,  and  4      halves  is  the  same  as  2  wholes,  etc.        If  necessary,  use  the  half  circles  to      demonstrate  the  area  model  on  the      number  line  (linear  model)    

Source:    E  deVries    2009    Varia)ons  &  Extensions  1.   Quarters  and  Thirds  and  FiMhs  Resources:  Quarters  Game;    Thirds  Game    Repeat  the  above  ac;vity  using  Quarters  and  Thirds.                2.   Collec3ons  Resources:    Collec;ons  of  objects  –  counters,  shapes,  

bujons  Ask  students  to  share  out  collec;ons  as  evenly  as  they  can  with  2  people,  then  3  people,  4  people  and  5  people.    Represent  this  as  a  frac;on.      

     2.   Fly  swaPer  frac3ons  

 Resources:    Frac;on  equivalence  cards  -­‐  1/2,  1/3,  1/4,  1/5    

Each  group  has  1  caller  and  4  players.  Each  player  has  a  fly  swajer.    Place  5  frac;on  equivalence  cards  in  a  row.  The    caller  calls  out  the  name  of  one  of  the  frac;ons.  The  first  to  swat  the  correct  frac;on  takes  the  card.  The  caller  replaces  the  card  with  a  new  card  from  the  pack.  The  game  con;nues  for  a  set  ;me  or  un;l  all  the  cards  have  been  used.    Each  player  records  the  number  of  cards  they  have  won,  and  ajempts  to  beat  this  score  in  the  next  game.      

 

Digital  Resources  hjp://www.ideal-­‐resources.com.au/index.php      Frac3on  maker                      Recognising  simple  frac3ons              ILLUMINATIONS:      hjp://illumina;ons.nctm.org/Ac;vityDetail.aspx?ID=11      Explore  different  representa;ons  for    frac;ons.  There  are  length,  area,  region,    and  set  models.  Adjust  numerators  and    denominators  to  see  how  they  alter  the    representa;ons  and  models.  Use  the    table  to  keep  track  of  interes;ng  frac;ons.    Contexts  for  Learning  Play:    Play  the  Colour  a  frac;on  game:  1/2  1/3  1/4  1/5  Real  life  experience:  When  sharing  out  equipment  in  the  classroom,  convert  the  sharing  to  a  frac;on,  for  example:  20  pencils  shared  among  5  students  –  each  child  will  get  1  group  of  the  5  equal  groups  –  or  1/5      Inves3ga3on:  How  many  different  designs  can  you  make  that  are  ¾  red  and  ¼  yellow?    Note  if  the  designs  are  simple  or  complex.  Are  they  crea;ve?  Ask  students  to  explain  how  they  know  ¾  is  red  and  ¼  is  yellow.    Source:  Sullivan  and  Lilburn.  2010.  Open  ended  maths  ac-vi-es.  Oxford:  South  Melbourne.  p23.  Rou3nes  and  Transi3ons:  Place  the    Frac;on  equivalence  cards  -­‐  1/2,  1/3,  1/4,  1/5    cards  in  rows.  Ask  students  to  find  two  that  mean  the  same  amount.