Achievement Targets (AC): By the end of Year 5, students solve simple problems involving the four operations using a range of strategies. They check the reasonableness of answers using estimation and rounding. Students identify and describe factors and multiples. They explain plans for simple budgets. Students connect three-dimensional objects with their two-dimensional representations. They describe transformations of two-dimensional shapes and identify line and rotational symmetry. Students compare and interpret different data sets. Students order decimals and unit fractions and locate them on number lines. They add and subtract fractions with the same denominator. Students continue patterns by adding and subtracting fractions and decimals. They find unknown quantities in number sentences. They use appropriate units of measurement for length, area, volume, capacity and mass, and calculate perimeter and area of rectangles. They convert between 12 and 24 hour time. Students use a grid reference system to locate landmarks. They measure and construct different angles. Students list outcomes of chance experiments with equally likely outcomes and assign probabilities between 0 and 1. Studentspose questions to gather data, and construct data displays appropriate for the data. English Program:

Number and Algebra Measurement and Geometry Statistics and Probability General  capabilities  and  cross-­‐curriculum  priorities  Content description Create simple financial plans Elaborations • creating a simple budget for a class fundraising event • identifying the GST component of invoices and receipts

Code ACMNA106 Content description Use estimation and rounding to check the reasonableness of answers to calculations Elaborations • recognising the usefulness of estimation to check

calculations

• applying mental strategies to estimate the result of calculations, such as estimating the cost of a supermarket trolley load

Code ACMNA099 Content description Identify and describe factors and multiples of whole numbers and use them to solve problems Elaborations • exploring factors and multiples using number sequences • using simple divisibility tests

Code ACMNA098 Content description Use efficient mental and written strategies and apply appropriate digital technologies to solve problems Elaborations • using calculators to check the reasonableness of answers

Code ACMNA291  

Content description Describe translations, reflections and rotations of two-dimensional shapes. Identify line and rotational symmetries Elaborations • identifying and describing the line and rotational

symmetry of a range of two-dimensional shapes, by manually cutting, folding and turning shapes and by using digital technologies

• identifying the effects of transformations by manually flipping, sliding and turning two-dimensional shapes and by using digital technologies

Code ACMMG114 Content description Apply the enlargement transformation to familiar two dimensional shapes and explore the properties of the resulting image compared with the original Elaborations • using digital technologies to enlarge shapes

• using a grid system to enlarge a favourite image or cartoon

Code ACMMG115 Content description Use a grid reference system to describe locations. Describe routes using landmarks and directional language Elaborations • comparing aerial views of Country, desert paintings and

maps with grid references

• creating a grid reference system for the classroom and using it to locate objects and describe routes from one object to another

Code ACMMG113 Content description Connect three-dimensional objects with their nets and other two-dimensional representations Elaborations • identifying the shape and relative position of each face

of a solid to determine the net of the solid, including that of

 Content description Construct displays, including column graphs, dot plots and tables, appropriate for data type, with and without the use of digital technologies Elaborations • identifying the best methods of presenting data to

illustrate the results of investigations and justifying the choice of representations

Code ACMSP119  

Identify  and  describe  the  general  capabilities  and  cross-­‐curriculum  priorities  that  will  be  targeted  in  the  unit.    Delete  those  that  do  not  apply.  

• Literacy  Word  Walls  and  Glossaries  will  be  built  for  all  main  concept  

areas.    • Numeracy  Being  a  Maths  program  it  predominantly  focuses  on  Numeracy                              

acquisition.    • Critical  and  creative  thinking  A  problem  solving  approach  and  ongoing  questioning  and  

encouragement  of      • Personal  and  social  capability  Working  in  groups  for  puppet  theatre  will  encourage  

communication  and  the  ability  to  work  as  a  team.    • Intercultural  understanding  Incorporating  Indigenous  and  Asian  perspectives  in  the  program  

will  broaden  children’s  understanding  of  numeracy  to  include  intercultural  perspectives  

• Aboriginal  and  Torres  Strait  Islander  histories  and  cultures  Aboriginal  Mapping  paintings  shown  to  link  to  maths  mapping  

and  coordinates.    • Asia  and  Australia’s  engagement  with  Asia  Shadow  Puppetry  developed  in  Asia-­‐  Use  videos  from  this  region  

 

MATHS This Unit Plan describes the school requirements and integrates these with history, art and science where possible. Maths skills are useful in a wide variety of human endeavours; including science, art and history.

Year Level: 5

prisms and pyramids • representing two-dimensional shapes such as

photographs, sketches and images created by digital technologies

Code ACMMG111 Content description Calculate the perimeter and area of rectangles using familiar metric units Elaborations • exploring efficient ways of calculating the perimeters of

rectangles such as adding the length and width together and doubling the result

• exploring efficient ways of finding the areas of rectangles

Code ACMMG109 Content description Choose appropriate units of measurement for length, area, volume, capacity and mass Elaborations • recognising that some units of measurement are better

suited for some tasks than others, for example kilometres rather than metres to measure the distance between two towns

• investigating alternative measures of scale to demonstrate that these vary between countries and change over time, for example temperature measurement in Australia, Indonesia, Japan and USA

Code ACMMG108 Content description Estimate, measure and compare angles using degrees. Construct angles using a protractor Elaborations • measuring and constructing angles using both 180° and

360° protractors

• recognising that angles have arms and a vertex, and that size is the amount of turn required for one arm to coincide with the other

Code ACMMG112

   

   

Prior  Knowledge   Resources,  Programs  and  Texts  

Students  have  been  engaged  in  whole  school  programs  so  theoretically  are  ready  for  the  material  in  the  identified  whole  school  programs.  There  are  a  number  of  students  who  do  “maths  Olympiad”  and  a  number  of  students  who  struggle  with  learning.  My  aim  is  to  provide  diverse  learning  experiences  which  will  engage  all  students  and  ensure  there  is  more  scaffolding  for  some  and  extension  activities  for  others.  Most  lessons  begin  with  the  basic  and  become  progressively  more  challenging.  Specific  challenges  can  be  set  for  the  more  capable  students  as  they  complete  the  easier  tasks.  These  tasks  can  be  set  discreetly  for  particular  students  instead  of  confusing  the  rest  of  the  class  with  too  many  instructions.  

 Whole  School  Programs  Signpost  Mental  Maths  Books  Signpost  Maths  Books  and  teacher  books  Elementary    Maths  Mastery  :  Mental  Maths  program    Angle  Dance  Video  http://thekidshouldseethis.com/post/49936880302    Maths  Greek  Geometry  video    http://thekidshouldseethis.com/post/79866139523    3D  objects  

Protractors    Painting  Country  –  Forms  of  Mapping  –  Cross  Curriculum  Priorities  http://aso.gov.au/titles/documentaries/painting-­‐country/clip3/      Online  Kids  Maths  Dictionary  and  ipad  app  http://www.amathsdictionaryforkids.com/dictionary.html    Symmetry  Video  https://www.youtube.com/watch?v=6qNB2LsgC8Y    (See  more  resources  below  in  resource  sections)  

Links  to  other  learning  areas  

Geometry  exercises  will  link  with  art  making  curriculum.  Coordinates  will  be  explored  through  maths,  mapping  and  choreography  of  puppet  theatre.  Measurement  and  translations  will  be  explored  through  shadow  puppet  project.  

Unit Overview Context/Intent   Deep  Knowledge  and  Understandings   Skills  Processes/Values/Attitudes  

This Unit Plan describes the school requirements and integrates these with history, art and science where possible. Using coordinates to map local places of historical significance can aid both numeracy, history and geography learning. Understanding and creating maps are important skills for general numeracy and literacy. The specialist science teacher is working on light this term. Maths activities will include translating and enlarging figures to appropriate sizes using grid paper and using coordinates to measure and choreograph puppet performance. Translations, reflections and rotations will be explored through the students own art and design work as well as the art of Escher. Literacy learning will be integrated with all of these activities through journal writing, word walls, mind maps, word sleuths and cross words.

Maths skills are useful in a wide variety of human endeavours; including science, art and history. Different people solve problems in different ways. Working together can achieve the most positive results.

 

Maths can be used to enhance learning and understanding in all the other key learning areas. People may have different ways of solving the same problem. Working as a team can solve problems faster. Maths can be creative and fun and help us solve problems in science. Asking questions and coming up with ways to test and try out our ideas is a good way of approaching maths problems as well as science and history problems.  

Program  Activities  

There  are  three  whole  school  Maths  programs  that  must  be  completed  on  a  daily  basis.    These  include  Signpost  Maths,  Signpost  Mental  Maths  and  Elementary  Maths  Mastery:  Mental  Maths.  Students  at  the  more  competent  level  of  maths  also  attend  extension  maths  :  “Maths  Olympiad”  once  a  week.  The  mental  maths  sessions  are  conducted  from  Elementary  Maths  Mastery  :  Mental  Maths  and  Signpost  Maths  :Mental  Maths  as  well  as  using  individual  laminated  white  boards  to  practice  with  chanting  tables  and  basic  facts.      Overall  Assessment  Systems    Formative  and  Summative  There  is  a  maths  test  every  Friday  which  covers  material  from  mental  maths  as  well  as  assessing  material  covered  in  the  signpost  maths.    

Work  sheets,  maths  books,  art  works  and  literacy  work  associated  with  the  language  of  each  maths  topic  will  also  be  assessed  and  noted.    Feedback  given  as  soon  as  possible  after  work  to  the  student.  And  outcomes  used  to  plan  next  phase  of  learning.    The  first  activity  in  any  concept  will  be  reviewed  promptly  as  diagnostic  assessment  in  order  to  choose  the  next  activity  and  prepare  the  following  lessons  with  the  appropriate  differentiated  activities.    Differentiation  All  lessons  will  include  a  number  of  different  activities.  Whole  class  activities  will  begin  the  lesson  and  then  different  activities  beginning  with  the  easiest  and  building  to  the  more  complex.  Once  students  have  finished  an  activity  and  it  has  been  checked  for  

accuracy  another  activity  which  is  slightly  more  challenging  will  be  given.  In  this  way  everyone  covers  the  same  material  and  some  are  offered  further  extension  than  others.  Some  students  second  activity  may  be  easier  rather  than  harder  depending  on  how  easily  they  completed  the  first  task.  Students  will  where  practicable  be  given  choices  as  to  the  order  in  which  they  complete  thins  and  the  difficulty  level  in  order  to  increase  engagement.    

 

Concepts  

Space  and  Geometry  

reflection,  rotation,  translations  

 

• Learning  Activities    • Signpost  Maths  Activities  expanded  • Watch  Escher  Videos  • Use  physical  actions  to  demonstrate:  

Translation  –  Slide  Reflection  –  two  people  face  each  other  –  two  hands  held  up.  Rotation  –  a  turn  around  with  one  arm  in  the  air.  

• Show  Arrow  example  on  the  board.  • Hand  out  photocopies  • Students  cut  out  images  • Trace  around  and  create  diagrams  of  reflection,  rotation  and  translations.  • Complete  worksheet  • Questions  • What  do  you  see  when  you  look  in  the  mirror?  • Is  it  the  same  as  what  you  actually  look  like/  what  you  see  in  a  photograph?  • How  else  do  we  use  the  word  rotation?  

• What  else  rotates?  

Group  Structure  

Whole  Class  

Individual  

Resources  

Escher  Videos  

Photocopies  of  Escher  designs  

Maths  books  

Pencils,  scissors,  glue  

 

Assessment  

Note  :  There  will  be  a  maths  test  every  Friday  in  which  work  from  both  the  EMMS  mental  maths  and  Signposts  maths  work  and  all  work  included  in  this  program  will  be  assessed.  Assessment  will  also  take  place  constantly  during  lessons  to  check  for  understanding  before  moving  to  the  next  phase.  

……………………………………………………………………..  

Worksheet  marked  and  clued  into  maths  book.  

Diagram  drawn  in  Maths  book  marked.  

Feed  back  given  as  close  as  possible  to  completion.  

Ongoing  questioning  in  the  classroom  using  named  paddle  pop  sticks  so  that  all  children  remain  accountable  for  their  learning.  

Space  and  Geometry  

3D  shapes  and  Nets  

 

• Show  students  weetbix  box.  • Ask  students  if  they  know  what  a  net  is.  • Ask  them  what  the  shape  of  the  box  would  be  if  you  pulled  it  apart.  • Instruct  them  to  individually  draw  their  answers  on  the  white  boards  –  allow  them  to  

chat  and  share  with  a  partner.  • Get  them  to  share  their  diagram  answers.  • ……………..  • Questions  • “Is  there  only  one  answer?”  • “Which  answers  do  you  think  would  make  a  box.  • ………………  • Pull  apart  the  weetbix  box  and  show  them  the  net  shape.  • Hand  out  an  assortment  of  templates  of  3D  nets  on  coloured  cardboard  • Differentiation  

If  students  finish  offer  a  challenge  to  those  who  finish.  How  could  they  use  a  3D  shape  (from  the  maths  kits)  to  create  a  net?  IE  trace  around  the  item  –  moving  the  shape  around  to  create  a  net.  

  Weetbix  box  

Scissors  

Assorted  photocopied  nets  on  coloured  cardboard  

Scissors    

3D  shapes    

plane  coloured  cardboard  

glue  

sticky  tape  

 

Made  shapes  –  checklist  of  completed  objects.  

Anecdotal  notes  on  how  children  complete  tasks.  

 

Space  and  Geometry  

Angles  and  Protractors    

 The  language  of  Geometry  –  Angle  Glossary    

• Show  Video  Angle  Dance:  https://www.youtube.com/watch?v=tqIki33mTgs&feature=kp  

• Ask  Students  to  note  down  all  the  words  they  hear  that  are  related  to  Geometry.  • Ask  students  individually  to  come  up  to  board  and  write  words  up  on  board  • Once  all  the  words  are  up-­‐  if  there  are  any  left  out  fill  them  in.  • Ask  children  to  rule  up  a  page  in  their  maths  book  and  write  down  words  to  create  a  

glossary.  • Use  a  literacy  lesson  to  fill  in  the  definitions  of  the  words.  • Introduce  protractors.  • Name  the  important  elements  of  a  protractor.  • Base  line,  centre  point,    • Define  steps  to  measuring  an  angle  using  interactive  white  board.  

Use  Prezi  (Like  powerpoint)    to  do  this  as  a  warm  up  • Students  write  steps  in  their  maths  book.  • Practice  measuring  angles  with  prepared  angle  sheets.  • Practice  measuring  angles  by  creating  angles  for  each  other  in  pairs  using  a  protractor.  • Use  a  clock  to  describe  angles.  • Use  compasses  to  explore  degrees  and  directions.  • Set  a  compass  quest  with  degrees  and  directions.  • Origami  folding  paper  and  identifying  angles.  

     

 Whole  Class  Individual  Pairs    

 Video  Angle  Dance:  https://www.youtube.com/watch?v=tqIki33mTgs&feature=kp    Maths  books  White  Boards.  Pencils  Protractor  Sets  Compasses  Clock  Sheet  with  angles  to  measure.    Steps  :  Measure  angles  steps  Step  one  –  Line  up  centre  point      AMSI  site  information    http://www.amsi.org.au/ESA_middle_years/Year5/Year5_md/Year5_1a.html#stucon-­‐2    Origami  angles    http://www.arvindguptatoys.com/arvindgupta/sastrymath.pdf  

 Folding  angles  and  making  an  equilateral  triangle  http://nrich.maths.org/5372    Angle  Game  Online  http://nrich.maths.org/1235    Good  way  of  explaining  online  http://www.amblesideprimary.com/ambleweb/mentalmaths/angleshapes.html  

 

Glossary  created  in  maths  book.  

 

Angle  Worksheets.  

 

Angle  section  in  Friday  maths  test.  

 

 

 

Coordinates    

 • Introduce  coordinate  grid  using  3D  object  chart.  Signpost  maths.  Work  as  a  whole  

class  with  exercise  on  the  electronic  board  • Use  coordinate  grid  for  shadow  puppet  choreography  –  students  work  in  teams  to  

create  a  short  shadow  puppet  play  • A  version  of  Battleship  on  the  Electronic  white  board  with  coordinates  • Practice  with  the  signpost  maths  worksheet  • Use  coordinates  for  mapping  exercise  in  History  and  with  white  board  /  laminated  

map  • Use  tarp  coordinates  to  explicitly  teach  how  to  map  shadow  puppet  choreography  • Incorporate  into  the  Friday  test  

 

 Whole  Class  Individual  Groups  

 Signpost  activities  for  white  board  White  board  /laminated  map  of  Australia  Tarp  with  coordinates  marked  on  with  masking  tape  (see  Science  Program  Resources)    Indigenous  Art  /Mapping  country/Cross  cultural  perspectives  on  knowledge  of  space  http://aso.gov.au/titles/documentaries/painting-­‐country/clip3/    

 

Coordinates  added  to  weekly  Friday    Maths  test  

Signpost  Maths  activity  sheets  glued  in  to  books  

 

Addition  and  Subtraction  of  money/decimals  

Simple  Budgets    

Understandings    

(  Taken  from  https://www.moneysmart.gov.

 • Elicit  current  knowledge  by  asking  students  questions  about  budgets  and  money.  • What  words  do  we  need  to  understand  in  order  to  communicate  about  money  and  

learn  about  how  to  manage  budgets?  Begin  to  create  a  word  wall  and  budget  glossary:  budget,  addition,  subtraction,  multiply,  divided  by  

• Talk  about  something  they  might  want  but  don’t  have  the  money  for.  Ask  them  to  think  of  something  and  to  give  an  estimate  of  how  much  it  might  cost.  

• Ask  students  to  consider  whether  they  get  pocket  money  or  not  –  or  birthday/  Christmas  money.  

 

Whole  Class  

Pairs  

Individual  

 Electronic  White  Board  active  inspire.    Pictures  of  desirable  objects-­‐  Loom  band  kits  Bicycles  Skateboards      

 

Problem  sheets  glued  into  Maths  books  and  marked.  

au/media/391824/5_3_mst_primary_maths5_unit.pdf)  

Budgets  are  a  way  to  plan  and  manage  spending  

Expenditure  can  be  classified  as  essential  or  optional,  and  choices  made  have  a  financial  impact  

Estimation  and  rounding  can  be  used  to  check  the  reasonableness  of  answers  

Accurate  calculations  are  important  when  planning  and  amending  a  budget  

• Do  an  example  on  the  electronic  white  board  of  a  new  skateboard  • Frame  it  as  a  word  problem  (see  literacy  program)  How  long  will  it  take  to  save  up  for  

a  particular  item  • Do  one  together.  Then  get  them  to  do  one  themselves  –  check  with    partner  -­‐  and  

then  write  one  for  each  other.  

Perimeter  and  Area  

Being  able  to  calculate  perimeter  and  area  have  many  practical  applications  for  students  and  their  families.  

• Use  the  front  student  desk  to  demonstrate    the  idea  of  perimeter.  Get  a  volunteer  to  come  up  and  measure  the  sides.  

• Remind  them  of  angles  as  the  diagram  and  number  sentence  is  written  on  the  board.  • Talk  about  different  measurements.  Why  do  we  need  different  measurements-­‐  could  

we  measure  an  oval  in  centremetres?  When  is  it  useful  to  be  able  to  work  out  perimeter  and  area?  Explicitly  teach  language  necessary  for  actvities  

• Use  a  selection  of  worksheets  and  problems.  Start  with  the  easy  ones  get  students  to  put  up  their  hand  when  they  have  finished.  Allow  them  to  choose  the  next  tasks  level  of  difficulty  as  long  as  the  first  task  shows  understanding.  

Whole  Class,  Individual     Formative  assessment  of  each  activity  before  moving  on  to  the  next  one.  

Add  maths  terms  to  the  weekly  spelling  words.  

Activities  posted  in  to  Maths  books.  

Perimeter  and  area  activities  included  in  weekly  test.