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maths program

VIEWS: 7 PAGES: 30

									            Mt Tarampa
           State School




            Mathematics
             Program



Mt Tarampa State School
Page 1 of 30
Our beliefs about teaching mathematics
The staff of Mt Tarampa State School believe that mathematics:
 is highly important for successful life beyond schooling
 should be taught everyday
 focuses on the development of higher order thinking within our students
 includes the explicit teaching of mathematical strategies and ways of working
 incorporates the use of materials at all year levels
 should be connected to the students’ real lives
 includes opportunities for teachers to continue learning.

Teaching mathematics at Mt Tarampa State School includes:
 a balanced mathematical learning approach which consists of
   o learning basic facts
   o applying basic facts and procedures to solve familiar problems
   o solving specific problems in novel situations
   o investigating issues and problem situations
 differentiated learning to meet the varied needs of our students
 embedding the effective use of information and communication technologies
 embedding Indigenous perspectives
 focusing on all forms of computation (mental, written and technology-assisted)
 First steps in mathematics strategies.

Cross-curricular priorities
Numeracy
We improve the numerate capabilities of students at Mt Tarampa State School by:
 fostering students to be confident in their use of mathematics
 encouraging students to be flexible in their mathematical thinking
 promoting higher-order thinking through a working mathematically approach
 applying mathematics through a range of contexts and key learning areas
 encouraging risk-taking in the use of mathematical knowledge, skills and thinking
 instilling persistence when problem-solving in mathematics.


Literacy
We improve the literacy capabilities of students at Mt Tarampa State School by:
 explicitly identifying and teaching the language demands of mathematics at all year levels
 ensuring students are exposed to and taught the conventions used by mathematicians
 applying skills learned at literacy training to the interpretation of word problems in mathematics (in
    particular, functional grammar)
 identifying the different visual representations used in mathematics e.g. number lines, tables, graphs,
    maps, networks, nets and 3D objects (refer to notes in the term breakdown for further details).

Our Maths Program Structure
The Mathematics program has been structured as follows:
    there will be a single curriculum focus for each year level during any teaching period
    Ways of working are embedded throughout the Teaching Focus section of the school
      mathematics program
    Mathematics will be allocated 5 hours per week
    Term programs work on 9 weeks to allow for other commitments such as assessment,
      review, consolidation and interruptions eg excursions, sports days



Mt Tarampa State School
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Pedagogy
At Mt Tarampa State School we encourage learning as an active process, and have designed our
mathematics program around the inclusion of interesting, fun and relevant learning experiences that will
help students develop a positive disposition towards mathematics.

To meet this aim, our program, planning, teaching and assessment include:
 a range and balance of learning experiences from focused skill development activities through to
   open-ended investigations and inquiry
 the provision of multiple opportunities for students to explore concepts so they can develop a deep
   knowledge and understanding
 planning units and lessons that are relevant and responsive to the needs, interests and capabilities of
   our students. This is achieved by starting with real world problems  materials and representations
    language  symbolic representations and abstract concepts
 an emphasis on challenging problems that promote higher order thinking skills, and the critical
   analysis of data and issues
 teaching a range of calculation strategies, such as mental computation, formal and informal jottings,
   calculators, computers and written algorithms
 a range and balance of teaching approaches, such as whole class–directed lessons, group/team work
   and individual work
 an embedded use of ICTs into all classrooms
 Indigenous perspectives embedded into all classrooms
 explicit teaching of specific mathematics language, diagrams, models and conventions used by
   mathematicians
 the provision of multiple opportunities for students to confidently, willingly and capably transfer
   their mathematics learning to a variety of contexts
 explicit advice to students about expected standards of achievement.


Assessment and reporting

Monitoring learning
Monitoring of student learning is integral to informing our planning so we develop students that have a
deep understanding of the concepts that make up number, algebra, measurement, chance and data, and
space.

At Mt Tarampa State School, monitoring occurs in the following ways:
 classroom observations
 checklists
 homework
 diagnostic tasks
 anecdotal records
 knowledge gained from assessment for reporting.

Immediate feedback to students is a priority, as this builds student confidence and a positive disposition.
It also assists students to manage their own learning.

Assessment for reporting (assessment of learning)
We believe that to learn mathematics, children must construct concepts, and relationships among
concepts, in their own minds. To do this, we must allow our children to explore and investigate, and
discuss and justify. As such, we have designed our teaching and assessment programs using these
tenants. The assessable elements (knowledge and understanding, thinking and reasoning,
communicating, reflecting) are considered, but not all are assessed on every task.

Each semester in each year level, we aim to have a range and balance of different types of tasks. As
such, our minimum assessment requirements for each class are listed below.

Mt Tarampa State School
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School-based assessment requirements

   Assessment type            Frequency                        Assessable elements
Short answer tests         1 per topic             Knowledge and understanding
                                                   Communicating
Open-ended                 1 per term              Thinking and reasoning
investigation                                      Communicating
                                                   Reflecting
Report                     2 per year              Knowledge and understanding
                                                   Thinking and reasoning
                                                   Communicating
                                                   Reflecting
QCAT (semester 2           1 per year           As per QCAT design brief — this will vary every
only)                                           second year
External assessment requirements
NAPLAN                                   To be completed in May of each year

This data is to be included in the student’s portfolio so that progress can be tracked.

Notes:
 In the early years of schooling, there will be a greater emphasis on the use of oral presentations,
   portfolios and checklists. As students progress through the school, there will be more balance
   between spoken and written forms of assessment.

National Assessment Program — Literacy and Numeracy (NAPLAN) data will be used to review our
program, and identify strengths and weaknesses, and professional development priorities for staff and
resource purchasing. Students that require targeted teaching can be identified.

                                       2009 NAPLAN results
(Reading, writing, spelling, grammar and punctuation, and numeracy results for Years 3, 5, 7 and 9)

Numeracy                                                Year 3 Year 5 Year 7
Avg. score for Mt Tarampa SS                            275.5  456.2  513.6
Avg. score for Australia                                393.9  486.8  543.6
Percentage of students at Mt Tarampa SS above benchmark  50     100    90.9

Year 2 Diagnostic Net Results (2008): Percentage of students not requiring additional support in
Number: 100%

Reporting
At Mt Tarampa State School, we will report student achievement and learning to parents on a regular
basis. This will include both written and oral reporting.
Specifically:
 quarterly written reports on a 5-point scale (end of each term)
 thrice yearly oral reporting (end of Terms 1, 2 and 3)
 informal reporting to parents (on a needs basis for those students requiring special programs, such
    as intervention or extension)

Note: Special programs may take a variety of forms (i.e. intensive and specialised teaching within the
classroom, targeted programs with specialist teachers or intensive one-to-one tutoring).




Mt Tarampa State School
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                                                        Mathematics Overview ~ Year P-3
                                                                 Semester 1

FOCUS CONCEPTS            ESSENTIAL LEARNINGS (Knowledge and                       TEACHING FOCUS P – 1                              TEACHING FOCUS 2-3
                          Understandings)
PATTERNS                  Algebra
                           Simple relationships between objects or numbers           Patterns                                         Patterns
                              can be described in terms of order, sequence             - patterns in our daily lives                     - repeating and non-repeating patterns
                              and arrangement                                          - repeating patterns including actions,             both number patterns and pictorial
                           Number patterns and sequences based on                       sounds and objects                                patterns
                              simple rules involve repetition, order and regular             recognises the pattern                           recognises the pattern
                              increases or decreases.                                        continues or extends the pattern                 identifies the repeating part
                                                                                             identifies the repeating part                    continues the pattern
                                                                                             creates a repeating pattern                      identifies the missing part
                                                                                             determines the missing part
MONEY                     Number
                           Money can be used to buy goods and services.              Knowledge                                        Knowledge
                           Transactions for goods and services can use                - coins and notes – sort; relative value of       - coins and notes - relationship between
                             different combinations of notes and coins of                 notes and coins (notes have more                  different coins and notes; justifies
                             equivalent value.                                            value than coins); visual recognition of          thinking
                                                                                          coins and notes                                - represents values in a variety of ways
                                                                                       - language – cost, price and names of                e.g. $5 can be made up of 2 $2 coins
                                                                                          coins and notes                                   and 1 $1 coin or 5 $1 coins
                                                                                      Financial decisions                              Financial decisions
                                                                                        - Uses of money                                  - Uses of money




Mt Tarampa State School
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FOCUS CONCEPTS            ESSENTIAL LEARNINGS (Knowledge and                    TEACHING FOCUS P – 1                               TEACHING FOCUS 2-3
                          Understandings)
CHANCE                    Chance and Data
                           Predictions about chance events can be made            Likelihood                                        Likelihood
                             using simple statements.                               - concept of likelihood linked to                  - concept of likelihood linked to
                                                                                       appropriate language                               appropriate language
                                                                                    - language – will happen, won’t happen,            - language – likely, unlikely, certain,
                                                                                       always, sometimes, never, will, will not,          impossible
                                                                                       might happen, maybe                            Judgements
                                                                                   Judgements                                         - uses language to describe different
                                                                                    - Classifications of the likelihood of daily          situations e.g. pulling a green marble
                                                                                       events                                             out of the bag, the chance of rain
                                                                                                                                          tomorrow etc.
TIME                      Number
                           Simple fractions, including half and quarter, and      Fraction                                          Fraction
                             mixed numbers can be represented in different          - parts of a whole (equal parts & not              - half is one of two-equal parts of the
                             ways.                                                     equal parts)                                       whole and quarter is one of four-equal
                          Measurement                                               - half = 1 of 2 equal parts                           parts of the whole
                           Hour, half-hour, and quarter-hour times and five-      Point in time                                      - identify half and quarter on a clock face
                             minute intervals are read using analogue clocks        - identify and sequence familiar daily            Duration of time
                             and all times are read using digital clocks.              events                                          - analogue and digital clocks.
                                                                                    - sequence daily events                            - read and record hour, half-hour and
                                                                                    - language – start, finish, later, earlier,           quarter-hour times and five-minute
                                                                                       slow, longer, shorter                              intervals on analogue clocks and all
                                                                                   Duration of time                                      times on digital clocks
                                                                                    - comment if something takes a long
                                                                                       time or not




Mt Tarampa State School
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FOCUS CONCEPTS            ESSENTIAL LEARNINGS (Knowledge and                   TEACHING FOCUS P – 1                              TEACHING FOCUS 2-3
                          Understandings)
3D OBJECTS                Space
                           Geometric names and properties are used to            Shape - 3D objects                               Shape - 3D objects
                             sort, describe and construct common 2D shapes         - recognition and identification of objects       - identification of object as prism,
                             including squares, rectangles, triangles and          - classification of everyday objects (see            pyramid, cone, cylinder, sphere
                             circles, and 3D objects, including prisms,               list in Essentials)                            - using verbal and written
                             pyramids, cones, cylinders and spheres.               - grouping boxes, cones and balls                    representations to identify and
                                                                                      according to their properties (including          communicate the properties of different
                                                                                      justification)                                    objects
                                                                                   - construction of models using play              Visualisation
                                                                                      dough                                          - identification of 2D shapes as faces of
                                                                                  visualisation                                        3D object
                                                                                   - description of properties (shapes,              - construct 3D objects according to
                                                                                      faces, pointy, smooth, rolling, sliding)          criteria
                                                                                                                                     - draw 3D shapes to show depth
VOLUME                    Measurement
                           Standard units, including centimetre, metre,          Understanding volume and associated              Understanding volume and associated
                             kilogram (half and quarter) and litre (half and       units                                             units
                             quarter), and non-standard units of                   - concept of volume                               - concept of volume
                             measurement can be used to measure attributes        Direct comparisons                                - non-standard units e.g. cups, cans,
                             of shapes and objects.                                - empty, full                                        buckets
                           Measurements of length, area, volume and               - order and sequence objects according            - standard units - litre including a half
                             mass of shapes and objects are compared and              to volume                                         and a quarter
                             ordered, using instruments                            - ways to measure volume                         Direct comparisons
                                                                                                                                     - determining appropriateness of
                                                                                                                                        standard or non-standard units
                                                                                                                                     - order objects based on their volume
                                                                                                                                     - measure volume using standard and
                                                                                                                                        non-standard units depending on
                                                                                                                                        accuracy required




Mt Tarampa State School
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FOCUS CONCEPTS            ESSENTIAL LEARNINGS (Knowledge and                   TEACHING FOCUS P – 1                                TEACHING FOCUS 2-3
                          Understandings)
LENGTH AND AREA           Measurement
                           Standard units, including centimetre, metre,          Understanding length and area and                  Understanding length, area and
                             kilogram (half and quarter) and litre (half and       associated units                                    associated units
                             quarter), and non-standard units of measurement       - concept of length                                  - concept of length and perimeter
                             can be used to measure attributes of shapes and       - non-standard units for length e.g.                 - standard units - metres, centimetres
                             objects.                                                 pencil, rake, foot                                - relationship between metres and
                           Measurements of length, area, volume and              Direct comparisons                                     centimetres
                             mass of shapes and objects are compared and           - bigger, smaller, longer, taller, shorter,          - conventions – m, cm
                             ordered, using instruments                               wider, longest, tallest, shortest, widest,        - concept of area
                                                                                      same length, near, far                            - non-standard units e.g. post-its, tiles,
                                                                                   - order and sequence objects according                 counters
                                                                                      to length                                       Direct comparisons
                                                                                   - ways to measure length                             - determining appropriateness of
                                                                                                                                          standard or non-standard units for
                                                                                                                                          length
                                                                                                                                        - order objects based on their length
                                                                                                                                        - order objects based on their area
                                                                                                                                        - measure or estimate length using
                                                                                                                                          standard and non-standard units
                                                                                                                                          depending on accuracy required
                                                                                                                                      Indirect measures
                                                                                                                                        - problem solving involving the perimeter
                                                                                                                                          of a range of 2D shapes




Mt Tarampa State School
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FOCUS CONCEPTS            ESSENTIAL LEARNINGS (Knowledge and                     TEACHING FOCUS P – 1                            TEACHING FOCUS 2-3
                          Understandings)
MULTIPLICATIVE            Number
THINKING                   Multiplication and division of whole numbers to         Number concepts                                Number concepts
                             10 can be calculated using arrays, skip counting,       - groups of                                     - conventions used to write number
                             doubles, double doubles, turnarounds and                - equal sharing                                   sentences involving grouping and
                             sharing of concrete materials                          Numeration                                        sharing
                                                                                     - counting in twos and fives                   Numeration
                                                                                    Number facts and strategies                     - skip counting
                                                                                     - using arrays to show groups of               Number facts and strategies
                                                                                    Problem solving                                 - arrays
                                                                                     - representation of groups of and sharing       - doubles, double doubles, …
                                                                                       problems using materials                      - multiplication facts for 1, 2, 5 and 10
                                                                                     - writing number sentences (using words        Problem solving
                                                                                       and symbols e.g. 5 groups of 2 = 10) to       - solving problems involving
                                                                                       describe thinking                               multiplication and division using basic
                                                                                                                                       facts and materials as appropriate for
                                                                                                                                       the situation and size of the numbers
                                                                                                                                     - writing number sentences (using words
                                                                                                                                       and symbols e.g. 5 groups of 2 = 10) to
                                                                                                                                       describe thinking




Mt Tarampa State School
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FOCUS CONCEPTS            ESSENTIAL LEARNINGS (Knowledge and                      TEACHING FOCUS P – 1                             TEACHING FOCUS 2-3
                          Understandings)
EQUATIONS                 Number                                                                                                      Number concepts
                           Addition and subtraction involving 2-digit whole         Number concepts                                  - place value
                              numbers can be calculated using concrete                - number representations - words,               Numeration
                              materials, mental computation and written                 symbols, pictorial and materials               - comparing and ordering
                              strategies.                                            Numeration                                      Number facts and strategies
                           Multiplication and division of whole numbers to           - grouping of items using blocks                 - doubles, double doubles, skip counting,
                              10 can be calculated using arrays, skip counting,      Number facts and strategies                         turnarounds
                              doubles, double doubles, turnarounds and                - counting - on and back in 1s, 2s, and          - mental computation
                              sharing of concrete materials.                            3s                                            Problem solving strategies that involve a
                           Problems involving operations can be explored             - simple addition and subtraction facts to       single operation
                              using concrete materials, sketches and                    10 e.g. 4+4=8 and 5+3=8                        - sketches and diagrams
                              diagrams.                                              Problem solving                                  - inverse relationship between +/- and
                           Problems using a single operation can be                  - problem solving with the use of                   x/
                              planned and solved.                                       materials                                      - using materials
                          Algebra                                                                                                      - written methods
                           Inverse relationships between addition and                                                                 - check for reasonableness
                              subtraction can be applied to find unknowns and                                                          - addition and subtraction problems
                              maintain equivalence in equations                                                                           involving 2-digit whole numbers
                                                                                                                                       - multiplication and division




Mt Tarampa State School
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FOCUS CONCEPTS            ESSENTIAL LEARNINGS (Knowledge and               TEACHING FOCUS P – 1                         TEACHING FOCUS 2-3
                          Understandings)
EQUIVALENCE               Number
                           Whole numbers (to 999) have position on a         Numeration                                   Numeration
                              number line and each digit has place value       - using a number line to order number (to     - using a number line to order numbers
                          Algebra                                                10)                                           (to 999)
                           Simple relationships between objects or           Number facts and strategies                  Number facts and strategies
                              numbers, including equivalence, can be           - counting on and counting back in 1s, 2s     - relationships between equations e.g. 6
                              represented using concrete and pictorial           and 3s - using materials, mentally and        + 3 = 9, 9 – 6 = 3 and 9 – 3 = 6
                              materials                                          in written form                            Problem solving
                                                                              Problem solving                               - justification of thinking
                                                                               - representations of numbers using            - representations of numbers and
                                                                                 pictorial and concrete material e.g. 5        equations of equivalence using pictorial
                                                                                 can be made up of 3 blue and 2 red            and concrete material representations
                                                                                 markers or 4 blue and 1 red marker            e.g. 14 + 8 = 10 + 12
                                                                                 without changing the total number           - recording equations (addition and
                                                                               - justification of thinking                     subtraction) using written, pictorial and
                                                                                                                               concrete representations




Mt Tarampa State School
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FOCUS CONCEPTS            ESSENTIAL LEARNINGS (Knowledge and                   TEACHING FOCUS P – 1                             TEACHING FOCUS 2-3
                          Understandings)
DATA                      Chance and Data
                           Data can be collected using simple surveys and        Collecting data                                 Collecting data
                             observations to respond to questions.                 - Gather a small amount of data to               - surveys and how to conduct one
                           Data can be organised in lists, tables, picture           support a class decision (hands up for        - determine data needed to support
                             graphs and bar graphs.                                   this decision, counts the hands)                 hypothesis e.g. if we survey the
                           Data can be explored for variation and adequacy.       - Observation to collect data to resolve            students at our school on what their
                                                                                      questions, issues of interest                    favourite ice-cream flavour is, is it
                                                                                  Displaying data                                     appropriate to comment that this is our
                                                                                   - Class generated data recording sheets             town’s favourite ice-cream flavour or do
                                                                                   - Can develop written observations: lists,          we need more evidence?
                                                                                      data displays, pictures                      Displaying data
                                                                                  Analysing data                                   - read and record results as a list, table,
                                                                                   - Classifies and sorts objects and                  picture graph or bar graph.
                                                                                      pictures and discusses the basis for          - differences and similarities between
                                                                                      their classification                             lists, tables, picture graphs and bar
                                                                                                                                       graphs
                                                                                                                                   Analysing data
                                                                                                                                    - compare data in a graph to analyse
                                                                                                                                       variation




Mt Tarampa State School
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                                                        Mathematics Overview ~ Year P-3
                                                                 Semester 2

FOCUS CONCEPTS            ESSENTIAL LEARNINGS (Knowledge and                 TEACHING FOCUS P – 1                              TEACHING FOCUS 2-3
                          Understandings)
MISCELLANEOUS             Review Measurement
                                                                                Review areas in need of assistance with          Angles
                                                                                 particular emphasis on Number                     - concept of angles in relation to turns
                                                                                                                                   - comparison of angles using non-
                                                                                                                                     standard units e.g. arms, right-angle
                                                                                                                                     checker (corner of a piece of paper)
TIME                      Measurement
                           Calendars can be used to identify specific          Duration of time                                 Duration of time
                             information about days and dates.                   - names of months in the year                     - names and sequence of the days in a
                                                                                 - names of days in the week                         week and months in the year.
                                                                                 - record familiar events on a simple              - names and sequence of the seasons
                                                                                   calendar                                        - read calendars e.g. identify the dates of
                                                                                 - names and characteristics of the                  all the Thursdays in a given month
                                                                                   seasons.                                       Time intervals
                                                                                                                                   - fortnight, annual, monthly etc.
                                                                                                                                   - calculate the date that is a week later,
                                                                                                                                     or earlier.
SYMMETRY                  Space
                           Flips, slides and turns are particular ways of      Visualisation                                    Transformations
                             moving shapes to explore symmetry.                  - making mental images of 2D shapes               - language - slide, turn
                                                                                    and 3D objects                                 - application of flip, slides, turns to
                                                                                Transformations                                      shapes and objects
                                                                                 - turn simple shapes to match other               - develop repeating patterns based on
                                                                                    shapes.                                           flip, slide, turn
                                                                                 - fold shapes that have line symmetry             - simple visual puzzles
                                                                                    e.g. a drawing of a heart with a line of
                                                                                    symmetry down the middle
                                                                                 - use materials including pattern blocks
                                                                                    to demonstrate flips and turns


Mt Tarampa State School
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FOCUS CONCEPTS            ESSENTIAL LEARNINGS (Knowledge and                   TEACHING FOCUS P – 1                             TEACHING FOCUS 2-3
                          Understandings)
POSITION IN SPACE         Space
                           Obvious features in everyday environments can         Location, direction and movement                Location, direction and movement
                             be represented and located on simple maps and         - simple sketches to represent objects           - construct birds-eye view to show
                             plans.                                                  e.g. can look at a drawing of 3 bottles          positions within a given area (e.g.
                           Directions can be given for moving and for               and place them in the correct order in           bedroom, classroom etc)
                             locating features within and environment.               real-life                                      - follow and give directions to move
                                                                                   - Birds-eye view to show relative position         forwards, backwards, left, right, half, full
                                                                                   - language – over, under, up, down, left,          and quarter turns (three-quarter turns)
                                                                                     right, forwards, backwards, sideways,
                                                                                     on, below, between, beside, near,
                                                                                     before, after, full turn, half turn
                                                                                   - simple directions - move forwards,
                                                                                     backwards, left and right
                                                                                   - non-verbal information (gestures) to
                                                                                     give directions
MASS                      Measurement
                           Standard units, including centimetre, metre,          Understanding mass and associated units         Understanding mass and associated units
                             kilogram (half and quarter) and litre (half and       - concept of mass                                - concept of mass
                             quarter), and non-standard units of measurement      Direct comparisons                               - non-standard units e.g. centicubes,
                             can be used to measure attributes of shapes and       - bigger, smaller, heavy, light, heavier,           marbles
                             objects.                                                 lighter, heaviest, lightest                   - standard units - kilogram including a
                           Measurements of length, area, volume and mass          - order and sequence objects according              half and a quarter
                             of shapes and objects are compared and                   to mass                                      Direct comparisons
                             ordered, using instruments                            - ways to measure mass                           - determining appropriateness of
                                                                                   - determining which object is lighter or            standard or non-standard units
                                                                                      heavier by hefting                            - order objects based on their mass
                                                                                                                                    - measure mass using standard and
                                                                                                                                       non-standard units depending on
                                                                                                                                       accuracy required




Mt Tarampa State School
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FOCUS CONCEPTS            ESSENTIAL LEARNINGS (Knowledge and                    TEACHING FOCUS P – 1                              TEACHING FOCUS 2-3
                          Understandings)
2D SHAPES                 Space
                           Geometric names and properties are used to             Shape – 2D shapes(see list in Essentials)        Shape – 2D shapes (see list in Essentials)
                             sort, describe and construct common 2D shapes          - recognition and identification of 2D            - properties of shapes e.g. right angles,
                             including squares, rectangles, triangles and              shapes                                            number of straight sides
                             circles, and 3D objects, including prisms,             - recognition of straight and curved lines,       - identify 2D shapes in different
                             pyramids, cones, cylinders and spheres.                   number of sides and corners                       orientations
                                                                                    - names of shapes                                Visualisation
                                                                                   Visualisation                                     - draw 2D shapes and identify properties
                                                                                    - make 2D shapes learnt with cord or                 of the shape
                                                                                       pipe cleaners                                  - draw 2D shapes according to criteria
EQUIVALENCE               Number
                           Whole numbers (to 999) have position on a              Numeration                                       Numeration
                              number line and each digit has place value            - using a number line to order number (to         - using a number line to order numbers
                          Algebra                                                     10)                                               (to 999)
                           Simple relationships between objects or                Number facts and strategies                      Number facts and strategies
                              numbers, including equivalence, can be                - counting on and counting back in 1s, 2s         - relationships between equations e.g. 6
                              represented using concrete and pictorial                and 3s - using materials, mentally and            + 3 = 9, 9 – 6 = 3 and 9 – 3 = 6
                              materials                                               in written form                                Problem solving
                           Inverse relationships between addition and             Problem solving                                   - justification of thinking
                              subtraction can be applied to find unknowns and       - representations of numbers using                - representations of numbers and
                              maintain equivalence in equations                       pictorial and concrete material e.g. 5            equations of equivalence using pictorial
                                                                                      can be made up of 3 blue and 2 red                and concrete material representations
                                                                                      markers or 4 blue and 1 red marker                e.g. 14 + 8 = 10 + 12
                                                                                      without changing the total number               - recording equations (addition and
                                                                                    - justification of thinking                         subtraction) using written, pictorial and
                                                                                                                                        concrete representations
VOLUME
MULTIPLICATIVE
THINKING                                                                        Review areas in need of assistance
EQUATIONS
DATA



Mt Tarampa State School
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                                                       Mathematics Overview ~ Year 4/5
                                                                Semester 1

FOCUS CONCEPTS            ESSENTIAL LEARNINGS (Knowledge and Understandings)                        TEACHING FOCUS 4-5
EQUATIONS                 Number
                           Place value of digits in whole numbers and decimal fractions               Number concepts
                              changes when they are multiplied and divided by 10 and 100.               - factors including prime numbers and composite numbers
                           Whole numbers (to thousands) and decimal fractions (to                     Numeration
                              hundredths) can be calculated using addition and subtraction.             - investigates the effect of multiplying a number by 10 and by 100
                           Whole numbers can be multiplied and divided by whole numbers to            Number facts and strategies
                              10                                                                        - mental computation strategies that rely on commutative,
                           Whole numbers have factors, prime numbers have only two distinct              associative, distributive and inverse laws e.g. 27 + 52 + 3 = 27 +
                              factors and composite numbers have more than two factors.                   3 + 52 = 30 + 52 = 82
                           Problems can be made manageable by using strategies involving               - adds and subtracts with and without regrouping
                              estimation, inverse operations, doubles, double doubles and halving       - multiplication facts to 10
                          Algebra                                                                      Problem solving
                           Rules can be developed to interpret a pattern and predict further           - reinforce problem solving strategies (refer to Year 2-3 notes)
                              elements                                                                  - discuss other strategies that could be used for solving problems
                           Generalisations associated with the four operations are built upon         Patterns
                              commutative, associative and distributive properties and inverse          - Growing patterns - identifies the rule; and continues the pattern
                              operations.




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FOCUS CONCEPTS            ESSENTIAL LEARNINGS (Knowledge and Understandings)                          TEACHING FOCUS 4-5
TIME                      Measurement
                           Analogue and digital clocks can be used to read time to the nearest          Duration of time
                             minute.                                                                      - hours, minutes and seconds
                           Timelines, clocks, calendars and timetables are used to sequence,             - read and record times on analogue and digital clocks to the
                             schedule and calculate timed events.                                           nearest minute
                           Standard units, including centimetre, metre, square centimetre,               - real-life applications of timelines, clocks, calendars and timetables
                             square metre, gram, kilogram, minute, degree, millilitre and litre,         Time intervals
                             and a range of instruments are used to measure and order attributes          - calculate the amount of time between one event and another
                             of objects, including length, area, volume, mass, time, and angles             using timelines, clocks, calendars and timetables
                           Links exist between different ways of recording the same                      - calculate the time of given events using hours, minutes and
                             measurement.                                                                   seconds
                           Reasonable estimates can be made using strategies that suit the               - estimate times taken for different situations e.g. I know it takes 2
                             situation.                                                                     hours to travel 212km so I estimate it will take 1hour to travel
                                                                                                            100km
2D SHAPES                 Space
                           Geometric features, including parallel and perpendicular lines, acute,       Shape - 2D shapes
                             right, obtuse and reflex angles, and vertex, edge and base, can be           - grouping shapes according to their properties (see list in
                             used to sort shapes and objects into broad family groups.                       Essentials)
                           Defining features, including edges, angle sizes and parallel lines, are       - parallel sides, congruent sides
                             used to make accurate representations of 2D shapes and 3D                    - using verbal and written representations to identify and
                             objects.                                                                        communicate the properties of different shapes
                                                                                                          - drawing accurate representations using appropriate tools
                                                                                                         Visualisation
                                                                                                          - draw 2D shapes according to criteria and using appropriate
                                                                                                             conventions
MASS                      Measurement
                           Standard units, including centimetre, metre, square centimetre,              Understanding mass and associated units
                             square metre, gram, kilogram, minute, degree, millilitre and litre,          - standard units - kilogram and gram
                             and a range of instruments are used to measure and order attributes          - relationship between kilograms and grams
                             of objects, including length, area, volume, mass, time, and angles.          - conventions to represent mass e.g. kg, g
                           Links exist between different ways of recording the same                     Direct comparisons
                             measurement.                                                                 - measure or estimate mass depending on accuracy required
                           Reasonable estimates can be made using strategies that suit the
                             situation.

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FOCUS CONCEPTS            ESSENTIAL LEARNINGS (Knowledge and Understandings)                        TEACHING FOCUS 4-5
MULTIPLICATIVE            Number
THINKING                   Common and mixed fractions involving denominators to tenths can             Fractions
                             be represented as a collection of objects, on number lines and as           - unit fractions to tenths
                             parts of measure to solve problems                                          - non-unit fractions
                                                                                                         - mixed numbers
                                                                                                         - compare and order common fractions and mixed numbers
                                                                                                         - operating with fraction problems with related denominators e.g. 1/2
                                                                                                            + 3/4
                                                                                                         - problem solving involving fractions
MISCELLANEOUS             Measurement
                           Standard units, including centimetre, metre, square centimetre,             Angles
                             square metre, gram, kilogram, minute, degree, millilitre and litre, and     - concept of angles
                             a range of instruments are used to measure and order attributes of          - types of angles - acute, right, obtuse, straight and reflex
                             objects, including length, area, volume, mass, time, and angles.            - standard units – degrees including the fact that there are 360
                                                                                                           degrees in a circle
                                                                                                         - measures and calculates angles using appropriate technologies
                                                                                                           (protractor)
MONEY                     Number
                           Financial records and simple spending and saving plans are ways to          Knowledge
                             check on available money and income.                                        - savings - methods of saving; interest may be earned on savings
                           Money can be saved and borrowed, and interest and fees may                   - borrowing - methods of borrowing; interest is applied to money
                             apply.                                                                         borrowed
                                                                                                         - income - money coming in
                                                                                                         - expenditure - money going out
                                                                                                         - ways to record these transaction amounts appropriately
                                                                                                        Financial decisions
                                                                                                         - decisions based on income and expenditure
                                                                                                         - borrowing - implications interest has on individuals




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FOCUS CONCEPTS            ESSENTIAL LEARNINGS (Knowledge and Understandings)                          TEACHING FOCUS 4-5
CHANCE                    Chance and Data
                           The likelihood of outcomes of events involving chance can be                 Likelihood
                             described using terms including “likely”, “more likely”, “most likely”       - concept of likelihood linked to appropriate language
                             and “never”.                                                                 - language – likely, more likely, most likely, never
                           Data collected from experiments or observations can be organised              - relate fractions to likelihood
                             in tables and graphs and used to respond to questions about the             Judgements
                             likelihood of possible outcomes of events.                                   - uses appropriate language to describe different situations
                                                                                                          - experiments of likelihood - collect data and discuss the likelihood
                                                                                                             of different events occurring e.g. pull a marble out of a bag 10
                                                                                                             times and comment on the likelihood of choosing a blue one next
                                                                                                          - represent data collected in a table and/or graph
VOLUME                    Measurement
                           Standard units, including centimetre, metre, square centimetre,              Understanding volume and associated units
                             square metre, gram, kilogram, minute, degree, millilitre and litre,          - standard units - litres and millilitres
                             and a range of instruments are used to measure and order attributes          - relationship between litres and millilitres
                             of objects, including length, area, volume, mass, time, and angles.          - conventions to represent volume e.g. L, mL
                           Links exist between different ways of recording the same                     Direct comparisons
                             measurement.                                                                 - measure or estimate volume depending on accuracy required
                           Reasonable estimates can be made using strategies that suit the
                             situation.
3D OBJECTS                Space
                           Geometric features, including edges, angle sizes and parallel lines,         Shape – 3D objects
                             are used to make accurate representations of 2D shapes and 3D                - language - edge, angle size, and parallel lines
                             objects.                                                                     - classify objects, in appropriate context, according to properties
                           3D objects can be visualised or constructed using nets.                          and using appropriate language/terminology to justify
                                                                                                             classifications
                                                                                                         Visualisation
                                                                                                          - nets - construct objects from a net; identify object that matches a
                                                                                                             given net
                                                                                                          - draw 2D representations of 3D objects




Mt Tarampa State School
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                                                       Mathematics Overview ~ Year 4/5
                                                                Semester 2

FOCUS CONCEPTS            ESSENTIAL LEARNINGS (Knowledge and Understandings)                      TEACHING FOCUS 4-5
SYMMETRY                  Space
                           Symmetry and transformations involving flips, slides, turns,             Visualisation
                             enlargements and reductions provide a basis for creating patterns,       - visualise single flips, slides and turns
                             designs and tessellations.                                              Transformations
                                                                                                      - demonstrate understanding of flip, slide, turn
                                                                                                      - enlarging and reducing shapes and patterns
                                                                                                      - investigating tessellating 2D shapes
POSITION IN SPACE         Space
                           Mapping conventions, including symbols, scales, legends and              Location, direction and movement
                             alphanumeric grids, are used to represent and interpret movements        - mapping conventions including symbols, scales, legends,
                             and to identify locations on maps and plans.                               alphanumeric grids.
                           Mapping conventions, including the four major compass points, are         - create maps that use mapping conventions
                             used to give direction and movement and can be linked to turns.          - calculate real-life distances from scale (e.g. 1cm is 1 km in real
                                                                                                        life therefore, 3cm is 3km in real life etc)
                                                                                                      - use a map to follow directions
                                                                                                      - relationship between North, South, East and West and quarter,
                                                                                                        half and three quarter turns
PATTERNS                  Algebra
                           Simple relationships are used to predict results of change               Patterns
                           Rules can be developed to interpret a pattern and predict further         - repeating and non-repeating number patterns
                              elements.                                                                     recognises the pattern
                                                                                                            identifies the rule e.g. 5, 7, 9, 11, …adds on 2
                                                                                                            uses the rule to continue the pattern
TIME                      Measurement
                           Timelines, clocks, calendars and timetables are used to sequence,        Duration of time
                             schedule and calculate timed events.                                     - real-life applications of timelines, clocks, calendars and timetables
                           Links exist between different ways of recording the same                 Time intervals
                             measurement.                                                             - problem solving using timelines, clocks, calendars and timetables
                           Reasonable estimates can be made using strategies that suit the           - 12 months = 1 year, 52 weeks = 1 year, 26 fortnights = 1 year, 10
                             situation.                                                                 years = 1 decade, 100 years = 1 century etc.


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FOCUS CONCEPTS            ESSENTIAL LEARNINGS (Knowledge and Understandings)                       TEACHING FOCUS 4-5
DATA                      Chance and Data
                           Data collected from experiments or observations can be organised          Collecting data
                             in tables and graphs and used to respond to questions about the            - experiments, simulations, surveys, research
                             likelihood of possible outcomes of events.                                 - determine data needed to justify statements or predictions (e.g.
                           Collected data can be used to justify statements and predictions.             more children in our town like riding motorbikes than horses)
                           Sets of data may contain expected or unexpected variation, and this         - new questions are developed as we collect data and these new
                             may mean that additional data are needed.                                    questions also need to be investigated
                                                                                                      Displaying data
                                                                                                        - record data appropriately in tables, bar graphs, line graphs
                                                                                                      Analysing data
                                                                                                        - interpret data in tables, bar graphs, line graphs
                                                                                                        - compare data in tables or graphs to analyse variation
LENGTH AND AREA           Measurement                                                                 Understanding length, area and associated units
                           Standard units, including centimetre, metre, square centimetre,             - standard units – metres, centimetres, millimetres, kilometres
                             square metre, gram, kilogram, minute, degree, millilitre and litre,        - relationship between metres, centimetres, millimetres and
                             and a range of instruments are used to measure and order attributes          kilometres
                             of objects, including length, area, volume, mass, time, and angles.        - conventions to represent length e.g. m, cm, mm, km
                           Links exist between different ways of recording the same                    - standard units – square centimetres, square metres
                             measurement.                                                               - relationship between square centimetres and square metres
                           Reasonable estimates can be made using strategies that suit the             - conventions – cm2, m2
                             situation.                                                               Direct comparisons
                                                                                                        - determining appropriateness of standard or non-standard units for
                                                                                                          area
                                                                                                        - measure or estimate area depending on accuracy required
                                                                                                      Indirect measures
                                                                                                        - problem solving involving the perimeter or area of a range of 2D
                                                                                                          shapes
                                                                                                        - rules for calculating the perimeter of square and rectangle




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FOCUS CONCEPTS            ESSENTIAL LEARNINGS (Knowledge and Understandings)                       TEACHING FOCUS 4-5
EQUIVALENCE               Number
                           Whole numbers (to 9999), decimal fractions (to at least hundredths),      Numeration
                              and common and mixed fractions have positions on a number line           - using a number line to represent and order numbers on a number
                           Equivalent fractions have easily related denominators that are used           line - whole numbers; common and decimal fractions; mixed
                              to assist mental calculations                                               numbers
                          Algebra                                                                     Fractions
                           Patterns in space and number, and relationships between quantities,        - numerators and denominators
                              including equivalence, can be represented using concrete and             - using related denominators to determine equivalence
                              pictorial materials, lists, tables and graphs                           Number facts and strategies
                           Generalisations associated with the four operations are built upon         - mental computation strategies
                              commutative, associative and distributive properties and inverse        Problem solving
                              operations                                                               - equivalence can be applied to quantities of measurement – these
                                                                                                          can be calculated and recorded in a variety of methods.
                                                                                                       - equations of equivalence can be represented using all four
                                                                                                          operations.
                                                                                                       - appropriate symbols can be used to represent relations of
                                                                                                          equivalence




Mt Tarampa State School
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                                                        Mathematics Overview ~ Year 6/7
                                                                 Semester 1
FOCUS CONCEPTS            ESSENTIAL LEARNINGS (Knowledge and Understandings)                        TEACHING FOCUS 6-7
EQUATIONS                 Number
                           Estimation strategies including rounding, and estimates based on           Number concepts
                              powers of 10, assist in checking for reasonableness of calculations       - place value relating to large numbers and decimals
                              involving whole numbers and common and decimal fractions.                Numeration
                           Problems can be interpreted and solved by selecting from the four           - comparing and ordering
                              operations and mental, written and technology-assisted strategies.        - representing numbers (place value)
                          Algebra                                                                      Number facts and strategies
                           Expressions and relationships, including formulas and simple                - order of operations
                              equations, can be demonstrated using words, diagrams, materials          Problem solving involving more than one operation
                              and symbols to represent variables.                                       - estimating - strategies for working with whole numbers, decimals
                           The order of operations identifies the appropriate sequence of                and fractions
                              operations used in calculations to obtain solutions.                      - reasonableness of answer when problem solving
                           Tables of values for functions using input-output rules can be              - connecting written words, numerical equations and pictorial forms
                              constructed and the resulting ordered pairs graphed.                        of the same problem
                                                                                                        - representing problems in words, as a numerical equation and in
                                                                                                          pictorial formats
EQUIVALENCE               Number
                           Whole numbers, including positive and negative numbers, and                Numeration
                              common and decimal fractions can be ordered and compared using            - using a number line to order and compare whole numbers,
                              a number line                                                                common and decimal fractions both positive and negative
                           Common fractions can be represented as equivalent fractions,               Fractions
                              decimals and percentages for different purposes                           - relationship between common fractions, decimals and
                          Algebra                                                                          percentages
                           Equations and expressions involving addition, subtraction and              Number facts and strategies
                              multiplication can be solved to establish equivalence                     - Mental computation
                                                                                                       Problem solving
                                                                                                        - Solve equations using addition, subtraction and multiplication to
                                                                                                           establish equivalence
                                                                                                        - Use appropriate symbols to represent equivalence in equations




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FOCUS CONCEPTS            ESSENTIAL LEARNINGS (Knowledge and Understandings)                       TEACHING FOCUS 6-7
2-D SHAPES                Space
                           Geometric conventions, including length, angle size and                   Shape – 2D shapes
                             relationships between faces, are used to classify 2D shapes and 3D        - properties of shapes and the similarities and differences between
                             objects, including part and composite shapes.                                these (e.g. types of triangles, quadrilaterals etc)
                           2D shapes can be sketched or accurately represented, using                Visualisation
                             drawing instruments and software, to reflect their geometric              - sketch and draw accurate representations of 2D shapes using
                             properties.                                                                  appropriate tools and software
                           Congruent shapes are the same shape and size and can be                   Transformations
                             superimposed on one another through a sequence of                         - language - congruent, reflections, rotations, translations
                             transformations, involving reflections, rotations and translations.       - identifying congruent shapes
TIME                      Measurement
                           Timetables and duration of events involving both 12- and 24-hour          Duration of time
                             time cycles and Australian time zones can be calculated.                  - read and record times in both 12- and 24-hour times
                           Appropriate instruments, technologies and scale are used when              - read a clock even though not all graduations are labelled
                             exploring measurement of length, area, volume, mass, time and             - time-zones
                             angles where not all of the graduations are numbered.                    Time intervals
                           Estimation strategies are used to identify a reasonable range of           - problem solve using both 12- and 24-hour times
                             values for a measurement.                                                 - problem solving involving the time taken to complete events on
                                                                                                         that use different time-zones e.g. the time taken to fly from the
                                                                                                         East coast to the West coast of Australia
                                                                                                       - estimation strategies




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FOCUS CONCEPTS            ESSENTIAL LEARNINGS (Knowledge and Understandings)                       TEACHING FOCUS 6-7
DATA                      Chance and Data
                           Data may be discrete and can be allocated to categories or                Collecting data
                             numbered.                                                                 - terminology – discrete, continuous, bias
                           Data may be continuous and described as distributions of quantities.       - collection methods for discrete and continuous data
                           Sample data drawn from a given population can be summarised,               - identify bias in samples
                             compared and represented in a variety of ways.                           Displaying data
                           Measures of location such as mean, median and mode, and                    - representations - two-way tables, pie charts, bar graphs, line
                             frequency and relative frequency, can be used to explore                     graphs
                             distributions of sample data.                                             - determine display/s most appropriate for discrete and continuous
                           Variation and possible causes of bias can be identified in data               data
                             collections.                                                             Analysing data
                                                                                                       - terminology - mean, median, mode, frequency, relative frequency
                                                                                                       - measures of central tendency – mean, median, mode
                                                                                                       - measures of spread - range
                                                                                                       - effects of central tendency and spread on distributions
MISCELLANEOUS             Measurement
                           Appropriate instruments, technologies and scale are used when             Angles
                             exploring measurement of length, area, volume, mass, time and             - concept of angles
                             angles where not all of the graduations are numbered.                     - types of angles - acute, right, obtuse, straight and reflex
                           Measurement involves error, which can be reduced through the               - standard units – degrees
                             selection and use of appropriate instruments and technologies.            - conventions - o
                           Estimation strategies are used to identify a reasonable range of           - geometric properties - 360 degrees in a circle, sum of angles in a
                             values for a measurement.                                                   triangle equal 180o, sum of angles in a quadrilateral equal 360o
                                                                                                       - measures the size of given angles using a protractor
                                                                                                       - calculates the size of given angles using knowledge of angles,
                                                                                                         circles, triangles and quadrilaterals




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FOCUS CONCEPTS            ESSENTIAL LEARNINGS (Knowledge and Understandings)                       TEACHING FOCUS 6-7
MULTIPLICATIVE            Number
THINKING                   Percentages, rate, ratio and proportion can be used to describe           Number concepts
                             relationships between quantities and to solve problems in practical       - key percentages
                             situations involving money, time and other measures                       - concept of rate
                                                                                                       - concept of ratio
                                                                                                       - conventions for rate and ratio e.g. km/h, km per h, 1:4, 1/4
                                                                                                       - concept of proportion as two or more equal ratios
                                                                                                      Numeration
                                                                                                       - compare and order percentages
                                                                                                       - estimating involving percentage problems
                                                                                                      Number facts and strategies
                                                                                                       - relationship between key percentages, common fractions and
                                                                                                         decimals
                                                                                                       - order of operations
                                                                                                      Problem solving
                                                                                                       - calculating involving percentage, rate, ratio and proportion in
                                                                                                         practical situations
MONEY                     Number
                           Financial decisions and transactions are influenced by a range of         Knowledge
                             factors, including value for money, discounts, method of payment,         - language - value for money, discount, method of payment,
                             and available income or savings.                                             income, savings, budget, cheque, EFTPOS, credit card, debit
                           Budgets and financial records are used to monitor income, savings             card, money order
                             and spending.                                                             - accessing money or the equivalent – discount; interest ; ATMs
                           Cashless transactions include the use of cheques, EFTPOS, credit          Financial decisions
                             and debit cards, and money orders.                                        - budgeting including saving and borrowing
                                                                                                       - developing a budget on given figures
                                                                                                       - managing personal budgets with reference to bank statements,
                                                                                                          ATM slips, credit card statements, etc.




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FOCUS CONCEPTS            ESSENTIAL LEARNINGS (Knowledge and Understandings)                        TEACHING FOCUS 6-7
POSITION IN SPACE         Space
                           Maps and plans can be constructed and interpreted to identify a            Location, direction and movement
                             specific location, to plan movement from one location to another,          - mapping conventions including coordinates (ordered pairs), scale
                             and to calculate distance between locations.                                 (1:20)
                           Mapping conventions, including coordinates, compass points and              - relationship between the 8 key compass points and amount of
                             scale, are used to specify and identify locations on maps and plans.         turn
                                                                                                        - construct maps and plans to identify a specific location, plan
                                                                                                          movement from one location to another, and to calculate distance
                                                                                                          between locations
                                                                                                        - identify the best route to follow within parameters e.g. most direct
                                                                                                          route, most scenic route, longest route etc




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                                                       Mathematics Overview ~ Year 6/7
                                                                Semester 2

FOCUS CONCEPTS            ESSENTIAL LEARNINGS (Knowledge and Understandings)                        TEACHING FOCUS 6-7
LENGTH AND AREA           Measurement                                                                Understanding length, area and associated units
                           Appropriate instruments, technologies and scale are used when              - International System of measures and relationships between units
                             exploring measurement of length, area, volume, mass, time and               e.g. metres, kilometre, millimetre, square centimetre, square
                             angles where not all of the graduations are numbered.                       metre, hectare, etc.
                           Relationships exist within the International System (SI) of measures,    Direct comparisons
                             including between mm, cm, m and km; kg and t; cm2 and m2; cm3             - measure accurately using standard units
                             and m3.                                                                   - estimate length or area when appropriate
                           Relationships between attributes of regular 2D shapes and 3D             Indirect measure
                             objects can be used to develop rules that allow perimeter, area and       - problem solving involving perimeter and/or area including the use
                             volume to be calculated.                                                    of ratio in scales
                           Measurement involves error, which can be reduced through the               - the relationship between the perimeter and area of a given shape
                             selection and use of appropriate instruments and technologies.              e.g. rectangle, triangle
                           Estimation strategies are used to identify a reasonable range of           - rules for calculating the perimeter and area of common 2D
                             values for a measurement                                                    shapes
3D OBJECTS                Space
                           Geometric conventions, including length, angle size and                    Shape – 3D objects
                             relationships between faces, are used to classify 2D shapes and 3D         - language - length, angle size, faces
                             objects, including part and composite shapes.                              - classify 3D objects
                           3D objects can be constructed from plans, nets and isometric               Visualisation
                             diagrams.                                                                  - plans, nets and isometric diagrams
                                                                                                        - construct models based on plans, nets and isometric diagrams
                                                                                                           (e.g. main street of town, school buildings etc)




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FOCUS CONCEPTS            ESSENTIAL LEARNINGS (Knowledge and Understandings)                        TEACHING FOCUS 6-7
CHANCE                    Chance and Data
                           Events have different likelihoods of occurrence and estimates of           Likelihood
                             probability can be expressed as percentages, common fractions or           - express probability on a scale from 0 to 1
                             decimal fractions between 0 and 1.                                         - express probability as a percentage, common fraction or decimal
                           Experimental data for chance events can be compared with                    - theoretical vs experimental probability
                             theoretical probability.                                                   - list the sample space for theoretical probability of an event
                                                                                                       Judgements
                                                                                                        - demonstrates understanding of experimental data and theoretical
                                                                                                           probability by conducting an experiment and commenting on the
                                                                                                           results e.g. tosses a coin 20 times and records the answers for
                                                                                                           experimental data whereas the theoretical probability states you
                                                                                                           should toss 10 heads and 10 tails
PATTERNS                  Algebra
                           Tables of values for functions using input-output rules can be             Functions
                              constructed and the resulting ordered pairs graphed.                      - input – output machines
                                                                                                             displays input and outputs in a table
                                                                                                             uses the input and the rule to find the output
                                                                                                             uses the output and the rule to find the input
                                                                                                             uses the inputs and outputs to find the rule
                                                                                                        - displays of data and their relationships – tables, graphs, rules
MASS                      Measurement
                           Appropriate instruments, technologies and scale are used when              Understanding mass and associated units
                             exploring measurement of length, area, volume, mass, time and               - concept of mass
                             angles where not all of the graduations are numbered.                       - International System of measures and relationships between units
                           Relationships exist within the International System (SI) of measures,          e.g. gram, kilogram, tonne
                             including between mm, cm, m and km; kg and t; cm2 and m2; cm3             Direct comparisons
                             and m3.                                                                     - measure accurately using standard units
                           Measurement involves error, which can be reduced through the                 - estimate mass when appropriate
                             selection and use of appropriate instruments and technologies.            Indirect measure
                           Estimation strategies are used to identify a reasonable range of             - problem solving involving the concept of mass
                             values for a measurement




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FOCUS CONCEPTS            ESSENTIAL LEARNINGS (Knowledge and Understandings)                        TEACHING FOCUS 6-7
VOLUME                    Measurement
                           Appropriate instruments, technologies and scale are used when              Understanding volume and associated units
                             exploring measurement of length, area, volume, mass, time and               - concept of volume
                             angles where not all of the graduations are numbered.                       - International System of measures and relationships between units
                           Relationships exist within the International System (SI) of measures,          e.g. litres, millilitres, megalitres
                             including between mm, cm, m and km; kg and t; cm2 and m2; cm3             Direct comparisons
                             and m3.                                                                     - measure accurately using standard units
                           Relationships between attributes of regular 2D shapes and 3D                 - estimate volume when appropriate
                             objects can be used to develop rules that allow perimeter, area and       Indirect measure
                             volume to be calculated.                                                    - problem solving involving the concept of volume
                           Measurement involves error, which can be reduced through the
                             selection and use of appropriate instruments and technologies.
                           Estimation strategies are used to identify a reasonable range of
                             values for a measurement.
DATA                      Chance and Data
                           Data may be discrete and can be allocated to categories or                 Collecting data
                             numbered.                                                                  - terminology – discrete, continuous, bias
                           Data may be continuous and described as distributions of quantities.        - collection methods for discrete and continuous data
                           Sample data drawn from a given population can be summarised,                - identify bias in samples
                             compared and represented in a variety of ways.                            Displaying data
                           Measures of location such as mean, median and mode, and                     - representations - two-way tables, pie charts, bar graphs, line
                             frequency and relative frequency, can be used to explore                      graphs
                             distributions of sample data.                                              - determine display/s most appropriate for discrete and continuous
                           Variation and possible causes of bias can be identified in data                data
                             collections.                                                              Analysing data
                                                                                                        - terminology - mean, median, mode, frequency, relative frequency
                                                                                                        - measures of central tendency – mean, median, mode
                                                                                                        - measures of spread - range
                                                                                                        - effects of central tendency and spread on distributions
SYMMETRY                  Space
                           Points, lines and planes of symmetry can be identified in shapes and       Transformations
                             objects and can be related to transformations and tessellations of         - points, lines and planes of symmetry
                             suitable shapes in the plane.                                              - identify congruent shapes


Mt Tarampa State School
Page 30 of 30

								
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