Smith 2014
1
WULUNGARRA COMMUNITY SCHOOL
WHOLE SCHOOL NUMERACY PLAN
Smith 2014
2
NUMERACY OUTCOMES ........................................................................................................................... 4
SCHOOL NUMERACY STRATEGIES ............................................................................................................. 4
NUMERACY ASPIRATIONAL TARGETS ....................................................................................................... 6
AGREED WHOLE SCHOOL APPROACH TO NUMERACY ............................................................................... 7
PURPOSE OF ASSESSMENT ....................................................................................................................... 8
AGREED WHOLE SCHOOL APPROACH TO PLANNING ................................................................................ 8
ESSENTIAL FRAMEWORKS ........................................................................................................................ 9
APPENDIX 1.0 ......................................................................................................................................... 11
APPENDIX 2.0 ......................................................................................................................................... 23
APPENDIX 3.0 ......................................................................................................................................... 27
APPENDIX 4.0 ......................................................................................................................................... 32
APPENDIX 5.0 ......................................................................................................................................... 35
APPENDIX 6.0 ......................................................................................................................................... 40
APPENDIX 7.0 ......................................................................................................................................... 42
APPENDIX 8.0 ......................................................................................................................................... 45
APPENDIX 9.0 ......................................................................................................................................... 47
APPENDIX 10.0 ....................................................................................................................................... 49
APPENDIX 11.0 ....................................................................................................................................... 53
APPENDIX 12.0 ....................................................................................................................................... 61
APPENDIX 13.0 ....................................................................................................................................... 65
APPENDIX 14.0 ....................................................................................................................................... 68
APPENDIX 15.0 ....................................................................................................................................... 78
APPENDIX 16.0 ....................................................................................................................................... 84
Smith 2014
3
APPENDIX 17.0 ....................................................................................................................................... 88
APPENDIX 18.0 ....................................................................................................................................... 91
APPENDIX 19.0 ....................................................................................................................................... 96
APPENDIX 20.0 ..................................................................................................................................... 101
APPENDIX 21.0 ..................................................................................................................................... 107
Smith 2014
4
WULUNGARRA COMMUNITY SCHOOL WHOLE SCHOOL PLAN NUMERACY
Rationale: To develop numeracy capabilities that all students need in their personal work and civic life by adopting agreed whole school approaches to the teaching and learning of Mathematics.
Numeracy Outcomes Numeration Calculate Measurement &
Geometry Statistics & Probability
Students are able to read and write numbers, say the number sequence, subitise and partition, count collections and understand place value with ongoing improvement.
Students can continuously improve their understanding of basic facts, addition and subtraction, multiplication and division, estimation and judging reasonableness.
Students have the understanding to use units, scale and estimation, depict shape, location, transformation, geometric reasoning and attribute and direct comparison.
Students have an ongoing understanding of chance, data collection, data representation and data interpretation.
Students also maintain an ongoing understanding of money and financial literacy.
OUR BELIEFS AND UNDERSTANDINGS Students learn best when: • Collaborating in a scaffolded environment. • Provided with optimal reading opportunities. • Part of an environment that encompasses Being,
Belonging and Becoming. • Students use mathematical language to understand,
develop and communicate ideas and information and to interact with others.
• Students select, integrate and apply numerical and spatial concepts and techniques.
• Students visualise consequences, think laterally, recognise opportunity and potential and are prepared to test options.
• Students become numerate as they develop the knowledge and skills to use mathematics confidently across all learning areas at school and in their lives more broadly.
• Students develop the capacities to use mathematical knowledge and skills purposefully.
• Their contributions are reflected upon, valued and shared.
• Appropriate teaching and learning strategies for ESL/EALD learners are employed.
• SMART goals are set. • Learning through differentiation. • Students recognise when and what information is
required, locate and obtain it from a range of sources and evaluate, use and share it with others.
• Students select, use and adapt technologies. • Students describe and reason about patterns,
structures and relationships in order to understand, interpret, justify and make patterns.
• Students recognise and understand the role of mathematics in the world.
• Provided with a ‘Keeping Safe’ environment.
SCHOOL NUMERACY STRATEGIES
• Teaching Maths through music using ‘Education Closet’ as a guide by making use of free resources including: Activity Cards, Lesson Plans & Charts for, ‘Core Strategies for Arts Integration’ E.g. ‘Equal Rhythms’: Math, Music & Movement & ‘Equation Time’: Math through Music.
• YouTube clips for counting to music and dancing.
• Teachers use Signpost Maths as an effective and valuable pedagogical resource to drive Teachers’ Mathematics teaching, learning and assessment programmes.
• Maths games.
• ICT used daily to reinforce student understanding of concept.
• ICT used each day (during ‘Morning Circle’) to reinforce ‘Life-Skill’ Maths i.e. calendaring (days of the week, months of the year, seasons).
• Concrete materials to be used regularly to reinforce skills & concepts.
• Opportunities to allow students to use ‘The Arts’ to demonstrate understanding through making, drawing and building wherever possible and appropriate, considering the topic.
• K-3 to focus on linking number senses and computational skills through daily opportunities in subitising, partitioning and manipulating small quantities linked to number problems.
Smith 2014
5
• Year 4-7 to focus on developing a repertoire of calculation strategies in mental and informal written methods.
• Year 6/7 will use calculators in their mathematics teaching and learning programs.
• Teachers to input student data using Wulungarra Community School tracking sheets & AICS Numeracy Tracking Tool (ANTT).
• ICT used daily to reinforce student understanding and learning.
• Teachers will explicitly teach techniques for Mental Calculations.
• Students to engage in ‘How Did You Do It?’ sessions weekly.
• Students to participate in ‘Level of Difficulty’ surveys to ascertain how they felt about the given task. Teachers will utilize Problem Solving scaffold with students.
• Teachers will provide opportunity for students to practise and consolidate problem-solving strategies.
• Teachers will use ‘Real life Maths’ problems across all mathematical outcomes.
• Maths games used weekly: Paul Swan’s Maths Collection e.g. ‘Dice Dilemmas’.
• Maths activity cards (Maths Links Plus-Mental Maths Discussions) to be used throughout the day as lesson breaks (one from each of the four levels).
• Scholastic Activities (Blackline Master Practice Activities) used regularly to reinforce skills & concepts.
• Education Closet App.
• Activity Cards, Lesson Plans & Charts from, Education Closet ‘Core Strategies for Arts Integration’ E.g. ‘Equal Rhythms’: Math, Music & Movement & ‘Equation Time’: Math through Music.
Smith 2014
6
NUMERACY ASPIRATIONAL TARGETS
These targets are set at school based level and not set against NAPLAN National Targets. They are based on research evidence and negotiation with staff, and will be monitored annually.
Numeracy • Students will have measureable gains in number & algebra, measurement & geometry, statistics &
probability. o See Student Analysis documentation and individual Education Support Plans.
Education Support Plans
• Wulungarra Community School operates under a modified curriculum where each student has an active individualised ‘Education Support Plan’ (ESP) (See Appendix 21.0). This adheres to The National Aboriginal and Torres Strait Islander Education Action Plan 2010-2014 (ATSIEAP), which aims to accelerate improvement in the educational outcomes of Aboriginal and Torres Strait Islander students.
Hotdogs and Homework
• Students are encouraged to attend weekly homework sessions (with a parent/guardian) “Hotdogs and Homework” run by the teaching staff.
Kids Matters
• Guiding Principles of the Kids Matters Program to be integrated on a daily basis. All teachers to have appropriate training in the Kids Matters Program.
Keeping Safe: Child Protection Curriculum
• Wulungarra Community School uses, promotes and integrates the Keeping Safe Curriculum and acknowledges its guiding principles
o The right to be safe o Relationships o Recognising and reporting abuse o Protective strategies
Smith 2014
7
AGREED WHOLE SCHOOL APPROACH TO NUMERACY
• Utilise the AICS Portal Scope & Sequence for Numeration. • Utilise the AICS Portal Scope & Sequence for Calculate. • AICS Portal activities & assessments (See Appendix 11.0 through 20.0 for sample assessments
from each Mathematical area). • Input student data using Wulungarra Community School tracking sheets & AICS Numeracy Tracking
Tool (ANTT). • Develop phase specific Problem Solving scaffolds for students to use. • Attend ongoing professional development for Mathematics. • Teachers will view planning as an ongoing process, using student performance data to plan, teach
and evaluate collaboratively. Regular curriculum planning meetings will include analysing work samples, plan strategies, share approaches, report results and anecdotal notes.
• Enrol in a Master Degree in Professional Studies (all work place based learning) to inform and guide an ‘Action Plan’ to plan & teach using music as the mode.
• Identify key concepts, ideas and skills as the focus for learning and what students will do or produce to demonstrate understanding of these.
• Consider student learning strengths and needs and available resources. • Plan using music as the vehicle for engagement, learning and understanding. • Identify connections with students’ prior knowledge (with the use of pre-assessments at the
beginning of each new learning cycle), their social and cultural background knowledge and contexts in which the learning would be applied.
• Ask the following questions to inform planning, practice and reflection. 1. What do we want the students to learn? 2. Why does the learning matter? 3. Which teacher(s) will teach the unit? 4. What collaborative planning needs to take place? 5. How will students’ social and cultural background knowledge, resources, current events,
opportunities, interests and goals for the future be used to engage students? 6. How will the learning be differentiated to meet needs of particular students? 7. How will we record variations from the planned teaching program?
• Formulate and monitor Whole School Numeracy Plan. • Monitor and Review School Data.
Smith 2014
8
ASSESSMENT RESOURCES
• AICS Numeration, Calculate, Measurement & Geometry, Statistics & Probability and Money Scope and Sequence documents (Appendix 2.0 through 6.0).
• Numeration and Calculate Success Indicators and Resources (See Appendix 10.0). • Numeracy Planning Documents (Appendix 7.0, 8.0 and 9.0).
Purpose of Assessment:
• All assessment is collated in Student Analysis folders. This data is used to adapt and modify individualised Education Support Plans (ESP), and inform pedagogy.
o For Individual Year Level Descriptions and Achievement Standards as recommended by the Australian Curriculum see Appendix 1.0.
• All assessments align with the School Curriculum and Standards Authority’s Curriculum and Assessment Outline document and therefore meet the Assessment Principles (See http://k10outline.scsa.wa.edu.au/Resources/downloadà Assessment Principles 1 – 6).
o Teaching Staff to utilise the AICS Numeracy Portal as a resource for planning, teaching and assessing. Appendices 11.0 through 20.0 depict samples from each Mathematical area.
AGREED WHOLE SCHOOL APPROACH TO PLANNING All unit, term, week and lesson planning is completed and implemented by the classroom teacher in collaboration with the Educational Staff. Each planning document adheres to the principles set by the Wulungarra Community School Whole School Numeracy Plan and follows themes and practices consistent with the Australian Curriculum, appropriate Scope and Sequence documents, other relevant materials, and modified to cater to all Education Support Plans in place. All planning is undertaken with student learning and outcomes as the highest priority.
Smith 2014
9
ESSENTIAL FRAMEWORKS All planning should be made on Wulungarra Community School templates (see Appendices 4.0 through 6.0) and follow the principles and practices of the Early Years Learning Framework as seen in the Kindergarten Curriculum Guidelines (DRAFT) (see Figure 1):
Figure 1: Principles and practices of the Early Years Learning Framework
The Wulungarra Community School Whole School Literacy Plan aligns with the seven (7) quality areas of the Quality Improvement Plan Framework as provided by the Australian Children’s Education & Care Quality Authority. All Wulungarra Community School Staff are required to understand and align to the Capability Framework: Teaching Aboriginal and Torres Strait Islander EAL/D Learners in conjunction with the Australian Professional Standards for Teachers (see Figure 2).
Figure 2: Table demonstrating how Capabilities relate to the Australian Professional Standards for Teachers
�
DRAFT FOR CONSULTATION November 2013 2013/40178v9
5
Educators are mindful that all curriculum decisions affect each child in some way. The key curriculum decisions (adapted from Queensland Studies Authority, 2010) are: • Plan and organise for learning and teaching - daily, short and long term plans. Educators strive to
provide relevant learning opportunities that take into account the experiences, interests and capabilities of individuals and groups of children.
• Enact, interact and respond thoughtfully using a number of strategies to engage children in learning experiences. They give feedback to strengthen learning.
• Monitor, assess and document children’s learning and participation in a variety of ways in diverse contexts over time.
• Analyse and evaluate to inform ongoing planning and share information with parents and colleagues. • Reflect on learning and practice to further professional growth. Interact with colleagues and identify
areas for further professional learning that will improve curriculum processes and practices. As educators work through each of the key curriculum decisions they are mindful of the five principles and eight practices of the EYLF. The principles and practices are synthesised below to enable quality curriculum development:
• Differentiation and inclusion • Early learning environments • Relationships and partnerships • Balanced content
• Contexts and strategies for learning • Child participation • Extension, engagement and enjoyment in children’s
learning
��
Using the Framework
This Framework is designed so that it can be used independently or alongside the Australian Professional Standards for Teachers (APST). It does not replace the APST.
The Framework has seven Capabilities. Each Capability is related to an APST Standard. The Capabilities provide supplementary information for the effective teaching of Aboriginal and Torres Strait Islander EAL/D learners.
Like the APST, the Capabilities in this framework are arranged into Domains of Teaching: Professional Knowledge, Professional Practice and Professional Engagement.
Framework Capabilities Related Standards from the APST
1. Identify Aboriginal and Torres Strait Islander EAL/D learners and understand EAL/D learning
1. Know students and how they learn
2. Know about language, Standard Australian English, and the language demands of the curriculum
2. Know the content and how to teach it
3. Plan for and implement effective teaching and learning for Aboriginal and Torres Strait Islander EAL/D learners
3. Plan for and implement effective teaching and learning
4. Create and maintain supportive and safe learning environments for Aboriginal and Torres Strait Islander EAL/D learners
4. Create and maintain supportive and safe learning environments
5. Assess, provide feedback and report on SAE learning
5. Assess, provide feedback and report on student learning
6. Engage in professional learning about teaching Aboriginal and Torres Strait Islander EAL/D learners
6. Engage in professional learning
7. Engage in respectful and reciprocal cross-cultural relationships
7. Engage professionally
Professional Knowledge
Professional Practice
Professional Engagement
Professional Knowledge
Professional Practice
Professional Engagement
The following table shows how the Capabilities relate to the APST Standards:
5 Capability Framework Teaching Aboriginal and Torres Strait Islander EAL/D learners
Smith 2014
10
All planning and curriculum development has been made in line with the Early Years Learning Framework (see Figure 3). Wulungarra Community School supports the principles of the Early Years Learning Framework and ensures all five (5) learning outcomes are met through planning, regular meetings, anecdotal notes, formative and summative assessment and modification/review of Education Support Plans:
1. Children have a strong sense of identity. 2. Children are connected with and contribute to their world. 3. Children have a strong sense of wellbeing. 4. Children are confident and involved learners.
5. Children are effective communicators.
Figure 3: Elements of the Early Years Learning Framework
10 BELONGING, BEING & BECOMING The Early Years Learning Framework for Australia
CURRICULUMDECISION
MAKING FORCHILDREN’SLEARNING
PRINC
IPLES
Secure relationships and positive interactions
Genuine partnerships w
ith families
Respect for diversity
Com
munity to equity
Reflective practiceLEA
RNIN
G O
UTC
OM
ES
Chi
ldre
n ha
ve a
stro
ng se
nse
of id
entit
y
Chi
ldre
n pa
rtici
pate
in c
omm
uniti
es
Chi
ldre
n ha
ve a
stro
ng se
nse
of w
ellb
eing
Chi
ldre
n ar
e co
nfid
ent a
nd in
volve
d le
arne
rs
Chi
ldre
n ar
e ef
fect
ive c
omm
unica
tors
PEDAGOGICAL PRACTICEPlay-based curriculum and intentional teaching
Physical and social learning environmentsContinuity of learning and transitions
Assessment for learning
BELONGING
BECOM
ING B
EING
CHILDREN’SLEARNING
PRINC
IPLES
Secure, resepctful and reciprocal relationships
Partnerships with fam
ilies
High expectations and equity
Respect for diversity
Ongoing learning and reflective practice
LEA
RNIN
G O
UTC
OM
ES
Chi
ldre
n ha
ve a
stro
ng se
nse
of id
entit
y
Chi
ldre
n ar
e co
nnec
ted
with
and
con
trib
ute
to th
eir w
orld
Chi
ldre
n ha
ve a
stro
ng se
nse
of w
ellb
eing
Chi
ldre
n ar
e co
nfid
ent a
nd in
volve
d le
arne
rs
Chi
ldre
n ar
e ef
fect
ive c
omm
unica
tors
PRACTICEHolistic approaches
Responsiveness to childrenLearning through playIntentional teaching
Learning environmentsCultural competence
Continuity of learning and transitionsAssessment for learning
BELONGING
BECOM
ING B
EING
Figure 1: Elements of the Early Years Learning Framework
Dispositions: enduring habits of mind and actions, and
tendencies to respond in characteristic
ways to situations, for example,
maintaining an optimistic outlook, being
willing to persevere, approaching new
experiences with confidence. (Carr, 2001)
Involvement: is a state of intense, whole hearted
mental activity, characterised by sustained
concentration and intrinsic motivation.
Highly involved children (and adults)
operate at the limit of their capacities,
leading to changed ways of responding
and understanding leading to deep level
learning. (adapted from Laevers 1994)
Smith 2014
11
APPENDIX 1.0
Smith 2014
12
FOUNDATION YEAR YEAR LEVEL DESCRIPTION The proficiency strands Understanding, Fluency, Problem Solving and Reasoning are an integral part of mathematics content across the three content strands: Number and Algebra, Measurement and Geometry, and Statistics and Probability. The proficiencies reinforce the significance of working mathematically within the content and describe how the content is explored or developed. They provide the language to build in the developmental aspects of the learning of mathematics. At this year level:
• Understanding includes connecting names, numerals and quantities. • Fluency includes readily counting numbers in sequences, continuing patterns, and comparing the
lengths of objects. • Problem Solving includes using materials to model authentic problems, sorting objects, using
familiar counting sequences to solve unfamiliar problems, and discussing the reasonableness of the answer.
• Reasoning includes explaining comparisons of quantities, creating patterns, and explaining processes for indirect comparison of length.
ACHIEVEMENT STANDARD By the end of the Foundation year, students make connections between number names, numerals and quantities up to 10. They compare objects using mass, length and capacity. Students connect events and the days of the week. They explain the order and duration of events. They use appropriate language to describe location. Students count to and from 20 and order small collections. They group objects based on common characteristics and sort shapes and objects. Students answer simple questions to collect information.
Smith 2014
13
YEAR ONE YEAR LEVEL DESCRIPTION The proficiency strands Understanding, Fluency, Problem Solving and Reasoning are an integral part of mathematics content across the three content strands: Number and Algebra, Measurement and Geometry, and Statistics and Probability. The proficiencies reinforce the significance of working mathematically within the content and describe how the content is explored or developed. They provide the language to build in the developmental aspects of the learning of mathematics. At this year level:
• Understanding includes connecting names, numerals and quantities, and partitioning numbers in various ways.
• Fluency includes counting number in sequences readily forward and backwards, locating numbers on a line, and naming the days of the week.
• Problem Solving includes using materials to model authentic problems, giving and receiving directions to unfamiliar places, and using familiar counting sequences to solve unfamiliar problems and discussing the reasonableness of the answer.
• Reasoning includes explaining direct and indirect comparisons of length using uniform informal units, justifying representations of data, and explaining patterns that have been created.
ACHIEVEMENT STANDARD By the end of Year 1, students describe number sequences resulting from skip counting by 2s, 5s and 10s. They identify representations of one half. They recognise Australian coins according to their value. Students explain time durations. They describe two-dimensional shapes and three-dimensional objects. Students describe data displays. Students count to and from 100 and locate numbers on a number line. They carry out simple additions and subtractions using counting strategies. They partition numbers using place value. They continue simple patterns involving numbers and objects. Students order objects based on lengths and capacities using informal units. They tell time to the half hour. They use the language of direction to move from place to place. Students classify outcomes of simple familiar events. They collect data by asking questions and draw simple data displays.
Smith 2014
14
YEAR TWO LEVEL DESCRIPTION The proficiency strands Understanding, Fluency, Problem Solving and Reasoning are an integral part of mathematics content across the three content strands: Number and Algebra, Measurement and Geometry, and Statistics and Probability. The proficiencies reinforce the significance of working mathematically within the content and describe how the content is explored or developed. They provide the language to build in the developmental aspects of the learning of mathematics. At this year level:
• Understanding includes connecting number calculations with counting sequences, partitioning and combining numbers flexibly, identifying and describing the relationship between addition and subtraction and between multiplication and division.
• Fluency includes counting numbers in sequences readily, using informal units iteratively to compare measurements, using the language of chance to describe outcomes of familiar chance events and describing and comparing time durations.
• Problem Solving includes formulating problems from authentic situations, making models and using number sentences that represent problem situations, and matching transformations with their original shape.
• Reasoning includes using known facts to derive strategies for unfamiliar calculations, comparing and contrasting related models of operations, and creating and interpreting simple representations of data.
ACHIEVEMENT STANDARD By the end of Year 2, students recognise increasing and decreasing number sequences involving 2s, 3s and 5s. They represent multiplication and division by grouping into sets. They associate collections of Australian coins with their value. Students identify the missing element in a number sequence. Students recognise the features of three-dimensional objects. They interpret simple maps of familiar locations. They explain the effects of one-step transformations. Students make sense of collected information. Students count to and from 1000. They perform simple addition and subtraction calculations using a range of strategies. They divide collections and shapes into halves, quarters and eighths. Students order shapes and objects using informal units. They tell time to the quarter hour and use a calendar to identify the date and the months included in seasons. They draw two- dimensional shapes. They describe outcomes for everyday events. Students collect data from relevant questions to create lists, tables and picture graphs.
Smith 2014
15
YEAR THREE LEVEL DESCRIPTION The proficiency strands Understanding, Fluency, Problem Solving and Reasoning are an integral part of mathematics content across the three content strands: Number and Algebra, Measurement and Geometry, and Statistics and Probability. The proficiencies reinforce the significance of working mathematically within the content and describe how the content is explored or developed. They provide the language to build in the developmental aspects of the learning of mathematics. At this year level:
• Understanding includes connecting number representations with number sequences, partitioning and combining numbers flexibly, representing unit fractions, using appropriate language to communicate times, and identifying environmental symmetry.
• Fluency includes recalling multiplication facts, using familiar metric units to order and compare objects, identifying and describing outcomes of chance experiments, interpreting maps and communicating positions.
• Problem Solving includes formulating and modelling authentic situations involving planning methods of data collection and representation, making models of three-dimensional objects and using number properties to continue number patterns.
• Reasoning includes using generalising from number properties and results of calculations, comparing angles, creating and interpreting variations in the results of data collections and data displays.
ACHIEVEMENT STANDARDS By the end of Year 3, students recognise the connection between addition and subtraction and solve problems using efficient strategies for multiplication. They model and represent unit fractions. They represent money values in various ways. Students identify symmetry in the environment. They match positions on maps with given information. Students recognise angles in real situations. They interpret and compare data displays. Students count to and from 10 000. They classify numbers as either odd or even. They recall addition and multiplication facts for single digit numbers. Students correctly count out change from financial transactions. They continue number patterns involving addition and subtraction. Students use metric units for length, mass and capacity. They tell time to the nearest minute. Students make models of three-dimensional objects. Students conduct chance experiments and list possible outcomes. They carry out simple data investigations for categorical variables.
Smith 2014
16
YEAR FOUR LEVEL DESCRIPTION The proficiency strands Understanding, Fluency, Problem Solving and Reasoning are an integral part of mathematics content across the three content strands: Number and Algebra, Measurement and Geometry, and Statistics and Probability. The proficiencies reinforce the significance of working mathematically within the content and describe how the content is explored or developed. They provide the language to build in the developmental aspects of the learning of mathematics. At this year level:
• Understanding includes making connections between representations of numbers, partitioning and combining numbers flexibly, extending place value to decimals, using appropriate language to communicate times, and describing properties of symmetrical shapes.
• Fluency includes recalling multiplication tables, communicating sequences of simple fractions, using instruments to measure accurately, creating patterns with shapes and their transformations, and collecting and recording data.
• Problem Solving includes formulating, modelling and recording authentic situations involving operations, comparing large numbers with each other, comparing time durations, and using properties of numbers to continue patterns.
• Reasoning includes using generalising from number properties and results of calculations, deriving strategies for unfamiliar multiplication and division tasks, comparing angles, communicating information using graphical displays and evaluating the appropriateness of different displays.
ACHIEVEMENT STANDARD By the end of Year 4, students choose appropriate strategies for calculations involving multiplication and division. They recognise common equivalent fractions in familiar contexts and make connections between fraction and decimal notations up to two decimal places. Students solve simple purchasing problems. They identify unknown quantities in number sentences. They describe number patterns resulting from multiplication. Students compare areas of regular and irregular shapes using informal units. They solve problems involving time duration. They interpret information contained in maps. Students identify dependent and independent events. They describe different methods for data collection and representation, and evaluate their effectiveness. Students use the properties of odd and even numbers. They recall multiplication facts to 10 x 10 and related division facts. Students locate familiar fractions on a number line. They continue number sequences involving multiples of single digit numbers. Students use scaled instruments to measure temperatures, lengths, shapes and objects. They convert between units of time. Students create symmetrical shapes and patterns. They classify angles in relation to a right angle. Students list the probabilities of everyday events. They construct data displays from given or collected data.
Smith 2014
17
YEAR FIVE LEVEL DESCRIPTION The proficiency strands Understanding, Fluency, Problem Solving and Reasoning are an integral part of mathematics content across the three content strands: Number and Algebra, Measurement and Geometry, and Statistics and Probability. The proficiencies reinforce the significance of working mathematically within the content and describe how the content is explored or developed. They provide the language to build in the developmental aspects of the learning of mathematics. At this year level:
• Understanding includes making connections between representations of numbers, using fractions to represent probabilities, comparing and ordering fractions and decimals and representing them in various ways, describing transformations and identifying line and rotational symmetry.
• Fluency includes choosing appropriate units of measurement for calculation of perimeter and area, using estimation to check the reasonableness of answers to calculations and using instruments to measure angles.
• Problem Solving includes formulating and solving authentic problems using whole numbers and measurements and creating financial plans.
• Reasoning includes investigating strategies to perform calculations efficiently, continuing patterns involving fractions and decimals, interpreting results of chance experiments, posing appropriate questions for data investigations and interpreting data sets.
ACHIEVEMENT STANDARD By the end of Year 5, students solve simple problems involving the four operations using a range of strategies. They check the reasonableness of answers using estimation and rounding. Students identify and describe factors and multiples. They explain plans for simple budgets. Students connect three-dimensional objects with their two-dimensional representations. They describe transformations of two-dimensional shapes and identify line and rotational symmetry. Students compare and interpret different data sets. Students order decimals and unit fractions and locate them on number lines. They add and subtract fractions with the same denominator. Students continue patterns by adding and subtracting fractions and decimals. They find unknown quantities in number sentences. They use appropriate units of measurement for length, area, volume, capacity and mass, and calculate perimeter and area of rectangles. They convert between 12 and 24-hour time. Students use a grid reference system to locate landmarks. They measure and construct different angles. Students list outcomes of chance experiments with equally likely outcomes and assign probabilities between 0 and 1. Students pose questions to gather data, and construct data displays appropriate for the data.
Smith 2014
18
YEAR SIX LEVEL DESCRIPTION The proficiency strands Understanding, Fluency, Problem Solving and Reasoning are an integral part of mathematics content across the three content strands: Number and Algebra, Measurement and Geometry, and Statistics and Probability. The proficiencies reinforce the significance of working mathematically within the content and describe how the content is explored or developed. They provide the language to build in the developmental aspects of the learning of mathematics. At this year level:
• Understanding includes describing properties of different sets of numbers, using fractions and decimals to describe probabilities, representing fractions and decimals in various ways and describing connections between them, and making reasonable estimations.
• Fluency includes representing integers on a number line, calculating simple percentages, using brackets appropriately, converting between fractions and decimals, using operations with fractions, decimals and percentages, measuring using metric units, and interpreting timetables.
• Problem Solving includes formulating and solving authentic problems using fractions, decimals, percentages and measurements, interpreting secondary data displays, and finding the size of unknown angles.
• Reasoning includes explaining mental strategies for performing calculations, describing results for continuing number sequences, explaining the transformation of one shape into another, explaining why the actual results of chance experiments may differ from expected results.
ACHIEVEMENT STANDARD By the end of Year 6, students recognise the properties of prime, composite, square and triangular numbers. They describe the use of integers in everyday contexts. They solve problems involving all four operations with whole numbers. Students connect fractions, decimals and percentages as different representations of the same number. They solve problems involving the addition and subtraction of related fractions. Students make connections between the powers of 10 and the multiplication and division of decimals. They describe rules used in sequences involving whole numbers, fractions and decimals. Students connect decimal representations to the metric system and choose appropriate units of measurement to perform a calculation. They make connections between capacity and volume. They solve problems involving length and area. They interpret timetables. Students describe combinations of transformations. They solve problems using the properties of angles. Students compare observed and expected frequencies. They interpret and compare a variety of data displays including those displays for two categorical variables. They evaluate secondary data displayed in the media. Students locate fractions and integers on a number line. They calculate a simple fraction of a quantity. They add, subtract and multiply decimals and divide decimals where the result is rational. Students calculate common percentage discounts on sale items. They write correct number sentences using brackets and order of operations. Students locate an ordered pair in any one of the four quadrants on the Cartesian plane. They construct simple prisms and pyramids. Students list and communicate probabilities using simple fractions, decimals and percentages.
Smith 2014
19
YEAR SEVEN LEVEL DESCRIPTION The proficiency strands Understanding, Fluency, Problem Solving and Reasoning are an integral part of mathematics content across the three content strands: Number and Algebra, Measurement and Geometry, and Statistics and Probability. The proficiencies reinforce the significance of working mathematically within the content and describe how the content is explored or developed. They provide the language to build in the developmental aspects of the learning of mathematics. At this year level:
• Understanding includes describing patterns in uses of indices with whole numbers, recognising equivalences between fractions, decimals, percentages and ratios, plotting points on the Cartesian plane, identifying angles formed by a transversal crossing a pair of lines, and connecting the laws and properties of numbers to algebraic terms and expressions.
• Fluency includes calculating accurately with integers, representing fractions and decimals in various ways, investigating best buys, finding measures of central tendency and calculating areas of shapes and volumes of prisms.
• Problem Solving includes formulating and solving authentic problems using numbers and measurements, working with transformations and identifying symmetry, calculating angles and interpreting sets of data collected through chance experiments.
• Reasoning includes applying the number laws to calculations, applying known geometric facts to draw conclusions about shapes, applying an understanding of ratio and interpreting data displays.
ACHIEVEMENT STANDARD By the end of Year 7, students solve problems involving the comparison, addition and subtraction of integers. They make the connections between whole numbers and index notation and the relationship between perfect squares and square roots. They solve problems involving percentages and all four operations with fractions and decimals. They compare the cost of items to make financial decisions. Students represent numbers using variables. They connect the laws and properties for numbers to algebra. They interpret simple linear representations and model authentic information. Students describe different views of three-dimensional objects. They represent transformations in the Cartesian plane. They solve simple numerical problems involving angles formed by a transversal crossing two parallel lines. Students identify issues involving the collection of continuous data. They describe the relationship between the median and mean in data displays. Students use fractions, decimals and percentages, and their equivalences. They express one quantity as a fraction or percentage of another. Students solve simple linear equations and evaluate algebraic expressions after numerical substitution. They assign ordered pairs to given points on the Cartesian plane. Students use formulas for the area and perimeter of rectangles and calculate volumes of rectangular prisms. Students classify triangles and quadrilaterals. They name the types of angles formed by a transversal crossing parallel line. Students determine the sample space for simple experiments with equally likely outcomes and assign probabilities to those outcomes. They calculate mean, mode, median and range for data sets. They construct stem-and-leaf plots and dot-plots.
Smith 2014
20
YEAR EIGHT LEVEL DESCRIPTION The proficiency strands Understanding, Fluency, Problem Solving and Reasoning are an integral part of mathematics content across the three content strands: Number and Algebra, Measurement and Geometry, and Statistics and Probability. The proficiencies reinforce the significance of working mathematically within the content and describe how the content is explored or developed. They provide the language to build in the developmental aspects of the learning of mathematics. At this year level:
• Understanding includes describing patterns involving indices and recurring decimals, identifying commonalities between operations with algebra and arithmetic, connecting rules for linear relations their graphs, explaining the purpose of statistical measures, and explaining measurements of perimeter and area.
• Fluency includes calculating accurately with simple decimals, indices and integers, recognising equivalence of common decimals and fractions including recurring decimals, factorising and simplifying basic algebraic expressions, and evaluating perimeters, areas of common shapes and their volumes and three dimensional objects.
• Problem Solving includes formulating, and modelling practical situations involving ratios, profit and loss, areas and perimeters of common shapes, and using two-way tables and Venn diagrams to calculate probabilities.
• Reasoning includes justifying the result of a calculation or estimation as reasonable, deriving probability from its complement, using congruence to deduce properties of triangles, finding estimates of means and proportions of populations.
ACHIEVEMENT STANDARD By the end of Year 8, students solve everyday problems involving rates, ratios and percentages. They recognise index laws and apply them to whole numbers. They describe rational and irrational numbers. Students solve problems involving profit and loss. They make connections between expanding and factorising algebraic expressions. Students solve problems relating to the volume of prisms. They make sense of time duration in real applications. They identify conditions for the congruence of triangles and deduce the properties of quadrilaterals. Students model authentic situations with two-way tables and Venn diagrams. They choose appropriate language to describe events and experiments. They explain issues related to the collection of data and the effect of outliers on means and medians in that data. Students use efficient mental and written strategies to carry out the four operations with integers. They simplify a variety of algebraic expressions. They solve linear equations and graph linear relationships on the Cartesian plane. Students convert between units of measurement for area and volume. They perform calculations to determine perimeter and area of parallelograms, rhombuses and kites. They name the features of circles and calculate the areas and circumferences of circles. Students determine complementary events and calculate the sum of probabilities.
Smith 2014
21
YEAR NINE LEVEL DESCRIPTION The proficiency strands Understanding, Fluency, Problem Solving and Reasoning are an integral part of mathematics content across the three content strands: Number and Algebra, Measurement and Geometry, and Statistics and Probability. The proficiencies reinforce the significance of working mathematically within the content and describe how the content is explored or developed. They provide the language to build in the developmental aspects of the learning of mathematics. At this year level:
• Understanding includes describing the relationship between graphs and equations, simplifying a range of algebraic expressions, explaining the use of relative frequencies to estimate probabilities, and the use of the trigonometric ratios for right-angle triangles.
• Fluency includes applying the index laws to expressions with integer indices, expressing numbers in scientific notation, listing outcomes for experiments and developing familiarity with calculations involving the Cartesian plane and calculating areas of shapes and surface areas of prisms.
• Problem Solving includes formulating, and modelling practical situations involving surface areas and volumes of right prisms, applying ratio and scale factors to similar figures, solving problems involving right-angle trigonometry, and collecting data from secondary sources to investigate an issue.
• Reasoning includes following mathematical arguments, evaluating media reports and using statistical knowledge to clarify situations, developing strategies in investigating similarity and sketching linear graphs.
ACHIEVEMENT STANDARD By the end of Year 9, students solve problems involving simple interest. They interpret ratio and scale factors in similar figures. Students explain similarity of triangles. They recognise the connections between similarity and the trigonometric ratios. Students compare techniques for collecting data in primary and secondary sources. They make sense of the position of the mean and median in skewed, symmetric and bi-modal displays to describe and interpret data. Students apply the index laws to numbers and express numbers in scientific notation. They expand binomial expressions. They find the distance between two points on the Cartesian plane and the gradient and midpoint of a line segment. They sketch linear and non-linear relations. Students calculate areas of shapes and the volume and surface area of right prisms and cylinders. They use Pythagoras’ Theorem and trigonometry to find unknown sides of right-angled triangles. Students calculate relative frequencies to estimate probabilities, list outcomes for two-step experiments and assign probabilities for those outcomes. They construct histograms and back-to-back stem-and-leaf plots.
Smith 2014
22
YEAR TEN LEVEL DESCRIPTION The proficiency strands Understanding, Fluency, Problem Solving and Reasoning are an integral part of mathematics content across the three content strands: Number and Algebra, Measurement and Geometry, and Statistics and Probability. The proficiencies reinforce the significance of working mathematically within the content and describe how the content is explored or developed. They provide the language to build in the developmental aspects of the learning of mathematics. At this year level:
• Understanding includes applying the four operations to algebraic fractions, finding unknowns in formulas after substitution, making the connection between equations of relations and their graphs, comparing simple and compound interest in financial contexts and determining probabilities of two and three step experiments.
• Fluency includes factorising and expanding algebraic expressions, using a range of strategies to solve equations and using calculations to investigate the shape of data sets.
• Problem Solving includes calculating the surface area and volume of a diverse range of prisms to solve practical problems, finding unknown lengths and angles using applications of trigonometry, using algebraic and graphical techniques to find solutions to simultaneous equations and inequalities, and investigating independence of events.
• Reasoning includes formulating geometric proofs involving congruence and similarity, interpreting and evaluating media statements and interpreting and comparing data sets.
ACHIEVEMENT STANDARD By the end of Year 10, students recognise the connection between simple and compound interest. They solve problems involving linear equations and inequalities. They make the connections between algebraic and graphical representations of relations. Students solve surface area and volume problems relating to composite solids. They recognise the relationships between parallel and perpendicular lines. Students apply deductive reasoning to proofs and numerical exercises involving plane shapes. They compare data sets by referring to the shapes of the various data displays. They describe bivariate data where the independent variable is time. Students describe statistical relationships between two continuous variables. They evaluate statistical reports. Students expand binomial expressions and factorise monic quadratic expressions. They find unknown values after substitution into formulas. They perform the four operations with simple algebraic fractions. Students solve simple quadratic equations and pairs of simultaneous equations. They use triangle and angle properties to prove congruence and similarity. Students use trigonometry to calculate unknown angles in right-angled triangles. Students list outcomes for multi-step chance experiments and assign probabilities for these experiments. They calculate quartiles and inter-quartile ranges.
Smith 2014
23
APPENDIX 2.0
Smith 2014
24
AICS NUMERATION SCOPE & SEQUENCE READING NUMBERS
F 1.1 F 1.2 Year 1.1 Year 1.2 Year 2.1 Year 3.1 Year 4.1 Year 5.1 Year 6.1 (a.) Recognises numbers in their environment. (b.) Distinguishes numbers from other written symbols.
Reads number symbols up to 10.
(a.) Reads whole number up to 50. (b.) Recognise and name coins, 5c, 10c, 20c, 50c, $1, $2.
(a.) Reads whole number up to 109. (b.) Knows that $ coins are worth more than cent coins.
Reads whole numbers up to 999 and simple decimals involving money.
Reads whole numbers up to 9 999 and decimals involving money.
Reads whole numbers up to 999 999 and decimals involving money and measures.
Reads whole numbers into the millions and decimals to two places.
Reads decimal numbers to three places.
ACMNA 001 ACMNA 001 ACMNA 002
ACMNA 013 ACMNA 017
ACMNA 013 ACMNA 017
ACMNA 027 ACMNA 034
ACMNA 052 ACMNA 059
ACMNA 072 ACMNA 079
ACMNA 072 ACMNA 079
ACMNA 104 ACMNA 105 ACMNA 131
WRITING NUMBERS
F 1.2 Year 1.1 Year 1.2 Year 2.1 Year 3.1 Year 4.1 Year 5.1 Year 6.1 Writes number symbols up to 10.
Writes whole numbers up to 50.
Writes whole numbers up to 109.
Writes whole numbers up to 999 and simple decimals involving money.
Writes whole numbers up to 9 999 and decimals involving Writes decimal numbers to three places involving money.
Writes whole numbers up to 999 999 and decimals involving money and measures.
Writes whole numbers into the millions including decimals to two places.
Writes decimal numbers to three places.
ACMNA 001 ACMNA 002
ACMNA 013 ACMNA 017
ACMNA 013 ACMNA 027 ACMNA 034
ACMNA 027 ACMNA 034
ACMNA 072 ACMNA 079
ACMNA 072 ACMNA 105
ACMNA 104 ACMNA 105 ACMNA 131
SAYING THE NUMBER SEQUENCE
F 1.1
F 1.2 Year 1.1 Year 1.2 Year 2.1 Year 3.1 Year 4.1 Year 5.1 Year 6.1
When asked to 'count' says the first few numbers
Says the number names in order (orally counts)
Says number names in order (orally counts)
Uses the patterns in the numeration system to
Uses the patterns in the numeration system to
Uses the patterns in the numeration system to
Uses the patterns in the numeration system
Uses the patterns in the numeration system
Uses the patterns in the numeration system to
Smith 2014
25
in order E.g. 1,2,3,4.
up to 29. Compares and orders numbers up to 10.
up to 50. Compares and orders numbers to 50.
say the numbers (count) forwards and backwards by ones and tens up to 109 and to compare and order them.
say the numbers (count) forwards & backwards by ones and tens up to 999 and compare and order them.
say the numbers forwards and backwards by ones, tens and hundreds up to 9 999and to compare and order them.
to: a) Say the numbers forwards and backwards by ones, tens and hundreds up to 999 999. b) Say decimal sequences involving familiar money and measures. c) Compare and order them.
to: a) Compare and order whole numbers into the millions. b) Say the decimal numbers forwards and backwards to two places. c) Compare and order them.
say decimal numbers forwards and backwards to three places and to compare and order them.
ACMNA 001 ACMNA 001 ACMNA 289
ACMNA 012 ACMNA 013
ACMNA 012 ACMNA 013 ACMNA 018 ACMNA 026
ACMNA 027 ACMNA 028
ACMNA 052 ACMNA 072 ACMNA 079
ACMNA 072 ACMNA 105
ACMNA 104 ACMNA 105 ACMNA 131
SUBITISING/PARTITIONING
F 1.1 F 1.2 Year 1.1 Year 1.2 Year 2.1 Uses comparative language to compare sets, including community language and English ('big mob', 'little one', 'more', 'lots'). Subitises (says how many without counting) small collections up to three.
Subitises (says how many without counting) up to 6.
Partitions small quantities (up to 10).
Partitions numbers up to 20 with the support of materials or drawings.
Uses visualisation and other mental strategies to partition two digit numbers.
ACMNA 003 ACMNA 003 ACMNA 014 ACMNA 015
ACMNA 014 ACMNA 015
ACMNA 014 ACMNA 015 ACMNA 028
COUNTING COLLECTIONS
F 1.1 F 1.2 Year 1.1 Year 1.2 Year 2.1 Knows that Counts collections Knows that objects Chooses to use Skip counts money
Smith 2014
26
numbers are used to say how many.
of up to 10 items placed in front of them. Counts collections of up to 30 items places in front of them. Knows the last number said tells how many items in the set. Uses counting to get or draw a quantity when requested, up to 30.
can be counted in any order. Knows that the collection can be rearranged without changing the total quantity. Chooses to use counting to solve problems where an exact quantity is needed. Uses skip counting by twos to say how many in small collections.
skip counting to say how many in a large collection (up to 100 items). Skip counts money with like coins/notes. E.g. 5c, 10c, 15c, 20c.
using combinations of coins and notes.
ACMNA 001 ACMNA 002
ACMNA 001 ACMNA 002
ACMNA 013 ACMNA 014 ACMNA 018 ACMNA 002
ACMNA 014 ACMNA 017 ACMNA 028
ACMNA 034
UNDERSTANDING PLACE VALUE
Year 1.2 Year 2.1 Year 3.1 Year 4.1 Year 5.1 Year 6.1 Knows that the order of the digits affects the size of the number.
Understands and uses place value partitions for two-digit numbers.
Understands and uses place value partitions for three-digit numbers. Understands and uses place value to rename two-digit numbers in different ways, egg 64 is 6 tens and 4 ones, 5 tens and 14 ones, etc.
Understands and uses place value partitions for four-digit numbers. Uses place value to rename three and four-digit numbers in different ways.
Understands and uses place value partitions for any whole number. Uses place value partitions of decimal numbers to two places.
Understands and uses place value partitions of decimals to three places.
ACMNA 013 ACMNA 014
ACMNA 013 ACMNA 014
ACMNA 027 ACMNA 028
ACMNA 052 ACMNA 028
ACMNA 072 ACMNA 073 ACMNA 105
ACMNA 104 ACMNA 105 ACMNA 131
Smith 2014
27
APPENDIX 3.0
Smith 2014
28
AICS CALCULATE SCOPE & SEQUENCE BASIC FACTS: + AND -
F 1.2 Year 1 Year 2 Year 3 Working towards Year 1. a) Know what number is
one/two more and one/two less for numbers to 10. b) Add and take zero from numbers to 10.
a) Know doubles (and near doubles) up to 10 + 10 (and related subtraction facts). b) Know the combinations to 10 (and related subtraction facts).
Know all addition facts to 10 + 10 and related subtraction facts.
ACMNA 055 ACMNA 055 ACMNA 055 ACMNA 055
BASIC FACTS: TABLES
Year 3 Year 4 Know the 2 x, 10 x, 5 x, 1 x, 0 x tables facts. a) Know the 4 x, 8 x, 3 x, 6 x tables facts.
b) Know all of their tables, including 9 x, 7 x tables facts.
ACMNA 056 ACMNA 075
ADDITION AND SUBTRACTION: MENTAL AND INFORMAL WRITTEN
F 1.1 F 1.2 Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Attempt to solve small number story problems using realistic materials, drawings and counting.
Use counting or subsidising to solve simple story problems using materials or drawings (for results up to 10).
Use counting or subitising to solve simple story problems using materials or drawings (for results up to 20).
a. Use partitioning and some basic facts to mentally solve problems involving small two-digit numbers b. Use efficient counting strategies to solve problems involving two-digit numbers using materials and diagrams.
Use basic facts, partitioning and other strategies to mentally add and subtract 'friendly' two-digit numbers, using informal written strategies to keep track.
Use basic facts, place-value partitioning and other strategies to mentally add and subtract 'friendly' three-digit numbers and simple decimals involving money, using informal written strategies to keep track.
Use mental strategies to add and subtract 'friendly' whole numbers and decimals involving money and measures (to two decimal places), using informal written strategies to keep track.
Use mental strategies to add and subtract any 'friendly' decimal numbers, using informal written strategies to keep track.
ACMNA 004 ACMNA 004 ACMNA 031 ACMNA 032
ACMNA 057 ACMNA 076 ACMNA 100 ACMNA 101
ACMNA 123 ACMNA 098
Smith 2014
29
ADDITION AND SUBTRACTION: CALCULATOR AND CHOOSE STRATEGIES
Year 2 Year 3 Year 4 Year 5 Year 6
Use the + and – and = buttons in the appropriate order.
Choose appropriately between mental informal written and calculator strategies to solve calculations involving ‘unfriendly’ two-digit numbers.
Choose appropriately between mental, informal written or calculator strategies to solve calculations involving ‘unfriendly’ three-digit numbers and simple decimal numbers involving money.
Choose appropriately between mental, written or calculator strategies to solve problems involving ‘unfriendly’ whole numbers an decimal numbers involving money and measures (to two decimal places).
Choose appropriately between mental, written or calculator strategies to solve problems.
ACMNA 291 ACMNA 291 ACMNA 291 ACMNA 291 ACMNA 291
ADDITION AND SUBTRACTION: WRITTEN STRATEGIES
Year 4 Year 5 Year 6 Working towards Year 5. Use written strategies for
calculations involving four-digit numbers and decimals involving money and measures (two decimal places).
Use written strategies for calculations involving large whole numbers and decimals.
ACMNA 291 ACMNA 291 ACMNA 123
MULTIPLICATION AND DIVISION: MENTAL AND INFORMAL WRITTEN
F 1.2 Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Attempt to solve simple and familiar sharing problems using realistic materials, drawings and counting.
Use counting to solve simple equal-group problems using realistic materials and drawings (up to 20).
Use counting to solve simple equal-group problems using materials and drawings (up to 50).
Use skip counting and doubling to solve simple equal-group problems involving materials and diagrams (including division without remainders, up to 100).
Use skip counting, doubling, halving, familiar basic facts, and place value partitioning to mentally solve problems involving ‘friendly’ small two-digit by one-digit numbers (division without remainders).
Use doubling and halving, basic facts, and place-value partitioning to mentally solve problems involving ‘friendly’ two-digit by one-digit numbers, and those involving multiples of 10 (E.g. 120 x 4), using informal written
Use doubling and halving, place-value partitioning and basic facts, to mentally solve problems involving ‘friendly’ numbers, using informal written strategies to keep track.
Use factors to mentally solve problems involving ‘friendly’ numbers, using informal written strategies to keep track.
Smith 2014
30
strategies to keep track (including division with remainders).
ACMNA 004 ACMNA 004 ACMNA 031 ACMNA 032
ACMNA 057 ACMNA 076 ACMNA 100 ACMNA 101
ACMNA 123 ACMNA 098
MULTIPLICATION AND DIVISION: WRITTEN STRATEGIES
Year 6 Year 7 Use written strategies for calculations involving up to three-digit numbers (mult = 3 x 2, div = 3 / 1 digits) and simple decimals involving money and measures.
Use written strategies for three- and four-digit numbers and decimals.
ACMNA 123 ACMNA 129
ACMNA 123 ACMNA 129
MULTIPLICATION AND DIVISION: CALCULATOR AND CHOSE STRATEGIES
Year 4 Year 5 Year 6 Year 7 Use the x and / and = buttons in the appropriate order.
Choose appropriately between mental, informal written and calculator strategies to solve calculations involving 'unfriendly' two-digit numbers, including division with remainders.
Choose appropriately between mental, informal written or calculator strategies for 'unfriendly' large numbers and decimals involving money and measures Choose appropriately between mental, written or calculator strategies to solve problems.
Choose appropriately between mental, written or calculator strategies to solve problems.
ACMNA 076 ACMNA 100 ACMNA 101
ACMNA 123 ACMNA 129
ACMNA 123 ACMNA 129
ESTIMATION
F 1.2 Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Working towards Year 3.
Working towards Year 3.
Working towards Year 3.
Round two digit numbers to check addition and subtraction.
Round three digit numbers and simple decimals involving money to check addition and subtraction.
Round large whole numbers and decimals to check addition and subtraction, and round two digit numbers to check multiplication
Round large whole numbers and decimals to check answers to problems.
Smith 2014
31
and division. ACMNA 099 ACMNA 099 ACMNA 099 ACMNA 099 ACMNA 099 ACMNA 099 ACMNA 128
ACMNA 156
JUDGING REASONABLENESS
Year 3 Year 4 Year 5 Year 6 Year 7 Know their answers to two-digit addition and subtraction problems make sense.
4a) Know their answers to three-digit addition and subtraction problems make sense 4b) Know that multiplication of whole numbers gives a bigger number and division of whole numbers gives a smaller number.
5a) Know their answers to addition, subtraction, and two-digit multiplication and division problems make sense. 5b) Can interpret remainders in division and round up or down to compensate.
Know their answers to multiplication or division problems make sense.
7a) Know their answers to problems involving decimal numbers make sense. 7b) Know that multiplication does not always give a bigger number and division does not always give a smaller answer (i.e. when working with decimal numbers).
ACMNA 099 ACMNA 051
ACMNA 099 ACMNA 071
ACMNA 099 ACMNA 099 ACMNA 128
Smith 2014
32
APPENDIX 4.0
Smith 2014
33
AICS STATISTICS AND PROBABILITY SCOPE & SEQUENCE CHANCE
Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Identifies possible outcomes of familiar events and describes them using everyday language.
Recognises events that involve chance. Classifies outcomes of events as possible/impossible, likely/unlikely, certain/uncertain. Explains reasoning for the classification.
Conducts chance experiments. Identifies and describes possible outcomes. Conducts repeated trails. Recognises variation in results they may obtain.
Describes possible everyday events. Orders their chances of occurring. Identifies mutually and non-mutually exclusive events.
Lists outcomes of chance experiments involving equally likely outcomes and represents probabilities of those outcomes using fractions. Recognises that probabilities range from zero to one.
Describe probabilities using fractions, decimals and percentages. Conducts chance experiments with both small and large numbers of trials with digital technologies. Compares observed frequencies with expected frequencies.
DATA COLLECTION
F 1.1 F 1.2 Year 1 Year 2 Year 3 Year 4 Year 5 Answer yes/no questions posed by teacher to collect information.
Answer yes/no questions posed by teacher to collect information.
Selects simple questions they have generated from which they may gather responses.
Identifies a question to be investigated with one categorical variable and gathers data. Collects, checks and classifies data. Uses tally marks.
Refines question to be asked so that they obtain most useful data. Plans an investigation and collects data. Organises data into categories.
Selects and trial methods for data collection to determine most effective method.
Poses questions an collects categorical or numerical data by observation or survey.
DATA REPRESENTATION
F 1.2 Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Creates simple displays of data.
Represents data with objects and drawings where one object or drawing represents on data
Creates displays of data using lists, table and picture graphs.
Creates displays using lists, tables, pictures graphs and simple column graphs with and without
Constructs suitable data displays from primary and secondary sources, with and without digital technologies.
Constructs most appropriate displays for collected data including column graphs, dot plots and
Constructs more sophisticated data displays such as side-by-side column graphs for two categorical
Smith 2014
34
value. digital technologies.
Includes picture graphs where one picture represents more than one data value.
tables with and without digital technologies.
variables.
DATA INTERPRETATION
F 1.1 F 1.2 Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Answers simple questions about data.
Answers simple questions about data.
Describes the displays they make. Identifies the category with the highest or lowest frequency.
Interprets data displays. Compares usefulness of different types of data displays.
Interprets and compares data displays.
Evaluates which data presents the data is the most useful way.
Describes and interprets different data sets in context.
Interprets these displays. Interprets secondary data presented in digital media and elsewhere. Identifies misleading data.
Smith 2014
35
APPENDIX 5.0
Smith 2014
36
AICS MEASUREMENT AND GEOMETRY SCOPE & SEQUENCE ATTRIBUTE AND DIRECT COMPARISON
F 1.1 F 1.2 Year 1 Year 2 Year 3 Compares objects by general ‘bigness’. E.g. Describing things as tall/short, fat thin. Visually compare without attempting to match.
Describes and compares objects by the most obvious attribute and explains reasoning in everyday language. Distinguish different forms of length. E.g. Wide from tall.
Responds to and uses everyday language associated with length, mass, capacity and time. Line up bases to compare lengths and superimpose to measure area.
Knows that the same objects can be ordered by different attributes. Directly compares and makes matching quantities.
Directly compares and describes length, capacity, mass and time using appropriate comparative language.
USING UNITS
Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Uses informal units to measure and compare. Count units and call it ‘measuring’.
Uses uniform informal units to compare and order several objects by length, mass, capacity, area and volume. Uses a balance scale to compare mass of objects. Use of ‘between’.
Uses familiar metric units to measure, order and compare objects.
Selects suitable objects to use a s uniform units to order length, mass, capacity and area. Attend to gaps and overlaps.
Selects and carefully uses suitable units to order length, capacity, mass, area, time and angle. Understands that using a uniform unit repeatedly to match an object gives a measure of the size of the object. Uses count of units to say which is ‘bigger’. Understands the difference between perimeter and area.
Understands the smaller the unit, the greater the number. Understands the unit can be cut and rearranged. Compose part-units into wholes. Has a sense of common standard units of length, mass, capacity and converts between them.
SCALE
F 1.1 F 1.2 Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Connect days of the week to
Compare and order the
Tells time to the half-hour.
Uses balance scales to
Tell time to the minute. Investigate
Connect the repetition
Understands and uses
Interpret the unnumbere
Smith 2014
37
familiar events and actions.
duration of events using the everyday language of time.
Describes duration using months, weeks, days and hours.
compare masses of objects. Recognise key times on analogue clock to quarter-hour and tell time on digital clocks. Name and order months and seasons. Use a calendar to identify date and number of days per month.
relationship between units of time.
of a unit with the numbers on a whole-number calibrated scale. Convert between units of time. Use am and pm notation.
standard scales to measure and compare length, mass, capacity and time (analogue and digital). Understand 24 –hour time and convert between 12- and 24-hour times.
d graduations on a familiar whole-number scale. Interpret and use timetables and programs.
ESTIMATE
F 1.1 F 1.2 Year 3 Year 4 Year 6 ‘Guess’ whether something is ‘bigger’/’smaller’ than an object.
Use appropriate language of approximation.
Attends to correct attributes when estimating.
Makes sensible numerical estimates to measure length, capacity and mass.
Estimates standard units using personal benchmarks. Estimates without units being present.
SHAPE
F 1.1 F 1.2 Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Sorts 2D shapes and 3D objects into groups by similarities. Describes and names groups of shapes and objects they can see and handle.
Identifies differences between 2D shapes and 3D objects. Copies simple figures and makes recognisable models of objects in the environme
Names many shapes. Describes features of familiar shapes in everyday words. Connects shape, movement and function.
Identifies key features and draws 2D shapes. Identifies and describes geometric features of 3D objects.
Makes models of 3D objects and describes key features.
Compares areas of regular and irregular 2D shapes counting the number of informal metric units taken to cover each. Uses more sophisticated
Describes the main features of 2D shapes and 3D objects in their drawings and models. Matches 3D objects with their nets by attending
Identifies 3D objects from descriptions. Matches 3D objects to skeletal frames. Selects suitable nets to fold to make simple prisms and
Smith 2014
38
nt. Describes some features of 2D shapes.
language to describe 2D and 3D. Compare and contrast 2D shapes. Creates 2D shapes from instructions. Identifies 2D shapes that are part of composite shapes.
to shape and relative position of the faces.
pyramids. Can produce nets for geometric shapes they can see and handle. Uses oblique lines to represent depth in drawing.
LOCATION
F 1.1 F 1.2 Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Follows simple directions related to position. Locates objects in a familiar environment.
Draws simple maps to represent the local area or story setting.
Gives and follows directions to familiar locations referring to turns, direction and distance.
Uses and interprets familiar everyday language for position of things. Interprets simple maps.
Represents order and betweeness on informal maps. Creates and interprets simple grid maps of familiar environment.
Uses simple scales, legends and direction to interpret information contained in basic maps. Uses birds-eye-view to represent features on maps and plans with rough sense of proximity.
Informally attends to proximity and direction. Uses grid references to describe location. Describes routes using landmarks and directional language.
Uses compass directions, half and quarter turns in directional language. Uses known distances to describe location. Represent location using the Cartesian co-ordinate system.
TRANSFORMATION
Year 2 Year 3 Year 4 Year 5 Year 6 Investigates the effects of one-step slides and flips with and without digital technology. Understands that objects can be moved but
Identifies and uses slide and turn symmetry to make patterns with and without digital technology.
Recognises flips, slides and turns. Makes symmetrical pictures.
Describes translation, reflection and rotation of 2D shapes. Identifies line and rotational symmetry.
Visualises and describes the effect of the range of transformation. Investigates combinations of transformations with and without
Smith 2014
39
changing position does not alter an object’s size or features. Identifies and describes half and quarter turns and uses this to predict and reproduce patterns.
Explores what happens when 2D shapes are enlarged. Uses a grid system to enlarge images.
digital technology.
GEOMETRIC REASONING
Year 3 Year 4 Year 5 Year 6 Identifies angles as measures of turn and compares angle size in everyday situations.
Compares angles and classifies them as equal to, greater than or less than a right angle.
Estimates, measures and compares angles using degrees. Constructs angles using a protractor.
Investigates, with and without digital technology, angles on a straight line, angles at a point and vertically opposite angles. Uses results to find unknown angles. Identifies the size of a right angle as 90 degrees and defines acute, obtuse, straight and reflex angles. Measures, estimates and compares angles in degrees and classifies angles according to their size.
Smith 2014
40
APPENDIX 6.0
Smith 2014
41
AICS MONEY AND FINANCIAL LITERACY SCOPE & SEQUENCE Lessons should provide opportunities for students to:
F 1.1 F 1.2 Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7
Play with coins in general classroom
activities. U
se coins and notes during play activities where using m
oney adds to the ‘realness’ of the scenario.
Recognise, describe and order Australian coins according to their value.
Use descriptive language w
hen talking about money.
Learn the language and concepts such as more/less, m
ost/least etc. in a variety of contexts.
Recognise, describe and order Australian coins according to their value.
Skip count money, both notes and coins to 100c or $100.
Engage in simple addition activities using m
oney. Trust the count using m
oney. Explore equivalent values. R
ead and write m
oney values using the $ and c symbols correctly.
Count and order sm
all collections of Australian coins and notes according to their value. C
ount forwards and backw
ards by ones and tens using money, both coins and notes.
Skip count money.
Simple addition and subtraction using m
oney. R
ead and write m
oney values using the $ and c symbols correctly.
Represent m
oney values in multiple w
ays and count the change required for simple transactions to the nearest five cent.
Engage in problem solving w
ith money.
Interpret questions involving money.
Write sim
ple number sentences using addition and subtraction w
ith money.
Solve problems involving purchases and the calculation of change to the nearest five cents w
ith and without digital technologies.
Be introduced to the language and concepts of budgeting, saving, rounding and estimating m
oney.
Create sim
ple financial plans. Becom
e aware of the need to plan to m
anage money effectively.
Investigate sources of income.
Become aw
are of the importance of saving m
oney. Investigate the process of opening a bank account.
Investigate and calculate percentage discounts of 10%, 25%
and 50% on sale item
s, with and w
ithout digital technologies. Explicitly connect concepts of fractions and percentage to m
oney. U
nderstand the concept of discounts and sales.
Investigate and calculate ‘ best buys’, with and w
ithout digital technologies. U
se copies of store magazines to ‘purchase’ item
s up to a certain value of money and com
pare the cost of items from
a range of suppliers. Evaluate best deals for a mobile phone.
Investigate online shopping – savings and ‘extra’ costs of shipping, insurance. Investigate the process of applying for a credit card and becom
e aware of the costs involved.
Smith 2014
42
APPENDIX 7.0
Smith 2014
43
WULUNGARRA COMMUNITY SCHOOL
!!!
!!This!unit!of!work!contains![number]!of!lessons.!It!provides!students!with!opportunities!to.......................................................................................................!!!CONTENTS!CURRICULUM!INFORMATION!Phase!of!development!…………………!!1!Major!learning!areas!….......................1!Values!………………………………..............1!!!TOPIC!INFORMATION!Purpose……………………………………..……2!Student!outcomes………………..…………2!Key!background!points………..………….2!Cultural!and!protocol!considerations.....................................2!!!TEACHING!AND!LEARNING!STRATEGIES!Teaching!resources!overview………….2!Lesson!1:![Title]…………….………………..3!Lesson!2:![Title]……………….……………..4!Lesson!3:![Title]!……………….…………….5!Lesson!4:![Title]!…………………….……….6!Lesson!5:![Title]!…………………….……….7!!PHOTOCOPIABLE!RESOURCES!Learning!guide!1:![Title]………………….8!Learning!guide!2:![Title]…………….……9!
CURRICULUM!INFORMATION!
Phase!of!Development!
Early!Childhood! !Middle!Childhood! !Early!Adolescence! !Late!Adolescence! !
!Key!Learning!Areas!
!The!Arts! !English! !Health!&!Physical!Education! !Languages! !Mathematics! !Science! !Society!&!Environment! !Technology!&!Enterprise! !
! !! !! !! !! !
!Values!
[Unit Plan Title]
Smith 2014
44
WULUNGARRA COMMUNITY SCHOOL
Wulungarra/Smith 2013/
TERM PLANNER
TERM 1, 2014
Theme: Year Levels: Combined K - 10
WEEK LITERACY NUMERACY MUSIC/LANGUAGE ICT
1
2
3
4
5
6
7
8
9
10 KLAs Science/History/Geography etc. are explicitly integrated into our literacy and numeracy planning and adhered to Australian Curriculum Framework where possible.
Smith 2014
45
APPENDIX 8.0
Smith 2014
46
WEE
KLY
SCHE
DULE
M
OND
AY
TUES
DAY
WED
NESD
AY
THUR
SDAY
FR
IDAY
7:00
Rou
tine:
Bru
sh te
eth,
was
h fa
ce, p
ut o
n sc
hool
shi
rt, y
ard
tidy.
7:
00 R
outin
e: B
rush
teet
h, w
ash
face
, and
put
on
scho
ol s
hirt.
7:
15 In
tegr
atio
n (n
umer
acy,
lite
racy
, scie
nce,
ICT,
hea
lth)
7:00
Rou
tine:
Bru
sh te
eth,
was
h fa
ce, p
ut o
n sc
hool
shi
rt, y
ard
tidy.
7:00
Rou
tine:
Bru
sh te
eth,
was
h fa
ce, a
nd p
ut o
n sc
hool
shi
rt.
7:15
Inte
grat
ion
(num
erac
y,
litera
cy, s
cienc
e, IC
T, h
ealth
)
7:00
Rou
tine:
Bru
sh te
eth,
was
h fa
ce, p
ut o
n sc
hool
shi
rt, y
ard
tidy.
7:15
Inte
grat
ion
(num
erac
y,
litera
cy, s
cienc
e, IC
T)
7:45
Gar
den
Writ
ing
8:00
Tea
cher
Rea
d Bo
ok +
Ac
tivity
7:15
Inte
grat
ion
(num
erac
y,
litera
cy, s
cienc
e, IC
T)
7:45
Gar
den
Writ
ing
8:00
Tea
cher
Rea
d Bo
ok +
Ac
tivity
7:15
Inte
grat
ion
(num
erac
y,
litera
cy, s
cienc
e, IC
T)
8:00
Gui
ded
Read
ing
(3 g
roup
s)
8:00
Gui
ded
Read
ing
(3 g
roup
s)
8:00
Gui
ded
Read
ing
(3 g
roup
s)
8:30
FIR
ST B
REAK
8:45
Num
erac
y
8:45
Num
erac
y
8:45
Wor
ds T
heir
Way
8:45
Gui
ded
Read
ing
9:15
Wor
ds T
heir
Way
8:
45 N
umer
acy
9:15
Inte
grat
ion
(lite
racy
, SO
SE)
9:15
Writ
ing
9:
45 L
itera
cy G
ames
9:
00 In
tegr
atio
n (n
umer
acy,
life
skills
, phy
sica
l edu
catio
n)
9:30
Num
erac
y 9:
15 W
ritin
g 9:
40 W
ords
The
ir W
ay
9:45
Wor
ds T
heir
Way
9:30
Inte
grat
ion
(lite
racy
, SO
SE)
10:0
0 FR
UIT
BREA
K
10:1
5 In
tegr
atio
n (m
usic,
liter
acy,
nu
mer
acy)
10:1
5 W
ords
The
ir W
ay
10:3
5 In
depe
nden
t Rea
ding
10
:15
Inte
grat
ion
(mus
ic, lit
erac
y,
num
erac
y)
10:1
5 W
ritin
g
10:1
5 In
tegr
atio
n (m
usic,
liter
acy,
nu
mer
acy)
10
:45
Inte
grat
ion
(num
erac
y, lif
e sk
ills, p
hysi
cal e
duca
tion)
11:0
0 W
ritin
g 10
:50
Num
erac
y 10
:45
Inte
grat
ion
(num
erac
y,
litera
cy, l
ife s
kills
, ICT
) 11
:15
Inte
grat
ion
(lite
racy
, SO
SE)
11:
00 N
umer
acy
11:2
0 Pa
ck-U
p Cl
assr
oom
11:3
0 LA
ST B
REAK
11:4
5 In
depe
nden
t Rea
ding
11:4
5 Ki
ngdo
m A
viatio
n
11:4
5 W
ritin
g 12
:15
Inde
pend
ent R
eadi
ng
11:4
5 In
tegr
atio
n (li
tera
cy,
num
erac
y, v
isua
l arts
) 12
:30
Pack
-Up
11:4
5 In
tegr
atio
n (n
umer
acy,
lite
racy
, life
skil
ls, I
CT)
12:0
5 In
tegr
atio
n (li
tera
cy,
num
erac
y, v
isua
l arts
) 12
:50
Pack
-Up
Clas
sroo
m
1:05
End
of D
ay R
evie
w an
d G
ame
12:3
0 Li
brar
y: S
elec
ted
Lite
racy
Ap
ps
12:3
0 Nu
mer
acy
12:4
5 Li
brar
y: S
elec
ted
Num
erac
y Ap
ps
12:3
0 W
ritin
g
1:00
Pac
k-Up
Cla
ssro
om
1:05
Pac
k up
Cla
ssro
om
2:00
BRE
AK
2:
00 B
REAK
3:00
Sta
ff M
eetin
g 3:
00 C
urric
ulum
Mee
ting
3:00
Por
tfolio
/ESP
Mee
ting
4:00
AAS
C
4:00
AAS
C 4:
00 A
ASC
4:00
Hot
dogs
& H
omew
ork
Smith 2014
47
APPENDIX 9.0
Smith 2014
48
Term 2 Resources/Integration Science/Lesson Plans
Monster Toothpaste
Science
Kindergarten – Year 10
Friday 9/5/14
Overview
Big messy science experiments are a fun way to get your students interested in how things work. This ‘Monster Toothpaste’ science experiment for kids is a great hands-on learning activity.
Objectives
To introduce students to simple chemical reactions.
Activities
1. Watch (Video) 2. Place the empty bottle in the centre of the sheets of newspaper. 3. In a small jug mix together the yeast and warm water. Agitate it until
bubbles form (you need to activate the yeast). 4. Use a funnel to pour ½ cup of hydrogen peroxide into the soda bottle.
Add some food colouring and a squirt of dishwashing liquid. 5. Now add the yeast mixture to the bottle. 6. Watch the monster toothpaste rise up and ooze out of the bottle. 7. Why is it so? Hydrogen Peroxide naturally breaks down into water
and oxygen. The yeast speeds up the reaction. Dish soap catches the oxygen particles as they are released by the ‘breakdown’ process and forms bigger bubbles. The foam and the bottle feel warm because it is an ‘exothermic’ reaction: meaning it releases energy as heat.
Adaptations
All students involved, older ones to do the tricky bits while younger students watch with Kylie.
Evaluation
Compare to Volcano Experiment from Monday, determine similarities and differences.
Materials
• Sheets of Newspaper
• 1 x Empty Soda Bottle
• Yeast
• Warm Water
• A Plastic Funnel
• Hydrogen Peroxide (6%)
• Blue Food Colouring
• Dishwashing liquid
Other Resources
www.kidspot.com.au
Smith 2014
49
APPENDIX 10.0
Smith 2014
50
NUMERATION SUCCESS INDICATORS
RESOURCES SCHOOL DATA
Reading Numbers • Students will have measureable gains in reading numbers
BOOKS & KITS • Signpost Maths Books • Discovering Number Patterns • Exploring Number Patterns • Investigating Number Patterns • AICS Portal Maths Book Activity
List • Developing Efficient Numeracy
Strategies Stage One and Stage Two
• Paul Swan’s Maths Collection: Games Based Activities, to Support Mathematical Understanding
1. Dice Dilemmas 2. Card Capers 3. Domino Deductions 4. Talking Tables 5. Kids Calculators & Classrooms
• Scholastic-Maths Focus (Kit 2) ‘Reinforcing Skills & Concepts’
ICT RESOURCES
• Dr Paul Swan Maths Games: Abacus www.drpaulswan.com.au/
• Developing Efficient Numeracy Strategies Books: Stage One and Stage Two www.curriculumsupport.education.nsw.gov.au/primary/.../index.htm
• Education Closet (Core Strategies for Arts Integration) http://educationcloset.com/music
• Cool Math for Kids Games http://www.coolmath4kids.com
• IXL Maths for Preschool to Year 11-‘Dynamic, Adaptive Learning’ http://au.ixl.com
• COPACABANA Public School http://www.copacabana-ps.com/
Foundation – Year 6 Data and testing on AICS Portal.
Writing Numbers • Students will have measurable gains in writing numbers
Foundation – Year 6 Data and testing on AICS Portal.
Saying the Number Sequence
• Students will have measureable gains in saying or singing the number sequence
Foundation – Year 6 Data and testing on AICS Portal.
Subitising/ Partitioning
• Students will have measureable gains in demonstrating subitising and partitioning
Foundation – Year 2 Data and testing on AICS Portal.
Counting Collections
• Students will demonstrate measureable gains in counting collections
Foundation – Year 2 Data and testing on AICS Portal.
Understanding Place Value
• Students will have measurable gains in demonstrating their understanding of place value
Year 1.2 - Year 6 Data and testing on AICS Portal.
Smith 2014
51
CALCULATE SUCCESS INDICATORS
RESOURCES SCHOOL DATA
Basic Facts + and -
• Students will demonstrate understanding of basic addition and subtraction facts
BOOKS & KITS • Signpost Maths Books • Discovering Number Patterns • Exploring Number Patterns • Investigating Number Patterns • AICS Portal Maths Book Activity List • Developing Efficient Numeracy
Strategies Stage One and Stage Two • Paul Swan’s Maths Collection: Games
Based Activities, to Support Mathematical Understanding
1. Dice Dilemmas 2. Card Capers 3. Domino Deductions 4. Talking Tables 5. Kids Calculators & Classrooms
• Scholastic-Maths Focus (Kit 2) ‘Reinforcing Skills & Concepts’
ICT RESOURCES
• Dr Paul Swan Maths Games: Abacus www.drpaulswan.com.au/
• Developing Efficient Numeracy Strategies Books: Stage One and Stage Two www.curriculumsupport.education.nsw.gov.au/primary/.../index.htm
• Education Closet (Core Strategies for Arts Integration) http://educationcloset.com/music
• Cool Math for Kids Games http://www.coolmath4kids.com
• IXL Maths for Preschool to Year 11-‘Dynamic, Adaptive Learning’ http://au.ixl.com
• COPACABANA Public School http://www.copacabana-ps.com/
Foundation – Year 3 Data and testing on AICS Portal.
Basic Facts Tables
• Students will demonstrate measurable gains in basic times tables
Year 3 and 4 Data and testing on AICS Portal.
Addition and Subtraction, Mental and Informal Written
• Students will demonstrate measureable gains in mental and informal written addition and subtraction
Foundation – Year 6 Data and testing on AICS Portal.
Addition and Subtraction, Written Strategies
• Students will show measureable gains in addition and subtraction using written strategies
Year 2 – Year 6 Data and testing on AICS Portal.
Addition and Subtraction, Calculator and Choose Strategies
• Students will demonstrate understanding of addition and subtraction, using a calculator and chosen strategies
Year 4, 5 and 6 Data and testing on AICS Portal.
Multiplication and Division, Mental and Informal Written
• Students will demonstrate measureable gains in mental and informal written multiplication and division
Foundation – Year 7 Data and testing on AICS Portal.
Multiplication and Division, Written Strategies
• Students will show measureable gains in multiplication and division using written strategies
Year 4 – Year 7 Data and testing on AICS Portal.
Multiplication and Division, Calculator and Choose Strategies
• Students will demonstrate understanding of multiplication and division, using a calculator and chosen strategies
Year 6 and 7 Data and testing on AICS Portal.
Estimation • Students show Foundation – Year
Smith 2014
52
measurable gains in understanding estimating answers to problems when an accurate answer is not necessary
6 Data and testing on AICS Portal.
Judging Reasonableness
• Students develop their ability to decide whether to estimate or to calculate and to judge reasonableness of answers to problems.
Year 3 – Year 7 Data and testing on AICS Portal.
Smith 2014
53
APPENDIX 11.0
Smith 2014
54
Calculate Addition and Subtraction: F–1
©AICS Numeracy Strategy Oct 2011
Frogs and Pencils Foundation–Year 1
Purpose To find out whether students can: Foundation 1.1
x attempt to solve small number story problems. Foundation 1.2
x use counting or subitising to solve simple story problems, using realistic materials or realistic pictures (for results up to ten).
Year 1
x use counting or subitising to solve simple story problems, using blocks, counters or drawings (for results up to 20).
Equipment Blocks, counters, teddies etc. or pictures of frogs, birds, etc. (see attached sheets) Paper and pencil
Procedure Individual interview Read the problem to the student or tell it as a story. Teachers may wish to change the wording according to the materials that are available, for example change frogs to teddies if teddies are available. Foundation 1.1 and 1.2: have realistic materials or pictures (photocopy the attached sheets) readily available for students to use. If the student cannot get started, prompt them to get out the first three frogs by saying: ‘Can you show me three frogs? Now two more frogs came over. How many frogs are there now?’ Year 1: encourage students to first draw a picture to solve the problem. If they cannot, then offer them materials (e.g. blocks, counters). Students can use either materials or drawings. Observe whether the student:
attempts to solve the first problem (Frogs 1) with the prompt, using either counting or subitising.
Evidence of F 1.1 checkpoint
solves the first two problems (Frogs 1–2) using realistic materials, drawing, counting or subitising, with prompt from above if needed.
Evidence of F1.2 checkpoint
Smith 2014
55
Calculate Addition and Subtraction: F–1
©AICS Numeracy Strategy Oct 2011
uses drawings or materials, counting or subitising to solve the four Pencils problems (Pencils 1–4). (If students need a prompt to get started, then this is not evidence)
Evidence of Year 1 checkpoint
Observe and comment on the strategies the student uses to count the collection (e.g. count all, count on, count up, count down, skip counting).
Smith 2014
56
Calculate Addition and Subtraction: F–1
©AICS Numeracy Strategy Oct 2011
Frogs Name: _______________________ Date: ______________
1. There were 3 frogs and 2 more frogs came over. How many frogs are there now?
2. There were 5 birds and 3 more birds joined them. How many birds are there now?
Smith 2014
57
Calculate Addition and Subtraction: F–1
©AICS Numeracy Strategy Oct 2011
Pencils Name: _______________________ Date: ______________
1. There were 12 pencils. 7 more pencils were added. How many pencils are there now?
2. Kimberlee had 16 stickers and the teacher gave her 4 more stickers. How many stickers does Kimberlee have now?
Smith 2014
58
Calculate Addition and Subtraction: F–1
©AICS Numeracy Strategy Oct 2011
3. There were 17 lollipops but I ate 3 of the lollipops. How many lollipops are left?
4. There were 16 snakes but 12 snakes slid away. How many are left?
Smith 2014
59
Calculate Addition and Subtraction: F–1
©AICS Numeracy Strategy Oct 2011
Below are some images you can print, laminate, cut out and use with students. It is important to offer MORE items than are in the story, NOT the exact amount.
Smith 2014
60
Calc
ulat
e Ad
ditio
n an
d Su
btra
ctio
n: F–1
©
AICS
Num
erac
y St
rate
gy O
ct 2
011
Frog
s an
d Pe
ncils
S
trate
gies
for s
olvi
ng a
dditi
on a
nd s
ubtra
ctio
n pr
oble
ms
Nam
e D
ate
F 1.
1 (F
rogs
1)
Atte
mpt
s to
sol
ve th
e pr
oble
m
F 1.
2 (F
rogs
1–2
)
Use
s co
untin
g or
su
bitis
ing
to s
olve
Fr
og p
robl
ems
Yea
r 1 P
enci
ls (1
–4)
Use
s co
untin
g or
su
bitis
ing
to s
olve
Pen
cil
prob
lem
s
+
–
Com
men
ts
x st
rate
gies
stu
dent
use
s x
prom
pts
need
ed
1
2
3
4
5
6
7
8
9
10
Smith 2014
61
APPENDIX 12.0
Smith 2014
62
Calculate Basic facts: Yr 2
© AICS Numeracy Strategy Oct 2011 Calculate: Basic facts
Double Rainbows Year 2
Purpose To find out whether students know:
x doubles (and near doubles) to 10 + 10 and related subtraction facts x ‘rainbow facts’ or complimentary numbers to 10 (e.g. 3 + 7).
Equipment List of basic facts on cards (see following sheet).
Procedure Tell the student you are going to ask them some number facts. Show the student each card as you ask them the fact. Show one card at a time.
Language Use language the student is familiar with, which may be, for example:
x double 2 x 2 and 2 x 8 plus 2 x 8 add 2 x 8 minus 2 x 8 take 2 x 2 less than 8.
Use the proforma to record the student’s answers and mark them against the following checkpoints.
NB: Basic facts should be automatic and should not require counting to work out. Students may need some thinking time to retrieve a fact or apply a strategy. Allow approximately 3 seconds per fact.
Knows doubles to 10 and related subtraction facts (without counting)
x Year 2 checkpoint
Knows combinations to 10 and related subtraction facts (without counting)
x Year 2 checkpoint
Smith 2014
63
© AICS Numeracy Strategy Oct 2011 Calculate: Basic facts
Double Rainbows
3 + 3
12 - 6
3 + 7
20 - 10
8 + 2
14 - 7
6 + 4
18 - 9
4 + 4
10 - 9
9 + 9
10 - 3
8 + 8
10 - 5
Smith 2014
64
© A
ICS
Num
erac
y St
rate
gy O
ct 2
011
C
alcu
late
: Bas
ic fa
cts
Doub
le R
ainb
ows
Year
2: K
now
s do
uble
s to
10
Year
2: K
now
s co
mbi
natio
ns to
10
Basi
c fa
cts
shou
ld b
e au
tom
atic
and
sho
uld
not r
equi
re c
ount
ing
to w
ork
out.
How
ever
, stu
dent
s m
ay n
eed
som
e th
inki
ng ti
me.
NAM
E
3 + 3
12 - 6
3 + 7
20 - 10
8 + 2
14 - 7
6 + 4
18 - 9
4 + 4
10 -9
9 + 9
10 - 3
8 + 8
10 - 5
Kno
ws
doub
les
to 1
0
(Yr 2
)
Kno
ws
com
bi-
natio
ns to
10
(Yr 2
)
Com
men
ts
1
2
3
4
5
6
7
8
9
10
11
12
Smith 2014
65
APPENDIX 13.0
Smith 2014
66
Understanding the Numeration System Counting Collections: Years 1.1–1.2
©AICS Numeracy Strategy October 2011 Understand Number: Counting collections
Skip Counting Years 1.1–1.2
Purpose Year 1.1: To find out whether students can use skip counting by twos to say how many in small collections. Year 1.2: To find out whether students choose to use skip counting to say how many in a large collection (up to 100).
Materials Year 1.1: 15 small things, e.g. 15 nuts, counters or blocks Year 1.2: A large collection of up to 100 nuts, counters or blocks
Procedure
Year 1.1 Give the child 15 small things, e.g. 15 nuts. Ask: Can you count the nuts (counters or blocks) by twos and tell me how many there are? Observe whether the child: x counts by ones
x counts by twos but says 12, 14, 16 instead of 12, 14, 15
x counts the nuts accurately by twos to 14, then adds the one and says 15
Year 1.1 checkpoint
Year 1.2 Tip the large collection of items out in front of the child and ask: How many nuts, (counters or blocks) do you think are there? Could you count them to say how many are there? Observe whether the child:
x counts by ones
x chooses to count by groups, e.g. twos, fives or tens Year 1.2 checkpoint
* Department of Education and Training of Western Australia (2006), First Steps in Mathematics: Number Course Book, Rigby Heinemann, Melbourne.
Adapted from First Steps in Mathematics: Number
Smith 2014
67
Unde
rsta
ndin
g th
e Nu
mer
atio
n Sy
stem
Co
untin
g Co
llect
ions
: Yea
rs 1
.1–1
.2
©AI
CS N
umer
acy
Stra
tegy
Oct
ober
201
1
Unde
rsta
nd N
umbe
r: Co
untin
g co
llect
ions
Skip
Cou
ntin
g Y
ear 1
.1: U
ses
skip
cou
ntin
g by
twos
to s
ay h
ow m
any
in s
mal
l col
lect
ions
Y
ear 1
.2: C
hoos
es to
use
ski
p co
untin
g to
say
how
man
y in
a la
rge
colle
ctio
n (u
p to
100
item
s)
NAM
E Ye
ar 1
.1
Can
use
ski
p co
untin
g by
twos
to s
ay h
ow
man
y in
sm
all
colle
ctio
ns
Year
1.2
C
hoos
es to
use
ski
p co
untin
g to
say
how
m
any
in a
larg
e co
llect
ion
(up
to 1
00)
Com
men
ts
(not
e th
e st
rate
gies
use
d by
stu
dent
s)
1
2
3
4
5
6
7
8
9
10
Smith 2014
68
APPENDIX 14.0
Smith 2014
69
Calculate Judging reasonableness of an answer: 3–7
©AICS Numeracy Strategy November 2012 Calculate: Judging reasonableness of an answer
It’s Around About Years 3–7
Purpose Year 3: It’s Around About (1) To find out whether students:
x Rounding—are able to round numbers to the nearest 10 to check answers to addition and subtraction problems.
x Making Sense—know if their answer to a two-digit addition or subtraction problem makes sense.
Year 4: It’s Around About (2) To find out whether students:
x Rounding—are able to round numbers to the nearest 100 and simple decimals involving money to the nearest 10 to check answers to addition and subtraction problems.
x Making Sense— (a) know if their answer to a three-digit addition or subtraction problem makes sense; (b) know that multiplication of whole numbers gives a bigger number and division of whole numbers gives a smaller number .
Year 5: It’s Around About (3) To find out whether students:
x Rounding—are able to round to the nearest 10 to check multiplication and division answers, and to the nearest 1000 for addition and subtraction.
x Making Sense—(a)know if their answer to an addition, subtraction, two-digit multiplication or division problem makes sense; (b) can interpret remainders in division and round up or down to compensate.
x
Year 6: It’s Around About (4) To find out whether students:
x Rounding—are able to round numbers to the nearest 100 or 1000 to check an answer.
x Making Sense—know if their answer to a multiplication or division problem makes sense.
Year 7: It’s Around About (5) To find out whether students:
x Making Sense— (a) know their answer to a problem involving decimals makes sense; (b) know that multiplication does not always give a bigger number and division does not always give a smaller answer, for example when working with decimals.
Equipment Worksheets, pencils
Smith 2014
70
Calculate Judging reasonableness of an answer: 3–7
©AICS Numeracy Strategy November 2012 Calculate: Judging reasonableness of an answer
Procedure Rounding Tell students that you do not want them to work out the answers. They are to decide which number in the box on the right-hand side is closest to the answer and then circle that number.
Making Sense Read the questions to the students. Ask them to circle the number they think is closest to the answer.
Students need to complete each section of the worksheet correctly to show evidence of the year level checkpoints. Students may find it difficult to write an answer to the ‘Explain how you know?’ section. If necessary, simply ask the students to explain why they circled the number that they did. They do not have to write an explanation to achieve this checkpoint. An oral explanation is sufficient.
Smith 2014
71
©AICS Numeracy Strategy November 2012 Calculate: Judging reasonableness of an answer
It’s Around About (1) Name: _______________________ Date: ______________
Do not work out the answers. Which number will be closest to the answer? Circle it.
Rounding
12 + 11 10 20 30 40 50
29 + 28 30 40 50 60 70
48 + 31 50 60 70 80 90
72 – 59 10 20 30 40 50
Making Sense
Shoes $39
Shorts $19
Shirt $29
1. How much money would you need to buy the shirt and the shorts? Circle one answer only.
$40 $50 $60 $70 $80 Explain how you know?
2. How much money would you need to buy the shoes and the shirt? Circle one answer only.
$40 $50 $60 $70 $80 Explain how you know?
Smith 2014
72
©AICS Numeracy Strategy November 2012 Calculate: Judging reasonableness of an answer
It’s Around About (2) Name: _______________________ Date: ______________ Do not work out the answers. Which number will be closest to the answer? Circle it. Rounding
121 + 113 100 200 300 400 500
417 + 396 500 600 700 800 900
816 – 593 100 200 300 400 500
21 x 3 20 30 50 60 70
44 ÷ 2 10 20 40 80 90
$21.50 + $37.20 $30 $40 $50 $60 $70
Making Sense
Television $399
Camera $289
Boots $159
1. How much money would you need to buy the camera and the boots? Circle one answer.
$400 $500 $600 $700 $800 Explain how you know?
2. How much money would you need to buy the television and the camera? Circle one
answer only. $400 $500 $600 $700 $800
Explain how you know?
Smith 2014
73
©AICS Numeracy Strategy November 2012 Calculate: Judging reasonableness of an answer
It’s Around About (3) Name: _______________________ Date: ______________ Do not work out the answers. Which number will be closest to the answer? Circle it. Rounding
42 x 3 20 40 100 120 140
65 ÷ 3 20 40 100 150 180
119 x 4 50 100 240 400 480
351 ÷ 5 10 50 70 100 150
$5776.75 + $3211.05 $5000 $6000 $7000 $8000 $9000
8875 – 3125 5000 6000 7000 8000 9000
Making Sense
Television $1099
Computer $2289
Football $28
1. How much money would you need to buy the television and the computer? Circle one answer only.
$1000 $2000 $3000 $4000 $5000 Explain how you know?
2. How much money would you need to buy 5 footballs? Circle one answer only.
$70 $80 $100 $ 120 $150 Explain how you know?
Smith 2014
74
©AICS Numeracy Strategy November 2012 Calculate: Judging reasonableness of an answer
It’s Around About (4) Name: _______________________ Date: ______________ Do not work out the answers. Which number will be closest to the answer? Circle it. Rounding
597 x 42 200 900 2000 2400 24 000
3156 x 39 9000 90 000 12 000 120 000 900 000
$28.50 x 18 30 60 300 600 700
$782 ÷ 7 10 100 150 200 700
Making Sense
Television $1099
Computer $2289
1. How much money would you need to buy five computers? Circle one answer. $1000 $1200 $12 000 $13 000
Explain how you know? 2. How many television sets could you buy with $8000? Circle one answer
4 5 6 7 8 9 10 Explain how you know?
Smith 2014
75
©AICS Numeracy Strategy November 2012 Calculate: Judging reasonableness of an answer
It’s Around About (5) Name: _______________________ Date: ______________ Do not work out the answers. Which number will be closest to the answer? Circle it. Making Sense
42 x 1.5 40 50 60 100 400
100 x 0.5 20 50 100 150 500
50 ÷ 0.5 1 10 20 50 100
2.94 x 80 80 160 240 320 400
250 x 0.46 125 250 500 1000 2000
1. A piece of wood is 4 metres long. How many pieces of
wood 0.5 metres long can you get from this piece of wood? Circle one answer only.
2 4 6 8 10 20 Explain how you know?
2. Seven people shared $200. About how much do they get each? Circle one answer
only. $14 $25 $50 $140
Explain how you know?
Smith 2014
76
©AI
CS
Num
erac
y St
rate
gy N
ovem
ber 2
012
Cal
cula
te: J
udgi
ng re
ason
able
ness
of a
n an
swer
It’s Aro
und Abo
ut
Yea
rs 3
& 4
Jud
ging
reas
onab
lene
ss o
f an
answ
er
Dat
e:__
____
____
____
____
____
___
NAM
E
Yr 3 Rounding— rounds numbers to the nearest 10 to check addition and subtraction answers.
Yr 3 Making Sense—knows their answers to two-digit addition and subtraction problems make sense.
Yr 4 Rounding—rounds numbers to the nearest 100 and simple decimals involving money to nearest 10 to check addition and subtraction.
Yr 4 Making Sense (a) knows their answers to three-digit addition and subtraction problems make sense.
Yr 4 Making Sense (b)—(Rounding Items 4 & 5)—knows that multiplication of whole numbers gives a bigger number and division of whole numbers gives a smaller number.
Com
men
ts
1
2
3
4
5
6
7
8
9
10
Smith 2014
77
©AI
CS
Num
erac
y St
rate
gy N
ovem
ber 2
012
Cal
cula
te: J
udgi
ng re
ason
able
ness
of a
n an
swer
It’s Aro
und Abo
ut
Yea
rs 5
, 6 &
7 J
udgi
ng re
ason
able
ness
of a
n an
swer
Date
:___
____
____
____
____
____
___
NAM
E
Yr 5 Rounding—rounds to the nearest 10 to check multiplication and division, and to the nearest 1000 to check addition and subtraction.
Yr 5 Making Sense —(a)knows their answers to addition, subtraction, two-digit multiplication and division problems make sense.
Yr 5 Making Sense —(b)can interpret remainders in division and round up or down to compensate
Yr 6 Rounding—rounds numbers to the nearest 100 or 1000 to check answers.
Yr 6 Making Sense—knows their answers to multiplication or division problems make sense.
Yr 7 Rounding—(b) (Table items 2 and 3)knows that multiplication does not always make bigger and division does not always make smaller, e.g. multiplying decimals.
Yr 7 Making Sense—(a) (all other items) knows their answers to problems involving decimals make sense.
Com
men
ts
1
2
3
4
5
6
7
8
9
10
Smith 2014
78
APPENDIX 15.0
Smith 2014
79
Calculate Multiplication and division: 3–4
©AICS Numeracy Strategy Oct 2011 Calculate: Multiplication and division
Numbers Galore Years 3–4
Purpose To find out whether students: Year 3
x use skip counting and doubling to solve simple equal-group problems with materials or diagrams (including division without remainders, up to 100).
Year 4
x use skip counting, doubling, halving, familiar basic facts and place value partitioning to mentally solve ‘friendly’ small two-digit by one-digit problems (division without remainders)
x use the x and ÷ buttons on a calculator in the appropriate order.
Equipment Worksheets, pencil, counters or materials (year 3), calculator (year 4).
Procedure Part 1—Individual or small group activity Ask students to try and solve the first part in their head. If they need to draw a picture, or use materials to count, this is acceptable.
Observe students and note whether they use:
materials or a drawing and some skip counting or doubling Evidence of Year 3
skip counting, doubling, halving, basic facts and place value partitioning. (Students must show at least two of these strategies.)
Evidence of Year 4
NB: You may need to interview students to find out which strategies they have used.
Part 2—Using the correct buttons on the calculator (individual interview) Give the student the two cards, 5 and 35, with the 5 on the student’s left hand side. Say, ‘Show me how you can multiply (or ‘times’) these two numbers on the calculator.’ After the student has completed this, say, ‘Show me how you can divide one of these numbers into the other one on the calculator.’ If the student puts in 35 ÷ 5 in this order then show them the 9 and 45, with the 9 on their left hand side. Say, ‘Show me how you can divide one of these numbers into the other one on the calculator.’
Smith 2014
80
Calculate Multiplication and division: 3–4
©AICS Numeracy Strategy Oct 2011 Calculate: Multiplication and division
Observe whether the student thinks to put the larger number first in the division example.
(Evidence of Year 4 Checkpoint) NB: The numbers could be entered into the calculator with the smaller number first, e.g., 5 ÷ 35 = 0.1428. However, this task is looking to see if students know that the order in which the digits are entered into a calculator makes a difference when working with division.
Smith 2014
81
©AICS Numeracy Strategy Oct 2011 Calculate: Multiplication and division
Numbers Galore—Part 1
Name: _______________________ Date: ______________
a) 9 x 5 = b) 7 x 4=
c) 12 x 3 = d) 36 ÷ 6 =
e) 24 ÷ 2 = f) 40 ÷ 5=
g) 50 ÷ 10 = h) 4 x 16 =
Smith 2014
82
©AICS Numeracy Strategy Oct 2011 Calculate: Multiplication and division
Numbers Galore—Part 2 Cards to be cut out.
5 35
9 45
Smith 2014
83
Calc
ulat
e M
ultip
licat
ion
and
divi
sion
: 3–4
©AI
CS N
umer
acy
Stra
tegy
Oct
201
1
Calc
ulat
e: M
ultip
licat
ion
and
divi
sion
Num
bers
Gal
ore
Year
s 3
and
4 S
trate
gies
for
solv
ing
mul
tiplic
atio
n an
d di
visi
on p
robl
ems
NAM
E Y
ear
3
Num
bers
Gal
ore
(1)
Mat
eria
ls a
nd
diag
ram
s
Yea
r 3
Par
t 2
Cal
cula
tor
Yea
r 4
Num
bers
Gal
ore
(1)
Men
tal
Com
men
ts
1
2
3
4
5
6
7
8
9
10
Smith 2014
84
APPENDIX 16.0
Smith 2014
85
Understanding the Numeration System Reading Numbers: Foundation 1.1
©AICS Numeracy Strategy October 2011 Understand Number: Reading Numbers
Recognise Numbers Foundation 1.1 (a)
Purpose To find out whether students recognise numbers in their environment.
Materials Picture of football match, enlarged to A3
Procedure
Show the child the picture of the football match and talk with them about what is happening in it. Encourage them to look in detail at various parts of the picture. For example, ask: Can you see the boy who has the football boots on? Then say: Can you see any numbers? Point to all the numbers you can see on the page. Observe whether the child:
x identifies some of the numbers in the picture
x points to the numbers or letters, or to other things that are not numbers or letters
When the child has finished, point to a mixture of numbers and letters and ask: Is this a number?
Observe whether the child:
x distinguishes which are numbers and which are not
If the child is able to identify the numbers in the picture, then go to the next task, entitled, Finding Numbers.
Foundation 1.1 (a)
Foundation 1.1 (a)
Smith 2014
86
©AICS Numeracy Strategy October 2011 Understand Number: Reading Numbers
Smith 2014
87
©AI
CS N
umer
acy
Stra
tegy
Oct
ober
201
1
Unde
rsta
nd N
umbe
r: Re
adin
g Nu
mbe
rs
Read
ing
Num
bers
: Fou
ndat
ion
1.1
a &
b a)
R
ecog
nise
s N
umbe
rs: R
ecog
nise
s nu
mbe
rs in
thei
r env
ironm
ent
b)
Find
ing
Num
bers
: D
istin
guis
hes
num
bers
from
oth
er w
ritte
n sy
mbo
ls
NAM
E Fo
unda
tion
1.1
a R
ecog
nise
s nu
mbe
rs in
thei
r en
viro
nmen
t
Foun
datio
n 1.
1 b
Dis
tingu
ishe
s nu
mbe
rs fr
om o
ther
sy
mbo
ls
Com
men
ts
1
2
3
4
5
6
7
8
9
10
Smith 2014
88
APPENDIX 17.0
Smith 2014
89
Understanding the Numeration System Saying the Number Sequence: Foundation 1.1– Yr1.1
© AICS Numeracy Strategy October 2011 Understand Number: Saying the Sequence
Oral Count Foundation 1.1–1.1
Purpose Foundation 1.1: To find out whether children can say number names in order to 5.
Foundation 1.2: To find out whether children can say number names in order to 29.
Year 1.1: To find out whether children can say number names in order to 50
Materials None needed
Procedure Ask: Can you count?
If the child responds with ‘yes’, say: Okay, start at one and see how far you can go. If the child responds with ‘no’, say: Let’s count together, one, two … Pause and see whether the child can continue. If they cannot, say three and then pause and see whether they can continue. If they cannot, then you have found out that they do not know the conventional counting sequence.
If students can get started, encourage them to count as far as possible.
Use the proforma to record the last number the child says correctly, and mark them against the checkpoints as follows: Student says number names in order to 5
Foundation 1.1 checkpoint
Student says number names in order to 29
Foundation 1.2 checkpoint
Student says number names in order to 50
Year 1.1 checkpoint
Smith 2014
90
© AI
CS N
umer
acy
Stra
tegy
Oct
ober
201
1
Unde
rsta
nd N
umbe
r: Sa
ying
the
Sequ
ence
Ora
l Cou
nt
Foun
datio
n 1.
1: S
ays
num
ber n
ames
in o
rder
to 5
Fo
unda
tion
1.2:
Say
s nu
mbe
r nam
es in
ord
er to
29
Year
1.1
: Say
s nu
mbe
r nam
es in
ord
er to
50
NAM
E La
st n
umbe
r sa
id in
cor
rect
or
der
Ove
r 5?
(F 1
.1 le
vel)
Ove
r 29?
(F 1
.2 le
vel)
Ove
r 50?
(Yea
r 1.1
leve
l) Co
mm
ents
1
2
3
4
5
6
7
8
9
10
11
12
Smith 2014
91
APPENDIX 18.0
Smith 2014
92
Understanding the Numeration System Subitising and Partitioning: 1.2–2
©AICS Numeracy Strategy October 2011 Understand Number: Subitising & Partitioning
How Many Ways? Years 1.2–2
Purpose Year 1.2: To find out whether children can partition numbers, using materials or drawings (numbers up to 20). Year 2: To find out whether children can partition numbers, using visualisation or mental strategies.
Materials The following recording sheet (one for each child)
Picture sheet and materials such as counters (Year 1.2 level)
Procedure Ask the child to show all the different ways they could put 16 monkeys in two trees.
Say: There are 16 monkeys jumping around in the jungle. When a crocodile comes, they will all climb up into two trees. There are lots of different ways the monkeys could be split up. We need to try and find all the ways.
Emphasise the need to find many different possibilities. You could say: There might be big mobs of monkeys in this tree, and only a little bit in the other tree. Or there might be about the same. There are lots of different ways.
At first, just give the child the recording sheet and encourage them to try and partition the numbers mentally. If they struggle, provide them with the picture and materials.
If a child successfully completes the task using materials, you may like to try this task again without materials on another day. You could use a different number or story.
Use the proforma to record the strategies the child uses and mark them against the following checkpoints.
Observe whether the child: uses materials or drawings, then counts and records their partitions
Year 1.2 checkpoint
uses mental partitioning strategies, moving one from the first number to the second, and/or basic facts to find many different combinations
Year 2 checkpoint
Smith 2014
93
Name: ___________________ Year level: __________ Date: _______________
©AICS Numeracy Strategy October 2011 Understand Number: Subitising & Partitioning
How Many Ways? How many different ways can the monkeys climb into the two trees? Write all the answers you can find in the spaces below.
Smith 2014
94
©AI
CS N
umer
acy
Stra
tegy
Oct
ober
201
1 U
nder
stan
d Nu
mbe
r: Su
bitis
ing
& Pa
rtitio
ning
Smith 2014
95
©AI
CS N
umer
acy
Stra
tegy
Oct
ober
201
1 U
nder
stan
d Nu
mbe
r: Su
bitis
ing
& Pa
rtitio
ning
How
Man
y W
ays?
Y
ear
1.2:
Par
titio
ns n
umbe
rs to
20
usin
g m
ater
ials
or d
raw
ings
Y
ear
2: P
artit
ions
num
bers
usi
ng v
isua
lisat
ion
or m
enta
l stra
tegi
es
NAM
E M
ater
ials
and
dr
awin
gs
(Yea
r 1.2
)
Bas
ic fa
cts
(man
y di
ffere
nt
com
bina
tions
)
(Yea
r 2)
Mov
ing
one
from
fir
st n
umbe
r to
seco
nd
(Yea
r 2)
Com
men
ts
1
2
3
4
5
6
7
8
9
10
11
12
Smith 2014
96
APPENDIX 19.0
Smith 2014
97
Understanding the Numeration System Understanding Place Value: Year 6
Decimal Models Year 6
Purpose To find out whether students can understand and use place value partitions to three decimal places.
Materials Attached worksheet
Coloured texta or pencil
Procedure This task can be completed with the whole class.
Give each student a worksheet and read through it with them. Ask students to colour the grids to show each of the three decimals, 1.9, 0.09, 0.009.
Ask students to draw arrows below the number lines to show each of the three decimals, 0.5, 0.05, 0.005, and then write a sentence to explain how each of the decimals is different.
1.9: students need to circle or colour one complete grid, and then 90 squares out of 100 on the second grid.
0.09: students need to colour 9 out of 100 squares on the grid.
0.009: students need to colour 9/10 of one square on the grid.
Evidence of Year 6 checkpoint
0.5: students need to draw an arrow showing the halfway mark between the 0 and the 1.
0.05: students need to show halfway between the zero and the first unit (line).
0.005: students need to think of finding one-tenth of the first unit, and then drawing an arrow to show half of this one-tenth.
Evidence of Year 6 checkpoint
Explanation: Students may say that 0.05 is half of the first unit, and that 0.005 is half of one-tenth of this unit.
Students may use the decimal place names to locate the numbers. For example, 0.05 is 5 hundredths, which is part of one tenth.
They might also say that 0.005 is 10 times smaller than 0.05.
Evidence of Year 6 checkpoint
Smith 2014
98
©AICS Numeracy Strategy October 2011 Understand Number: Place Value
Decimal Models Name _____________________________________ Date ______________
Colour the grids below to show these decimals:
1.9 0.09 0.009
Smith 2014
99
©AI
CS N
umer
acy
Stra
tegy
Oct
ober
201
1 Un
ders
tand
Num
ber:
Plac
e Va
lue
Deci
mal
Mod
els
Nam
e _
____
____
____
____
____
____
____
____
____
Dat
e _
____
____
____
_
On
the
num
ber l
ine
belo
w, u
se a
n ar
row
↓ to
sho
w th
ese
deci
mal
s:
0.
5
0.0
5
0.0
05
0
1
Wha
t is
the
diffe
renc
e be
twee
n 0.
5, 0
.05
and
0.00
5?
W
rite
a se
nten
ce to
exp
lain
.
#
Smith 2014
100
©AI
CS N
umer
acy
Stra
tegy
Oct
ober
201
1 Un
ders
tand
Num
ber:
Plac
e Va
lue
Deci
mal
Mod
els:
Yea
r 6
Und
erst
ands
and
use
s pl
ace
valu
e pa
rtitio
ns fo
r dec
imal
num
bers
to th
ree
plac
es
Nam
e Da
te
1.9
0.
09
0.0
09 0
.5
0.0
5
0.00
5 Ex
plan
atio
n Co
mm
ents
(n
ote
the
stra
tegi
es u
sed
by s
tude
nts)
Smith 2014
101
APPENDIX 20.0
Smith 2014
102
Understanding the Numeration System Writing Numbers: Years 2–6
©AICS Numeracy Strategy October 2011 Understand Number: Writing Numbers
Writing Numbers Years 2–6
Purpose Year 2: To find out whether students can write whole numbers up to 999 and simple decimal numbers involving money. Year 3: To find out whether students can write whole numbers up to 9 999 and decimal numbers involving money. Year 4: To find out whether students can write whole numbers up to 999 999 and decimal numbers involving money and measures. Year 5: To find out whether students can write whole numbers into the millions and decimals to two places. Year 6: To find out whether students can write decimal numbers to three places.
Materials Answer sheet Pre-organised task for students exiting the task early
Procedure Call out the numbers in order of the year level (see tables below).
Ask students to write the correct number onto their answer sheet.
Say: I am going to read out some numbers and would like you to write them on your answer sheet. Listen carefully to what I say … e.g. (see tables) In the Triangle column, I would like you to write the number eighty-nine. Give students time to think and then repeat the number.
When students make two errors, ask them to stop and go on with a pre-organised task.
Observe whether the child is able to write the numbers correctly:
x up to 999 and simple decimal numbers involving money
x up to 9 999 and decimal numbers involving money
x up to 999 999 and decimals involving money and measures
x into the millions, including decimals to two places
x decimals up to three places
Note: If students write 6 250.05 (Year 6) or 61.005, 1.012 (Year 7) as fractions, then ask: Can you write this as a decimal?
Year 2 checkpoint
Year 3 checkpoint
Year 4 checkpoint
Year 5 checkpoint
Year 6 checkpoint
Smith 2014
103
©AICS Numeracy Strategy October 2011 Understand Number: Writing Numbers
Year 2 Say:
1. 89 eighty-nine
2. 101 one hundred and one
3. 213 two hundred and thirteen
4. 790 seven hundred and ninety
5. 818 eight hundred and eighteen
6. $307 three hundred and seven dollars
7. $1.50 one dollar fifty
Year 3 Say:
1. 1 004 one thousand and four
2. 2 019 two thousand and nineteen
3. 5 106 five thousand, one hundred and six
4. 7 013 seven thousand and thirteen
5. 9 098 nine thousand and ninety-eight
6. $13.15 thirteen dollars and fifteen cents
7. $23.65 twenty-three dollars and sixty-five cents
Year 4 Say:
1. 15 099 fifteen thousand and ninety-nine
2. 95 501 ninety-five thousand, five hundred and one
3. 150 000 one hundred and fifty thousand
4. 705 804 seven hundred and five thousand, eight hundred and four
5. $106.25 one hundred and six dollars and twenty-five cents
6. $15.05 fifteen dollars and five cents
7. 10.5 m ten point five metres
Smith 2014
104
©AICS Numeracy Strategy October 2011 Understand Number: Writing Numbers
Year 5 Say:
1. 1 000 101 one million, one hundred and one
2. 53 201 099 fifty-three million, two hundred and one thousand and ninety-nine
3. 8 063 969 eight million and sixty-three thousand, nine hundred and sixty-nine
4. 12 003 003 twelve million, three thousand and three
5. 56.23 secs fifty-six point two three seconds
6. $86.02 eighty-six dollars and two cents
7. 6 250.05 six thousand, two hundred and fifty and five hundredths
Year 6 Say:
1. 3.233 three point two three three
2. 61.005 sixty-one and five thousandths
3. 0.102 zero point one zero two
4. 1.012 one and twelve thousandths
Smith 2014
105
©AICS Numeracy Strategy October 2011 Understand Number: Writing Numbers
Answer Sheet Name: _________ Grade: _______
1.
1. 1.
2.
2. 2.
3.
3. 3.
4.
4. 4.
5.
5. 5.
6.
6. 6.
7.
7. 7.
1. 1.
2. 2.
3. 3.
4. 4.
5.
6.
7.
Smith 2014
106
©AI
CS N
umer
acy
Stra
tegy
Oct
ober
201
1
Unde
rsta
nd N
umbe
r: W
ritin
g Nu
mbe
rs
Writ
ing
Num
bers
: Yea
rs 2–6
Y
ear 2
: Writ
es w
hole
num
bers
up
to 9
99 a
nd s
impl
e de
cim
al n
umbe
rs in
volv
ing
mon
ey
Yea
r 3: W
rites
who
le n
umbe
rs u
p to
9 9
99 a
nd d
ecim
al n
umbe
rs in
volv
ing
mon
ey
Yea
r 4: W
rites
who
le n
umbe
rs u
p to
999
999
and
dec
imal
num
bers
invo
lvin
g m
oney
and
mea
sure
s Y
ear 5
: Writ
es w
hole
num
bers
into
the
mill
ions
and
dec
imal
s to
two
plac
es
Yea
r 6: W
rites
dec
imal
num
bers
to th
ree
plac
es
NAM
E DA
TE
Year
2
Year
3
Year
4
Year
5
Year
6
Com
men
ts
Smith 2014
107
APPENDIX 21.0
Smith 2014
108
WU
LUN
GA
RR
A C
OM
MU
NIT
Y S
CH
OO
L
E
DU
CA
TIO
N S
UPP
OR
T PL
AN
- 2
014
I
NSE
RT
PH
OT
O H
ER
E
Th
e E
duca
tion
Sup
port
Pla
n is
a d
ocum
ent u
sed
to re
cord
any
adj
ustm
ents
the
scho
ol/te
ache
r is
curr
ently
mak
ing
to a
ssis
t the
iden
tifie
d st
uden
t to
achi
eve
succ
ess.
Th
is d
ocum
ent w
ill id
entif
y ad
just
men
ts m
ade
in th
e fo
llow
ing
area
s:
- C
urric
ulum
-
Com
mun
icat
ion
- S
ocia
l par
ticip
atio
n/em
otio
nal w
ell b
eing
-
Hea
lth a
nd p
erso
nal c
are
- S
afet
y -
Lear
ning
env
ironm
ent/a
cces
s Th
e cl
assr
oom
teac
her w
ill id
entif
y ar
eas
for a
djus
tmen
t in
cons
ulta
tion
with
spe
cial
ists
and
sup
port
staf
f. Th
is is
a c
olla
bora
tive
proc
ess
and
incl
udes
the
pare
nt/c
areg
iver
. C
lass
room
Tea
cher
: Thi
s do
cum
ent s
houl
d be
upd
ated
at t
he b
egin
ning
and
end
of e
ach
term
(at a
min
imum
) in
cons
ulta
tion
with
the
Prin
cipa
l and
Sup
port
Sta
ff.
NA
ME
OF
ST
UD
EN
T
TE
AC
HE
R
YE
AR
LE
VE
L
Smith 2014
109
2
C
RIT
ICA
L IN
FOR
MA
TIO
N
TEA
CH
ER O
BSE
RVA
TIO
NS/
AN
ECD
OTA
L EV
IDEN
CE:
PL
EASE
ATT
AC
H A
NY
SUPP
OR
TIN
G D
OC
UM
ENTA
TIO
N A
FTER
TH
IS P
AG
E (A
LSO
IDEN
TIFY
AN
D IN
CLU
DE
CO
NTA
CT
DET
AIL
S/C
OR
RES
PON
DEN
CE
FOR
AN
Y PE
RSO
NS
INVO
LVED
IN C
ON
SULT
ATI
ON
)
Smith 2014
110
3
Impa
cts
on le
arni
ng
Ada
ptat
ions
Mad
e
TE
AC
HER
CO
MM
ENTS
:
Smith 2014
111
4
AIM
S/G
OA
LS
St
uden
t Com
pete
ncie
s
(E.G
. acr
oss
curr
icul
um –
wha
t is
this
stu
dent
goo
d at
) Id
entif
ied
Goa
ls/A
spira
tions
(E
.G. w
hat a
re th
e go
als
for t
his
stud
ent)
Goa
ls/A
spira
tions
K
ey S
trat
egie
s fo
r Goa
l Ach
ieve
men
t
Smith 2014
112
5
SUM
MA
RY
OF
OU
TCO
MES
FO
R T
HIS
TER
M: C
omm
ents
to d
iscu
ss im
pact
of a
dapt
atio
ns m
ade
and
wha
t wor
ked
or n
eeds
reth
inki
ng/m
odifi
catio
n
__
____
____
____
____
____
___
___
____
____
____
____
____
____
_
___
____
____
____
____
____
_
Cla
ssro
om T
each
er
P
rin
cip
al
D
ate