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LODGE Education Training & Consultancy Services © 2005
Primary School
Mathematics Syllabus Framework
2005
Edited by: Phil Lodge
LODGE Education Training & Consultancy ServicesIntroduction
Explanatory Notes:
This document is the:
A Primary School Mathematics Syllabus Framework.
The basis of this syllabus is the Ohio, Academic Content Standards K-7 Mathematics Benchmark and Indicators.
The School has adapted the Ohio program and matched it with the Victorian Essential Learning Standards which are also included for each Level.
This is a prescribed program content syllabus for all year level teachers but is not restrictive. Teachers are encouraged and expected to provide learning experiences in addition to and beyond what has been prescribed after the essential aspects of this document have been introduced, reinforced and assessed.
This framework document is to be used as a resource for planning learning and teaching programs and for assessing student performance against the Standards.
Assessment Protocols are also included at the end of each year level program content section. These are to be used as a reference for determining student performance in Primary School Mathematics to ensure rigour, uniformity and consistency in teacher judgements.
The syllabus is a collection of statements and examples which specify:
- Skills, knowledge and understandings (SKUs) which should be taught at each year level and;
- Behavioural expectations for students – which the teacher has facilitated and encouraged as a consequence of instruction and learning experiences provided.
- Enquiries regarding this document should be directed to:
Phillip Lodge: LODGE Education Training & Consultative Services
Phone: Australia - 03 9789 4080, Email:
Maths
LEVEL 1
Learning focus
Standards
Prep
Number Dimension
Measurement, Chance and Data Dimension
Space Dimension
Working Mathematically Dimension
ASSESSMENT PROTOCOLS (Year Prep Level 1)
LEVEL 2
Learning focus
Standards
Year One
Number Dimension
Measurement , Chance and Data Dimension
Space Dimension
Working Mathematically Dimension
ASSESSMENT PROTOCOLS (Year 1 Level 2)
Number -
Year Two
Number Dimension
Measurement, Chance and Data Dimension
Space Dimension
Working Mathematically Dimension
ASSESSMENT PROTOCOLS (Year 2 Level 2)
LEVEL 3
Learning focus
Standards
Year Three
Number Dimension
Measurement, Chance and Data Dimension
Space Dimension
Working Mathematically Dimension
ASSESSMENT PROTOCOLS (Year 3 Level 3)
Year Four
Number Dimension
Measurement Dimension
Space Dimension
Working Mathematically Dimension
ASSESSMENT PROTOCOLS (Year 4 Level 3)
LEVEL 4
Learning focus
Standards
Year Five
Number
Space
Location
Measurement and Data
ASSESSMENT PROTOCOLS (Year 5 Level 4)
Year Six
Number
Space
Location
Measurement and Data
Assessment Protocols (Year 6 Level 4)
LEVEL 5
Year Seven
Number Dimension
Measurement, Chance and Data Dimension
Space Dimension
Working MathematicallyDimension
LEVEL 1
Learning focus
In Number and Space, students manipulate concrete and visual models to develop understanding of the fundamental mathematical concepts and objects of natural number, numeral, shape and location. They relate counting of discrete objects in sets to spatial patterns and arrangements of 1 to 20 objects with physical, visual and written representations including numerals. They apply number to establish sequence and order with respect to the elements of sets and model addition and subtraction by grouping together or by moving apart elements of sets.
They manipulate everyday objects to identify and describe the features of common two- and three-dimensional shapes that correspond to the spatial concepts of point, line, boundary, face, interior and exterior. They follow simple instructions for the location of objects and movement from one place to another in familiar situations. Students learn fundamental concepts related to Measurement, chance and data in situations where they need to measure and compare length, capacity, mass, time and temperature using descriptive terms such as hot or fuller than and/or by counting of informal units such as the length of a row of paperclips. They learn to make and check rough estimates of quantitative measurements. Students begin to recognise unpredictability and uncertainty in chance events such as a game of ‘Snakes and Ladders' and identify and gather data required for a birthday party.
Students learn about fundamental aspects of Structure and Working mathematically by matching elements of different sets according to given instructions, such as one-to-one correspondence in a simple card game of memory, or a many-to-one correspondence between the students in a class and the first letter of their name. They explore patterns in number and space by manipulating objects according to simple rules and test the truth or otherwise of simple conjectures with respect to number, shape, pattern, measurement and data, simple time structures and the sequence of daily events. Students work with calculators to check the results of simple addition and subtraction and use drawing tools and geometry software to create and colour simple two-dimensional geometric shapes and visual patterns and composite objects based on these shapes.
In learning activities at Level 1, Structure provides notions of set, logic, function and algebra fundamental to the development of mathematical concepts, skills and processes in Number, Space, Measurement, chance and data and Working mathematically. The related s for Structure are embedded across these dimensions to underpin an integrated approach to student learning.
Standards
Number
At Level 1 students:
- construct small sets of objects and elements according to simple descriptions and form correspondences between these sets based on simple relationships.
- use one-to-one correspondence to identify when two sets are equal in size or when one set is larger than another set or smaller than another set.
- form collections of sets of equal size.
- place sets in sequence of increasing size and use the numbers 0 to 20 to count and to determine the size of a given set, including zero for the empty set.
- describe the position of an element in an ordered set using ordinal numbers up to ten.
- use materials to model addition and subtraction by the aggregation (grouping together) and dis-aggregation (moving apart) of elements in sets.
- add and subtract by counting forward and backward using the natural numbers from 0 to 20.
Space
At Level 1 students:
- recognise, copy and draw points, lines and simple free-hand curves and identify interior and exterior, edges; basic two-dimensional shapes such as triangles, circles and squares and basic three-dimensional solids and objects such as boxes and balls.
- use attributes of shapes to construct small sets of geometric objects according to simple descriptions and form correspondences between these sets based on simple relationships.
- place and orientate shapes according to simple descriptions of relative location such as next to, beside, in front of, behind, over, under, and give and follow simple directions for locating an object and for movement from one place to another over a short distance.
- develop and follow simple instructions to move and place shapes and objects in familiar situations in relation to what they can see, and to move themselves from one place to another.
Measurement, Chance and Data
At Level 1 students:
- measure and compare length, area, capacity and mass in relation to various familiar objects that are seen and handled using descriptive terms and/or informal units such as the length of a line segment using steps or paces, simple area covered such as a shape by two handprints, the capacity of containers such as half a glass of water, the weight of common objects such as a heavy schoolbag and duration such as the number of days until a birthday.
- recognise the flow and continuity of time and the use of natural cycles such as day/night, the seasons, and informal units such as heartbeats and hand claps at regular intervals to segment and describe the passage of time.
- recognise and respond to unpredictability and variability in events, such as getting or not getting a certain number on the roll of a die in a game.
- identify and describe the outcomes of simple chance events such as the toss of a coin, and collect and display these using simple pictograph data related to their own activities which may include games or events such as a birthday party.
Working Mathematically
At Level 1 students:
- make and test simple conjectures such as ‘the larger an object the heavier it is', ‘it is likely to rain after school today' and ‘nine is four more than five'.
- make rough estimates and check their work with respect to computations and constructions in Number, Space, Measurement, chance and data and Structure.
- devise and follow ways of recording computations involving the use of materials, mental calculations and the digit keys and +, - and = keys on a four function calculator.
- use drawing tools such as simple shape templates and geometry software to draw points, lines, shapes and simple patterns and to copy a picture of a simple composite shape such as a child's sketch of a house using these shapes.
In this domain, s for the Structure dimension are introduced at Level 3.
Prep
Number Dimension
Number and Number SystemsMeaning of Operations
Computation and Estimation /
- Compare and order whole numbers to 20.
- Explain rules of counting, such as each object should be counted once and that order does not change the number.
- Count to twenty; e.g., in play situations or while reading number books.
- Determine “how many” in sets (groups) of 10 or fewer objects.
- Relate, read and write numerals for numbers (0 to 20).
- Construct multiple sets of objects each containing the same number of objects.
- Compare the number of objects in two or more sets when one set has one or two more, or one or two fewer objects.
- Represent and use whole numbers in flexible ways, including relating, composing and decomposing numbers; e.g., 5 marbles can be 2 red and 3 green or 1 red and 4 green.
- Identify and state the value of all coins.
- Model and represent addition as combining sets and counting on, and subtraction as take-away and comparison. For example:
- Combine and separate small sets of objects in contextual situations; e.g., add or subtract one, two, or another small amount.
- Count on (forward) and count back (backward) on a number line between 0 and 10.
- Demonstrate joining multiple groups of objects, each containing the same number of objects; e.g., combining 3 bags of candy, each containing 2 pieces.
- Partition or share a small set of objects into groups of equal size; e.g., sharing 6 stickers equally among 3 children.
- Recognize the number or quantity of sets up to 5 without counting; i.e conservation, e.g., recognize without counting the dot arrangement on a domino as 5.
Measurement, Chance and Data Dimension
Measurement UnitsUse Measurement Techniques and Tools
Data Collection
Statistical Methods
Probability /
- Identify units of time (day, week, month, year) and compare calendar elements; e.g., weeks are longer than days.
- Compare and order objects of different lengths, areas, weights and capacities; and use relative terms, such as longer, shorter, bigger, smaller, heavier, lighter, more and less.
a.how many paper clips long is a pencil;
b.how many small containers it takes to fill one big container using sand, rice, beans.
4. Order events based on time. For example:
a.activities that take a long or short time;
b.review what we do first, next, last;
- recall what we did or plan to do
5. Tell the time using analogue and digital
clocks – hour (o’clock) and half hour.
1. Gather and sort data in response to questions posed by teacher and students; e.g., how many sisters and brothers, what color shoes.
2. Arrange objects in a floor or table graph according to attributes, such as use, size, color or shape.
3. Select the category or categories that have the most or fewest objects in a floor or table graph.
- Identify and describe the outcomes of simple chance events such as the toss of a coin.
- Collect and display data using simple pictograph data related to their own activities which may include games or events such as a birthday party.
Space Dimension
Characteristics and PropertiesSpatial Relationships / 1. Identify and sort two-dimensional shapes and three-dimensional objects. For example:
a.Identify and describe two-dimensional figures and three-dimensional objects from the environment using the child’s own vocabulary.
b.Sort shapes and objects into groups based on student-defined categories.
c.Select all shapes or objects of one type from a group.
d.Build two-dimensional figures using paper shapes or tangrams; build simple three-dimensional objects using blocks.
2. Name and demonstrate the relative position of objects as follows:
a. place objects over, under, inside, outside, on, beside, between, above, below, on top of, upside-down, behind, in back of, in front of;
- describe placement of objects with
Working Mathematically Dimension
Use Patterns, Relations and FunctionsUse Algebraic Representations / 1. Sort, classify and order objects by size, number and other properties. For example:
- Identify how objects are alike and different.
- Order three events or objects according to a given attribute, such as time or size.
- Recognize and explain how objects can be classified in more than one way.
- Identify what attribute was used to sort groups of objects that have already been sorted.
3. Describe orally the pattern of a given sequence.
4. Model a problem situation using physical materials.
ASSESSMENT PROTOCOLS (Year Prep Level 1)
Abbreviation and Terminology Key:
In Italics: ‘Primary Assessment Measure’ – to be initial and foremost measurement criteria for assessing student performance against Assessment Focus.
# SKUs: Skills, Knowledge and Understandings detailed in this Syllabus Framework. To be regarded by teacher when making ‘on-balance’ judgements about student performance.
- The Assessment Protocols are not a complete assessment tool for classroom teachers.
- The Protocols do not cover all dimensions of the Standards or the school Mathematics Syllabus.
- Those dimensions that are not included in the Protocols, as well as more detailed aspects of the Mathematics Syllabus, will be assessed cumulatively by the classroom teacher and form a basis on which the classroom teacher will make final, on-balance judgements about a student’s performance.
- The Performance Measures in these Protocols are the essential and readily assessable aspects of the Number and Measurement and Chance and Data Dimensions. These are the two dimensions which are required for systemic school data processing and student reporting purposes.
- The intention of these Protocols is to provide a consistent framework for student assessment in these two dimensions across all year levels of the school.
- Teachers at each year level will devise and apply Common Assessment Tasks which specifically focus on the aspects of mathematics detailed in these protocols.
Mathematics
ASSESSMENT FOCUS / PERFORMANCE MEASURES / Weight1 / Number - Knowledge and understanding of relationships between ordinal and cardinal number, numerals and
numeration.
Operations- addition,
Subtraction.
Operations-multiplication, division
Working Mathematically – Operations and Applications) – apply knowledge of number operations and processes
Spatial Awareness – awareness of relative relationships and position.
Properties of Shapes /
- Counts, recognises, models and writes numerals to 20, and words to 10.
- Makes, counts, records and estimates size of small collection of objects.
- Orders and compares collections of objects.
- Counts forwards and backwards to 20.
- Performs and describes simple mental calculations – “more than, less than, bigger than, smaller than, longer than, shorter than, shortest” etc..
- Copies and repeats counting patterns.
- Models and describes appropriately groupings of objects – e.g. “three groups of two”.
- Understands concept of ‘0’..
- Solve simple addition and subtraction problems within the counting range of 0 –20.
- Count on to solve addition problems, modelling with materials.
- Count back to solve subtraction problems, modelling with materials.
- Verbally explains mathematical strategies involved.
- Joins multiple groups, shares into equal groups a small number of objects.
- Can join together a small number of equal groups to find total.
- Share a small number of objects equally.
- Can discuss, describe and model addition and subtraction concepts.
- Verbally explains mathematical strategies involved.
- Draws conclusions based on logical reasoning.
- Uses concrete materials, objects, etc to model addition and subtraction concept.
- Describes consequences of adding to or taking away from as more or less, bigger or smaller etc.
- Describes collections of objects as more or less than, and can equalise by adding to or taking away.
- Appropriately describes objects relative to position or proximity.
- Conceptualisation of over, under, next to after, near, far, inside, outside etc.
- Demonstrates relationship between characteristics of 2 and 3 D shapes.
- Draw and name 2D shapes
- Use 2D paper shapes to represent 3D objects.
- Cover given area with designated shape.
15%
5%
2 / Measurement, Chance and Data – is aware of basic time, linear and area size and relationships in life situations. /
- Can describe, discuss and apply understanding of time, size and length to every day situations.
- Understands concept of time and relationship to clocks for daily activities e.g. Play, lunch, home time, dinner, bedtime etc.
- Understands relativity of hours, days and weeks.
- Recognises analogue time on the hour and half past.
- Is aware of months and seasons.
- Aware of age in terms of years.
- Can model and describe objects and areas in terms of long, longer, short, small etc.
- Understands and can describe area in special describers – wide, long, little, big, smaller than etc.
- Understands the concept of what happens next, what might or could happen next e.g. toss of coin, repetition as in patterns/sounds/actions etc.
- Can interpret pictographs.
- Contribute to simple class data collection and graphing.
- Answer questions based on data shown in graphs.
- Recognise chance or variability in events.
- Can use language of chance in everyday situations.
5%
5%
LEVEL 2