The Primary Years Programme (PYP) views mathematics not as a fixed body of knowledge to be transmitted, but as a way of thinking and a language for understanding meaning. Traditionally, mathematical knowledge has been disassembled in schools broken into unrelated skills-based activities. Our vastly expanded knowledge base about learning mathematics however, tells us that people assemble, or construct, mathematical knowledge. This requires us to look at mathematics not as a fixed body of knowledge to be transmitted, but as a language and a way of thinking. By engaging in various activities and discussions, students construct meaning, using multiple strategies, developing an understanding of which strategies are most effective and efficient.
Cognitive psychologists have described the stages through which children learn
mathematics:
Constructing meaning |
Transferring meaning into signs and symbols |
Understanding and applying |
Teachers plan activities, through which students construct meaning from direct experience, by using manipulatives and conversation. |
Teachers connect the notation system with the concrete objects and associated mathematical processes. The teacher provides the symbols for the students. Students begin to describe their understanding using signs and symbols. |
Teachers plan authentic activities in which students independently select and use appropriate symbolic notation to process and record their thinking. |
The
following expectations are arranged in five interwoven strands of knowledge.
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These are the expectations for each year group in Mathematics
Number |
Pattern and function |
Data handling |
Measurement |
Shape and Space |
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The students in Early childhood will: |
Read, write and model numbers to 20
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Find and describe simple patterns
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Sort and label real objects into sets by attributes
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Identify, compare and describe attributes of real objects and situations: longer, shorter, heavier, empty, full, hotter, colder
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Sort, describe and compare 3-D shapes according to attributes such as size or form
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Number |
Pattern and function |
Data handling |
Measurement |
Shape and Space |
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The students in Year 1 will: |
Begin to read, write and order all numbers from 0 to 100;
Understand and use the vocabulary of comparing and ordering these numbers Count forwards and backwards from any small number, and in fives and tens from zero to one hundred
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Create, describe and extend patterns
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Solve simple problems by sorting, classifying and organizing information in various ways
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Estimate, measure, label and compare using non-standard units of measurement: length, mass or capacity
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Use everyday language to describe features of familiar 3-D and 2-D shapes
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Number |
Pattern and function |
Data handling |
Measurement |
Shape and Space |
|
The students in Year 2 will: |
Count, read, write and order whole numbers to at least 100; know what each digit represents (including 0 as a place holder). Read,
write and model numbers, using the base 10 system.
Read, write and model addition and subtraction to 20 (with and without
Understand that subtraction is the inverse of addition.
Use knowledge that addition can be done in any order to do mental calculations
more efficiently.
Understand the operation of multiplication as repeated addition or as
describing an array in real world contexts, using manipulatives, diagrams,
and symbols. Use fraction names (half and quarter) to describe part and whole relationships. |
Create,
describe and extend patterns.
Recognize, describe and extend patterns in numbers: odd and even, skip
counting, 2s, 5s and 10s, counting on, counting back. Explore patterns in fact families.
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Record,
organize, classify, display and understand data in a variety of simple
ways
Discuss, interpret and compare data represented in teacher generated
diagrams: tree, Carroll and Venn
Understand the purpose of graphing data
Create a pictograph and simple bar graph from a graph of real objects,
and interpret data by comparing quantities: more, fewer, less than,
greater than Discuss, identify, predict and place outcomes in order of likelihood: impossible, unlikely, likely, certain |
Estimate, measure and compare lengths, masses and capacities, using standard units Understand
why we use standard units of measurement to measure
Use a calendar to determine the date and to identify and sequence days
of the week and months of the year
Read a simple scale to the nearest labelled division, including using
a ruler to draw and measure lines to the nearest centimetre
Estimate, identify and compare lengths of time, second, minute, hour,
day, week, month Read and write the time to the hour, half hour and quarter hour |
Use the mathematical names for common 2-D and 3-D shapes; sort shapes and describe some of their features
|
Number |
Pattern and function |
Data handling |
Measurement |
Shape and Space |
|
The students in Year 3 will: |
Read, write and order numbers to 1000 and understand what each digit represents
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Choose and use appropriate operations to solve word problems, explaining methods and reasoning
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Discuss, compare and create sets from data that has subsets using tree, Carroll, Venn and other diagram
Collect and display data in a bar graph and interpret results
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Read and write the time to the minute using intervals of fifteen minutes, ten minutes and five minutes on a 12-hour clock
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Identify right angles
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Number |
Pattern and function |
Data handling |
Measurement |
Shape and Space |
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The students in Year 4 will: |
Read, write and model numbers, using the base 10 system, to 1000
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Analyse patterns in number systems to 100
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Discuss, compare and create sets from data that has subsets using tree, Carroll, Venn and other diagrams
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Estimate, measure, label and compare using formal methods and standard units of measurement: length, mass, time and temperature
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Sort, describe and model regular and irregular polygons: triangles, hexagons, trapeziums
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Number |
Pattern and function |
Data handling |
Measurement |
Shape and Space |
|
The students in Year 5 will: |
Read,
write and model numbers using base ten system up to one million
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Recognise,
describe and extend more complex patterns in numbers
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Design surveys and collect, organise and record data in displays
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Estimate,
measure, label and compare length, mass, time, temperature
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Combine and transform 2-D shapes to make another shape
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Number |
Pattern and function |
Data handling |
Measurement |
Shape and Space |
|
The students in Year 6 will: |
Read, write and model numbers to one million and beyond
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Understand and use the relationship between the four operations
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Display and interpret data in a variety of ways, compare data display
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Estimate, measure, label and compare perimeter, area and volume
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Use the mathematical vocabulary of 2-D and 3-D shapes and angles
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Demonstrations of deeper learning in responsible behaviour through positive action and service; a manifestation in practice of the other essential elements | Powerful ideas which have relevance within and across the disciplines and which students must explore and re-explore in order to develop understanding | Significant, relevant, subject matter which students are expected to explore and know about Click here to find out more about the 6 themes Click here to find out more about the 6 subject areas
| Those things which the students need to be able to do to succeed in a changing, challenging world | Dispositions which are expressions of fundamental values, beliefs and feelings about learning, the environment and people |
updated 16 fÈvrier, 2007