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 skillsbased 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.

These are the expectations for each year group in Mathematics
Number 
Pattern and function 
Data handling 
Measurement 
Shape and Space 

The students in Early childhood will: 
Read, write and model numbers to 20

Find and describe simple patterns

Sort and label real objects into sets by attributes

Identify, compare and describe attributes of real objects and situations: longer, shorter, heavier, empty, full, hotter, colder

Sort, describe and compare 3D shapes according to attributes such as size or form

Number 
Pattern and function 
Data handling 
Measurement 
Shape and Space 

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

Create, describe and extend patterns

Solve simple problems by sorting, classifying and organizing information in various ways

Estimate, measure, label and compare using nonstandard units of measurement: length, mass or capacity

Use everyday language to describe features of familiar 3D and 2D shapes

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.

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 2D and 3D 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

Choose and use appropriate operations to solve word problems, explaining methods and reasoning

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

Read and write the time to the minute using intervals of fifteen minutes, ten minutes and five minutes on a 12hour clock

Identify right angles

Number 
Pattern and function 
Data handling 
Measurement 
Shape and Space 

The students in Year 4 will: 
Read, write and model numbers, using the base 10 system, to 1000

Analyse patterns in number systems to 100

Discuss, compare and create sets from data that has subsets using tree, Carroll, Venn and other diagrams

Estimate, measure, label and compare using formal methods and standard units of measurement: length, mass, time and temperature

Sort, describe and model regular and irregular polygons: triangles, hexagons, trapeziums

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

Recognise,
describe and extend more complex patterns in numbers

Design surveys and collect, organise and record data in displays

Estimate,
measure, label and compare length, mass, time, temperature

Combine and transform 2D shapes to make another shape

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

Understand and use the relationship between the four operations

Display and interpret data in a variety of ways, compare data display

Estimate, measure, label and compare perimeter, area and volume

Use the mathematical vocabulary of 2D and 3D shapes and angles

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 reexplore 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