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Mathematics Overview

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.

In number and pattern and function, students inquire into our number system, and its operations, patterns and functions.

The remaining strands, data handling, measurement and shape and space, are the areas of mathematics that other disciplines use to research, describe, represent and understand aspects of their domain.

These are the expectations for each year group in Mathematics

Jump to the expectations for Early Childhood    Year 1    Year 2    Year 3    Year 4     Year 5     Year 6
           

Number

Pattern and function

Data handling

Measurement

Shape and Space

The students in

Early childhood

will:

Read, write and model numbers to 20


Count, compare and order numbers to 20


Estimate quantities to 10


Use ordinal numbers to describe the position of things in a sequence


Model number relationships to 10: “Show me one more than three, take two cubes away from these cubes”


Use language of mathematics: more, less, number names, total


Use 1:1 correspondence


Explore the conservation of number through the use of manipulatives (xxxx = x x x x)


Select and explain an appropriate method for solving a problem

Find and describe simple patterns


Create simple patterns using real objects

 

 

Sort and label real objects into sets by attributes


Create a graph of real objects and compare quantities using number words


Discuss and identify outcomes that will happen, won’t happen and might happen

 

Learning to count

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


Identify, compare and sequence events in their daily routine: before, after, bedtime, storytime, today, tomorrow

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


Explore and describe the paths, regions and boundaries of their immediate environment (inside, outside, above, below) and their position (next to, behind, in front of, up, down)

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


Estimate quantities to 50


Understand the operation of addition, and of subtraction (as 'take away' or 'difference'), and use the related vocabulary and symbols


Begin to memorize simple number facts


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 by 5s and 10s


Identify simple patterns and rules for addition and subtraction

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


Discuss, interpret and compare data represented in teacher generated diagrams: tree, Carroll and Venn
Begin to understand the purpose of graphing data

 

 

data gathering Year 1

Estimate, measure, label and compare using non-standard units of measurement: length, mass or capacity


Begin to understand why we use standard units of measurement to measure


Use a calendar to determine the date and to identify and begin to sequence days of the week and months of the year


Tell time to the hour

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


Sort and label 2D and 3D shapes using appropriate vocabulary: sides, corners, circle, sphere, cube


Create 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
regrouping).

Understand that subtraction is the inverse of addition.
? Recall addition and subtraction facts to 10.

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.

 

 

patterns

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

pattern Year 2

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


Find and explain symmetry in their immediate environment


Create and explain simple symmetrical patterns


Use mathematical vocabulary to describe position, direction and movement

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


Estimate quantities to at least 100


Count on or back in tens or hundreds from any two- or three-digit number
Count in 3s, 4s, 5s, and explore other numbers


Recognize unit fractions such as 1/2, 1/3, 1/4, 1/5, 1/10, and begin to use them to find fractions of shapes and numbers


Add and subtract mentally a 'near multiple of 10' to or from a two-digit number


Reasonably estimate answers to 100, using rounding and approximation


Know by heart all addition and subtraction facts for each number to 20


Know by heart facts for the 2, 3, 4, 5 and 10 multiplication tables

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


Understand and be able to explain the relationship between the number operations., addition and subtraction, multiplication and division


Identify patterns in number systems to 100

 

 

 

graph on water use Year 3

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


Design a survey, process and interpret the data


Solve a given problem by organizing and interpreting numerical data in simple lists, tables and graphs

Collect and display data in a bar graph and interpret results


Use the scale on the vertical axis of a bar graph to represent large quantities

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


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


Select appropriate tools and units of measurement
Begin to understand and use monetary notation

 

number drawing

Identify right angles


Identify lines of symmetry in simple shapes and recognize shapes with no lines of symmetry

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


Count, compare and order numbers to 1000


Estimate quantities to 1000


Count in 3s, 4s, 5s, and explore other numbers


Use number patterns to learn multiplication tables: 1s, 2s, 5s, 10s


Automatically recall basic addition and subtraction facts


Model addition and subtraction equations to 1000 (with and without regrouping)


Use mathematical vocabulary and symbols of multiplication and division: times, divide, product, factors, x ÷


Use and describe multiple strategies to solve addition, subtraction, multiplication and division problems


Read, write and model multiplication and division problems


Compare fractions using manipulatives and using fractional notation


Use mathematical vocabulary and symbols of fractions: numerator, denominator, equivalence


Understand and model the concept of equivalence to 1: two halves = 1, three thirds = 1


Reasonably estimate answers: rounding and approximation


Select and explain an appropriate method for solving a problem

Analyse patterns in number systems to 100


Recognize, describe and extend more complex patterns in numbers


Understand and use the relationship between addition and subtraction: 4 + 3 = 7, 7 – 3 = 4


Identify patterns and rules for multiplication and division: 4 x 3 = 12, 3 x 4 = 12 and 12 ÷ 3 = 4, 12 ÷ 4 = 3


Model, with manipulatives, the relationship between multiplication and division model, with manipulatives, the relationship between multiplication and addition (repeated addition)


Model, with manipulatives, the relationship between division and subtraction
Model multiplication as an array


Understand and use number patterns to solve problems (missing numbers)

 

Fractions

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


Collect and display data in a bar graph and interpret results


Use the scale on the vertical axis of a bar graph to represent large quantities


Find, describe and explain the mode in a set of data and its use
Understand the purpose of a database by manipulating the data to answer questions and solve problems


Use probability to determine mathematically fair and unfair games and to explain possible outcomes

 

representing place value

 

 

 

multiplication squares

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


Select appropriate tools and units of measurement


Describe measures that fall between numbers on a measure scale: 31/2kg, between 4cm and 5cm


Estimate, measure, label and compare perimeter and area


Model addition and subtraction using money


Read and write the time to the minute, using intervals of 10 minutes, 5 minutes and 1 minute, on 12-hour analogue and digital clocks

 

 

clocks

 

 

 

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


Identify, describe and model congruency in 2-D shapes


Combine and transform 2-D shapes to make another shape


Create symmetrical patterns, including tessellation


Identify lines and axes of reflective and rotational symmetry


Understand an angle as a measure of rotation by comparing and describing rotations: whole turn; half turn; quarter turn; north, south, east and west on a compass


Locate features on a grid using coordinates

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

Count, compare and order numbers up to one million


Estimate quantities beyond a thousand


Automatically recall addition, subtraction, multiplication and division facts


Create and solve using multiple strategies, addition, subtraction multiplication and division problems


Use number patterns to solve problems involving larger numbers


Read, write, model and compare fractions
Understand and model equivalence

Reasonably estimate answers using rounding and approximation


Select, explain and defend various methods for solving problems

Recognise, describe and extend more complex patterns in numbers

Model and explain number patterns and use patterns to solve problems


Understand and use the relationship among the four operations - addition, subtraction, multiplication and division


Use real-life problems to create a number pattern following a rule

Design surveys and collect, organise and record data in displays


Create, interpret, discuss and compare data displays

Use a scale on a graph to represent large quantities


Find, describe and explain the mode in a set of data


Discuss, identify, predict and place outcomes in order of likelihood: impossible, unlikely, likely and certain

Fraction equivilants

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

Select and use appropriate standard units of measurement


Use measuring tools accurately


Develop procedures for finding perimeter, area and volume

Measure and construct angles in degrees using a protractor


Use and construct time-lines


Read and write the time to the minute and second, using intervals of 10, 5 and 1 minute on twelve and 24-hour clocks

 

 

 

 

 

Combine and transform 2-D shapes to make another shape


Create symmetrical patterns, including tessellation


Identify lines and axes of reflective symmetry


Understand that an angle is a measure of rotation


Locate features on a grid using co-ordinates


Use geometric vocabulary of 2-D and 3-D shapes and angles


Classify, sort and label different types of triangles and quadrilaterals


Use a pair of compasses

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


Automatically use number facts


Read, write, model and compare fractions, decimals and percentages
Interchange fractions, decimals and percentages


Add and subtract decimals to the thousandths


Find and use ratios


Read, write and model additional and subtraction of integers


Use exponential notation


Describe strategies to create and solve more complex problems

Understand and use the relationship between the four operations


Model and explain number patterns and use real-life problems to create a number pattern following a rule


Develop, explain and model simple algebraic formulas
Model exponents as repeated multiplication


Understand and use exponents and roots as inverse functions

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


Find, describe and explain the range, mode, median and mean in a set of data
Use a numerical probability scale 0-1 or 1%-100%


Determine theoretical probability of an event and explain why it might differ from the experimental probability

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


Develop procedures for finding perimeter, area and volume


Use the correct tools for any measurement with accuracy


Measure and construct angles in degrees using a protractor


Use and construct 12-hour and 24-hour timetables


Be able to determine time world-wide

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


Classify, sort and label all types of triangles and quadrilaterals


Turn a 2-D net into a 3-D shape and vice versa
Use scale and ratio to enlarge and reduce shapes


Read and plot coordinates in four quadrants

equivalent fractions poster

5concepts

Action

Concepts

Knowledge

Skills

Attitude

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

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updated 16 fÈvrier, 2007