Match, Sort & Compare

Talk about measure and patterns

It’s me 1, 2, 3

Circles and triangles

1, 2, 3, 4, 5

Shapes with 4 sides

Alive in 5

Mass & Capacity

Growing 6, 7, 8

Length, height and time

Building 9 and 10

Explore 3D shapes

To 20 and beyond

How many now?

Manipulate, compose and decompose

Sharing and grouping

Visualise, build and map

Make connections

Place Value
(within 10)

Addition & Subtraction (within 10)

Addition & Subtraction (within 10)

Shape

Place Value (within 20)

Addition & Subtraction
(within 20)

Place Value (within 50)

Length & Height

Mass & Volume

Multiplication & Division

Fractions

Position & Direction

Place Value (within 100)

Money

Time

Place Value

Addition & Subtraction

Addition & Subtraction

Shape

Money

Multiplication & Division

Multiplication & Division

Length & Height

Mass, Capacity & Temperature

Fractions

Time

Statistics

Position & Direction

Place Value

Addition & Subtraction

Addition & Subtraction

Multiplication & Division

Multiplication & Division

Length & Perimeter

Fractions

Maths & Capacity

Fractions

Money

Time

Time

Shape

Statistics

Place Value

Addition & Subtraction

Addition & Subtraction

Area

Multiplication & Division

Multiplication & Division

Length & Perimeter

Fractions

Decimals

Decimals

Money

Time

Shape

Statistics

Position & Direction

Place Value

Addition & Subtraction

Multiplication & Division

Multiplication & Division

Fractions

Multiplication & Division

Fractions

Decimals & Percentages

Decimals & Percentages

Perimeter & Area

Statistics

Shape

Position & Direction

Decimals

Decimals

Negative Numbers

Converting Units

Volume

Place Value

Addition, Subtraction, Multiplication & Division

Fractions

Converting Units

Ratio

Algebra

Decimals

Fractions, Decimals & Percentages

Area, Perimeter & Volume

Statistics

Shape

Position & Direction

Financial Education

Young Enterprise

Mathematical Vocabulary

Communication and Language

We learn to:

• Use a wider range of vocabulary
• Understand ‘why’ questions

We enable this by:

• Adults modelling high expectations of mathematical vocabulary.
• Providing children with opportunities to use mathematical vocabulary in a context relevant to them.

Number and Place Value

Counting

We learn to:

• Recite numbers past 5
• Say one number name for each item in order: 1,2,3,4,5 (one-one principle)
• Know that the last number reached when counting a small set of objects tells you how many there are in total (cardinal principle)

Vocabulary:

count, one, two, three, four, five, all together, total, how many, number, next, forwards, backwards

We learn it by:

• Regularly saying the counting sequence in a variety of playful contexts.
• Saying the counting sequence both forwards and backwards.
• Counting a vast range of objects in different contexts and repeating the last number, including fingers.
• Collecting a number of objects, both mathematical manipulatives and toys.
• Singing songs and rhymes and playing games in relevant contexts.

Identifying Representing and Estimating Numbers

We learn to:

• Recognise with pace up to 3 objects, without having to count them individually (subitising).
• Show finger numbers up to 5.
• Link numerals and amounts.
• Experiment with our own symbols and marks as well as numerals.

Vocabulary:

number, amount, how many, all together, total, match, guess

We learn it by:

• Being provided with small groups of two or three objects and children to tell you how many are in each group.
• Playing games in a range of different contexts.
• Estimating a number of objects before counting to confirm.
• Matching written numbers to amounts in a range of different contexts.
• Recording an amount in our own ways e.g. wooden numerals, number track.

Compare and Order Numbers

We learn to:

• Compare quantities using language; ‘more than’, ‘fewer than’.
• Solve real world mathematical problems with numbers up to 5.

Vocabulary:

different, more than, fewer than, more, less, the same as, solve, amount, quantity

We learn it by:

• Creating different amounts using mathematical manipulatives and other resources.
• Identifying differences between 2 amounts.
• Identifying changes in amounts through stories e.g. The Enormous Turnip
• Using fingers, objects and marks to solve mathematical problems in a familiar and relevant context.

Addition and Subtraction

We learn to:

• Practically add more items to a group.
• Practically take away items from a group.
• Recognise that when we add, we end up with more than we started with.
• Recognise that when we take away, we end up with less than we started with.

New vocabulary taught in Foundation Stage 1

add, more, take away, less, how many, all together

We learn it by:

• Listening to stories and songs in which items are added and taken away.
• Discussing what happens when we add, the amount gets bigger.
• Discussing what happens when we take away, the amount gets smaller.
• Being provided with a range of resources, both inside and outside, to add to and take away from.

Measurement

Describe, Measure, Compare and Solve

We learn to:

• Make comparisons between objects relating to size, length, weight and capacity.

New vocabulary taught in Foundation Stage 1

long, short, same, bigger, smaller, heavy, light, exactly, same, different

We learn it by:

• Being provided with a range of everyday experiences of size changes e.g. when you squeeze a sponge does it stay small? What happens when you stretch Play-Doh?
• Model specific techniques. E.g. When comparing the length of different ribbons, model lining the ends up, straightening them out.

Time

We learn to:

• Begin to describe a sequence of events, real or fictional.

New vocabulary taught in Foundation Stage 1

First, last, then, after, before, earlier, later, morning, afternoon, evening, night-time, today, yesterday, tomorrow.

We learn it by:

• Talking about patterns of events in daily tasks e.g. getting dressed.
• Use of daily visual timetable in classroom, talking through the day as a class. What lesson is next? What lesson is before lunch?
• Discussing the sequence of events in stories.

Properties of Shapes

We learn to:

• Talk about and explore 2D and 3D shapes using informal and mathematical language.
• Select shapes appropriately.
• Combine shapes to make new ones.

New vocabulary taught in Foundation Stage 1

circle, square, rectangle, triangle, cuboids, sides, corners, straight, flat, round, build, make

We learn it by:

• Being encouraged to play freely with blocks, interlocking bricks, shapes, shape puzzles and shape-sorters.
• Creating dens using natural resources.
• Constructing indoors and outdoors.
• Identifying the similarities and differences between different shapes.
• Talking informally about the properties of the shapes being used e.g. pointy, curvy, sharp, and straight.
• Recognising that some shapes are better suited to different jobs when building e.g. flat triangular shapes for a roof, cuboids for towers.
• Discussing how properties of shapes suit the purpose.
• Providing shapes that combine to make other shapes for children to play freely with.
• Being challenged to build increasingly more complex and different constructions.
• Using tidy-up time to match blocks to silhouettes or fit things in containers.

Position and Direction

We learn to:

• Understand position through words alone (with no pointing).
• Describe a familiar route.
• Discuss routes and locations.

New vocabulary taught in Foundation Stage 1

under, above, on top of, next to, beside, over, down, off, on, inside, outside, in front of, behind, below.

We learn it by:

• Discussing position in real contexts e.g. how to move leaves off of the path, sweep water away down the drain.
• Using spatial words in play.
• Recalling the route taken to get to a known location (this could be within school e.g. hall or pond area).
• Participating in obstacle courses, interesting pathways and hiding places and when appropriate describe the route taken and give directions to each other.
• Being provided with complex train tracks with loops and bridges, or water-flowing challenges with guttering that direct the flow to a water tray.
• Listening to stories about journeys such as ‘Rosie’s Walk’.

Patterns

We learn to:

• Talk about and identify the patterns around us.
• Extend and create patterns.
• Notice and correct an error in a repeating pattern.

New vocabulary taught in Foundation Stage 1

pattern, spots, stripes, zig-zag, before, next, make

We learn it by:

• Being exposed to different patterns from different cultures e.g. fabrics, artwork.
• Interacting and play freely with a range of natural and everyday objects and materials, as well as blocks and shapes to make patterns with.
• Continuing patterns and spotting mistakes in patterns.
• Following and inventing movement and music patterns e.g. clap, clap, stamp.

Mathematical Vocabulary

Communication and Language

We learn to:

• Use a wider range of vocabulary
• Use new vocabulary throughout the day

We enable this by:

• Adults modelling high expectations of mathematical vocabulary throughout the day.
• Providing children with opportunities to use mathematical vocabulary in a mathematical context as well as a day-to-day context.
• Encouraging children to ask questions about what they see using mathematical vocabulary.

Number and Place Value

Counting

We learn to:

• Count objects, actions and sounds.
• Count beyond 10.
• Match one number name to each item (one-one principle)
• Understand that the last number of the count indicates the total number in a group.
• Count out a smaller number from a larger group

Pre-taught vocabulary form Foundation Stage 1

count, one, two, three, four, five, all together, total, how many, number, next, forwards, backwards

New vocabulary taught in Foundation Stage 2

count on, count back, missing, six, seven, eight, nine, ten

We learn it by:

• Regularly saying the counting sequence in a variety of playful contexts.
• Saying the counting sequence both forwards and backwards.
• Counting a vast range of objects in different contexts and repeating the last number, including fingers.
• Collecting a number of objects, both mathematical manipulatives and toys.
• Identifying a missing number within a number sequence.
• Counting out a smaller number from a larger group, knowing when to stop. (Cardinal Principle)
• Sing counting songs and number rhymes and read stories involving counting.
• Playing games in a range of different contexts.
• Practicing counting during every day routines e.g. register time, tidy up time.
• Providing images such as number tracks, calendars and hundred squares, inside and outside so children become familiar with 2-digit numbers and can start to spot patterns within them.

Identifying Representing and Estimating Numbers

We learn to:

• Subitise to 5.
• Link the numeral with its cardinal number value.

Pre-taught vocabulary form Foundation Stage 1

number, amount, how many, all together, total, match, guess

New vocabulary taught in Foundation Stage 2

numeral, subitise, estimate, record, quantity, digit, tally

We learn it by:

• Being exposed to small quantities in familiar patterns e.g. dice and random arrangements.
• Playing games which involve quickly revealing and hiding numbers of objects.
• Estimating a number of objects.
• Putting objects into five frames and then ten frames to begin to familiarise children with the tens structure of the number system.
• Showing a number of fingers ‘all at once’ without counting.
• Putting numerals in order alongside dot quantities or tens frames arrangements.
• Play card games such as snap or matching pairs with cards where some have numerals and some have dot arrangements.
• Recording quantities in different ways e.g. tallies, dots and using numeral cards.

Compare and Order Numbers

We learn to:

• Compare numbers
• Order numbers and quantities

Pre-taught vocabulary form Foundation Stage 1

different, more than, fewer than, more, less, the same as, solve, amount, quantity

New vocabulary taught in Foundation Stage 2

greater than, less than, equal to, compare, fewer, between

We learn it by:

• Comparing collections with a very different number of things.
• Comparing collections which are presented in very different ways e.g. objects that are larger, smaller, close together, spread out.
• Comparing collections with the same number of things.
• Correcting mistakes made by adults and explaining why they are wrong.
• Listening to stories in which characters distribute snacks unfairly and we can explain how to correct this.
• Ordering mathematical manipulatives and toys
• Identifying when objects are in the wrong order and correcting this.

Understanding Place Value

We learn to:

• Understand the one more than / one less than relationship between consecutive numbers.
• Explore the composition of numbers to 10.

New vocabulary taught in Foundation Stage 2

more than, less than, add, take away, number bonds, partition, number line

We learn it by:

• Making predictions about what the outcome will be in stories, rhymes and songs if one is added or if one is taken away.
• Seeing ‘staircase’ patterns which show that the next counting number includes the previous number plus one.
• Using manipulatives to physically see one being taken away and one being added.
• Focusing on composition of 2,3,4 and 5 before moving onto larger numbers.
• Seeing a range of visual models of numbers both in familiar patterns and random arrangements. E.g. on a dice 6 = 3 and 3. One hand and one finger = 6. (Conceptual subitising)
• Seeing numbers being physically broken down into 2 parts (partitioning).
• Recombining two sets to make the whole.
• Creating numbers to 10 using different mathematical manipulatives.
• Recognising that numbers can be made up in different ways (number bonds within 10, not just to 10).

Addition and Subtraction

Mental Calculations

We learn to:

• Automatically recall number bonds for numbers 0 – 10.
• Add and subtract one digit numbers.
• Understand that we can swap the order of numbers in an addition number sentence and we will still get the same answer (Commutative Law).
• Recognise that the biggest number in an addition number sentence is the answer.
• Recognise that the biggest number in a subtraction number sentence is at the start.
• Read and write addition and subtraction number sentences.

Pre-taught vocabulary form Foundation Stage 1

add, more, take away, less, how many, all together

New vocabulary taught in Foundation Stage 2

addition, equals, number sentence, total, partition, recombine, sum, plus, difference, subtract, minus

We learn it by:

• Having a sustained focus on each number to 10.
• Playing hiding games with a number of objects in a box/under a cloth.
• Intentionally being given the wrong number of things so we can explain how many more we need.
• Placing objects into a five frame and talking about how many spaces are filled and unfilled.
• Manipulating a variety of resources in a range of different contexts to understand what happens when we add numbers together.
• Having repeated experiences in different contexts to ensure depth of knowledge; with deep understanding comes automaticity.
• Listening to adults modelling the correct mathematical vocabulary when reading number sentences.
• Writing number sentences to describe a story, an image or a practical situation. E.g. There are 3 red pens and 2 blue pens, we have 5 pens altogether (children to know this is 3 + 2 = 5).
• Having visual and practical displays to support children in seeing the different ways of making numbers to 10.
• Play games which involve partitioning and recombining sets. E.g. throw 5 bean bags aiming for a hoop. How many go in and how many do not?

Solve Problems

We learn to:

• Link the number symbol (numeral) with its cardinal number value.
• Explore patterns within numbers to 10.
• Begin to recognise odd and even numbers.
• Begin to recognise double facts within 10.

New vocabulary taught in Foundation Stage 2

pattern, odd, even, half, double, problem, pair, calculate, sets, lots, share

We learn it by:

• Putting objects into ten frames to begin to familiarise ourselves with the tens structure of the number system.
• Manipulating a range of mathematical resources and toys to investigate patterns within 10.
• Using Numicon to recognise odd and even numbers.
• Discussing the pattern of odd and even numbers with 10.
• Sharing objects in a practical context to identify when an amount is odd or even.
• Predicting whether a number will be odd or even and then proving it.
• Understanding that double means 2 sets / lots of something.
• Exploring doubling in a range of different contexts, with deep understanding comes automaticity.
• Beginning to recognise the link between addition and doubling.

Measurement

Describe, Measure, Compare and Solve

We learn to:

• Compare length, weight and capacity.

Pre-taught vocabulary form Foundation Stage 1

longer, shorter, same, bigger, smaller, heavy, light, exactly

New vocabulary taught in Foundation Stage 2

than, longer, shorter, heavier, lighter, full, empty, half full, compare, accurate

We learn it by:

• Adults modelling comparative language using ‘than’.
• Making predictions before testing them.
• Being provided with a range of everyday experiences in which children can explore and investigate through play.
• Discussing the accuracy of comparisons.

Time

 We learn to:

• Begin to sequence events in chronological order.
• Name the days of the week.
• Start to recognise the months of the year.
• Recognise the numbers on a clock and their position.

Pre-taught vocabulary form Foundation Stage 1

First, last, then, after, before, earlier, later, morning, afternoon, evening, night-time, today, yesterday, tomorrow.

New vocabulary taught in Foundation Stage 2

We learn it by:

• Ordering events from a familiar story using appropriate vocabulary.
• Ordering events relevant to our own lives using appropriate vocabulary.
• Singing songs to help us remember the days of the week.
• Discussing what things we normally do on each of the days of the week e.g. PE day, what days we stay at home.
• Understanding that clocks are used to help us tell the time.
• Discussing why time is important, linking this to everyday scenarios in the classroom e.g. we eat lunch at 12pm, we finish school at 3pm.
• Counting down forthcoming events on the calendar in terms of number of days or sleeps.
• Identifying which day it is and that the day before was yesterday and the next day is tomorrow.

Properties of Shapes

We learn to:

• Select, rotate and manipulate shapes in order to develop spatial reasoning skills.
• Compare and classify shapes.
• Recognise a shape can have other shapes within it, just as numbers can.

Pre-taught vocabulary form Foundation Stage 1

circle, square, rectangle, triangle, cuboids, sides, corners, straight, flat, round, build, make

New vocabulary taught in Foundation Stage 2

2D, 3D, edges, hexagon, pentagon, cube, cuboid, sphere, pyramid, cone, construct, sort

We learn it by:

• Interacting with high-quality pattern and building sets, including pattern blocks, tangrams, building blocks and magnetic construction tiles as well as found materials.
• Copying increasingly complex 2D pictures and patterns with a range of resources.
• Solving a range of jigsaws of increasing challenge.
• Investigating how shapes can be combined to make new shapes.
• Exploring and investigating how many different ways a shape can be made.
• Predicting what shapes can be made when folding paper.
• Identifying 2D shapes within 3D shapes through printing activities or shadow play.

Position and Direction

 We learn to:

• Draw information from a simple map.
• Respond to simple directions.
• Give simple directions.
• Use positional and directional language with some accuracy.

Pre-taught vocabulary form Foundation Stage 1

under, above, on top of, next to, beside, over, down, off, on, inside, outside, in front of, behind, below.

New vocabulary taught in Foundation Stage 2

near, far away, close, nearby, forwards, backwards, left, right, 2 steps, turn.

We learn it by:

• ving our attention drawn to the immediate environment.
• Knowing where our school is.
• Recognising where things are in relation to others.
• Drawing maps of our immediate environment or drawing a map from a familiar story.
• Being given verbal instructions to reach a target.
• Giving verbal instructions to others in order to reach a target.
• Describing where items are on a treasure map.
• Programming BeeBots to reach a target.

Patterns

We learn to:

• Continue, copy and create repeating patterns.

Pre-taught vocabulary form Foundation Stage 1

pattern, spots, stripes, zig-zag, before, next, make

New vocabulary taught in Foundation Stage 2

repeating pattern, continue, same, different, mistake, correct, between

We learn it by:

• Making patterns with varying rules (AB, ABB, ABBC).
• Making patterns with a range of different resources, both mathematical and every-day objects.
• Continuing patterns.
• Identifying the mistakes within a pattern and knowing how to correct it.
• Engaging with physical and pictorial patterns.

Abstraction principle

An understanding that anything can be counted including things that cannot be touched including sounds and movements.

Cardinal Principle

The number name assigned to the final object in a group is the total number of objects in that group.

Conservation (of number)

The recognition that the number stays the same if none have been added or taken away.

Integer

A whole number (not a fraction).

Numeral 

The written symbol for a number e.g. 3, 2, 1

One-one principle

Assigning one number name to each object that is counted. (Children need to ensure that they count each object only once ensuring they have counted every object.

Order-Irrelevance principle

The order we count a group of objects in is irrelevant, there will still be the same number.

Ordinal

A number denoting the position in a sequence e.g. 1^st, 2^nd, 3^rd or page 1, page 2, page 3 etc.

Partition

Split a number into parts.

Quantity 

The amount you have of something.

Stable-Order principle

When counting, the numbers have to be said in a certain order.

Subitise

Instantly recognise the number of objects in a small group without needing to count. 

Addend

A number to be added to another.

Aggregation 

Combining two or more quantities or measures to find a total.

Augmentation 

Increasing a quantity or measure by another quantity.

Commutative Law

Numbers can be added in any order.

Complement

In addition, a number and its complement make a total e.g. 300 is the complement to 700 to make 1,000.

Difference 

The numerical difference between two numbers is found by comparing the quantity in each group.

Exchange

Change a number or expression for another of an equal value.

Inverse 

Using the opposite operation e.g. + and – or x and ÷

Minuend 

A quantity or number from which another is subtracted.

Reduction 

Subtraction as take away.

Subtrahend 

A number to be subtracted from another.

Sum 

The result of an addition.

Total 

The aggregate or the sum found by addition.

Array

An ordered collection of counters, cubes or other items in rows and columns.

Commutative Law

Numbers can be multiplied in any order.

Cube numbers

The product of three numbers which are the same.

Dividend

In division, the number that is divided.

Divisor

In division, the number by which another is divided.

Factor

A number that multiplies with another to make a product.

Multiple

The result of multiplying a whole number by another whole number.

Multiplicand

In multiplication, a number to be multiplied by another. 

Prime number

A number that is only divisible by itself and one.

Product

The result of multiplying one number by another.

Quotient

The result of a division.

Remainder

The amount left over after a division when the divisor is not a factor or the dividend.

Scaling

Enlarging or reducing a number by a given amount, called the scale factor. 

Square numbers

The product of a number multiplied by itself.

Denominator

The number below the line in a fraction.

Equivalent fractions

Fractions which have the same value even if they look different. E.g. 

Improper fraction

A fraction in which the numerator is greater than the denominator. E.g. 

Mixed numbers

A number consisting of an integer and a fraction. E.g. 

Non-unit fractions

A fraction that has a numerator larger that one. E.g. 

Numerator

The number above the line in a fraction.

Simplify (fractions)

Reduce a fraction by dividing the numerator and denominator by the same number E.g. 

The numerator and denominator have both been divided by 5.

Unit fractions

A fraction that has one as the numerator. E.g. 

Acute angles

Angles that measure less than 90°.

Area

The amount of space inside a 2D shape.

Circumference

The distance around the edge of a circle.

Diameter

The length of the line through the centre of a circle that touches two points on the edge of the circle.

Obtuse angles

Angles that measure more than 90° but less than 180°.

Parallel lines

 Two straight lines that are at equal distance from each other and never meet. 

Perimeter

The distance around a 2D shape.

Perpendicular lines

Two straight lines that meet at right angles.

Radius

The length of the line from the centre of a circle to the edge of the circle.

Reflex angles

Angles that measure more than 180° and less than 360°.

Right angles

Angles that measure 90°.

Volume

The amount of space a 3D shape takes up.