Category: Maths news

Let’s continue by looking at the expectations for children at the end of year 2 (6 to 7 years old). This is a year where a huge amount of new maths is introduced. However, it is still important to keep the maths in a practical context using real life situations. One of the most important developments is that children are expected to work with larger numbers, up to 100 and whole hundreds. Partitioning (or splitting numbers) is introduced with questions such as 36 = ? + 6.
Remember to look at the year 1 expectations to see the progression.

Counting and understanding number:

By the end of year 2 children should
• be able to read and write 2-digit numbers in figures and words.
(eg read ‘thirty six’.)

• be able to read and write 3-digit numbers in figures and words.
(eg read ‘360’.)

• be able to continue number sequences by counting on and back in steps of 1, 10 or 100.
(eg count on in tens from 50 to 100.)

• be able to recognise odd and even numbers.
(eg which of these numbers is odd 8, 9, 10 ?)

• be able to count up to 100 objects, by grouping them into tens.

• be able to group objects into twos and fives.

• understand place value. Children should know what each digit in a 2-digit number represents.
(eg the 2 in 27 represents 20.)

• through an understanding of place value, be able to partition a 2-digit number.
(eg 54 = 50 and 4 or 54 = 40 + 14.)

• be able to compare two numbers, saying which is more or less.
(eg which is more 27 or 72?)

• be able to put 4 or 5 numbers in order, largest/smallest first.
(eg put these numbers in order, smallest first: 6, 3, 9, 1.)

• be able to position a 2-digit number on a number line.

• understand two new signs: the greater than (>) and less than (<) signs.

• develop the language of estimation to include: roughly, nearly, close to, about the same as, estimate, too many, too few, enough, not enough.

• be able to make estimates of numbers up to about 50.
(eg the number of potatoes on a shelf.)

• round a number to the nearest ten.
(eg is page 43 in a book is closer to page 40 or page 50?)

• develop their vocabulary for fractions, recognising ½ and ¼ .

• be able to find half and find quarters of shapes and sets of objects.

Knowing and using number facts:

By the end of year 2 children should
• know all addition facts for two numbers up to a total of 10.
(eg 4 + 5.)

• be able to derive subtraction facts for numbers up to 10.
(eg if they know that 6 + 3 = 9, they can instantly work out that 9 – 6 = 3.)

• know all the pairs of whole numbers which total 20.
(eg 16 + 4.)

• know all the pairs of multiples of 10 which total 100.
(eg 30 + 70.)

• know the doubles of whole numbers up to a total of 20.
(eg double 7.)

• understand that halving is the inverse of doubling and hence derive halving facts from their knowledge of doubling.
(eg if double 8 is 16, then half 16 is 8.)

• recall 2, 5 and 10 times-tables.
(eg know 5 x 6.)

• work out related division facts.
(eg if 5 times 2 is 10, then 10 divided by 5 is 2.)

• be estimating answers to calculations and checking their answers by using the inverse operation.

Calculating:

By the end of year 2 children should
• be able to mentally add a single digit to any 2-digit number.
(eg 24 + 5.)

• be able to mentally add a single digit to a multiple of 10.
(eg 30 + 9.)

• be able to add a multiple of 10 to any 2-digit number.
(eg 34 + 50.)

• be able to mentally subtract a single digit from any 2-digit number.
(eg 44 – 5.)

• be able to mentally subtract a multiple of 10 from any 2-digit number.
(eg 43 – 20.)

• be using practical and informal methods to add or subtract two 2-digit numbers. This means making their own jottings rather than the standard written method.

• by understanding that subtraction is the inverse of addition, be able to work out related addition and subtraction sentences.
(eg if 9 + 5 = 14, then 5 + 9 = 14, 14 – 5 = 9 and 14 – 9 = 5.)

• be able to recognise multiplication as repeated addition.
(eg 4 added together 3 times is 4 + 4 + 4, or 3 lots of 4, or 3 times 4, or 3 x 4.)

• also be able to represent multiplication as an array
eg
3 x 2 = 6

2 x 3 = 6

• recognise division as sharing.
(eg share 8 sweets between 2 children.)

• recognise division as grouping.
(eg there are 12 sweets in a bag. How many bags of 3 sweets can be filled?)

• recognise all four symbols +, -, x and ÷ and use them in number sentences.

Understanding shape:

By the end of year 2 children should
• be able to visualise 2-D shapes and 3-D solids. (See earlier years for vocabulary).

• be able to identify shapes from pictures in different orientations.

• be able to make shapes and patterns with increasing accuracy.

• be able to recognise reflective symmetry and begin to draw a line of symmetry in shapes.

• have developed further their vocabulary for describing position, including clockwise and anti-clockwise.

• be able to give instructions involving position, direction and movement.
(eg give instructions for following a path through a simple maze.)

• also be able to recognise and use whole, half and quarter turns and know that a right angle represents a quarter turn.

Measuring:

By the end of year 2 children should
• estimate lengths, weights and capacities more accurately.

• compare lengths, weights and capacities.

• choose a sensible standard metric unit to measure and suitable measuring instruments.

• read the numbered divisions on a scale and interpret the divisions between them.
(eg on a jug read the intervals between numbered divisions.)

• use a ruler to draw and measure lines to the nearest centimetre.

• use units of time.
(eg know that 60 seconds = 1 minute, 60 minutes = 1 hour, 24 hours = 1 day.)

• read the time to the quarter hour and work out time intervals including those that cross the hour.
(eg how long is it from 3.50 pm to 4.10 pm?)

Handling data:

By the end of year 2 children should
• answer a question by collecting, and recording data in lists and tables.

• know how to use block graphs or pictograms to show their results.

• present data using ICT.

Using and applying mathematics:

By the end of year 2 children should
• solve problems using their knowledge of addition, subtraction, multiplication and division, including money and measures problems.

• solve problems and puzzles, identifying and recording the information needed.

• follow lines of enquiry, choose suitable equipment and present results.

• describe patterns involving shape and make predictions which can be tested.

• present solutions to puzzles and problems in an organised way.

To be able to successfully help your child with maths at home it is important to have a good idea of what is expected in school. Remember, we divided all the maths content into 7 strands. Let’s take each of the strands in turn to see what the Primary Framework for Mathematics suggests for children aged between 5 and 6 years old.

Counting and understanding number

By the end of year 1 children should

• know the number names (one, two, three etc) up to at least 20 and tens up to 100
(eg twenty, thirty, forty etc).

• be able to count up to 20 objects reliably. If the objects (eg buttons on a tray) are moved around they should be able to say that the total number has not changed without recounting. (Younger children will count them again if they have been moved around.)

• be able to read and write numerals up to 20
(eg 3, three, 4, four, 5 five, etc).

• be able to place numbers on a blank number line in the correct order.

• be able to say the number that is one more than or one less than any given number up to 20
(eg one less than 7).

• be able to say the number ten more than or ten less than a multiple of 10
(eg ten more than 30).

• recognise the equals sign (=) and understand it means “..is the same as..”

• use the terms, half and quarter in a practical sense
(eg give me a quarter of the orange).

Knowing and using number facts

By the end of year 1 children should

• know addition facts up to a total of 5
(eg 3 + 2).

• know all pairs of numbers with a total of 10
(eg 1 and 9, 2 and 8 etc).

• be able to work out subtraction facts from the addition facts they know.
(eg 5 -2 = 3 because 3 + 2 = 5)

• be beginning to count on and back in twos, fives and tens.

• know the doubles of all numbers up to 10
(eg double 6 is 12).

Calculating

By the end of year 1 children should

• know that addition can be done in any order.

• be able to write simple number sentences using the + and = signs
(eg 3 + 4 = 7).

• use practical methods (eg using counters) to help with addition of a 1-digit number to a 1-digit or 2-digit number
(eg 10 + 4 =).

• use informal written notes to help with addition
(eg jotting down the answer to adding 2 numbers before trying to add the third).

• understand that subtraction can mean ‘take away’.

• understand that subtraction can mean ‘find the difference between’.

• be able to use practical methods to help with subtraction of a 1-digit number from a 1-digit number
(eg using counters).

• use informal written notes to help with subtraction
(eg jotting down 5 circles and crossing out 3 for 5 – 3).

• be able to write simple number sentences using the – and = signs
(eg 7 – 4 = 3).

• understand and use the vocabulary related to addition and subtraction, including: more, add, sum, total, altogether, equals, =, take away, subtract, difference between, how much more/less, how many are left?

• be able to combine groups of 2, 5 and 10 in a practical situation
(eg combining marbles into groups of 5 marbles).

• be able to share a group of objects into 2 equal parts
(eg sweets shared equally).

Understanding shape

By the end of year 1 children should

• be able to visualise and name common 2-D shapes, including circle, triangle, rectangle and square. This includes activities such as “Find a shape which has 3 corners and 3 sides”.

• be able to visualise and name common 3-D shapes, including, cube, cuboid, sphere, cone and cylinder. This includes activities such as describing the properties of a shape by the feel of it, before seeing it.

• be able to make patterns and pictures with 2-D shapes and make models with 3-D shapes such as Lego.

• begin to describe the position of shapes, using terms such as: over, under, underneath, above, below, outside, inside, in front, behind, beside, before, after, next to, opposite, between, middle, centre, edge, corner, top, bottom, side. This is where activities such as moving furniture around a toy house are very important or placing counters on a board game.

• be using everyday language to describe direction, such as: left, right, up, down, forwards, backwards, sideways, across, along, through, to, from, towards, away from.

• begin to be able to describe movements in a straight line and turning. At first turning will only be by whole and half turns but it is important to recognise shapes that turn about a point, such as a pair of scissors.

• Once again it must be emphasised that most of this work is done orally with practical equipment. Toys, board games, may seem like playing to us but are invaluable learning experiences.

Measuring

By the end of year 1 children should
• understand and use the basic vocabulary related to length, mass and capacity.
For length: long, short, tall, high, low, wide, narrow, deep, shallow, thick, thin, far, near and words of comparison eg longer.
For mass: weight, weighs, heavy light, balances.
For capacity: full, empty, half full, holds.

• be able to make direct comparisons between two items eg comparing the length of two pencils, the weight of two parcels, the capacity of two cups. A set of balance scales is very useful for this kind of work.

• begin to use non-standard measures
(eg the jug holds 6 cups of water, the table is about 7 rulers long).

• be making sensible estimates and guesses related to length, mass and capacity. Standard units such as cm, km, kg are not used at this stage.

Using and applying maths

By the end of year 1 children should

• solve problems involving counting, addition, subtraction, doubling, halving, measures and money
(eg a toy shop, paying and giving change with numbers up to 10).

• describe and solve simple puzzles or problems
(eg How many ways can you score 4 rolling two dice?).

• sort information, shapes or objects and display the results using pictures
(eg sort cubes by colour).

• describe simple patterns involving numbers or shapes
(eg continue a pattern of repeated squares and circles).

• describe ways of solving a puzzle or problem orally
(eg talk about or draw what coins could be used to make 6p).

By year 5 children are expected to know the basic number facts, including tables up to 10. They should also have rapid recall of addition and subtraction facts. We have some excellent pages to help with this, using known facts to rapidly work out answers.
Firstly there are tasks such as ‘making 50’, which include writing all the pairs of even numbers that make 50.

Then there are ‘find the difference’ questions, involving whole tens such as 150 and 80. There should be little or no time spent working this out as a previously learnt fact that 8 and 7 make 15 comes instantly to mind. After all, they have been working on questions such as these for over 2 years.

Similar techniques can be used when finding the difference between two decimals, such as 10 and 8.1. Just think of the difference between 100 and 81 for a clue to the answer.

We also include several calculator multiplication games. The point of these is not to let the calculator do the calculation, but to use it as a check for your own mental calculation. Those with a good mental knowledge will be able to pick the answers they want rather than keying in numbers haphazardly.

Go to our Year 5 Knowing Number Facts category