2013 | Maths Blog

New Maths Curriculum: Year 2 Measurement

The statutory requirements for Year 2 Measurement :

Pupils should be taught to:

• choose and use appropriate standard units to estimate and measure length/height in any direction (m/cm); mass (kg/g); temperature (°C); capacity (litres/ml) to the nearest appropriate unit, using rulers, scales, thermometers and measuring vessels

• compare and order lengths, mass, volume/capacity and record the results using >, < and =

• recognise and use symbols for pounds (£) and pence (p); combine amounts to make a particular value

• find different combinations of coins that equal the same amounts of money

• solve simple problems in a practical context involving addition and subtraction of money of the same unit, including giving change

• compare and sequence intervals of time

• tell and write the time to five minutes, including quarter past/to the hour and draw the hands on a clock face to show these times.

Main changes and comments

One of the key changes is the use of the < > signs when comparing lengths, mass, volume/capacity.

Children should use standard units of measurement and mental calculations strategies to solve various number problems involving length, mass, capacity and time.

They should be encouraged to explain orally how the problems were solved and begin to write a simple number sentence on paper:

e.g. 12 cm + 6 cm = 18 cm

Children should also be reminded about abbreviations such as cm for centimetre,
kg for kilogram and g for gram.

They will also be expected to become fluent in telling the time on analogue clocks to five minutes.

New Maths Curriculum: Year 2 Measurement

New Maths Curriculum: Year 2 Fractions

$204 fractions$ Fractions are seen as a completely separate area now, rather than being within Number or Division and Fractions.

The statutory requirements for Year 2 Fractions :

Pupils should be taught to:

• recognise, find, name and write fractions 1/3, 1/4, 2/4 and 3/4 of a length, shape, set of objects or quantity

• write simple fractions e.g. 1/2 of 6 = 3 and recognise the equivalence of 2/4 and 1/2.

Main changes and comments
Quite a few new targets in this category.
Counting in fractions up to ten is a new target for this year.
Much practical work should continue to be done using shapes and objects so that children understand what finding a half or a quarter of a quantity means.

Thirds are introduced in Year 2 now. This enables children to work with fractions other than halves and quarters at an earlier age. (Some children do so much work with halves that they think all fractions can be worked out by dividing by two!!)

Three quarters is also introduced; the first time children come across a non-unit fraction (where the top number is more than one).

A new target is counting up to ten in quarters. This process has two purposes:

a. so that children see the equivalence between a half and two quarters
b. so that children see that fractions can add up to more than one whole one.

New Maths Curriculum: Fractions

Count on in tens (Christmas)

We are rapidly approaching the Christmas season in schools, with plenty of work going on preparing concerts, nativities etc. but the maths work still needs to go on, so here are a couple of worksheets for Year 1 children with a Christmas feel to them.

They look at counting on in whole tens from any 2-digit number, with answers up to 100. It is important that children are confident and happy with counting in ones up to 100 before starting this and some children may still need a number square to help them with this. Counting on in tens also helps with the understanding of partitioning numbers into tens and units and it is important to ask children what is happening, both to the tens and the units.

Count on in tens (pg 2)

New Maths Curriculum: Year 2 Multiplication and Division

Year 2 Multiplication and Division

It’s time to start learning those times tables off by heart; beginning with the 2x, 5x and 10x tables.
The statutory requirements for Year 2 Multiplication and division :

Pupils should be taught to:

recall and use multiplication and division facts for the 2, 5 and 10 multiplication tables, including recognising odd and even numbers

calculate mathematical statements for multiplication and division within the multiplication tables and write them using the multiplication (×), division (÷) and equals (=) signs

show that multiplication of two numbers can be done in any order (commutative) and division of one number by another cannot

solve problems involving multiplication and division, using materials, arrays, repeated addition, mental methods, and multiplication and division facts, including problems in contexts.

Main changes and comments

This is the year that children begin to learn multiplication tables, starting with the two, five and ten times tables. Remember, it is not enough to just count up in fives (5, 10, 15, 20 etc.) the whole sentence needs to be learned (5 times 2 equals 10 etc).
Perhaps the main change is that tables are meant to be learned up to 12 times, rather than just 10.

As with addition, it is important to know that multiplication can be done in any order, but not division. The relationship between multiplication and division is now stressed more, with inverse operations for checking made more explicit in the Guidance.

Year 2 multiplication and division statutory requirements

New Maths Curriculum: Year 2 Addition and Subtraction

Year 2 Addition and subtraction

The emphasis is on mental arithmetic this year, as children become fluent and confident adding and subtracting small numbers.

The statutory requirements for Year 2 Addition and Subtraction are:

Pupils should be taught to:

• solve problems with addition and subtraction:

using concrete objects and pictorial representations, including those involving numbers, quantities and measures

applying their increasing knowledge of mental and written methods

• recall and use addition and subtraction facts to 20 fluently, and derive and use related facts up to 100

• add and subtract numbers using concrete objects, pictorial representations, and mentally, including:
a two-digit number and ones
a two-digit number and tens
two two-digit numbers
adding three one-digit numbers

• show that addition of two numbers can be done in any order (commutative) and subtraction of one number from another cannot

• recognise and use the inverse relationship between addition and subtraction and use this to check calculations and missing number problems.

Main changes and comments

The key this year is to really learn basic number facts off by heart and then use them to work out other facts.
A great deal of emphasis is put on mental arithmetic so that by the end of the year children are responding quickly and accurately to oral and written questions. Three key areas are:

a. using known facts to work out other facts e.g. knowing 4 + 5 = 9 can be used to work out
quickly 40 + 50. This relates to knowledge of place value in number work.

b. knowing that addition of numbers can be done in any order but subtraction cannot. This is very
handy when adding more than two numbers; looking for pairs that make 10 etc.

c. using inverse operations to check answers e.g. to check 10 – 7 = 3 by adding 7 and 3 to make 10.

In the Guidance section there is also mention that children should record addition and subtraction in columns to support place vale and ready for formal written methods.

New Maths Programme of Study: Year 2 Addition and Subtraction

New Maths Curriculum: Year 2 Number and Place Value

There are some tough challenges in the new Year 2 Programme of Study. Let’s begin by looking at ‘Number and place value’.
The statutory requirements for Year 2 Number and Place Value are:

Number and place value

Pupils should be taught to:

• count in steps of 2, 3, and 5 from 0, and in tens from any number, forward or backward

• recognise the place value of each digit in a two-digit number (tens, ones)

• identify, represent and estimate numbers using different representations, including the number line

• compare and order numbers from 0 up to 100; use <, > and = signs

• read and write numbers to at least 100 in numerals and in words

• use place value and number facts to solve problems.

Main changes
Most of this looks very similar to the old curriculum. The main difference is the introduction of the < and > signs. Remembering which is which could prove very tricky.
Writing numbers to at least 100 in words is a real challenge which quite a few children will not be able to manage by the end of the year.
A key idea in this category is partitioning numbers in different ways. For example:
24 can be split up or partitioned into 20 + 4 or 10 + 14.
This is important to understand as it helps with written addition and subtraction in later years. Also it is important to begin to understand zero as a place holder; i.e. the 1 in 100 has a value ten times the 1 in 10, with the zeros being used as place holders.
Counting in multiples of 3 is a new target, introduced to help later with understanding the concept of a third.
Also note that this new programme will not become a statutory requirement until 2015.

Year 2 Number and Place Value

New Maths Curriculum: Year 1 Geometry

Geometry replaces the old shape and space categories and is in two parts:

a. properties of shapes
b. position and direction.

The statutory requirements for Year 1 Geometry are:

Properties of shapes

Pupils should be taught to:

• identify and describe the properties of 2-D shapes, including the number of sides and symmetry in a vertical line

• identify and describe the properties of 3-D shapes, including the number of edges, vertices and faces

• identify 2-D shapes on the surface of 3-D shapes, for example a circle on a cylinder and a triangle on a pyramid

• compare and sort common 2-D and 3-D shapes and everyday objects.

Position and direction

Pupils should be taught to:

• order and arrange combinations of mathematical objects in patterns

• use mathematical vocabulary to describe position, direction and movement including distinguishing between rotation as a turn and in terms of right angles for quarter, half and three-quarter turns (clockwise and anti-clockwise), and movement in a straight line.

Two really useful practical items to help with shape are:

a. Cubes: many shapes can be made from cubes. In year 2 keeping to a small number of cubes, e.g. four, and exploring all the possibilities, is better than using a much larger number in a more random way.
b. Pinboard: a pinboard is very useful for exploring all the possible four and five sided shapes. This may be simply made by nailing panel pins or small nails into a piece of plywood approximately 24cm × 24cm.

Position and direction
Clockwise and anti-clockwise turns are introduced including quarter, half and three-quarter turns.

Year 1 Geometry: statutory requirements

New Maths Curriculum: Year 1 Measurement

Here are the statutory requirements for Measurement in Year 1. There is a great deal more in Measurement now, including money and time.

Measurement

Pupils should be taught to:

• compare, describe and solve practical problems for:
lengths and heights (e.g. long/short, longer/shorter, tall/short, double/half)
mass or weight (e.g. heavy/light, heavier than, lighter than)
capacity/volume (full/empty, more than, less than, quarter)
time (quicker, slower, earlier, later)

• measure and begin to record the following:
lengths and heights
mass/weight
capacity and volume
time (hours, minutes, seconds)

• recognise and know the value of different denominations of coins and notes
sequence events in chronological order using language such as: before and after, next,
first, today, yesterday, tomorrow, morning, afternoon and evening

• recognise and use language relating to dates, including days of the week, weeks, months and years

• tell the time to the hour and half past the hour and draw the hands on a clock face to show these times.

Main changes

Much of the early work on measurement should to be done on a practical basis, with children comparing simple lengths, heights and weights, saying which is bigger or smaller, longer, shorter. Also with mass, comparing the mass of parcels wrapped up, using scales to balance objects etc should be done on a practical basis. At this stage the terms mass and weight are used interchangeably.

With capacity it is a good idea to fill various different jugs with water – many young children are convinced that the taller the jug the more it holds, and need a lot of practice to judge how much a container holds.

Standard measures are introduced, including the metre, litre and kilogram.

Year 1 Measurement statutory requirements

New Maths Curriculum: Year 1 Fractions

$104 fractions$ Fractions is a brand new category for Year 1: in the past this was part of the division section.

The statutory requirements for Year 1 Multiplication and Division are:

Fractions

Pupils should be taught to:

• recognise, find and name a half as one of two equal parts of an object, shape or quantity

• recognise, find and name a quarter as one of four equal parts of an object, shape or quantity.

Main changes

Nothing much new for this year and to begin with, work on fractions will be based on practical activities.

There are a large number of activities that can be undertaken, including:

a. filling jars, cups, containers half full with water/sand etc.

b. shading half of shapes

c. dividing an apple, pear etc in half

d. cutting a bar of chocolate in half

e. cutting string in half

f. learning nursery rhymes involving halves

g. moving half way towards something

At first all these activities should involve dividing one object into two halves, rather than counting several things (e.g. sweets) into two equal piles.

After a good deal of work on dividing small numbers of objects in half, children can then move onto the idea of finding half of a number: e.g. what is half of six? As part of their mental arithmetic work they should be encouraged to learn what half of any even number up to 10 is.

Work on quarters will develop in the same way, and one of the main concepts to re-inforce is that two quarters are the same as a half. This is a very early introduction to equivalent fractions – a crucial concept if children are to understand more complex fraction work in later years.

A further idea to develop is that two halves make a whole and that four quarters make a whole.

Year 1 Fractions: statutory requirements

New Maths Curriculum: Year 1 Multiplication and Division

Let’s look at the new targets for year 1 multiplication and division. A lot of the work this year should be practically based.

The statutory requirements for Year 1 Multiplication and Division are:

Multiplication and division

Pupils should be taught to:

• solve one-step problems involving multiplication and division, by calculating the answer using concrete objects, pictorial representations and arrays with the support of the teacher.

Main changes

Multiplication and division problems including arrays are now included, whilst previously these were expectations for Year 2 onwards.

Grouping and sharing small quantities forms the major part of the work.

Doubling small numbers is an important part of this year’s work. Plenty of opportunity should also be given to counting, using 2p, 5p and 10p pieces, both counting up and down. Similar activities can be carried out with pairs of socks, gloves etc. Once again, it is better to use real life objects when beginning to combine groups.

Practice should be given at counting up in twos before moving on to fives or tens and can be shown as arrays or number patterns.
Remember, division can be understood in two ways:

1. Sharing equally e.g. 6 bars of chocolate are shared between 2 people.
How many bars does each person get?

This concept is best introduced with practical apparatus – bowls of sweets, counters, buttons etc. are ideal for sharing into equal groups, and then counting the number in the group.

2. Grouping, or repeated subtraction e.g. 8 divided by 2
can be seen as how many lots of two can I take from eight?

Again, this is best done with apparatus at first and it is a slightly different process to sharing equally (where one item is given to each person in turn).

This can be answered by repeatedly taking two from the pile and then counting how many lots of two have been taken altogether.

Multiplication and division in Year 1