1. 3-D and 2-D shape

Children should understand and begin to write, the following words:
shape, pattern, flat, solid, hollow, side, edge, face, straight, curved, round, circular, triangular, rectangular, pentagonal, hexagonal, octagonal, right-angled, vertex, vertices, layer, diagram, surface, point, pointed, corner, sort, make, build, draw, cube, cuboid, sphere, cone, cylinder, prism, hemi-sphere, circle, triangle, rectangle, square, pyramid, hexagon, octagon, quadrilateral, semi-circle.

In 3-D shape work, the main new concept is that of a prism. A prism is a shape that has the same cross-section and same size throughout its length. Some shapes such as cones and square based pyramids have the same shape throughout their length (ie circle and square respectively), but they are not prisms because the size of the circle or square changes as you move from one end to the other.

There are many near prisms in real life (e.g. rulers, pencils, cans, chocolate boxes, rolls of sticky tape and exercise books), although they often have a small part such as the point of a pencil which prevents it being a pure prism. Children can generally be taught to ignore these annoying parts that manufacturers will insist on adding to spoil our maths lessons!
Children should also continue to describe solid shapes with increasing definition and precision and be more able to recognise similarities and therefore be more able to classify shapes according to their properties.

In 2-D shape work, the main new concept is that of a quadrilateral. A quadrilateral is a flat shape with four straight sides. Examples that are already familiar to children are squares, rectangles, rhombuses and parallelograms (although they may not yet know the names of the more difficult ones).

They should be able to recognise more difficult properties, in particular the right angle, and be able to classify shapes according to more difficult properties.

They should also realise that some shapes belong to larger families, e.g. squares are really just a special type of rectangle and rectangles are just a special type of quadrilateral.

In year 3 children will continue to make shapes and patterns, these becoming more complex and more accurate.

3D shapes should be related to 2D representations of them, as children match familiar solids to their pictures.

Drawing round shapes such as triangles, rectangles and hexagons and then cutting them out to make repeated patterns should be encouraged. When describing the patterns created, children should be encouraged to name the shapes.

Often children will need to copy a pattern before they feel confident enough to create their own. When drawing round shapes the emphasis should be on accuracy and care, both in placing the shape in the right position and drawing round it.

2. Symmetry

Symmetry is continued in year 3. Children should use and read terms such as:
line of symmetry
mirror line
reflection

Mirrors are essential for this work so that children can see the reflection of the shape in the mirror – they often find great difficulty predicting the mirror image without this help.

Whether shapes are symmetrical can be tested using a mirror, and a line of symmetry can be drawn where the mirror has been placed.

Further practical work should be continued, developing from that covered in years 1 and 2, such as making symmetrical patterns using ink blots or paint across a folded edge.

Other symmetrical patterns can be made with cubes, sticky gummed paper, plastic shapes etc.

Children should be encouraged to find examples of pictures, signs, letters of the alphabet etc which have a line of symmetry and to make a scrapbook up of these.

Sketching the other half of a shape is very difficult, but a few examples have been included in this module. They can also create their own ‘half’ pictures and try to draw the mirror image.

3. Describe position and direction

Children should understand and be able to use in practical contexts the following words. Where possible, they should be taught to read the words.

position, over, under, underneath, above, below, on, in, outside, inside, in front, behind, beside, before, after, higher, lower, next to, opposite, between, close, far, apart, middle, centre, edge, corner, top, bottom, side, direction, left, right, up, down, forward, backwards, sideways, across, along, around, through, to, from, towards, away from, clockwise, anticlockwise, journey, route, grid, row, column, map, plan, compass point, north, south, east, west, horizontal, vertical, diagonal, descend, ascend.

In addition to describing position in terms of ‘behind’, in front of’ etc, they should now be becoming confident with describing position in an absolute sense, ie on a grid or map. They should be able to say how many squares from a zero point horizontally and vertically an object is and give these labels when appropriate (square B3, F5 etc).

They should know the difference between a column and a row. Columns are vertical (as in the old Greek buildings), rows are horizontal (imagine standing at the front of a cinema and looking out at the rows of seats).

They should understand that a diagonal goes from one corner of a grid to the opposite corner eg bottom left to top right.
They should know the directions North, South, East and West and that on a map or plan, the North direction is almost always towards the top. The North direction should, in any case, always be indicated. North and South are generally easy to remember, but most children will mix up East and West for a long time.

They should know the meaning of the words ‘ascend’ and ‘descend’.

4. Understand angle

Children should understand and use in practical contexts the following vocabulary:

slide, roll, turn, whole turn, half turn, quarter turn, angle, right angle, straight line, is a greater/smaller angle than.

Children should recognise quarter and half turns and know that a quarter turn is a right angle and that  a half turn (or straight line) is two right angles.

They should understand the directions N, S, E and W and be able to face one direction, turn a quarter or half turn and say which way they are then facing.

They should know that turning a half turn or two quarter turns results in you facing in the opposite direction.

Children should be able to sort shapes according to the number of right angles they have and be able to fold a piece of paper to give a right angle with which they may test for right angles in other shapes.

They should be able to use a template to draw right angles and test angles to see if they are smaller, equal to or larger than right angles.

Go to year 3 shape

1. Sharing equally
e.g. 8 bars of chocolate are shared between 2 people.
How many does each person get?
2. Grouping, or repeated subtraction
In the same way that multiplication can be seen as repeated addition, so division can be seen as repeated subtraction.

e.g. 8 divided by 2, can be seen as how many twos in eight?

Children will still need practical apparatus to help them understand and work out division questions.  Hopping along a number line is especially helpful.

Also, in discussion, the idea that you cannot reverse division should be introduced; in other words 12 divided by 2 is not the same as 2 divided by 12.

Understanding that division is the inverse of multiplication is very important and children need a lot of work in making calculations up, having been given some information:

e.g.   if 2 x 6 = 12 then two division sums can be made from this:
12 divided by 6 = 2 and 12 divided by 2 = 6.

It is better to keep working with tables that children are familiar with, especially 2s, 5s and 10s, although others can be used when hopping along a number line.

Several key mental strategies are used in Year 3, including:

1. The effect of dividing by 1.
Know that dividing a whole number by 1 leaves the number unchanged.

2. The effect of dividing by 10.
As division is the reverse of multiplication, to divide by ten, numbers can be moved one place to the right. To avoid confusion with the decimal point, keep to multiples of 10 in year 3.

3. Dividing by 4 by halving and halving.

4. Rapid recall of halves
It is very important that children know the halves of numbers below 20 and have quick strategies for finding others.

Much of the work in Year 3 is re-enforcement of year 2 work, however, the more practice, the better.
Concepts covered include:
1.  dividing a three digit multiple of 100 by 1, 10 or 100
2.  halving multiples of 10 and 100
3. giving whole number remainders
4. rounding down and rounding up
By the end of year 3 children should be able to count forwards or backwards in halves and quarters from small whole numbers such as 10 and they should be able to mark wholes, halves, quarters and eighths on a number line from 0 to 5.
Pupils should be able to find a unit fraction of a familiar quantity such as one tenth of 30 or 100 or 500 and one quarter of 8 or 12 or 20.
They should be able to find simple fractions of £1 and one metre and be able to say what fraction of a large shape is a smaller shape.

Go to Year 3 Division concepts

In oral work the terms multiple and product can be introduced.

A key concept for children to understand is that multiplication can be done in any order, unlike division.

Tables are continued, especially the twos, fives and tens, with threes, fours and sixes introduced.

When learning a table it is important to say the number sentence and not just the list of answers:

i.e.  2 times two is 4, three times two is 6  ( not just 2, 4, 6 – which is counting in twos).

Several key mental strategies are used in Year 3, including:

1. The effect of multiplying a number by 10.
Many children are told that all you have to do to multiply by ten is ‘add a nought’. This is disastrous! When they move on to multiplying decimals, for instance, adding a nought gives an incorrect answer.  ( 2.4 x 10 = 24, not 2.40)

They should understand that the units digit moves one place to the left, into the tens column and a nought is placed in the empty units column.

2. Multiplying by 4 by doubling and doubling.
This is a very effective mental strategy. Having a sound knowledge of the double of all numbers up to ten can speed up mental calculations enormously.

3. Inverse
Finally there is re-enforcement of the relationship between multiplication and division, and how this can lead to other statements
e.g. if 24 divided by 6 = 4 then 6 multiplied by 4 = 24 etc.

Much of the work in Year 3 is re-enforcement of year 2 work, however, the more practice, the better.

Concepts covered include:

1.  multiplying a single digit by 1, 10 or 100

2.  doubling multiples of 5: exactly as for year 2, but children should now be more
confident.

3.  multiplying a two digit multiple of 10 by 2, 3, 4, 5

4.  multiply a two digit number by 2, 3, 4 or 5

Year 3 multiplication concepts

A similar list of words and phrases should be used as for year 2, including:
take away,   subtract,   how many are left,   less than,
what is the difference between,   more than,  how many more to make ….
It is expected that the minus (–) sign can be read and written.

Most of the work will still be done orally. All kinds of opportunities arise where simple subtraction questions can be posed, but, again, the numbers do need to be kept simple.

A number line or a number square is useful for harder examples so that children can see the  movement down the line as numbers are subtracted. Coins, counters or cubes are also excellent resources for practical subtraction exercises.

Children should understand that subtracting from a positive number makes the number less and that subtraction is the opposite, or inverse of, addition.

The idea that subtracting 0 leaves a number unchanged also needs to be re-enforced and children need to realise that 40  –   30  is not the same as  30  –  40.

Subtraction – oral questions
Examples of the type of question to ask include:

1. What is 30 take away 12 ?
2.  Take 14 from 40.
3.  60 subtract 41.
4.  What is 12 less than 40  ?
5. What number must I take from 30 to leave 9  ?
6. What must I add to 13 to make 50 ?
7. What is the difference between 11 and 50  ?
8.   How many more is 60 than 18  ?
9. 17 taken from a number is 23. What is the number?
10.  60 added to a number is 84. What is the number?
11. Find a pair of numbers that have a difference of 41.
12. Find two numbers which have a difference of 33.

Children continue to be expected to work out more complex subtraction in their heads.
Subtracting 19, 29, 39 etc from any two digit number is the next step
e.g. 58 – 29.

Because it is usually easier to subtract whole tens or a single digit the most effective method involves several steps:
58 – 29
1. adjusting the second number to the nearest whole ten: e.g. 29 to 30
2. subtracting the 30 from 58 leaves 28
3. readjusting by adding 1 makes 29.
58 – 29 = 29

Subtracting a single digit from a multiple of 100 is also introduced eg 300 – 5. This some children find quite difficult and they need to be confident in counting up and down crossing the hundreds boundary. Other skills taught will include:
subtracting a pair of multiples of 100 crossing 1 000   eg 1 300 – 500
subtracting 100 from any three digit number
Finding small differences between two numbers either side of 100 is extended to multiples of 100, up to 1 000.
Written methods

In year 3 children are encouraged to make jottings to help them with more difficult subtractions, leading to a more efficient method later.
Three different approaches are suggested, each one reliant on previously learnt mental methods.

At first children need to practice the methods, even though they may be confident enough to find the answer without resorting to pencil and paper jottings. To find out more about the three methods click the link below.

Go to the Year 3 subtraction pages

The words below should be understood and written correctly.

more    add    sum   total    altogether    equals    sign

Most of this work can be done orally, with increasing speed of recall.

Once the addition of single digits is secure, this knowledge can be applied to two digit and three digit problems with confidence. All kinds of opportunities arise where simple addition questions can be posed but the numbers do need to be kept simple.

Mental work will concentrate on smaller numbers, usually tens and units or whole hundreds.
Rapid recall is expected for answers up to 20. ‘Rapid’ means almost instant, where the child knows the answer rather than having to work it out.

A number line from 0 to 100 is still a useful resource.

It is also important to discuss how the sum has been done. Very often, when working mentally, it is easier to start with the tens and then add the units – the opposite to the usual pencil and paper method.

Again it is important to talk about how children add in their heads. Ask questions all the time such as:

“How did you work that out?”
“What did you start with?”
“Can you explain what you did?     etc.

In year 3 children should be encouraged to use a variety of strategies when adding, including:

Looking for pairs of numbers that make 10.
Looking for pairs of numbers that make 9 or 11.
Starting with the larger number and counting on, whichever way the sum is written or asked.
Use knowledge of doubles such as 6 + 6.
Use knowledge of doubles to find near doubles and then add or subtract 1.

When finding the difference between two numbers which are quite close to each other eg 198 and 202 it is often easiest to start with the lower number and count on, rather than to start with the higher number and count back. Subtraction problems can often be made into ‘counting on’, or addition!
Children continue to be expected to work out more complex addition in their heads.
Adding 9  is extended to any three digit number.
Adding 19, 29, 39 etc to any two digit number without crossing the hundred boundary is the next step e.g. 37 + 29.
Because it is usually easier to add whole tens or a single digit the most effective method involves several steps:
1. adjusting a number to the nearest whole ten: e.g. 39 to 40
2. adding the 40
3. readjusting by subtracting 1.

In year 3 addition of a single digit is extended to hundreds, for example 345 + 4, but the tens boundary is not crossed.

Further developments include adding a two digit number to any multiple of 100, such as 500 + 34 and adding a two digit number to a multiple of ten where crossing the hundred boundary does occur e.g. 60 + 55.
The second of these is much harder and children need to be secure in their knowledge of adding a pair of multiples of ten that cross the hundreds boundary e.g. 50 + 70 before they move on to this.

In year three progressively more difficult mental addition continues, including:
1.    adding 10 to any two digit number with answers going up to and beyond the  hundreds
2. adding a pair of multiples of 10, beyond the hundreds e.g. 80 + 50
3. finding pairs of multiples of 10 that make the next multiple of 100  e.g. 230 and 70
4. add a multiple of 10 to any two digit number, crossing 100 e.g. 46 + 70
5. add a pair of multiples of 100, with answers crossing 1 000
6. add 100 to any three digit number, not crossing 1 000

All these are extensions of the work covered in year two. If children find them difficult it is strongly recommended that the year two work is re-enforced.

Written methods

Pencil and paper methods of addition are encouraged in year 3. To begin with ‘jottings’ can be used to help with the mental methods that children are already familiar with, leading to a more efficient method later.
Hopping along a number line is a useful way to introduce these ‘jottings’.

Go to Year 3 addition concepts

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