The Year 4 questions are all on subtraction. The first few are relatively easy, subtracting, 11, 21 or 41 from 2-digit numbers where no adjustment is needed. The later questions are harder, including subtracting 19 and 29 from 2-digit numbers. Children should be developing their own fast, accurate strategies for doing this type of question, including subtracting 29 by subtracting 30 and adjusting by adding one to the answer. This is not always the best way e.g. where the number to be subtracted from has a nine in the units e.g. 39 – 29.

In Year 5 there are some tricky addition and doubling questions involving decimals. It is always interesting to think how we tackle questions ‘in our heads’ and then discussing this with children. For instance, ‘Double 3.5′. I must admit that I doubled 35, (70) which I pretty much know off by heart and then divided by 10,converting it back to the original question (7).

Finally the Year 6 questions concentrate on multiplication and division of decimal fractions. One question which might cause problems is ‘Double 5.5′ which can be tackled in the same way as mentioned above.

Go to Year 4 mental arithmetic

Go to Year 5 mental arithmetic

Go to Year 6 mental arithmetic

The numbers  650 and 900 should be circled.One mark for circling both the correct numbers.

Other unambiguous answers can be accepted, such as ticking, underlining or incorrect numbers crossed out.

Suggested method:
The clue for this question is that the sequence shows all the possible tens and units which can occur; i.e. 25, 50, 75 and 00. This makes it easy to spot the correct numbers in the list.
10.   This is a much harder question and those of us who don’t have great spacial awareness may well make a mistake with it.

The diagram should be completed as shown below.

Suggested method:

Symmetrical designs are a favourite with the SAT writers and here is another typical example. Because the mirror line runs diagonally it makes it harder to make the pattern symmetrical.

Children should have had a lot of practice with this type of question and a mirror is handy to complete the pattern. Folding along the dotted line is also an option which helps to see how the pattern is reflected.

Go to Questions 9 and 10 Paper A 2011

Interestingly, some of the addition statements can be answered by subtraction and some of the subtraction statements can be completed by addition. For example: 35 + ?? = 75 can be done by subtracting 35 from 75. An equally good method would be to add on in tens from 35 to 75.

In the same way 36 – ?? = 20 can be completed by adding on from 20 up to 36, or simply by subtracting 20 from 36. This all helps with understanding the relationship between addition and subtraction.

This set of worksheets, which because it involves both addition and subtraction is slightly harder than just dealing with one, can be found in the Year 4 addition category.

Go to Year 4 addition and subtraction questions

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

We start with some straightforward worksheets which are all linked to essential mathematical terms that children are expected to know. For example we have a Year 1 word search on Length, using terms such as short, high, narrow etc.

Once children in year 1 have got a really good knowledge of numbers they can start to look at ordinal numbers. Whilst young children are not expected to know the term ‘ordinal numbers’ they are expected to know and understand terms such as first, second, third etc. This language can be developed during the playing of games whilst discussing who should go first, second etc.

We have a simple word search using these terms. All the words can be found either going across or down – there are no diagonals. It is good practice to help with reading and writing these words as some of them are quite tricky.

Also we have published other similar pages on the vocabulary of measures and months of the year for year 2 and fraction terms for year 5.

Similar to the word searches are our tables number searches, but the times tables are hidden away rather than vocabulary. At the moment we have 3 times and 4 times table searches for Year 3, 6 times table for year 4 and 7 times table for Year 5.
Hardest of all are our wordsnakes which are rather like a maze. Start at the arrow to find the first word, moving across or down, but not diagonally, rather like a snake. The word will not be in a straight line so might be quite tricky to find, although the first word is often given to make it a little easier.

The second word follows on immediately from the first; the third word from the second and so on until each letter in the grid has been used once. The last letter of the last word is where the arrow exits the maze.

Write the words down in the spaces provided. The number of dashes shows how many letters are in each word. The initial letters of the second and third words have also been given.

All the words in the wordsnakes come from the vocabulary lists for the corresponding year group.

Go to wet break resource for year 1

The year 4 questions should prove popular with children as they are a nice and easy set of addition of 2-digit questions. 64 + 29 might at first glance look hard to do ‘in your head’ but children should be using all kinds of strategies to make it easier e.g. add 64 and 30 to make 94 and then subtract 1 to make 93.

The year 5 questions are on completely different themes, including place value, number sequences, rounding and percentages. The place value questions look at decimal fractions and the value of the the digit such as the 7 in 3.367. Knowing the value of digits to three decimal places is important when converting metric measures such as litres to millilitres etc.The final two questions look at finding simple percentages of amounts of money.

Finally, the year 6 questions again concentrate on fractions, percentages and rounding, including rounding fractions to the nearest whole number. Several of the questions ask for decimal fractions to be written as fractions e.g 0.33 can be written as 33/100.

Go to Year 4 mental arithmetic

Go to Year 5 mental arithmetic

Go to Year 6 mental arithmetic

The answer is:

3 + 7

1 + 8

2 + 4

Award two marks for all three pairs of numbers correct as shown above. The numbers within the pairs may be given in either order.
Award one mark if two out of the three pairs are correct..
Suggested method:
There appears to be only one way to complete this correctly, so a little bit of strategy needs to be employed. Take a look at the numbers involved and it can be seen that:
1. The two larger  numbers must go in the top two rows as they are both too large to go in the third row.
2. Given that the bottom row numbers must come from 1, 2, 3 or 4 and must total 6 then there is only one combination that works: 2 + 4.
That leaves 1, 3, 7 and 8 to make the totals up to 12 for the other two rows.
The top row needs 10 more so the only combination for this is 3 and 7.
That leaves 1 and 8 for the middle row, which is correct.
Probably the trickiest part of this question is not to assume that you can work out the top row first. The inclination is to think that because it needs the highest total it must include the highest digit (8) and therefore the other digit must be 2. Putting 2 and 8 in the top row will lead to a lot of unsatisfactory fiddling with the other numbers and time will pass by which should be saved for later questions in the test.

Go to Question 8 paper A 2011

1 kilometre = 1 000 metres

1 metre = 100 centimetres

1 kilogram = 1 000 grams

1 litre = 1 000 millilitres

They are also expected to recognise half units, such as half a kilometre and that this can be written as ½ km, or 0.5 km or 500 m.

Problems involving comparisons continue in length, capacity and mass, and once again most of these should be on a practical basis.

One of the most useful benefits of the metric system is the relationship between the units:

a litre of water can be contained in a 10 cm cube (1 000 cubic cm) and has a mass of 1 kg. Hence a 1 cm cube of water has a mass of 1 gram and is known as 1 ml.

Choosing suitable units continues from year 2, with many similar activities, but a greater emphasis on standard units and mathematical language.
It is an excellent idea to have a collection of pots, cartons etc which show the capacity and wrappers which show weight. These can be grouped in various ways and comparisons made.
Choosing the correct unit to measure is important and practice can be given orally on these questions – hold up a pot and ask what you would measure the capacity in as part of the daily mental arithmetic.
In Year 3 children measure and draw lines to the nearest half centimetre. It is important that they have rulers which include millimetres and that they understand that 0.5 is the same as a half.

Much more can be found in our measurement for Year 3 pages here.

It’s mainly fractions for the year 5 sets  of questions. Questions such as ‘How many sixths are there in one third?’ can cause confusion for children and highlights the importance of understanding equivalent fractions.

The year 6 questions again look at equivalent fractions and writing fractions as decimals. There are a lot of interesting patterns that can be made from converting fractions to decimals when using a calculator.

Go to Year 4 mental arithmetic

Go to Year 5 mental arithmetic

Go to Year 6 mental arithmetic

1. Counting

Making progress with counting will still be important in year 3, using up to three digit numbers. Grouping into tens or fives and using tally charts are both effective ways of counting larger sets of objects.

In Year 3 work on counting in tens will cross the hundreds boundary (eg count on from 285:  295, 305 etc).  This is harder than we might think and requires a good understanding of counting. A lot of oral work is necessary if children are to become confident with this and it will help a great deal with mental arithmetic if children can count up and down in tens from any starting point.
Having counted from one number to another it is a good idea to ask how many tens they have counted.

Counting on and back will progress to larger numbers. Starting with any small number, it is expected that children will be able to count on in steps of 2, 3, 4, 5, as well as 10.

Counting on and back in whole hundreds, up to 1 000, is also introduced in year 3.

Simple sequences, or patterns of numbers, which go up or down in equal steps should be recognised and children should continue to try to say what the rule is when they recognise a sequence.

They should also begin to make up their own sequences of numbers, given certain conditions eg ‘make a sequence that has a 4 and a 12 in it’ or ‘make a sequence which goes up in twos’.

Work will continue with multiples, extending to multiples of 50 and 100.

2. As well as reading and writing numbers up to 1 000 children are also expected to understand what any digit in a three digit number represents.

3. Comparing and ordering numbers

Children are expected to be more confident in  their knowledge and use of the vocabulary which is used when comparing and ordering numbers.

4. Rapid mental response

Rapid mental response to questions involving the addition and subtraction of 1,  10  and 100 is expected by the end of year 3. Building on earlier work questions will now involve crossing the hundreds boundary.

e.g. what is one less than 400?

5. Estimating and rounding

In year three children will continue to make estimates of numbers and measurements, usually up to about 100. This could involve the number of marbles in a jar, counters in a pile, lines on a page, words in a paragraph etc and a great deal of practice at estimating can be done in the outside environment.

6. Understanding Fractions

In year 3 children will be introduced to the fraction 1/10 (one tenth), as well as fractions such as 1/3 (one third) and 3/4 (three quarters), where the numerator (top number) is more than one.

Get more information on Year 3 Counting and Number