This is a brief summary of some of the most important maths concepts to be taught in Year 3 by way of challenges and investigations.
1. Choosing appropriate number operations
An important aspect of Using and Applying Maths is concerned with children choosing and using the most appropriate number operations to answer questions and solve problems.
A good way to introduce this is to ask children to make up number stories from given maths statements, using all four rules. In this way children can show that they understand the meaning of the number sentences and can put them into a real context.
When asking which number operation is best, activities can arise easily from practical work and everyday situations and can be answered orally.
Children should be starting to make more complex, and more interesting, number stories corresponding to the sums.
Another activity, following on from year 2, is a where a sign has been omitted or replaced by a star or shape . This again makes children think what is happening in the sum and is a good introduction into algebra.
2. Open and closed questions
Solving problems and investigating continue in three year. Some of these problems are ‘closed’, in other words they only have one, or a few possible answers. Others are ‘open’ and can have many possible answers.
The open questions are ideal for assessing how well children use their knowledge and how imaginative they can be.
Exercises such as the magic triangle look closed to begin with but there is plenty of potential to change totals or even change the numbers that are put in.
Because of the open nature of most of these problems we have not included answers for the majority – it is an excellent idea for children to check both their own and other children’s solutions to see if they fit the criteria.
3. Working in a systematic way
A key feature of this work is that children should become more systematic in their approach, checking as they go and looking for answers which are the same. They should be able to talk about their work, especially about how they are tackling the investigation, what the rules are and any findings they have.
Children should be given the opportunity to give examples to match statements. It should help them clarify some of the basic concepts, such as an even number and an odd number will always add up to an odd number etc. It also re-inforces much of the mathematical language used so far, such as multiple, odd, even, right angle etc.
4. Solving problems
In year 3 children are expected to use any of the four operations to solve ‘story’ problems.
Once again, these problems can be divided into one step and two step problems – the latter meaning that two calculations have to be done in order to get the answer.
Children should explain orally how they set about answering the questions and then move on to written methods using simple number sentences.
There are also similar modules on money, time and measurement.
Money continues to be an important area of work in year 3, especially as a means of re-enforcing place value. Working with coins should remain a priority, and children will begin to give change for amounts up to £1.
An emphasis is made on converting pounds to pence and vice versa. Especially important is to recognise the need to place a nought in the ten pence column when converting amounts such as 203p into pounds.
When working out change, ‘counting on’ from the units should be encouraged,
eg: Change from £1 when spending 67p
3p makes 70p, add another 30p to the 70p to make 100p: answer 33p
Note: Working in this way should avoid the all too common erroneous answer of 43p, which is reached by adding 40 to 60 and then a further 3 to the 7 to make 10 (in reality this comes to 110p)
Go to Year 3 Challenges: Using and Applying Maths
A brief summary of some of the most important maths concepts to be taught in Year 3.
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 have just begun a brand new section of the site called Wet Break/Holiday Activities which will contain short, fun activities with a mathematical slant. They are aimed at those odd quarters of an hour when there’s nothing else to do, such as a wet playtime or all other work has been finished early.
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
Posted in What's new!
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