## 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.

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 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

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.

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

## Perpendicular lines

The term perpendicular was usually introduced to children in the upper primary years and indeed into secondary school, but it is now thought that it should be introduced in year 3. At this stage children just need to be able to recognise two lines which are perpendicular to each other and to make it easier all the pairs of lines shown on the worksheet either cross or touch.

Of course, the key to being able to do this is to recognise a right angle and plenty of practice with recognising right angles must be done before going on to using the term perpendicular.   When the lines are vertical and horizontal it is quite easy to spot perpendicular lines but other placements make it more difficult to see just by looking and there is no harm in using the corner of a piece of paper to judge whether this is the case.

Perpendicular lines

## Year 6 resource of the week: factors

Understanding factors and multiples is something many children fail to grasp. Here we have a page on factors and how to find all the factors of a number. The process is fairly straightforward, but can be quite time consuming. A good knowledge of tables and division is also needed. So if children’s knowledge of tables is weak, if they find division difficult and if they have little staying power then it is unlikely that they will enjoy trying to find factors of numbers!

One point that even brighter children take a while to understand is that you only need to continue to divide up to when the number squared is larger than the original number eg to find the factors of 62 you only need to divide 62 by numbers up to 7 because eight eights are 64. It is a good idea to spend some time explaining and showing the logic of this to children.

This can be found in our Year 6 Understanding Number section.

Factors 1

## Roman numeral clock faces (2)

Our Roman numerals clock face worksheet has proved very popular so I thought I would post another similar page, but including quarter to and quarter past the hour times. I have also been asked why the clock face shows IIII for four o’clock rather than IV. In fact most Roman clockfaces do show the four Is and nobody is sure why.

One reason is that when looking at the numerals opposite to each other – all of them are in perfect balance, except for the ‘heavy’ VIII and the ‘light’ IV; optical balance is re-established by printing an also ‘heavy’ IIII.

Another reason which has been given is to do with the old casting process of the numerals; ‘ Since some numerals were cast out of metal, or carved out of wood or bone, you need 20 I’s, 4 V’s, and 4 X’s, even numbers of each, if you use four I’s for “four”. The molds would produce a long centre rod, with 10 I’s, 2 V’s, and 2 X’s on each side.’

A third possibility is that clocks use IIII rather than IV out of respect for the Roman God Jupiter, the king of the Gods,  whose name, in Latin, begins IV (the V being the U we now use, the I the J). Very old sun dials seem to use the IIII and early clocks followed suit; it has also been suggested that Wells Cathedral clock, one of the earliest cathedral clocks used the IIII and everyone copied this, and yet another reason is that Louis XIV preferred IIII over IV and ordered all clocks to be made in this way, and it has remained like this ever since.

Finally it has also been suggested that Romans were not great at subtraction so IIII was easier to work out than IV! I have no idea which, if any of these has the best claim to being true but interestingly Big Ben uses the IV convention.

Roman numerals clock  2

## Resource of the Week: Year 5 Number Challenge

I really like this challenge, partly because there is no, one right way to answer it and partly because it really makes children think.

There are 10 digits, from zero to nine to be placed in the 10 boxes in such a way that the targets can be matched as closely as possible. The catch is that each number can only be used once!

Now the obvious way to start is to make 98 the largest even number, but immediately that means that you can not have 97 as the largest odd number. By the time you reach the last target, number closest to 30, you have only two digits left and only two choices!

But what counts as the best possible answers? This is as big a challenge, if not bigger. I have had a class try to make a set of rules to try to be as fair as possible, but it involved a great deal of addition and subtraction. One group made a set of rules that went like this:

1. Find the difference between 98 and the answer given.

2. Find the difference between 99 and the answer given.

This will give your total so far – the larger the total, the worse you have done.

I won’t continue with this as it might spoil the fun!

This page can be found in our Year 5, Using and Understanding Maths category.

## Subtracting mentally in Year 4

Making the correct choice in deciding how to work out an answer is the key to fast mental arithmetic. Many children are unaware that there are often several ways of working out a calculation and that those who choose the best methods find maths easier and are able to answer questions more quickly and more accurately.

Let’s look at ‘Subtract 38 from 63.

This should be done, ‘in your head’ and will involve several stages, depending on the method used.

First, I could take 30 from 63 to leave 33. Then I could count back 8 from 33 which gives me 25.

Secondly, I could take 40 from 63 leaving 23 and then compensate by adding 2, which gives me 25.

Thirdly, I could take 38 from 68, leaving 30 and then compensate by subtracting 5 (because 63 is 5 less than 68).

There are several other ways very similar to these, but this does show that there is no ‘one right way, when it comes to mental arithmetic.

Quite hard mental arithmetic:_subtraction (1)