## Year 3 mental arithmetic: Sets 9 and 10

This week the mental arithmetic for Year 3 concentrates on writing whole numbers in digits, counting on and back, addition, subtraction and place value.

These questions can either be done quite quickly, taking up just a few minutes or in more detail, depending on the time available. By more detail I mean talking through each question and asking how they were done. For example: How do you add 40 and 70 in your head? Is it the same as you would do it if writing it down?

When writing down a number such as four hundred and ten in figures watch out for a common mistake of writing 40010.

Year 3 mental arithmetic: sets 09 and 10

## Year 5 maths worksheet: 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.

## Year 4 maths worksheet: decimal fractions and money

Money is a great way to reinforce place value with decimals. For example in the total £3.45 the digit 4 has a value of 4 tenths or 40p. Money makes it very easy to show tenths (a 10p coin is one tenth of a pound) and hundredths (a one pence coin is one hundredth of a pound).

This page looks at this in more detail, showing that ten pence can be written in two ways; either as 10p or as part of a pound £0.10. There are two further things to remember here:

1. that we should always have two digits after the decimal point when writing fractions of a pound eg £0.30 not £0.3.

2. that we should not include both the pound and pence sign when writing amounts in pounds eg £0.30 is correct but £0.30p is not. it is 0.30 of a pound, not 0.30 of a penny.

This is just one worksheet from a great selection in our Counting and Understanding Numbers section within our year 4 maths worksheets. Why not go and have a look at what else is freely available?

Decimal fractions and money

## What maths should children know by the end of reception?

Let’s begin by looking at what is expected by the end of the Reception year – that’s children aged between 4 and 5 years old. This is sometimes called the Foundation Stage. Yes, even our 5 year olds have targets to reach!
I will take each of the strands in turn, but as you go through them it will become clear that the most important thing of all is to talk with your children and use the vocabulary of simple maths to help them describe the world around them.

Counting and understanding number:

• Children should be able to say and use number names up to 10. A good example of this would be to join in nursery rhymes or songs such as:
“One, two three, four, five. Once I caught a fish alive.”

• Children should be beginning to count up in ones, up to 10 objects. This would be in a practical sense of counting a number of objects that they can touch (pieces of a jigsaw, coins, hats etc). Later they can count things they can see, but not touch (panes in a window, cows in a field etc).They can then begin to count down from a small number eg 5,4,3,2,1,0.

• They should be beginning to use mathematical language to compare two numbers. Words to include are: bigger/smaller, more/less, first/last.

• Recognise the numerals 1 to 9. Birthday cards with the age on is always a good starting point. Make a set of numbers from 0 to 9 on card. Pick out the numbers in a story: 3 Billie Goats Gruff etc.

Knowing and using number facts:

• Children should know one more or one less than a number between 1 and 10. In other words they know that 5 is one more than 4 etc. Again, the real world is the best learning environment – laying the table, in the kitchen etc.

Calculating:

• Children should begin to see addition as the combining of two groups of objects. (An example of this might be “Show me 3 fingers on your right hand. Show me two fingers on your left hand. How many fingers are showing altogether? Count 123….12….12345. They will need the oral prompt of “so 3 fingers and 2 fingers make 5 fingers” after the counting.)

• Children should begin to see subtraction as ‘taking away’. (When asked how many are left after eating 2 of our 5 cakes to begin with children will do this by counting how many are left. Having counted what is left, they need the reinforcement orally -“let’s say together 5 take away 2 is 3”.

• Through practical activities they will begin to use the vocabulary of addition and subtraction: add, make, more, take away, how many are left?

• A further extension is to begin to share objects into equal groups and count how many there are in each group.

Understanding shape:

• Children are expected to be able to create simple patterns. Much of this might be described as art work – using sets of shapes, printing, beads, cotton reels etc to create simple patterns and talk about them.

• Children are expected to be able to use the vocabulary of shape to describe the shape and size of solid and flat shapes: circle, triangle, square, rectangle, cube, cone and sphere. These could be shapes they make themselves or familiar shapes found around the home: mats, boxes etc.

• Use everyday words to describe the position of objects. A wide vocabulary including: over, under, above, below, next to, in front, behind, outside, inside, next to, left, right, up, down, forwards, backwards, across. Reading books are excellent for this type of work: looking at a picture in a book such as “Where’s Spot”.

Measuring:

• Children are expected to use the vocabulary of simple measurement, such as: more or less, longer or shorter, greater or smaller, heavier or lighter, thick, thin, tall, high, low, full, empty. Much of this is in the form of comparisons and needs to be done on a practical basis: a pair of balance scales and empty containers which can be filled with sand/water are really useful for this.

• Children are expected to use the vocabulary of time. They are expected to begin to know the days of the week, morning, afternoon, night, today, tomorrow, yesterday, now, soon, later, before, after, next, last. Again, story books are a superb resource such as The Very Hungry Caterpillar by E Carle. They should be beginning to use hours of the day: my bedtime is 8 o’clock etc.

Handling data:

• Children are expected to be able to sort familiar objects according to simple criteria – colour, shape, size etc. A tray of beads, lego, coins, marbles etc are all useful for this.
• They will count the number of objects which share a particular property (eg red crayons)
• They will also begin to present results of their counting using pictures or drawings

Using and applying mathematics:

• Use mathematical ideas to solve simple practical problems
• Match sets of objects to numerals
• Sort objects
• Talk about patterns in number
• Talk about how to solve a simple practical problem.

## Coming soon: tables, calculator game and probability

What have we got next week? we have the second in our multiplying by 3, 4, 6, 8 and 10 worksheets, suitable for year 4 children or those who are beginning to know their tables. The best way to learn tables is to recite them out loud eg ‘4 times 3 is 12, then shorten it to,  ‘4 3s are 12’, with the ultimate aim of being able to say the product for any two single digits without having to work it out – just like knowing your own name!

If you want further practice on tables then our calculator games are ideal. The idea of the game is to make a row of 4 in any direction before your opponent. Take it in turns to use the calculator to multiple chosen numbers to match numbers on the grid. This is excellent practice at multiplying and dividing by 5 mentally and then using the calculator to check answers. Suitable for year 3 upwards.

For Year 6 we have a probability page that looks at writing the probability of events happening as a fraction or a decimal fraction.

For example, the probability of getting a head when tossing a coin is 1/2, but this can also be written as 0.5. That one is easy, but many others are much trickier.

## Learning tables: grids

Multiplication tables are the basis for a huge amount of maths, ranging from simple sums to division and cancelling fractions.

Use these sheets as timed practice, with the aim of getting a quicker time for each and, of course, all correct. A limit on time can be given. A good 11 year old would need 2 minutes or less; most children would need between 10 to 15 minutes to begin with.

The grids can be approached in a variety of ways; completing in strict order or picking out the ones you know (such as 1x and 10x) first and then filling the gaps.

There are lots more like this at mathsphere.co.uk

All tables grids