Here we have a brief summary of some of the most important maths concepts to be taught in Year 3. More detail is available via the link below and on the urbrainy.com website.
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.
As we get well into the summer term here are the next sets of mental arithmetic questions for Years 4, 5 and 6.
The Year 4 questions concentrate on fractions and decimals, together with a little bit of counting, addition and subtraction. To answer the fraction questions correctly children will need a knowledge to know what fraction of a pound is 10p and what fraction of a metre is 10 cm. Luckily the metric system makes these answers quite easy.
The Year 5 questions are all about doubling, halving and multiplication. Children are expected to be able to double any 2-digit number and halve any even 2-digit number ‘in their heads’. Questions 5, 6 and 7 look at multiplying multiples of 10 which they should find straightforward if times tables are known.
The Year 6 questions follow a similar pattern, but with harder numbers. For example, multiplying 6.55 by 100 just needs a good understanding of place value as each digit moves two places to the left. There are also a couple of questions finding half of decimal fractions which could prove quite tricky.
This week we are publishing a set of pages which look specifically at dividing 3-digit numbers by single digits, concentrating on the 5, 6, 7 and 8 times tables to do this. This is to practise the ‘short’ division method.
When I was young I was taught the short method before the long method and by repeated practice learned the method, although probably not knowing why it works. Today the long method is usually introduced first as a means of showing exactly how it works, usually with easier numbers. The key to both methods is, of course, a good knowledge of tables, although on these pages the table has been written out to help.
For example: 7)627
‘How many sevens in 62?’
’7 times 8 is 56, 7 times 9 is 63.’
’7 goes into 62, 8 times with 6 left over.’
Write the 8 in the answer above the 2.
Write the remainder 6 beside the 7 units, making 67.
‘How many sevens in 67?’
’9 times 6 is 63.’
’7 goes into 67, 9 times with 4 left over.’
Write the 9 in the answer in the units and write rem 4 next to it.
It should be pointed out that children need a very good knowledge of tables in order to be successful with this method of division.
The year 3 work on division builds on the foundations built in year 2. Again, division can be seen in two ways:
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.
Here we have the latest batch of mental arithmetic questions for Years 4, 5 and 6. There are two sets of questions for each age group, with ten questions in each set.
The Year 4 questions include finding missing numbers in sequences and working out money problems. There is also a question involving negative numbers in the context of temperature measurement.
The Year 5 questions include a couple on factors which are quite hard if the questions are read out and children do not get to see the numbers involved. There are also some easy multiplications and finding tenths of numbers. two of the questions involve writing fractions as decimals, but as the fractions are tenths this should prove to be straightforward.
Finally the Year 6 questions are all about doubling and halving and making good use of knowledge of times tables. It is worth asking children how they work out the answer in their heads to questions such as ’16 times 15. One of the easiest ways is to halve one number and double the other, making a calculation of ’8 times 30′.
More mental arithmetic pages can be found in the links below.
This set of addition worksheets has a mixed selection of questions to stretch the capabilities of most children in Year 4. At this stage we are looking for rapid responses using a variety of different skills depending on the type of question.
Let’s look at some of the different types of question and some possible approaches.
a. 400 + 355. An instant recognition that just the hundreds need to be added and the tens and units will remain the same. Should be very quick.
b. 450 + 18. This is probably best done by ‘adding on’ add 10 to 450 makes 460 plus the 8 making 468.
c. 430 + ??? = 580. Either done as a subtraction taking 430 from 580, or by adding on. If doing the subtraction it is quite usual to start with the hundreds 500 take 400 is 100; then the tens 80 take 30 is 50; answer 150. (The reverse of doing this on paper.) If adding on children may well start with adding either the hundreds or the tens as both are equally good.
d. ??? + 50 = 460. Again this can be done by adding on from 50. Add 10 to make 60. Add 400 to make 460. Answer 110. It can also be done just as quickly by subtracting 50 from 460.
Year 3 is the year that children really begin to take off with multiplication. One of the key things is the understanding that multiplication is repeated addition. Also the multiplication sign is used and understood as meaning, ‘lots of’.
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
With the start of the summer term comes the next in our sets of mental arithmetic worksheets for years 4, 5 and 6.
The year 4 questions concentrate on multiplying and dividing by ten as well as place value. It is always worth reinforcing the idea that to multiply by ten move each digit one place to the left and to divide by ten move each digit one place to the right.
The year 5 and 6 questions are of a similar kind, although the numbers are larger. The first two questions of the year 5 sets look at writing large numbers in figures, including millions. Writing a number such as one million two hundred thousand in figures can prove to be quite tricky, with many adults getting into a muddle as well as children. It is best to remember that numbers come in sets of three:
hundreds, tens and units e.g. 123
hundreds, tens and units of thousands e.g. 123 123
hundreds, tens and units of millions e.g. 123 123 123
so 123 123 123 is one hundred and twenty three million one hundred and twenty three thousand one hundred and twenty three.
There has been a great deal of interest in the Titanic during the last few weeks, as the 14/15th April 2012 approaches, exactly one hundred years after the disaster.
The Titanic was built by Harland and Wolff for the White Star Line as the largest passenger ship in the World, and was thought to be unsinkable. However, at 11.40 pm on the 14th April 1912 the Titanic hit an iceberg in the cold North Atlantic Ocean which ripped holes into the side of the ship. The water flooded in much faster than the crew could pump it out. Unfortunately many of the lifeboats had never been installed because it was thought that they would never be needed and they would clutter up the deck of the new ship!
The Titanic sank just over 2 ½ hours after it hit the iceberg, in the early morning of the 15th April. The nearest ship to the Titanic, the Carpathia, was some distance away and the survivors had to wait in their lifeboats for several hours before being rescued. The Carpathia then took the survivors to their destination in New York. Many stories and films have been produced since that fatal night.
We have had many requests for comprehension pages and thought that now was a great time to launch the first of a brand new series, to coincide with the Titanic disaster! Comprehension is important because just identifying words on a page does not make for successful reading. It is vital to be able to understand the written words, engage with them and think about their meaning.
Over the months to come we will be producing a series of comprehension worksheets linked to historical events which we hope you will find useful. This first set of pages on the Titanic has three short comprehensions on aspects of the Titanic, giving practice at reading and understanding texts together with a fact sheet which provides a useful starting point for further research.
One of the most famous 800 metre finals in history took place in 1980 where three British runners were meeting, two of them with an excellent chance of winning. The athletes were Steve Ovett and Seb Coe and Dave Warren.
Coe was the favourite as he already held the World Record for the 800 metres. Ovett was favourite for the 1500 metres to be run a few days later.
The final was a tense affair, with Ovett only in sixth place after one lap. But he managed to force himself through the field to reach second place with about 100 metres left. He then raced into the lead and held off Coe over the last few metres to win the Gold Medal. Coe came second and Dave Warren came 8th.
This maths worksheet looks at the final places and times with some tricky questions to follow. Probably the hardest question looks at the average time that Ovett took to run each 100 metres of the race. This requires converting the minutes and seconds into seconds, then dividing by 8. Interestingly the average time he took to run each 100 metres of the race was 13.2 seconds – a time that not many people could achieve over just one 100m race, let alone doing this for 8!
