Resource of the week: partitioning large numbers

Our resource of the Week looks at place value with larger numbers, something that many children find tricky.

By year 5 children are expected to be able to read and write some seriously large numbers. A really good understanding of place value is needed to read large numbers successfully. The key to looking at a number and working out how to say it lies in separating the number up into a series of hundreds, tens and units.

Let’s look at 123 456 789

Take the first set of three digits (on the right:789) as a set of hundreds tens and units: that is seven hundred and eighty nine.

Take the second set of three digits (456): that is four hundred and fifty six; but it is four hundred and fifty six thousand.

Take the third set of three digits (123): that is one hundred and twenty three; but it is one hundred and twenty three million.

Put them together to make one hundred and twenty three million our hundred and fifty six thousand and seven hundred and eighty nine.

An abacus is a really good way to look at how to read numbers and is a very powerful mathematical tool – anyone who has been to Hong Kong or China and seen how they calculate with an abacus will be amazed!

 

Partition up to 5-digit numbers (pg 2)

Year 2 Counting and Number

A great deal is expected of children by the end of Year 2 and we have some great maths worksheets to help them on their way.

It all begins with counting on in steps of one. When children are really confident with this and have mastered reading 2-digit numbers they move on to counting on and back in steps of 10. Other activities included, are completing missing numbers on a number square, estimating on a number line and recognising halves of shapes and numbers.

Go to our year 2 Counting and Number worksheets

Year 4 maths worksheet on time

days-and-hours

By year 4 children are expected to know that:

1 week = 7 days
1 day = 24 hours
1 hour = 60 minutes
1 minute = 60 seconds

This maths worksheet uses this knowledge to answer  some straightforward questions. It also requires a calculator so more detailed information can be found, such as the number of minutes in a week. This, in turn, can lead on to some interesting investigative work, such as finding out how long a year is in minutes, and then how many minutes you have been alive (not forgetting leap years). It is quite an eye opener to realise how many precious minutes have been taken up in queues, traffic jams etc!!

This worksheet can be found in our Year 4 resources, under Measures

Days, hours, minutes and seconds

Old school methods better for learning?

Two studies recently published in the Science Journal would suggest that a couple of ‘old fashioned’ methods of learning are more effective than many of those used today.

Firstly, a study from the University of Stavanger suggests that writing things down rather than by typing helps with learning. Our brains receive more feedback from muscles and fingertips when writing rather than touching a keyboard. Also, it takes more mental effort and time and this is thought to help ‘imprint’ memories. I must admit to always thinking that recording on paper was a good way to learn and spent much of my time when revising for exams writing down what I knew. This would suggest that writing answers in maths is better done in a maths book, or worksheet than just keying in answers on a keyboard.

The second piece of research, from Purdue University, Indiana, says that reciting facts shortly after learning them is better than many newer educational methods such as mind mapping. Constant informal testing and reciting helps to reconstruct knowledge, both for short term and long term memory.

Year 3 maths worksheets: Know Number facts

Year 3 is a time when children make huge strides forward in their mathematical thinking, as long as they have got a secure background knowledge. With over 20 pages to choose from, our worksheets in the Know Number Facts reflect this development. We have worksheets on knowing addition and subtraction facts with numbers up to 20,  doubling numbers and subtracting from a teen number.

We also have a number of pages dedicated to calculator games. The aim of these is to use the calculator as a means of showing knowledge of tables and multiples of 3, 4, 5 and 10, not just as a means of working an answer out.

Division, of course, is much easier if tables are known and we have a growing number of pages of division questions.

Go to our Year 3 maths worksheets on knowing number facts

Year 6 maths worksheets: Understanding Number

The Mathsblog section on year 6 maths worksheets, Understanding Number, has a growing number of worksheets covering a wide range of topics. The work expected in Year 6 is very challenging as numbers are used in ever increasing and decreasing sizes. Rounding numbers right up to millions is included, together with rounding decimals and estimating and approximating numbers.

There is also some excellent pages on fractions, as well as relating fractions, percentages and decimals. Prime factors are also introduced. Keep an eye out on this section as it is updated with new worksheets being added on a regular basis.

For a lot of Year 6 children this work will prove too tricky and I would advise looking at some of the earlier year groups for suitable material, in particular year 4 and 5.

Go to our Year 6 Understanding Number worksheets

The year 2011

A very happy new year to everyone. The new year will begin with a real mathematical twist as 2011 is a Prime Number. (Remember a prime number has just two multiples, itself and 1). Whilst there are an infinite number of prime numbers they are not easy to find. The last prime year was 2003 and the next will be 2017.

There is quite a lot of time in 2011, although the older you are the quicker it seems to pass by! The total time from 01-01-2011 to 01-012012 is 8,760 hours.
This is equivalent to 525,600 minutes.
You can also convert 365 days to 31,536,000 seconds.

We can also look forward to some spectacular dates this year such as 11th November 2011 which will be 11.11.11, but more of that as we go through the year. We can start with the first second of the first minute of the first hour of the first day of the first month of the new year, which will be:

1.1.1.1.1.11 (127 is 1111111 in binary)

As for the Chinese Calendar, 2011 will be the Year of the Rabbit: According to the Chinese this will be a placid year, very much welcomed and needed after the ferocious year of the Tiger.

Year 2 maths worksheet: multiplication in any order

multiplication_in_any_order_large

Children in Year 2 are expected to know and understand an awful lot about how numbers work. Here we have a maths worksheet, one of a set from urbrainy.com, which looks at a vital part of understanding the process of multiplication: that it can be done in any order. This is also true of addition, but not of subtraction or division.
This page shows that ‘2 lots of 4’ is the same as ‘4 lots of 2’, therefore 4 x 2 is the same as 2 x 4. It does not matter which way the answer is worked out, it will be 8.
This little piece of knowledge helps children with mental arithmetic and with learning tables. Each table which is learned gives further knowledge of other tables. Eg If you know 5 x 4 = 20 then you can quickly reverse the number sentence to 4 x 5 = 20.

Multiplication in any order (pg 1)

New Education White Paper

I knew that it wouldn’t be long before the present government wanted to stamp its authority on education by bringing in new reforms, and here they come!

One of the main targets is discipline and they hope that by encouraging school uniforms, house systems and prefects that a back to basics approach will improve disciple. They seem to be ignoring that a vast number of schools already have these in place!

Perhaps more importantly, heads will have the final say on expulsions, stopping independent appeals by panels which often go against the school’s wishes. However, there is a twist in that the school must find alternative education for these expelled pupils and their performance in tests will still be included in the original school’s league tables.

The White Paper also announced plans to encourage servicemen leaving the forces to re-train as teachers under a “Troops to Teachers” programme, saying that troops had a lot to offer. I imagine adults from many other walks of life have just as much to offer, if not more, but perhaps I am biased as I still remember a couple of my Grammar School teachers who were retrained after the war, and good teachers they were not!

Gove has also given himself more power over schools; through the Academies Act he can order any school to be converted to one of his academies.

There were also hints that the curriculum might be freed up from the constraints of the National Curriculum, with only core subjects being mandatory.

There is plenty more, but much of it seems to be ‘hot air’ which will make little difference to the average school. No doubt the significance of the White Paper will become clearer over the next few weeks.

Katharine Birbalsingh: making children responsible

Katharine Birbalsingh has certainly caused a stir in Education circles with her views on what is the best way to help children succeed. She states that the education system is broken, because it keeps poor children poor by making excuses for them.

She believes that certain values are important, including being responsible for yourself and not allowing children to excuse away bad behaviour. Children should be held to account for what they do, so that they can be responsible for themselves.

She sees failure as an important part of the learning process and argues that because we don’t want children to fail we keep making excuses for them. She also believes that exclusions are not helpful as it gives children yet another excuse for failure.

Children should feel responsible for their own results, not the teachers. Until we get children to feel this responsibility then schools will continue to fail. This is a very different viewpoint than that held in many schools, and a very challenging one. Where does this responsibility come from? Certainly the home for most children and it is very difficult for schools to change attitudes without the backing of the home.