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Resource of the Week: short division of decimals
This week I would like to look at a page of practice on using the short method of division of decimals. The numbers being divided are just units and tenths which helps with getting the method correct.
There are arguments for and against putting the decimal point in before you start, or leaving it until you have reached that point in the question. it does not matter as long as it is inserted correctly.
One of the best ways to be fluent with this method is to talk it through out loud. If we look at question 2 which is 4.5 divided by 3, the verbal stages are:
a. How many 3s in 4?
b. 1 times 3 is 3 so there is 1 with a remainder of 1.
c. Place the 1 on the answer line, immediately above the 3.
d. Place the decimal point just above the answer line so it can be clearly seen.
e. The remainder 1 is placed just in front of the 5 (usually written smaller).
f. How many 3s in 15?
g. 3 x 5 is 15 so the answer is 5.
h. Place the 5 on the answer line, immediately above the 5 (tenths).
i. Answer 1.5
This page can be found in our Four Rules, Division category.
Year 3 Maths: Find the missing numbers
What looks like a very simple worksheet is actually rather tricky. There are six statements about pairs of numbers, along the lines of:
Find a pair of numbers with a sum of 8 and a product of 15.
Firstly, children need to know that the sum of two numbers is found by adding up. Secondly, they need to know that to find the product of two numbers they need to multiply them together.
It is then a matter of some ‘trial and error’ work, finding two numbers which meet one of the criteria and then seeing if they meet the other. For those who are good at times tables it is more efficient to start with finding products, as there are less possible answers.
Resource of the Week: know number facts in year 2
A lot is expected of children in Year 2, especially what they should know off by heart when calculating. By the end of the year they should:
• know all addition facts for two numbers up to a total of 10. (eg 4 + 5.)
• be able to derive subtraction facts for numbers up to 10. (eg if they know that 6 + 3 = 9, they can instantly work out that 9 – 6 = 3.)
• know all the pairs of whole numbers which total 20. (eg 16 + 4.)
• know all the pairs of multiples of 10 which total 100. (eg 30 + 70.)
• know the doubles of whole numbers up to a total of 20. (eg double 7.)
• understand that halving is the inverse of doubling and hence derive halving facts from their knowledge of doubling. (eg if double 8 is 16, then half 16 is 8.)
• recall 2, 5 and 10 times-tables. (eg know 5 x 6.)
• work out related division facts. (eg if 5 times 2 is 10, then 10 divided by 5 is 2.)
Now, that is quite a lot to know with instant recall, and they will need plenty of practice to achieve this. Why not go to our Year 2 Knowing and Using Number facts to help them on their way?
Year 4: What sign?
Children in Year 4 will be investigating a whole range of problems involving number and being able to recognise and explain patterns. Children should then be able to extend the ideas presented and use these to make predictions and ask ‘What if….?’ questions.
Problems may appear in many forms such as the following:
Find numbers that satisfy a particular relationship such as totalling a given number.
Adding operations of addition, subtraction, multiplication and division to a given set of numbers to make a given answer.
Fill in missing digits or missing signs.
This page looks at finding missing signs. The calculations probably don’t need to be worked out, especially if the child has a ‘feel’ for numbers.
A good extension of this is to have three or four number cards and signs and see what whole number answers can be made.
Resource of the week: adding 2-digit numbers mentally
One of the keys to success with maths is being able to calculate mentally. There should be no need to resort to written methods or to a calculator to add two 2-digit numbers; mental calculations should rule!
Having said that, these are not easy, and a number of skills need to have been learned to do these in an efficient manner.
For example: looking at ‘add 46 to 67′.
There a a number of ways to do this. Perhaps the most efficient is to add 40 to 67 to make 107 and then add on the extra 6 to make 113.
The second part of the sheet is a reminder of some of the ways that addition questions can be phrased.
Division: 3-digit numbers divided by 8
Here is another page for practising the short division method, this time just using the eight times table. The key to this method is, of course, a good knowledge of the 8 times table, as without this the solution can take an awfully long time and lots of errors may occur. The table has been written out as a helpful starting point, so that the method can be concentrated on.
For example: 8)659
‘How many eights in 65?’
’8 times 8 is 64, 9 times 8 is 72 which is too much.’
’8 goes into 65, 8 times with 1 left over.’
Write the 8 in the answer above the 5.
Write the remainder 1 beside the 9 units, making 19.
‘How many eights in 19?’
’2 times 8 is 16.’
’8 goes into 19, 2 times with 3 left over.’
Write the 2 in the answer in the units and write rem 3 next to it.
Answer: 82 remainder 3
Measuring in kilometres
Children in the UK get far less experience at using kilometres than most Euoropeans because we have decided to keep with the mile for most of our longer measuring. Of course this is a nonsense: to start with a system using mm, cm and metres and then switch to a completely different system ie miles does not make any sense at all! Until our road signs are changed there is little hope of any improvement in this situation.
Whilst there are 1760 yards in a mile the much simpler metric system has the easy to calculate 1000 metres in a kilometre.
At this stage children should be beginning to write half a kilometre as 0.5 km but 1/2 km is acceptable. This free maths worksheet concentrates on writing half kilometres as decimal fractions.
Reading and writing larger numbers
In Year 4 children are expected to be working with larger numbers, including thousands. However, it is often presumed that they can read and write these numbers without any practice. This is not the case, as many children find difficulty with this and often demonstrate the problem when asked to write down a number such as six thousand and five. They will write:
60005
What they have done here is write the whole of the 6000 and then added the 5 on at the end rather than 6 005.
When reading numbers it is best to start working them out from the first three numbers on the right and block the numbers into hundreds, tens and units. Then do the same with the next three, remembering that they are hundreds tens and units of thousands – these even bigger numbers will come into Year 5.
It is a good idea to separate each block of HTU in some way: a popular convention in the UK is to use a comma or a small space.
Scalene triangles
A lot of work is done on triangles in Primary Schools and by year 5 and 6 most children are familiar with the properties of right angled triangles, equilateral triangles and isosceles trinagles. However, fewer children know about the scalene triangle. A scalene triangle is one which has no sides the same length and no equal angles. It is worth pointing out that right angled triangles could also be scalene if all the sides are different lengths.
Thanks to MathSphere Ltd for this worksheet: and there are many more similar pages, both on their site and part of the ‘It’s All Figured Out’ CD.
Maths Board Game: Deadly red
Board games are a great way to improve logical thinking and maths concepts. This is a favourite of mine, which I call Deadly Red as the person who takes the red counter at the end loses!
Not a lot of equipment is needed, just:
12 coloured counters, one red counter and a playing board.
The rules of the game are straightforward:
This is a game for two people, but could be played by three.
Place a red counter on the middle dot and the 12 black counters on all the other dots.
The player going first takes away any number of counters – but they must all be from a straight line.
Then the second player has his/her turn.
The player who takes the red counter loses.
On the next page you will find a board which can be printed out onto card. It is a good idea to cut out and either laminate or ‘sticky back’ this board.
Alternative rules:
1.The player taking the last counter (red) is the winner.
It might appear at first that it is luck as to who wins, but with after playing a few times you might be able to work out a few strategies which will ensure you win most of the time.
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