It is important that children become familiar with calculators as they will be using them more and more as they progress through High School. There are many skills to learn and in this activity it is certainly a great help to be able to work out mentally division calculations. as the calculator will only confirm or otherwise your calculation.
This is the final game in our calculator series looking at tables and multiples. Once again the idea of the game is to get four counters in a row, this time on a multiples of 9 grid. Recognising multiples of 9 is relatively easy as the digits always add up to 9 or a multiple of 9. But knowing exactly which multiple is needed is much harder. Why not challenge your children?!!
Some children do not realise that a fraction such as 2/10 can also be written as a decimal i.e. 0.2. In one sentence we have two of the major sticking points in maths, but here we have a maths worksheet which neatly combines the two, showing the equivalence between fractions and decimal fractions.
One way to show this is to use the fraction as a division sum. 2/10 can be seen as 2 divided by 10. Do this on a calculator to get 0.2. Also remember, to divide by ten mentally, just move each digit one place to the right, putting in the decimal point if moving from units to tenths. This page can be found in our year 4 resources.
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.
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.
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?
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.
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.
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
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.
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:
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.
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