Maths help for parents of children aged 5 to 11
The latest draft version of the Primary Maths Programme of Study includes counting to and across 100, which has usually been left until year 2. It is quite tricky and shouldn’t be covered until you are certain that children can count confidently up to 100.
Here is a worksheet aimed at helping with this, counting three, four or five more in steps of one and crossing the hundred boundary in each case. Thanks to urbrainy.com for letting me adapt one of their pages.
There is no doubt that most children find division harder than multiplication, yet there is little real reason for this to be so. Most division questions can be turned on their head and knowledge of times tables used to work them out. For example:
30 ÷ 5 =?? can be thought as what number times 5 makes 30?
?? ÷ 6 = 7 can be thought of as 6 times 7.
60 ÷ ?? = 10 can be thought of as what number times 10 makes 60?
The key to success with division is to have a really good knowledge of times tables.
This worksheet looks at these types of division question, all with easy numbers and no remainders and is a good assessment sheet to see if division is understood and tables known. if times tables are not known sufficiently well children will spend more time than necessary trying to work these out.
This can be found in our Year 5 Knowing Number Facts category.
I have had a number of requests for more pages similar to the ‘Find the Missing Numbers’ published in May, so here is another.
The questions are all similar:
e.g. Find a pair of numbers with a sum of 7 and a product of 12.
Pairs of numbers with a sum of 7 are:
1 and 6
2 and 5
3 and 4
(it is not necessary to go on to 4 and 3 etc) as these have already been found.
Pairs of numbers with a product of 12 are:
1 and 12
2 and 6
3 and 4
Look for the same pair and the answer is 3 and 4.
To be able to successfully help your child with maths at home it is important to have a good idea of what is expected in school. This is a list of the targets expected of children by the end of Year 1 and most teachers will be planing their work around these. Of course this does not mean that all children will achieve these targets; some will find them impossible whilst many will be able to go on further. However, they do act as good starting point.
Counting and understanding number
By the end of year 1 children should
• know the number names (one, two, three etc) up to at least 20 and tens up to 100
(eg twenty, thirty, forty etc).
• be able to count up to 20 objects reliably. If the objects (eg buttons on a tray) are moved around they should be able to say that the total number has not changed without recounting. (Younger children will count them again if they have been moved around.)
• be able to read and write numerals up to 20
(eg 3, three, 4, four, 5 five, etc).
• be able to place numbers on a blank number line in the correct order.
• be able to say the number that is one more than or one less than any given number up to 20
(eg one less than 7).
• be able to say the number ten more than or ten less than a multiple of 10
(eg ten more than 30).
• recognise the equals sign (=) and understand it means “..is the same as..”
• use the terms, half and quarter in a practical sense
(eg give me a quarter of the orange).
Knowing and using number facts
By the end of year 1 children should
• know addition facts up to a total of 5
(eg 3 + 2).
• know all pairs of numbers with a total of 10
(eg 1 and 9, 2 and 8 etc).
• be able to work out subtraction facts from the addition facts they know.
(eg 5 -2 = 3 because 3 + 2 = 5)
• be beginning to count on and back in twos, fives and tens.
• know the doubles of all numbers up to 10
(eg double 6 is 12).
Calculating
By the end of year 1 children should
• know that addition can be done in any order.
• be able to write simple number sentences using the + and = signs
(eg 3 + 4 = 7).
• use practical methods (eg using counters) to help with addition of a 1-digit number to a 1-digit or 2-digit number
(eg 10 + 4 =).
• use informal written notes to help with addition
(eg jotting down the answer to adding 2 numbers before trying to add the third).
• understand that subtraction can mean ‘take away’.
• understand that subtraction can mean ‘find the difference between’.
• be able to use practical methods to help with subtraction of a 1-digit number from a 1-digit number
(eg using counters).
• use informal written notes to help with subtraction
(eg jotting down 5 circles and crossing out 3 for 5 – 3).
• be able to write simple number sentences using the – and = signs
(eg 7 – 4 = 3).
• understand and use the vocabulary related to addition and subtraction, including: more, add, sum, total, altogether, equals, =, take away, subtract, difference between, how much more/less, how many are left?
• be able to combine groups of 2, 5 and 10 in a practical situation
(eg combining marbles into groups of 5 marbles).
• be able to share a group of objects into 2 equal parts
(eg sweets shared equally).
Understanding shape
By the end of year 1 children should
• be able to visualise and name common 2-D shapes, including circle, triangle, rectangle and square. This includes activities such as “Find a shape which has 3 corners and 3 sides”.
• be able to visualise and name common 3-D shapes, including, cube, cuboid, sphere, cone and cylinder. This includes activities such as describing the properties of a shape by the feel of it, before seeing it.
• be able to make patterns and pictures with 2-D shapes and make models with 3-D shapes such as Lego.
• begin to describe the position of shapes, using terms such as: over, under, underneath, above, below, outside, inside, in front, behind, beside, before, after, next to, opposite, between, middle, centre, edge, corner, top, bottom, side. This is where activities such as moving furniture around a toy house are very important or placing counters on a board game.
• be using everyday language to describe direction, such as: left, right, up, down, forwards, backwards, sideways, across, along, through, to, from, towards, away from.
• begin to be able to describe movements in a straight line and turning. At first turning will only be by whole and half turns but it is important to recognise shapes that turn about a point, such as a pair of scissors.
• Once again it must be emphasised that most of this work is done orally with practical equipment. Toys, board games, may seem like playing to us but are invaluable learning experiences.
Measuring
By the end of year 1 children should
• understand and use the basic vocabulary related to length, mass and capacity.
For length: long, short, tall, high, low, wide, narrow, deep, shallow, thick, thin, far, near and words of comparison eg longer.
For mass: weight, weighs, heavy light, balances.
For capacity: full, empty, half full, holds.
• be able to make direct comparisons between two items eg comparing the length of two pencils, the weight of two parcels, the capacity of two cups. A set of balance scales is very useful for this kind of work.
• begin to use non-standard measures
(eg the jug holds 6 cups of water, the table is about 7 rulers long).
• be making sensible estimates and guesses related to length, mass and capacity. Standard units such as cm, km, kg are not used at this stage.
Using and applying maths
By the end of year 1 children should
• solve problems involving counting, addition, subtraction, doubling, halving, measures and money
(eg a toy shop, paying and giving change with numbers up to 10).
• describe and solve simple puzzles or problems
(eg How many ways can you score 4 rolling two dice?).
• sort information, shapes or objects and display the results using pictures
(eg sort cubes by colour).
• describe simple patterns involving numbers or shapes
(eg continue a pattern of repeated squares and circles).
• describe ways of solving a puzzle or problem orally
(eg talk about or draw what coins could be used to make 6p).
Sometimes it is much easier to carry out a calculation mentally (in your head) than to use the standard written method. This page of questions illustrates this perfectly. It looks at taking a one-digit number away from a multiple of a thousand.
if this was written down on paper it would involve considerable amounts of crossing out and ‘borrowing’ from thousands to hundreds and then from hundreds to tens; a potential minefield for children. However, if they just count back from the whole thousands, even using fingers to check that they have counted back the correct number, hey presto, the answer is found in seconds.
Similarly, with a question such as 4 000 – ??? = 3993 adding on can be employed: start with 3993 and counting on until 4 000 is reached. Simple.
This page can be found in our Year 4 Calculating category.
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.
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.
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?