Complete multiplication number sentences (3)

This is the third worksheet in the mini series looking at using different strategies to work out missing numbers in multiplication number sentences. Again, it is worth pointing out that people who say they, ‘can’t do maths’, probably don’t have a wide range of mental strategies to tackle questions. All the questions on this worksheet look very similar but if you analyse how the brain works to answer them you will see what I mean.

Let’s look at a couple of examples:

1. Question: ? x 6 = 360

I instantly recognise the relationship between 6 and 36, knowing that 6 x 6 = 36. it then becomes very easy to multiply by 10 to reach the answer 60. This is all done in less than a second.

2. Question: 26 x ? = 104

This takes a little longer and at first glance I’m not certain. I then realised that 25 is a quarter of 100, so 25 x 4 is 100,therefore 26 x 4 would be 104.

In the first question I am making use of knowing the 6x table. In the second question I am rounding a number, working out the answer and adjusting.

Of course, there are other ways, probably just as good  and don’t forget to ask the children how they worked out the answers. You might be surprised!

Complete multiplication number sentences (3)

Maths for Halloween

More Halloween worksheets can be found on the site – well worth a visit.

Nobody seems to be sure about the origins of Halloween but celebrations in the UK seem to be on the increase, perhaps following its popularity in the USA. We do know that it is always on the eve of All Saints Day and that pumpkins, apple bobbing, dressing up and demanding sweets seem to be important modern features.

So why not try a maths worksheet on Halloween? With less emphasis on the government’s planning more schools are developing themes for their maths. This page is suitable for older children who have a grasp of multiplication. A number is put through the two pots, firstly multiplying by 3 and then adding 9. The second set of questions show the resulting number and have to be worked backwards to find the number that is inputted.

Finally there are some missing digit questions. All very spooky!

This page can be found in my Year 5 calculating category.


More Halloween worksheets can be found on the site – well worth a visit.

Completing multiplication number sentences

This maths worksheet is suitable for Year 5 children who have a good knowledge of the times tables and can manipulate numbers ‘in their heads’.

It is surprising the number of different strategies we use to calculate mentally. The same type of question can be processed several different ways, often depending on the numbers being use. If we look at some of the questions on this worksheet it will become clearer as to what I mean, as I try to explain how I go about answering them, although you may well have different (and better) alternatives.

Question 1: ? x 2 = 120

Looking at the question I immediately think that I have to halve 120 to get the answer. I do this by halving 12, which is 6 and multiplying by 10, making 60. This is all done in a split second, and I might be tempted to think I did it in one, but it is important to stop and think of the steps that you go through.

Question 3: ? x 4 = 48

I could have halved and halved, or divided by 4, but, in fact, I learned my 12 times table many years ago and I know, instantly,  that 12 x 4 = 48 so the answer of 12 came immediately.

Question 4: 41 x ? = 205

The answer was not immediately obvious. I looked at the unit (1) and the unit in the answer (5) and it struck me that I need to multiply by 5. A quick check that4 x 5 will give me 20 confirmed this.

These are just a few of the ways of working out the answers and it is well worth asking children how they go about finding the answers.

Complete multiplication number sentences (1)


Resource of the Week: Congruent shapes and scalene triangles

Today we look at two mathematical terms which are less commonly known. Firstly, congruent is a word to conjure with! In fact it has a very simple meaning. If two shapes are congruent then they are identical in every way, including size.

Whilst this is very straightforward, unfortunately people who design maths tests papers make this as difficult as possible, as children are expected to be able to spot congruent shapes even when one of a pair has been turned. By far the easiest way to spot two congruent shapes is to cut one out, or trace it and see if it fits exactly over the other – if it does it is congruent. On this worksheet the aim is to find pairs of shapes which are congruent, and as always, the answers are provided! I do recommend the tracing option!

The second term is scalene. Most people are familiar with equilateral triangles and isosceles triangles but the term scalene triangle is the one that is most frequently forgotten. Quite simply, a scalene triangle is one which has no sides the same length and no equal angles.

These two worksheets can be found in the Year 5, Shape and Measures category.

Congruent shapes

Scalene triangles

Year 5 Calculating

There is a great deal expected of children in year 5 when it comes to calculating. Mental methods of calculating with whole numbers are extended to include addition of three small numbers, knowing tables and multiplying by 25. Efficient written methods of addition and subtraction of both whole numbers and decimals is expected as well as refining written methods of multiplication and division.

I have a growing range of worksheets covering these topics which can be found in the Year 5 Calculating category. Further worksheets on written methods can also be found in the Four Rules category.

Go to Year 5 calculating worksheets

Year 5 maths worksheet: multiplication and division hops

Each of the questions on this page has two sets of coloured arrows above the spaces which need to be filled in. The arrows give the instruction, red for multiplication and yellow for division. There are eight hexagons, one of which has been filled in. The aim is to complete the other seven using the arrows to work out what to put inside each hexagon.

Sounds complicated but it is easier to complete than to explain!

This is good practice for

a. knowing tables

b. knowing division facts

c. knowing that multiplication and division are the inverse of each other.

This page can be found in the Year 5 Know Number Facts category.

Multiplication and division hops

Year 5 Maths Worksheet: More In Out Function Machines

I have had several requests from people for another page of In Out tables, so here it is. Each table has a set rule. A number goes in, the rule is applied and a number comes out. Straightforward if you are given the number that goes in, but a little harder if you are given the number that comes out. In that case a reverse calculation has to be done.

Some children get into a muddle with these and it is a good idea to point out that if the rule is to add then the OUT number will always be larger than the IN number. If the rule is subtract, then the OUT number will always be smaller than the IN number.

This and lots more worksheets can be found in the Year 5 Calculating category.

In out function machines (2)

Year 5 Maths Worksheets: In-Out function machines

Whilst this worksheet appears to be very simple it is surprising how many children get into a bit of a muddle with such activities. A table is shown with a rule for completing it, such as ‘Add 34’. All that has to be done is complete the missing cells of the table following the rule. If the second (OUT) number has to be found then it is a straightforward matter of using the rule. If the first (IN) number has to be found then the rule has to be reversed: it becomes clear as you do the worksheet!

The fourth question does not give the rule, but it can be found by seeing what has happened from the IN number (40) to the OUT number (25); in this case it is subtract 15.

This is well suited to Year 5 children who are good at adding and subtracting two digit numbers mentally. It can be found in our Year 5, Calculating category.

In out function machines (1)

Year 5: Knowing Division Facts (2)

By Year 5 children should have a good knowledge of tables and this division page will show whether tables are known. It is also important to understand the relationship between division and multiplication as some children see the two as completely separate processes.

It is the second page on this knowing division facts as I have had several requests for more on dividing mentally. They can both be found in the Year 5 Maths Worksheets, in the Knowing Number Facts category.

Know division facts (2)

Year 5 probability

Probability, or chance,  is one of the more misunderstood areas of maths and one which has only crept into the Primary curriculum in the last 20 years or so. It brings with it a whole new set of vocabulary and concepts which are very precise in their meaning.

By the end of year 5 children should have come across the following terms:
perhaps, might, fair, unfair, likely, unlikely, equally likely, chance, certain, uncertain, probable, possible, impossible, good chance, poor chance, no chance, equal chance, even chance, evens, fifty-fifty chance, likelihood, probability, possibility.
The first two worksheets I have published look at events which are impossible (such as my talking to Henry V111 this evening), unlikely (such as throwing a die and getting a 1), likely (such as waking up tomorrow) or certain (such as throwing a normal die and getting a number from 1 to 6). Finding events which are either certain or impossible are often much harder than you might think.

The second pair of worksheets look at events that have an even chance of happening (such as tossing a coin and getting a head). However, care has to be taken to understand that, if there are two possibilities, they are not necessarily equally likely. For example, there are two possibilities – I might buy a new Rolls Royce today or I might not. Unfortunately, these two events are not equally likely. Another example of this is I choose a number between 1 and 5. Is the number I choose a prime number? As there are three prime numbers between 1 and 5 (2, 3 and 5) and two numbers that are not, there is not an even chance that I will choose a prime number.
Sometimes further investigations have to be carried out before a probability question can be answered. Take the possibility of a factor of 16 being even. Probably the best way of doing this is to first find all the factors of 16, group them into even or odd and then work out the probability.

Go to Year 5 probability worksheets