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 3 Mental Arithmetic: Sets 11 and 12

Two more sets of mental arithmetic questions to add to our growing collection. Today’s questions concentrate on addition, subtraction, multiplication and division.

Hopefully these questions will provide a confidence boost for those children who are not quite as secure in their knowledge as they should be as all the questions are worded in a very straightforward way. By Year 3 children should be familiar with the term ‘multiple’ and be able to use their knowledge of the 2, 3, 4, 5, 6 and 10 times table to work out simple division problems.

These sets of questions and other similar can be found in our Year 3 categories.

Year 3 mental arithmetic: sets 11 and 12

2010 Maths SAT Paper A: question 3

The second in my series on the KS2 SAT papers which looks at question 3 of the 2010 paper A and gives answers and suggested best ways to approach the questions.

If you are looking for much more on the KS 2 Maths SAT papers and an excellent revision programme then I would highly recommend: ks2-maths-sats.co.uk

Tables and charts are a real favourite with the SATs testers. Children should have had plenty of practice at interpreting this type of table in school so it should provide easy marks: marks which should not be lost through carelessness.

To answer the question: ‘What type of cat is found only in Africa?’ requires two steps.

Firstly, identify those cats found in Africa. Secondly check across to find the cat that is not found in Asia or Europe.

To answer the question: ‘Which types of cat are found in all three parts of the world?’ requires scanning the table looking for three ticks in a row across. Sometimes with this type of question it is worth using a ruler to slide down the rows to check, but probably not necessary in this case.

Question 3 from Maths SATs Paper 2010

Paper A Question 3 answers and suggested method.

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)

9x table space challenge

Continuing with my series of tables space challenges, we reach the 9x table. because there is a regular pattern to the answers to the 9x table it is one of the easier tables to learn. Of course, the digits of the answers always add up to 9 and the tens go up one at a time whilst the units decrease one at a time (only up to 90).

This worksheet can be used as a fun test to see how well knowledge of the times table can be put into practice. Because the table is jumbled up it becomes slightly harder and takes longer to do, especially if the table is not known ‘off by heart’. Remember, when learning the table say the whole of it (eg one times 9 is 9) and not just the answers, which is counting up in nines, not saying the table.

9x tables space challenge

Resource of the Week: Year 3 maths investigation

across-and-down

In year 3 children are expected to be able to solve problems involving numbers, follow a line of enquiry, identify patterns and organise information. Investigations are a great way to do this as well as developing logical thinking.
This is a fun investigation for children from Year 3 upwards (7+ yrs) which encourages children to organise their thoughts as there are enough different answers to make it interesting. It is also excellent for adding several small numbers.

The task is simple:
Put in the numbers 0, 1, 2, 3 and 4 in the squares on the grid so that the total across is the same as the total going down.
Children will probably start this mini investigation with a lot of ‘trial and improvement’ and then come up with some correct solutions.

To make it easier there is also a print-out of large numbers which can be cut out to help children move the numbers about without having to write down everything they do. I would recommend this approach for any similar activity, such as magic squares.

After a while some key aspects to the logical thinking behind this may arise, including:
1. Add up the total of 0, 1, 2, 3 and 4. It comes to 10.
2. This means that if the total across and the total down are equal and the corner number is zero, they must both add up to 5.
3. By working methodically with zero in the corner 8 arrangements can be found.

 

Investigation: across and down

Year 3 mental arithmetic: Sets 9 and 10

This week the mental arithmetic for Year 3 concentrates on writing whole numbers in digits, counting on and back, addition, subtraction and place value.

These questions can either be done quite quickly, taking up just a few minutes or in more detail, depending on the time available. By more detail I mean talking through each question and asking how they were done. For example: How do you add 40 and 70 in your head? Is it the same as you would do it if writing it down?

When writing down a number such as four hundred and ten in figures watch out for a common mistake of writing 40010.

Year 3 mental arithmetic: sets 09 and 10

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

2010 Maths SAT Paper A: answers questions 1 and 2

This is the first of a series which will look more closely at the KS2 Maths SAT papers for 2010. Taking one or two questions at a time I will show  suggested methods for answering and what is accepted as an answer. This should build into a very useful resource over the following weeks.

If you are looking for much more on the KS 2 Maths SAT papers and an excellent revision programme then I would highly recommend:

ks2-maths-sats.co.uk

The first question on Paper A looks at a series of five amounts of money, one shown in pence, the rest as pounds, which has to be put in order, smallest amount first.

Suggested method:

The best way to do this type of question is to search for the lowest possible amount, which is £0.27 (or 27p) and place this in the answer, at the same time as putting a thin line through that amount on the question sheet. This then eliminates this amount, making the others easier to see.

The second question is all about adding 2-digit numbers and rounding. The key is to carry out an ordered trial and error approach to this question. Starting with one number add it to each of the others in turn and see if the rounded result is 60.

Questions 1 and 2 from SATS test 2010 Paper A

Questions 1 and 2 answers

 

Maths game: Criss Cross 3 Addition (1)

This is a simple 2 player game suitable for children who are learning single figure addition facts.

Two sets of coloured counters and a calculator are needed.

Player 1 chooses two numbers from the list below.
Add the two numbers on the calculator. If the answer is on the grid place a red counter on that square.
Player 2 chooses two numbers from the list below and adds them on the calculator.   If the answer is on the grid place a blue counter on that square.
Once a number has been covered it cannot be covered again.
The winner is the first person to put three counters in a row, across, down or diagonally.

There is obviously a clear advantage in going first, but it also helps to know addition facts, as this takes the guesswork out of playing the game, which is really an advanced noughts and crosses.

Criss cross 3: Addition (1)