Month: July 2011

Resource of the Week: Maths from Stories

Maths from stories.
Hidden away on the mathsblog site is a superb selection of story books to help with early reading. These are all great books for young children to read, but an added bonus is that they all have a mathematical aspect to them. One of my favourites is The Very Hungry Caterpillar which I am sure you are all familiar with.
Another favourite is The Shopping Basket by John Burningham which is a great little book which will be thoroughly enjoyed by young children whilst at the same time helping them with counting and subtraction. Steven is a little boy who is asked by his mum to go round to the local corner shop, taking the shopping basket with him to bring back 6 eggs, five bananas, four apples….etc

Others include Mr Wolfe’s Week by Colin Hawkins, Jim and the Beanstalk by Raymond Briggs which helps with the mathematical language of shape and size, Two by two by Barbara Reid and Ten, Nine, Eight by Molly Bang.
To find this colection you need to go to the Top Maths Book heading at the top right of the blog and scroll down past the less interesting maths books. Some of the books are quite obscure and difficult to buy new copies, but they are all highly recommended and worth the effort to find.

Go to Maths from Stories

Year 2 Maths worksheet: missing numbers on a number square

The third in my series on missing numbers on a number square which can be found in the Year 2 Counting category. Each grid shows a different section from a 1-100 number grid, with only a couple of the numbers filled in. The task is to complete the number grid.

This is very good practice at counting on and back in ones, from any 2-digit starting number. It is also very good at showing the patterns in numbers, for example by moving down the grid one space the number increases by ten.

Missing numbers on a number square (3)

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