Carroll diagrams: Year 2 Handling Data

Carroll diagrams are named after the famous writer, Lewis Carroll and are a way of grouping things in a ‘yes or no’ way. They can be as simple as just two boxes but usually they are seen as four boxes with two attributes. In this case the two attributes are swimming and riding a bike and the children either can or can’t do each.

Carroll diagrams are introduced in Year 2 as a means of sorting, but it is not until towards the end of the year, or Year 3 where they would meet these types of diagram. The second page has a set of questions about the diagram and suggests that children then go on to try to collect their own data and make their own Carroll diagram from this data.

Thanks to urbrainy.com for this particular set of pages and they have  a great selection of Handling data resources at their site.

Carroll diagrams 1

Resource of the Week: Year 6 converting metric units

Children in Year 6 still need plenty of practice using the metric system, in particular converting larger metric units to smaller ones. Here we are highlighting a page which looks at converting metres to centimetres, kilos to grams and litres to millilitres.

One of the trickier aspects of this is to convert a weight such as 6.09 kg into grams, which of course is 6090 g. watch out for common mistake children make of writing just 609 g.

This is one of several similar pages found in our Year 6 Measuring section of the site.

Year 6 Larger units to smaller units (1)

Impossible question in the Maths AS paper

Well, it is not uncommon for me to make a mistake with the articles and worksheets published here, but I don’t have a team of proof readers to help me. Far more serious was the error in this years Maths AS Paper.

Over 6000 students took the paper and the question with the highest number of marks was impossible to answer! The question carried 8 marks out of 72 being awarded for the whole paper. This meant that many students would have agonised over the question, wasting many minutes in futilely trying to reach a correct answer.

A spokesperson for the exam board said,

“We very much regret that there was a mistake… and that our quality assurance procedures failed to identify this error.

“Because we have been alerted to this so early, we are able to take this error into account when marking the paper. We will also take it into account when setting the grade boundaries. We have sent a letter to all schools and colleges explaining in more detail what we shall do.

“We do apologise again that this has happened.”

Obviously some of the students think that this is a less than satisfactory outcome as some would have spent much longer than others on the question, leaving less time for the rest of the exam.

Read more

 

6 times table space challenge

Children need as many opportunities as possible to practise their knowledge of tables and teachers are always on the lookout for something slightly different to maintain interest. Hopefully this page will be useful as it is a bright and fun way to show how well the 6 times table is known and it could also be used as a timed challenge.

Beginning at the start move to the first box and write the number 6 times that shown on the left hand side, then move on to the next box and so on. There are 20 questions altogether; some children may become ‘stuck’ on a question, encourage them to move on and then return to it at the end. If they are stuck remind them, for example, that if they cannot remember 6 x 6 it is only six more than 5 x 6 which they should be able to remember.

This page can be found in our Maths worksheets, Four Rules, multiplication section and hopefully I will be adding similar pages for other times tables before long.

6x tables space challenge

Year 5 Line Graphs

With a lovely hot summer ahead of us what better way to spend a maths lesson than looking at line graphs of temperatures?

In year 5 children are expected to construct and interpret line graphs. The important aspect of a line graph is that each point on the line will have a value. The graph on this worksheet shows the minimum and maximum temperatures each month for London. It would be well worth finding other temperature graphs for cities around the world and comparing them.

Another great idea is to find data for countries in the southern hemisphere and compare the shape of the line graph to London.

Why not go to our Handling data and probability page for year 5?

Stern equipment from MathsExtra

 

By far the best the best maths equipment that I have come across over the years is the Stern Structural Arithmetic programme, which encourages children to reason rather than just rote learn. This approach was designed to follow a child’s natural stages of learning and development in the early years upward, to develop a number sense, number knowledge, concepts and number relationships, as well as ensuring that the pre-requisite skills are soundly in place prior to any formal work. It is also ideal for SEN children where little or no progress has been made in the past and for children who have been ‘moved on’ to the next stage, clearly before understanding the earlier stages.

Stimulating a child’s cognitive processing functions sits at the heart of the programme; the range of equipment provides wonderful ‘pictures’ which develop visual and auditory perceptual processing.


One example is the ‘stair’ in the 10-Box, where adding one more cube makes it the same ‘size’ as the next number. The concept then is explicit – adding one to any number will always result in the next number.

The Counting Board introduces position and sequence. The simple task, when asked to find a block to fit into an empty groove indicated, naturally develops a child’s judging, scanning and discrimination ability. Children discover that each block has its own special place in the series of blocks to 10. This means that it is not necessary only to work with numbers to 5.  Number relationships are a vital building block. Instead, children see the small numbers all ‘live’ at the beginning, and bigger ones ‘live’ at the end, (later to become on the left/right).

As an example of the Structural Arithmetic approach, look at 3 + 7 = 10. Children discover all the combinations that make 10 by fitting combinations of blocks into the 10-box. They reason that if 9 needs 1 to make 10, then 8 needs 2, and 7 needs 3 to make 10. By switching the blocks around, they discover that the order of the addends can be changed without changing the sum. Thus, they grasp that addition can be done in any order and can put it to use, reasoning that if 7 + 3 = 10, then 3 + 7 = 10. This fact has not been learned in isolation, but has been studied in a context where its relatioship to the other facts can be seen.

When children see an example such as 5 + 4 = and don’t know the answer, they often respond by counting “6, 7, 8, 9.” Teachers may assume that encouraging children to count, will one day result in their stopping counting and saying, ‘9’. Stern argues that, in fact, each time they see + 4 (as in 6 + 4 or 9 + 4), they automatically practise counting. The numbers themselves don’t have meaning. For the counting child, 5 plus 4 does not equal 9; it makes 9 by counting. No picture in the child’s mind makes the number fact 5 + 4 = 9 unforgettable. Furthermore, if children count the total incorrectly as 10, they have no certain way to check that result except by another uncertain counting procedure. On the other hand, in Structural Arithmetic, the two addends 5 and 4 actually measure 9 in the Number Track.

The Stern kits are not cheap, but I would recommend having a further read at

http://www.mathsextra.com/

Year 3 maths: Pairs that make 100

shape imageWhen working out how many more to make a number up to 100 it is important not to mix up two different ways of doing it. Let’s take the question:

‘How many more is there from 45 to 100?’

One way of doing this is to add 5 to 45, making 50 and then counting on 50 to make 100. That’s 55 in total.

Another way is to count on in tens from 45 to 95, which is 50, and then add on the extra 5, again making 55.

Watch out for children who get slightly confised, add on from 40 to 100, making 60 and then adding on another 5. This method will always result in ten more than the correct answer.

The ultimate aim of questions like these is to make the answers second nature or even to know them ‘off by heart’.

This page can be found in our Year 3, Calculating section.

Complete number sentences (pg 2)

More year 4 mental arithmetic: subtraction

This is the second page of ‘quite hard’ subtraction questions for year 4, which should be answered using mental arithmetic methods, although many adults would struggle to reach the correct answers: they really are quite hard!

Once again it shows that there are several possible ways to approach each question; the key is to choose a method which is efficient and quick. For example, they can all be done by counting on, but this may well not be the quickest way and it is speed and accuracy that we are looking for.

It is also always a really good idea to check answers by carrying out the inverse operation; in this case an addition of the answer and smallest number should give the largest number.

This, and other similar pages can be found in our Year 4 Calculations category as well as in the Four Rules section.

Quite hard mental arithmetic: subtraction_(2)

What boosts school performance?

We all know that smaller classes, uniforms and primary homework are ways of boosting schools’ performance. Or are they? Not according to a recent report from the Sutton Trust. In fact, reducing class sizes, setting homework during primary school, and introducing school uniforms are among the least effective ways of improving school results.

Looking at class sizes they found that benefits, “are not particularly large or clear, until class size is reduced to under 20 or even below 15”.

Another myth seems to be that hiring more classroom assistants is effective. This is at odds with what most teachers think as 44% said that hiring more teaching assistants was one of their top three priorities. The report says that hiring more teaching assistants  is associated with “very small or no effects on attainment”.

Significant gains in attainment meanwhile come from proven classroom approaches – providing effective feedback on pupil’s performance, encouraging students to think about their own learning strategies, and getting pupils to learn from each other. Implemented correctly, these approaches can increase pupils’ performance by an extra eight or nine months in a school year for a very low cost, according to the guide.

Key findings include:

On effective feedback – “One study even estimates that the impact of rapid feedback on learning is 124 times more cost effective that reducing class sizes.”

On peer tutoring – “Benefits are apparent for both tutor and tutee, though the approach should be used to supplement or enhance normal teaching, rather than replace it.”

On meta-cognitive approaches – “Studies report substantial gains equivalent to moving a class from 50th place in a league table of 100 schools to about 25th.”

On homework – “It is more valuable at secondary school level and much less effective for children of primary school age.”

On teaching assistants – “Most studies have consistently found very small or no effects on attainment.”

On school uniforms – “No robust evidence that introducing a school uniform will improve academic performance.”

On reducing class sizes – “Overall the benefits are not particularly large or clear, until class size is reduced to under 20 or even below 15.”

On one-to-one tuition – “Pupils might improve by about 4 or 5 months during the programme, but costs are high as the support is intensive.”

On ability grouping – “There may be some benefits for higher attaining pupils, but these are largely outweighed by the negative effects on attitudes for middle and lower performing learners.”

The full report can be found at:

The Sutton Trust

 

Reading, writing and ordering numbers at level 1

To attain maths level 1 children need to be able to recognise the number names up to 20, say them clearly and write them. They will be counting forwards and backwards up to 20, starting at any whole number.

To enable this to happen the numerals need to be displayed clearly on a wall so that they can be frequently referred to. Every opportunity needs to be given to count on and back in practical situations, around the home, in the kitchen, at the supermarket, in the car etc. There are lots of games which involve counting and using dice. Number lines and number tracks are really useful; pointing at each number before it is said whilst counting up and down. Eventually the number track can be visualised in a child’s head, helping with fast mental arithmetic.

To herlp with all of this, I have a good selection of worksheets for counting in:

Reception

Year 1

and Year 2 which will help with this process.