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]]>Compare numbers by picking the correct sign to make the number sentence. e.g. >, <, =
Practice or complete against the clock. Lots of levels of difficulty, increasing size of numbers.
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]]>Place Value – Create numbers from their parts. Write the completed number.
Number randomised each time. Accompanying worksheet to record answers.
National Curriculum – Read, write, order and compare numbers to at least 1,000,000 and determine the value of each digit
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]]>Place Value – determine value of each digit. Great for plenary.
Beware, harder questions include decimals and millions!
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]]>2x Table Bar demonstrates the bar method of visualising multiplication. Drag the bar to be multiplied and then click it the required number of times. Resize the top section to match. Repeat with the equivalent calculation. Aids understanding of concept as well as recall.
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]]>The post The Long Division Problem – Getting It Right appeared first on Maths Zone Cool Learning Games.
]]>I personally have no problem completing long division questions. I don’t have a problem with it being on the curriculum. I don’t even have a problem with Junior School children having a go, I suppose.
What I do have a problem with is the number of text books and websites which, I think, miss the point.
Long division is a system or algorithm normally used for solving problems which involve larger numbers. It is learnt after pupils have already experienced short division and have a good knowledge of multiplication facts. Pupils are generally required to work out the multiples of the divisor in order to answer the question, so you could end up trying to work out your 17 times table or worse. What we are asking pupils to do is not a simple task, but a quite ‘long’ series of steps which lead to a solution. Moreover we know that it can cause confusion and there are many points at which a pupil can make a wrong turn.
… DON’T DO IT, IF YOU DON’T HAVE TO!
And this is where my problems begin. Division problems can often be simplified in a number of ways, and searching thorough numerous text books, even new ones from popular publishers, I find that many, and sometimes most, of the questions can be performed much more easily by simplifying them first.
Some examples…
A fairly popular maths website starts with the following example 5568÷ 16 =
This can be factorised to become 2784÷ 8 followed by 1392 ÷ 4, then 696 ÷ 2 and finally giving 348.
The page has one more ‘good’ example which does not factorise at all, but then sets the pupils 9 questions to do, all of which can be simplified by factorisation. 7 of them then turn out to be short division problems, and only two end up as long divisions problems, however now much easier to solve.
That’s the Internet. The publishers must be better.
Well, a few years back a new scheme came out for the 2014 curriculum which many schools bought into. It had 15 questions on long division for pupils on one page, and again all but 2 could be completed by means of factorising to simplify the question. Many of my level 5 pupils could do them in their heads.
Surely the Government know what they’re doing! I mean, since they are insisting that pupils use long division to gain the extra mark if they don’t get the correct answer, they must .
I’m afraid there is no better news here. Back in 2014 the government produced sample materials to show teachers the new requirements, layout and mark schemes.
The only division question on the example paper (Q5) was 1652 ÷ 28 laid out encouraging pupils to perform long division.
Erm this is just 826 ÷ 14, or 413 ÷ 7 (by removing a factor of 2 from both numbers each time)
As 420 ÷ 7 = 60… the answer is 59.
Why do you want me to do long division? Why would you reward a pupil for making a mistake when they have chosen probably the worst method of performing this question?
There was this comment in the mark scheme…
Commentary: This question illustrates the increased demand of dividing a 4-digit number by a 2-digit number. It is presented vertically, to encourage pupils to use a formal written method. Only the use of a formal written method will gain the method mark should the pupil calculate incorrectly.
© Crown copyright 2014 Key stage 2 mathematics sample questions, mark schemes and commentary Electronic version product code: STA/15/7205/e ISBN: 978-1-78315-407-4
So let’s give pupils a division toolkit.
In it we’ll put estimation, multiplication facts, inverse operations, multiples, factorising, partitioning, short division, long division and a whole host of other useful devices. Let’s encourage knowledge and understanding as well as skills and procedures.
And surely let’s remove straight jackets which say that problems must be solved with a hammer, even if the screwdriver might have been a better option.
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]]>The post Squares in Squares appeared first on Maths Zone Cool Learning Games.
]]>I have just spent a lesson this week with my class discussing how we might know that there are only 11 nets of a cube.
The problem was that we could find 11 nets, we knew they were all different, and we couldn’t find anymore.
But is the lack of another solution proof enough that you have them all?
Last night, I came across this article from NRich…
In the article he discusses the question:-
Into how many squares can you cut a square?'
What a superbly simple question, and perhaps one you could try out with younger children.
However, there’s still quite a bit of thinking to do.
Perhaps one to try out on a GeoBoard…
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]]>Geoboard is a tool for exploring a variety of mathematical topics introduced in the primary school. Children stretch bands around the pegs to form line segments and polygons and make discoveries about perimeter, area, angles, congruence, fractions, and more.
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]]>The post The Maths Question of the Year 2016! appeared first on Maths Zone Cool Learning Games.
]]>Here is a question which has intrigued me for a few years now, but this year it seems most pertinent!
2016 is the product of two 2-digit numbers. What are they? Can you find all the possibilities?
The interesting aspect to the question is the way it is worded. It suggests to many pupils, particularly those trained in calculations, that they should begin to try lots of multiplication calculations. They begin a trial and improvement method, often starting with 44 x 54 (as 40 x 50 = 2000 and 4 x 4 = 16). They will often come up with one answer after some furious pencil scribblings, and then struggle on to find some more.
When questioned about how they will know when they have got them all, there is normally a silence or blank face. If not, a lot of ‘ums’ and ‘ers’.
It is usually the less trained student that will step back from the question and think about what they actually can do. Sometimes those among the least able in the class will say, well I know 2016 = 2 x 1008… This simple step leads them on a journey of discovery to their first answer, and it doesn’t take too long to discover some more. Clearly using factorising to prime factors is the best approach to a complete solution, and it is often less confident pupils who will happen upon this.
So why use this sort of question? Firstly, it teaches children that a question is not always asking you to do what it seems. It teaches children that Maths is about connections as much as calculations. This type of open ended question often requires curiosity and perseverance in order to achieve. It links to division and factors, and opens up lots of discussion about how seemingly difficult multiplication or division problems can be simplified.
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]]>sort shapes by rectangles and red in a Carroll diagram. No errors possible.
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