Fractions and quantities

[Wildflowers]

In the National Curriculum guidance to the Year 1 maths it states:

Pupils are taught half and quarter as 'fractions' of discrete and continous quantities by solving problems using shapes, objects and quantities.

Pupils connect halves and quarters to equal sharing and grouping of sets of objects and to measures.

1. Discrete and continuous quantities 2. objects and quantities 3. sets of objects and measures - Do they mean the same thing? And do they mean number of objects and amounts, i.e. countable and uncountable quantities?

We have two children who can find and name a half and a quarter of an object, shape and number of objects which can be divided by four, but is unable to find and name a quarter of an amount of water or sand. I can't find anything online explaining what discrete and continuous quantities are in relation to Year 1 maths. Do you primary teachers teach quarters of amounts/uncountable quantities? And is that the same as continuous quantities?

 

 

 

 

[mundia]

Hi wildflowers. You are on the right track, discrete quantities are those that can be counted..number of things..3 apples, 2 tins of beans etc. Continuous quantities are things like weights, measurements, sand, playdough.

Can you make the link between sharing and factions? So sharing out the dough or flour for baking between two people so that they have the same amount each gives them half each? Can you use lots of hands on materials and get the children to find ways of sharing out equally..halves first then quarters. There's an element of critical thinking and problem solving as they work out how to share out the dough (or anything else) fairly.

 

When my grandson does this (also in year one) he cuts it by eye first then weighs the bits to see if they are the same, then he adjusted. He does a lot of cooking so this would be obvious to him. Others might do it in a different way eg rolling it into a sausage then bending it in half.

 

Have fun with it but keep it practical.

[Wildflowers]

Thanks Mundia.

So a continous quantity is that which you say 'less' and 'least' for when comparing, and a discrete quantity is that which you say 'fewer' and 'fewest'.

Can one replace the concepts 'discrete and continous quantities' with 'numbers of objects and amounts', as parents may not be familiar with the former? Or should it be 'numbers of objects and measures'?

Regarding fractions: When you teach finding a quarter of a continuous quantity - do you always encourage children to first halve and then halve again? That is easier with playdough than with water, unless you pour out rather than to fill...

Edited June 17, 2016 by Wildflowers

[finleysmaid]

Thanks Mundia.

So a continous quantity is that which you say 'less' and 'least' for when comparing, and a discrete quantity is that which you say 'fewer' and 'fewest'.

 

Does this always work? only I was thinking about pizza maths and you could have less than a friend or fewer pieces than your friend?

[Wildflowers]

If playdough, sand and water are continuous quantities, then I assume pizza is as you can share it out in parts. An object, such as a stick or a ball is not a continous quantity, is my guess.

Regarding correct use of 'less' and 'fewer': http://blog.oxforddictionaries.com/2012/08/less-or-fewer/

[finleysmaid]

thanks wildflowers so I was correct then in assuming that less and fewer are not always correct as it states at the end of the article you posted regarding money/miles etc etc

[mundia]

The proper 'rules' about less and fewer are, as many things in our wonderful language, are quite complex but in general, wildflowers, that's right fewer when talking numbers and less when talking amounts. The maths curriculum uses mostly 'less'. The pizza example from Finleysmaid is also correct, less pizza because it's not countable but once you have slices of pizza, they are now countable so they can be fewer, but again depends on context.

 

But we could go on all day about the complexities of our language.

 

In terms of teaching halves and quarters, yes I would teach half and half again for quarter but only after children have lots of practical experience 'seeing' what happens when you cut the sandwich in half and then cut them again. Otherwise you end up with children learning some strange 'rule' in maths that has no meaning to them. But the idea of half of half is such an important aspect of handling larger numbers and dividing by 4, something I still use if I'm calculating in my head, I would still often halve and halve again.

 

I'd give children lots of examples, so how do we find half the cup of water, snack time may lend to this, one jug, 2 cups or 4 cups. I personally believe one of the reasons we're not great as a country at maths is because we take away the practical far too soon, and many of these things I'd be doing in reception, when we're looking at doubles and halves.

 

And I'd bet my pension on there being a strong link between a child's conceptual understanding of halves thirds and quarters and the number of children in the family...children have a very strong sense of fair when it comes to their siblings.

 

Oops I love to waffle.

[Wildflowers]

Is the maths curriculum mostly using 'less' also when it should be 'fewer'? I work in a preschool with a few reception-aged children and thought it would be important to teach them the correct usage of language, even if not always used in society.

[mundia]

I think the EYFS doesn't state fewer at all and yes the pedant in me thinks it should. On the one hand grammatical rules would be happy with one more than or one less than (the ELG), if you are comparing plates of biscuits, I would definitely say this was has fewer biscuits than that one.

 

Wildflowers when you mentioned the year one curriculum I assumed the children you were talking about were in year one? Are they in preschool?

[Wildflowers]

Some of our so called reception-aged children are beyond the ELG in some areas.

I'm not a primary teacher (I work with one) and have found it helpful to get to know what is to come in later. It has affected the comments I make in practical or play contexts, e.g. 'that puddle is shallow, so I think we can walk through it' or 'I think we are getting too many characters' when making up a story together and a child adds another animal. (Though that may be YR.) Our children half-fill cups of water to drink, so following on the theme of the thread: 'He can have less water because he is younger. He is half your age, so he an have just a quarter.' I'm just seeing and taking opportunities more, e.g. naming body parts, materials, 3D shapes, parts of plants etc and using simple scientific language, talking about properities of materials etc. I read somewhere that the awareness of concepts broaden children's experiential world, so thought that may be a good thing to bring them in whenever there is a natural opportunity.

[mundia]

Absolutely, correct mathematical language is something I don't hear a lot of when I am out and about, and time spent exploring mathematical ideas, and extending language in maths, is time well spent in my mind.