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# Examples of conceptual and procedural variation with measurements year 1

criberaud1 14 March 2020 16:37
Posts3
Joined14/03/20

Hi,

I have just started using Maths Mastery in January.  I am getting the hang of it ,( well I think I do...)  I am teaching measurements using non-standard units of measure at the moment  but I am struggling to find ways to show conceptual and procedural variations with this topic.  Can anybody help?  Some ideas or  advice please?

Many thanks

Corine

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Rebecca_Hanson 14 March 2020 17:22
Posts1120
Joined28/01/08

I've just published a video about this on YouTube Corine.    I think I'm not allowed to publish a link.  Try searching for my name year 1 measure maths or something like that.  Let me know if you get stuck.

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Laurie_Jacques 15 March 2020 20:59
Posts549
Joined27/06/06

Hi Corine,

The purpose of using variation is for pupils to be able to discern the sameness against the background of variation or variation against a background of sameness.

I am assuming in Y1 that you are working on measuring length at the moment.

Conceptual variation might be to measure the same thing with different non-standard units. This will enable the children to notice that when the unit of measure varies the 'amount' of units will also vary even when the object that is being measured is the same. Here variation is being discerned against a background of sameness and will help to establish that having a single unit of measure that is consistent is most reliable.

You can begin by using distinuishablely different objects to measure with e.g. round buttons/ counters or cubes or paperclips etc.

You can then make the units the same 'thing' but of different sizes. e.g. measuring the side length of the table with small buttons then big buttons. (The bigger the button the fewer the number that fit along the table). Or foot prints. Or handspans. This too is conceptually varying the unit of measure but the 'variation' (in hand size or button size) is far more subtle.

Conceptual variation also involves non-concept variation. In the case of measuring length this can mean comparing two lengths that do not share a common starting point (i.e. later leading to always position a ruler at 0 at the beginning of what you want to measure). Choose two children who differ in height in your class and ask one of them to stand on a chair next to the other on the floor. Who is the taller person? Is it possible to know? How? Exploiting misconceptions that because the child on the chair is taller than the child on the floor is the taller child challenges the concept of comparing heights and emphasises the need to compare from the same starting point.

For procedural variation you may want the children to consider how the measurement of length can vary. So changing what you measure but keeping the unit of measure the same. So this time what is kepy invariant is the unit of measure but what is measured varies. i.e. you are practising the measuring of length in different contexts.

Try lining a set of identical buttons on the table/ carpet and laying a toy car along the button but not starting at the first button. Can the children still say how long the car is? What if we move the car along to the beginning of the line? Or the other end of the line of buttons? This will enable the children to notice that when the unit is same an object will remain the same length whereever the measuring start point is chosen.

You may also want to offer a 'how could we measure' type task for something that is difficult to measure. E.g. something curved or large (where there are not enough single units to measure the entire length. Ten you can compare the children's different stratgies and see what characteristics of their strategies are the same or different.

I hope this doesn't make this sound too complicated. The key idea for conceptual variation is that when you choose examples for your children to think about, try to make a concious decision about what you will change and what you keep the same when you move from one example to another. Then by asking what is the same? what is different? You will be able to notice those important features and how what is the same is the focus of attention and what is different is arbitary.

For procedural variation you want the pupils to notice what is 'changing' and what is remaining the same in successive examples.

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criberaud1 15 March 2020 21:16
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Joined14/03/20

Hi Laurie,

The examples you gave are brilliant and make total sense!
Thank you so very much.

kind regards

Corine

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criberaud1 15 March 2020 21:19
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Joined14/03/20

Hi Rebecca,

I love the measuring worms!  Your video was really useful.
many thanks.

Corine

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