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Progression in Multiplication


Created on 13 March 2013 by ncetm_administrator
Updated on 30 June 2014 by ncetm_administrator

Progression in Multiplication

Introduction

This suite of videos looks at elements of progression in multiplication across the primary school. In the context of children practising table facts and developing fluency, Sam, a Key Stage 1 teacher reinforces children’s understanding of the concept through pictures and symbols. Later in her lesson she introduces the commutative law for multiplication through the image of an array. Richard, in Lower Key Stage 2, links the array to the grid method as an interim step for multiplication and Debbie, in Upper Key Stage 2, successfully introduces the children to the compact algorithm.

You can also find the videos on our YouTube channel - and you may find it useful to download them to your own device, using the links given beneath each video. If you encounter any problems, please contact us.

Multiple Representations of Multiplication

This video can also be watched on Vimeo, the video hosting site, where it is also possible to download a copy for your own use.

The commutative law for multiplication

This video can also be watched on Vimeo, the video hosting site, where it is also possible to download a copy for your own use. 

Grid multiplication as an interim step

This video can also be watched on Vimeo, the video hosting site, where it is also possible to download a copy for your own use. 

Moving from grid to a column method

This video can also be watched on Vimeo, the video hosting site, where it is also possible to download a copy for your own use. 

 
 

 


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Comments

 


29 January 2017 16:56
Where we use manipulative or a context, then the concrete examples will determine which is the multiplier and which is the multiplicand. These can be written in any order and would be mathematically correct
29 January 2017 15:34
In The Commutative Law for Multiplication video:

The teacher introduced the use of the 'times' x sign, which we later see being used.

From about 3 m 50s in, we hear that '2 times 3' is represented by an array of 3 rows and 2 columns, and we hear and see that '2 times 3' and '2x3' both refer to 2+2+2. also described as 'three two's'. This interpretation is contrary to that allowed in the 2016 KS1 SATS Reasoning paper. In Q26, one length of 10m, repeated 4 times, had to be either 4 x10 or 10+10+10+10 i.e. 4 lots of 10, 4 groups of 10, 4 times 10: the first number in 4 x 10 is the multiplier (number of groups) and the second number is the multiplicand (number of items in, or value of, the group). Another interpretation of the x sign, as used in the video, Grid Multiplication as an Interim Step' is 'multiplied by' where a number/quantity (the multiplicand) is multiplied (repeated) by another number (the multiplier) - this is the more usual format and usage in the UK, as referred to by authors such as Derek Haylock.

The point of the lesson was to guide pupils to discovering that 3x4 = 4x3, in that both result in the same total. However, if are to teach children through the use of manipulatives, then we need to have conformity on the meaning/structure of the language and the associated symbols.
By bjwestacott
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11 November 2015 21:24
Really useful video (moving from grid to column method), thank you. NQT in Year 5.
By gvickers
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02 June 2015 19:11
Sorry but the NCETM do not have the presentation. This was produced by the school
02 June 2015 15:50
It would be really helpful to have a link to the excellent smartboard presentation that this teacher was using. It would save us from having to reinvent the wheel!
By ClaireOc
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17 January 2015 04:08
wonderful! Its the stuff which I have been looking for to share with my teachers. Thankyou
By heylhi1234
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11 October 2014 21:00
This nrich link has some useful ones that can be played on line or downloaded

http://nrich.maths.org/8283
11 October 2014 16:19
Hi I'm looking for some matching cards used in this video. Does anyone know if there are any pre-made to go with this before I go and make my own?

Thanks :)
By shawksley.hi
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06 June 2014 14:00
That is a great way of representing the commutative law.
By laurencear
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04 June 2014 19:36
Great video, very effective, I wanted to see the rest of the smart board with the calculations and images!! Thanks.
By blacksheep2
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14 March 2014 14:42
Very clear and precise visual demonstration. It's a thumbs up from me!

A Bradley
By a10103312b
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23 November 2013 15:31
Very useful video
By AGoodwin
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11 June 2013 17:29
I am an FE Tutor and was looking for resources to use in a Teaching Maths for TAs course. THis looks excellent!

Thank You

Gaye Noel

Leeds City College
By GayeNoel
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12 April 2013 17:15
Excellent video, very clear use of language by the teacher as well as manipulatives used to promote an understanding of commutative law.
By lisaholt
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