This investigation offers rich opportunities to develop essential mathematical language connected to learning multiplication facts.
1. Using equal sized cubes or tiles (preferably of the) same colour) take a handful. This should be more than you can accurately estimate; probably between 15 – 25). DON”T COUNT THEM! You need this to be number ‘x’ (for the time being anyway).
2. Investigate how many rectangular arrays you can construct using ALL of your cubes or tiles. You must use them all as this will help reveal certain properties of ‘x’. For example, if you can create equal columns of 4 then you know ‘x’ is a multiple of 4 and has 4 as one of it’s factors. If you can create columns of 4, you must also be bale to see that ‘x’ can be divided into quarters and you’ll therefore be able to describe how much 3/4 of x is for example.
3. What if you can only create one array? What could you say about this number’s properties and how would we classify this mathematically? What kind of investigations could grow from this about even just the numbers from 1-20?
4. Most numbers will create more than one array though so you could then look carefully at the shape you’ve created and consider how you could rearrange it using what you know about 4. If there are two groups of 2 in 4 then what could you do to your array and what multiple, factor and fraction facts would you discover?
5. What if you can create columns and rows with the same number in each? What shape does this produce and has anyone else produced this shape with a different number of cubes?
6. What doesn’t work and why?
7. This could all be recorded pictorially using either squared paper or as labelled rectangles on plain paper. By creating the corresponding equations you’ll have the whole ‘Concrete- Pictorial – Abstract’ journey.
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Thank you so much Karen. I enjoyed the training this morning tremendously and tried out the ideas straight after lunch with my class leading to 20 mins of enthusiastic discussion! Brilliant!
The children said they really enjoyed it and wanted to do more so I am definitely going to be changing my teaching!’
Thank you for showing us HOW to change. So many courses just tell us what isn't working but not how to go about addressing this. Your approaches make so much sense! Thank you.
Just to say thank you again for 3 really brilliant talks at SGIS. We're a small school near Basel and we’d be interested in anything you’re doing nearby (Zurich way) so please let us know!