What happens when children begin by focusing on ‘noticing and understanding’ rather than calculating…
What can I see and explain?
I can see 4 ‘displays’ of tomatoes. Each ‘display’ has 4 rows of 3 tomatoes and 3 rows of 4 tomatoes
So that’s 4 multiplied 3 times and then this total multiplied 4 times! Or 3 multiplied 4 times and then this total multiplied 4 times!
Or, 4 x 3 plus 4 x 3 plus 4 x 3 plus 4 x 3 or 3 x 4 plus 3 x 4 plus 3 x 4 plus 3 x 4!
I can see each display has 2 groups of 6 tomatoes
So that’s 6 multiplied 8 times!
If there’s 2 groups of 6 in each display that must be 12
So that’s 12 x 4!
So if I wanted to work out how many tomatoes on 8 displays…I’d double it!
What is this total a multiple of…?
Well I can see equal groups of 3 so the total number of tomatoes must be a multiple of 3
And it’s a multiple of 2, 4 and 6, an 12 …oh, and 1…and 24, and 48! Wow! Have I missed any?
Ok, what about factors?
Well I can see that the total can be divided into equal groups of 2 with no remainder so 2 is a factor of this total.
What other equal groups without remainders can I divide this total into? 3? 4? 6? 12? 24? 48?
What about 8’s? Can I see groups of 8?
So, if I can see multiples and factors I must be able to see fractions. Let’s have a closer look…
The total number of tomatoes (the whole) is divided into 4 equal groups so this is quarters.
Each quarter has 12 tomatoes.
So that means four quarters = 48, three quarters =36, 2 quarters (or half) = 24 and one quarter = 12!
Let’s look for another fraction….
I can see there are equal groups of 6. How many groups can I see? 8
So the whole is split in to eight equal parts so each part is an eighth.
So eight eights = 28, what about 5 eighths? This would be 5 groups of 8 so that’s 40 out of 48 tomatoes. Wait, that’s an equivalent fraction! ⅝ = 40/48!
And all of this from a photo taken at the Malvern Autumn Show!
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S Thomas, Key Stage 2 Teacher, West Midlands
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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!