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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