‘WEDWK?’ The interconnectedness of mathematical knowledge.

WEDWK? Or… ‘What Else Do We Know?’

It’s one of those dreaded acronyms, buzz words and well-worn phrases that blight our screens and twitter feeds.

Actually… I made it up*

But WEDWK? (pronounced ‘wedwik’) has come in very useful in my KS2 teaching. It is a quick (and rather lazy) way of prompting deeper thinking and numerical fluency.

Example 1:

Pupils have been given a warm-up test of multiplication facts. They complete the test as quickly and accurately as possible, but are then asked to choose one fact, e.g. 4 x 8 = 32, and set up a WEDWK? bubble to generate related facts. The obvious, inverse-operational ones should necessarily come first, i.e. 8 x 4 = 32, 32 ÷ 4 = 8 and 32 ÷ 8 = 4

So far, so standard, right?

But then they should be encouraged to take the fact a step further and begin to relate it to all the other operations:

4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 = 32
8 + 8 + 8 + 8 = 32
32 – 8 – 8 – 8 – 8 = 0
32 – (8 x 4) = 0
8 + (8 x 3) = 32
(7 x 4) + 4 = 32

They may then extend to shifting the digits to incorporate decimal fractions and large numbers:

0.8 x 4 = 3.2
32 ÷ 0.4 = 80
3.2 ÷ 8 = 0.4
80 x 400 = 32,000

…And then they may explore links to whichever areas of maths they need to practise: a pupil who struggles with fractions may explore this meaning by drawing diagrams:

32 ÷ 4 = 32/4

Or a child who struggles with area may draw, annotate and tinker with compound and regular shapes whose area is 32 cm^2.

You get the picture.

Example 2:

When marking any child’s maths work, preferably alongside them in class, I simply write ‘WEDWK?’ next to an answer, particularly if it has come as a result of a paired discussion (or is devoid of written workings).

So, when their answer to…

Mr Dexter buys a TV and a bike
The TV costs £130 more than the bike.
Their total cost is £420.
How much does the TV cost? (White Rose problem)

TV = £275

… is recorded, they are allowed to deepen their understanding with WEDWK? statements.

Bike is £145
B = T+130
Two bikes and two TVs would be double £420 = £840

Or, better still, they write further questions to test on a classmate:

If the total cost was reduced by £100 but the difference between costs was still £130, how would the prices of the bike and TV adjust?
A 25% sale starts. Does the word problem above still make sense? Explain why/why not.

WEDWK? It’s a fluency-encourager, a deep-thinking-prompter and a humble insight into the interconnectedness of knowledge. Try it!

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This was my first blog. Any constructive comments or thoughts you have are very welcome.

* No, really – I did. It started out as ‘WEDIK’ (‘What Else Do I Know?’), but 5 minutes into its introduction to a lively class, I changed the personal pronoun. But yes, it’s based on well-trodden teaching principles and in no way revolutionary or particularly clever. It’s just memorable and useful.