Thread by @ThatMathsMan

Numberless Word Problems 🧵

Numberless Word Problems are a relatively new thing for many schools in the UK, so here's a short thread with links if you'd like to get started.

First, big praise goes to @bstockus and his blog:
bstockus.wordpress.com/numberless-wor…

#numberlesswp
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Numberless word problems are both a reasoning and a problem solving routine.

They help to address the problem that children sometimes just look at the numbers in a word problem and calculate, without thinking about the context.

NWP provides time to think and discuss first.

2/n

NWP also aim to help to overcome one of the other issues caused by problem solving: cognitive load.

Solving unfamiliar problems with unclear starting points can be mentally taxing, and therefore less accessible than other tasks.

Slowing down and directing thinking can help.
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In @bstockus' blog, he talks about how @reginarocks came up with the idea of replacing the numbers in a problem with the words 'some', 'fewer' and so on.

The account of how the children responded to this is well-worth the read, especially before you try it yourself.
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While it might seem simple (replacing the numbers with words for untold quantities) it can be alien to the children at first.

Therefore you will need to think about how and when you incorporate these into your lessons as this unfamiliarity may cause teething problems.
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Using a new routine such as NWP can be a challenge for all involved. But it can be helpful to watch how someone else does it.

Start here with where @mel0dyb0yd builds students' familiarity of the problem structure.
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Examining word problem structure and naming problem types helps us to better generalise about how we can apply our understanding to problems in the future.

For example, NWP allow us to talk about joining/separating/grouping problems with result/change/start unknowns.
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How about a basic example? I want the class to discuss this:
Tickets for the cinema cost £9 each. How much would it cost to buy 6 tickets?

So my NWP would read:
Tickets for the cinema cost □ each. How much would it cost to buy ■ tickets?

After initially discussing...
8a/n

...the structure of the problem, and identifying that we are going to multiply □ and ■ to find the total cost, I would share the first value.

By replacing □ with £9, the problem now reads:
Tickets for the cinema cost £9 each. How much would it cost to buy ■ tickets?
8b/n

The children now know that every part is worth £9 and that the total cost will be a multiple of 9.

But we still can't draw an array or part-whole model because we don't know how many parts there are.

Next we reveal that ■ is 6. So the children can see the full problem.
8c/n

However, we don't stop here.

This routine becones purposeful and worthwhile if we then consider how changing one of the elements in the problem would change the solution.

For example:
> What would happen to our model if the value of □ or ■ increased/decreased?
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This conversation about variables inevitably leads to more questions. For example:
> In this problem there was one ticket price. What if the price was different for adults and children?

Chn can then solve more and write their own, and then we can change the context.
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To find out more check out:

○ bstockus.wordpress.com/numberless-wor…
○ #numberlesswp on Twitter
○ @gareth_metcalfe's webinars on problem solving
○ Mixandmath.com/blog/numberles…
○ Or search for more inspiration on YouTube
11/n

If this is something you already do and you're looking to expand your reasoning repertoire, or to broaden your children's problem solving diet you might next look into "Goal free problems", "Data Talks" and/or "3 Act Tasks".

Please share your thoughts and experiences below
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@threadreaderapp please unroll.