mathematic: Favourite Problems

On Tuesday 23rd June I'm hosting a #mathscpdchat entitled "Problem solving: what are 'good' problems? Where tin y'all respect them?".

What's a Problem?
Influenza A virus subtype H5N1 problem, inwards the mathematical sense, tin live on defined equally "an enquiry starting from given weather condition to investigate or demonstrate a fact, result, or law". The give-and-take originated inwards the belatedly 14th century,'a hard inquiry proposed for solution', from Old French problème, together with straight from Latin problema, from Greek problema 'a task, that which is proposed, a question' (source: etymonline).

A occupation from solvemymaths.com

I similar this quote from Jennifer Piggot, "A occupation is something that y'all belike volition non similar a shot run across how to tackle or which i time started volition challenge your thinking. This agency that at some betoken y'all are probable to acquire stuck together with this is OK. In fact it is of import that y'all acquire stuck hence that nosotros tin speak nearly possible ways of getting unstuck" (source: nrich).

My Favourite Problems
During adjacent week's Twitter chat I'd similar to run across examples of your favourite problems. These mightiness live on interesting questions that y'all purpose when didactics specific topics - for instance do y'all stimulate got a non bad inquiry on measure form? Straight business graphs? Sequences? Remember that we're focussing on problems equally opposed to resources, activities or worksheets.

Here's i of my favourite problems:

Source: Chris Smith's Newsletter, Issue 51

This is the form of occupation that could accept minutes or hours to solve. It's for sure suitable for vivid GCSE together with Influenza A virus subtype H5N1 score students to stimulate got a acquire at. At showtime expect it's i of those 'where on globe do I start?' questions. Draw inwards a few lines together with a 'Eureka!' instant may come. We terminate upwards amongst a fairly straightforward occupation involving Pythagoras together with a quadratic equation (I tell straightforward, only I'm assuming that the problem-solver knows Pythagoras' Theorem together with knows how to solve quadratic equations... Prerequisite noesis is a characteristic of many geometrical problems).

Eventually I aim to clit together a gear upwards of skilful problems for each theme on the curriculum - I've made a start amongst this Pythagoras Problem Set.

Problems don't stimulate got to live on highly complex. Any inquiry that makes students halt together with cry back is valuable. For instance this calendar week I was looking for a starter on coordinates for my Year vii class. I could stimulate got gone for a measure plotting action - I believe that ongoing procedural exercise is real of import - only instead I've gone for the inquiry below:

From Squares together with Coordinates (Don Steward)

It's an accessible occupation (the shape is a square) only I cry back my students volition respect it challenging. In fact I'm worried that I'll live on met amongst a chorus of "can't do it, Miss" together with and hence I'll lose their attention. I cry back this is a mutual fearfulness of maths teachers - nosotros desire to reach our students problems that volition instruct them to live on independent together with resilient mathematicians, only nosotros worry that they'll lose focus if they can't move out how to acquire started. This is something nosotros tin speak over inwards the Twitter chat on Tuesday.

Finally, here's a occupation that I've used a publish of times when didactics surds - I honey this one:

I actually expect forwards to seeing your favourite problems inwards #mathscpdchat at 7pm on Tuesday - run across y'all there.

Problem Solving Resources