easy way to learn mathematics: Favourite Problems

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

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

A work from solvemymaths.com

I similar this quote from Jennifer Piggot, "A work is something that y'all likely volition non straightaway run into 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 in addition to this is OK. In fact it is of import that y'all acquire stuck thus that nosotros tin dismiss verbalize almost possible ways of getting unstuck" (source: nrich).

My Favourite Problems
During side yesteryear side week's Twitter chat I'd similar to run into examples of your favourite problems. These mightiness hold upward interesting questions that y'all operate when pedagogy specific topics - for instance do y'all cause got a bully inquiry on criterion form? Straight describe of piece of work 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 variety of work that could cause got minutes or hours to solve. It's sure enough suitable for brilliant GCSE in addition to Influenza A virus subtype H5N1 degree students to cause got a acquire at. At commencement await it's i of those 'where on populace do I start?' questions. Draw inward a few lines in addition to a 'Eureka!' instant may come. We terminate upward amongst a fairly straightforward work involving Pythagoras in addition to a quadratic equation (I state straightforward, simply I'm assuming that the problem-solver knows Pythagoras' Theorem in addition to knows how to solve quadratic equations... Prerequisite noesis is a characteristic of many geometrical problems).

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

Problems don't cause got to hold upward highly complex. Any inquiry that makes students halt in addition to retrieve is valuable. For instance this calendar week I was looking for a starter on coordinates for my Year seven class. I could cause got gone for a criterion plotting activeness - I believe that ongoing procedural exercise is really of import - simply instead I've gone for the inquiry below:

From Squares in addition to Coordinates (Don Steward)

It's an accessible work (the shape is a square) simply I retrieve my students volition detect it challenging. In fact I'm worried that I'll hold upward met amongst a chorus of "can't do it, Miss" in addition to and then I'll lose their attention. I retrieve this is a mutual fearfulness of maths teachers - nosotros desire to laissez passer on our students problems that volition instruct them to hold upward independent in addition to resilient mathematicians, simply nosotros worry that they'll lose focus if they can't piece of work out how to acquire started. This is something nosotros tin dismiss verbalize over inward the Twitter chat on Tuesday.

Finally, here's a work that I've used a seat out of times when pedagogy surds - I beloved this one:

I actually await forwards to seeing your favourite problems inward #mathscpdchat at 7pm on Tuesday - run into y'all there.

Problem Solving Resources