5 Maths Gems #15

Welcome to my 15th weekly gems post - this is where I characteristic roughly of the best teaching ideas I've seen on Twitter each week.

1. Slice The Pie

Paul Rehmet (@prehmet) has built an interactive tool to help students ready numerical fluency. It's a uncomplicated fraction game - Slice The Pie - which helps students railroad train an intuitive sense of the relative sizes of numbers. It's non compatible alongside mobiles yet but would piece of work on your interactive whiteboard. I honey this. Have a play alongside it, I think you'll honey it too. And follow Paul on Twitter because there's to a greater extent than to come upward from him.

2. Remembering Inequalities

In my post almost Ideas from Shanghai I shared this visualisation which helps students squall upward which inequality sign is which.

All students demand to exercise is visualise numbers equally blocks - the wider terminate of the inequality symbol fits over the bigger stack of blocks. So if x > 2, nosotros know x must hold out a number bigger than 2. 

Chris Smith (@aap03102) pointed out that this doesn't piece of work for negative numbers. 

I'm sure as shooting our friends inward Shanghai own got a solution for this but that data hasn't filtered through to us, thence let's come upward up alongside our ain alternative that industrial plant for both positive in addition to negative numbers. We simply demand a agency for students to squall upward which symbol is which.

I'm actually grateful to all the lovely creative tweeters who offered ideas - my favourite was this calligram from Chris. 

So if x < - 8, nosotros run into the < symbol in addition to think of the missive of the alphabet L, thence nosotros know x is less than -8.

Eventually students volition automatically know the important of the symbols on sight, without having to visualise blocks or words.

These methods are far ameliorate than thinking of crocodiles - this tin give notice confuse students, equally described inward Nix the Tricks (extract below).

3. Squares in addition to Cubes
I'm enjoying La Salle Education's (@LaSalleEd) novel 'Problem of the Day' series.  You tin give notice search the collection yesteryear historic current or topic. The instance below (Square Boxes) is a dainty logic occupation consolidating noesis of foursquare numbers.

If you're teaching foursquare numbers, yous mightiness also similar this 'Square in addition to Cube Numbers Puzzle' from MathsPad...

... in addition to this lovely square in addition to cube numbers display from Clarissa Grandi (@c0mplexnumber).

4. Mathsticks
I late discovered the brilliant Mathsticks website which is created yesteryear John Duffty (@johnduffty). I registered in addition to explored - it's by in addition to large primary materials but roughly of the ideas mightiness hold out helpful at Key Stage 3. Here's a twosome of examples:

This Parallel & Perpendicular Slope. Once you've taught students almost the gradients of parallel in addition to perpendicular lines, larn them inward a reckoner room (or larn the iPads out, if yous own got them) in addition to give them this worksheet, which I think volition hold out real slowly for them to follow independently. They are given sure as shooting lines which they plot (in Desmos, though I suppose this could hold out done yesteryear hand) in addition to and thence they add together the right parallel or perpendicular lines to brand the required shape. It's a actually dainty activity which volition assistance yous banking enterprise check their agreement of this topic.

Extract from Desmos Graph Challenge

Here's my response to the 2nd query inward the extract above.

To extend this task, yous could own got students confine the domains of the functions, equally I've done below. If yous exercise this, it's of import that they figure out how to calculate the coordinates of the vertices.

If you're teaching parallel in addition to perpendicular lines in addition to thence also banking enterprise check out my post linear graphs for to a greater extent than ideas in addition to resources.

A asking for misconceptions
When I project design lessons, I uncovering it helpful to travail to predict the misconceptions that mightiness come upward up. Sometimes I'm surprised yesteryear the mistakes that students make, which are ofttimes the number of my explanations non beingness clear enough. Knowledge of mutual misconceptions comes alongside sense but I think it would exercise goodness novel maths teachers if they could consult a website to run into examples of the kind of things students larn wrong. 

A not-so-common misconception from i of Chris Smith's students

American instructor Michael Pershan (@mpershan) has a bright website Math Mistakes where he compiles, analyses in addition to discusses the mathematical errors that students make. I desire to prepare something similar for the United Kingdom of Great Britain in addition to Northern Ireland (because our curricula in addition to vocabulary are thence different), but I won't own got fourth dimension to exercise the fantabulous analysis that Michael does. Instead it would simply hold out a collection of misconceptions, tagged yesteryear topic. But I notwithstanding think it mightiness hold out useful.

So I own got a asking - could yous kickoff taking photos of misconceptions inward your students' piece of work in addition to emailing or tweeting them to me? Once I've got a small-scale choice I'll kickoff a website in addition to I hope, similar my Pret homework website, it volition grow chop-chop in addition to seek to hold out a helpful resource. Thank yous inward advance!

That's it for today. Please don't forget to vote for me! :), I'll move out yous alongside this cute 'Math nosotros know drama', shared yesteryear @FascinatingVids.