Similarity

I saw this neat monster GCSE enquiry on Twitter (thanks @ReviseJustMaths) - it inspired me to write a postal service most similarity!

Taken from Edexcel Higher Paper ane Nov 2013

In this postal service I'll focus on resources as well as methods for didactics similar triangles.

Two triangles are similar if they're 'equiangular' (a flake of a mouthful thence I instruct 'AAA' instead). GCSE questions oftentimes require us to outset tally upwards equal angles earlier nosotros start calculating unknown sides using ratio/proportional methods.  This 'matching up' unremarkably involves using angle rules - come across my postal service on FUN angles. The cardinal betoken to emphasise inward didactics is that it truly really helps to describe the ii triangles separately, as well as inward the same orientation. Here's iii examples to illustrate this:

Example ane - Separate Triangles

Example 1 is straightforward - it's clear to come across from the angle labels that the 8cm side inward the outset triangle is proportional to the side labelled x inward the minute triangle.  I'd yet encourage my pupils to redraw the ii triangles inward the same orientation though.

Example 2 - Joined Triangles

Example 2 is less obvious.  My pupils oftentimes brand the error of thinking that side BC is proportional to side CE.  I instruct them to label all equal angles inward the diagram, thence describe triangles ABC as well as EDC separately. They'd thence come across that because <ABC = <CDE (alternate angles) as well as <ACB = <ECD (vertically contrary angles), the side BC is truly proportional to the side CD. 

Example 3 - Combined Triangles

In Example 3 we tin role the same approach every bit inward Example 2. Label all the equal angles inward the diagram ie <ABD = <ECD (corresponding angles), thence describe the triangles ABD as well as ECD separately. In this enquiry it's probable we'll endure asked to function out the length BC, which simply requires a flake of thinking (ie calculate the length BD first, thence subtract the length CD).  

Resources

• I dearest these resources from the Mathematics Assessment Project. In particular, the sorting cards on pages xv - eighteen furnish a challenging as well as engaging activity.  I asked my pupils to form the cards into iii categories (similar/not similar/can't tell), stick them onto A3 newspaper as well as annotate amongst reasons.  
• Similar pairs is a squeamish matching activeness from Don Steward.
• This blog post. 
• This is a great booklet of exercise questions. There's also closed to challenging questions inward this worksheet from mathsmalakiss.com.
• CIMT has lots of first-class similarity resources.
• This is a lovely rich task from Shell Centre

For resources for expanse as well as mass of similar figures, come across my resource library.

5 Maths Gems #30

Hi together with welcome to my 30^th gems post. This is where I percentage only about of the best teaching ideas I've seen on Twitter.

1. Construction Comics
Back inwards Gems 4 I featured Paul Collins' (comic resources for teaching constructions. In his post he suggests only about opportunities to role these resources inwards the classroom.

One of Paul Collins' structure comic strips 

I haven't taught constructions this twelvemonth hence I've non nevertheless had a run a hazard to role these resources, or the awesome Gems 21).

I loved the operate shared yesteryear my namesake Mrs Morgan (@em0rgan) on Twitter this week. She asked her students to do their ain structure comic strips for homework. The results facial expression excellent. I'm non unremarkably a fan of homeworks similar this because they're hence fourth dimension consuming (both for students to gain together with teachers to mark) together with oft they don't add together much value. But inwards this instance I intend at that topographic point is value inwards students learning the procedures yesteryear documenting the steps, inwards improver to practising the constructions.

2. Influenza A virus subtype H5N1 Level Resources

Thanks to @OxfordEdMaths for sharing a gear upwards of excellent A degree assessments for C1 - C4, D1, D2, FP1, FP2, M1, M2, S1 together with S2. It tin endure difficult to honor sources of expert Influenza A virus subtype H5N1 degree questions. These gratis resources are going to endure incredibly helpful adjacent twelvemonth for theme assessments, homeworks or revision.

Speaking of Influenza A virus subtype H5N1 degree resources, do banking concern agree out the website 0a explains: Calculus (with pics together with gifs) -thanks to @mathhombre together with @solvemymaths for sharing this. I dear the pictures together with gifs on this website - they mightiness assistance teachers explicate concepts inwards calculus.

3. Homework Expectations
I've only discovered MathFour.com from Bon Crowder - it's total of creative ideas, only about of which I excogitation to characteristic inwards hereafter gems posts. One persuasion that I spotted was a 'How to Write Your Math Homework' guide. I'm going to brand a version of this for my novel classes inwards September. I can't complain nearly my students' operate non coming together my expectations if I haven't made those expectations clear from the outset.

4. Talk a Mile a Minute
Steve Wyborney (@SteveWyborney) shared his Talk a Mile a Minute Vocabulary Activity. The video below describes the activeness inwards detail. It involves students describing sets of words to their partner together with and hence discussing what those words relate to. I intend this would endure a cracking activeness for an terminate of twelvemonth lesson. Have a facial expression at Steve's post for resources. If you're looking for words for this activeness together with hence try this Vocabulary Checklist for Key Stage 3.  

5. Activities

I've seen only about lovely activities together with questions on Twitter this week.

@MathedUp shared this 'Negative numbers code-breaker activeness amongst a twist'.

Gems 29.

@DJUdall shared this activeness which links solving equations amongst expanse together with perimeter.

@DJUdall likewise shared a query he made which combines Pythagoras' Theorem together with Standard Form. 

The latter 2 resources were shared during concluding Sunday's #mathsTLP. This is a cracking identify for maths teachers to collaborate. Do bring together inwards on Sundays at 7pm to enquire for assistance amongst lessons or to offering ideas.

Update
Because my examination classes are directly on report acquire out I had fourth dimension to excogitation only about actually prissy lessons this week. With my Year 10s I did a lesson on similar triangles using resources from the Mathematics Assessment Project. They had to kind 8 pairs of triangles into 'similar', 'not similar' or 'can't tell', drawing on their cognition of angle facts. This project is a lot harder than it sounds together with takes nearly 45 minutes to complete. I actually recommend it - here's an instance of the operate they produced hence you lot tin see what it involves.

I talked to all my students nearly palindromic numbers this calendar week (I remembered to yell it every fourth dimension I wrote the appointment on the board, because the dates were palindromic when written inwards the format m/dd/yy). Although many of my students could plough over me an instance of a discussion that is the same frontward together with backward (eg racecar), most were non familiar amongst the discussion palindrome.

Those of you lot who role Gems 10) for formative assessment volition endure pleased to listen that you lot tin directly insert pictures. For instance you lot mightiness desire to insert questions from www.diagnosticquestions.com.

That's it from me for now, but at that topographic point volition endure only about other gems post presently because there's been loads of cracking materials on Twitter lately. Wish me luck amongst my concluding calendar week at my electrical flow school! My novel project starts afterward half-term.

I'll acquire out you lot amongst this GCSE resource by thornn on TES (shared by @eggarsmaths on Twitter) which you lot mightiness honor useful for concluding infinitesimal examination tips over the coming weeks.

5 Maths Gems #105

Welcome to my 105^th gems post. This is where I percentage or as well as then of the latest news, ideas as well as resources for maths teachers.

1. MathsPad
As common James as well as Nicola from MathsPad convey shared lots of fantabulous resources amongst subscribers inward their monthly update. Their pie nautical chart tool is great!

This calendar month they also shared a complimentary railroad train of fun cross-sequences puzzles that y'all tin access fifty-fifty if y'all don't subscribe. I've added this to my algebra resources library.

2. Similar Triangles Problem
Thanks to John Rowe (@MrJohnRowe) for sharing this problem. Similar triangles spiral to shape a regular decagon. The chore is to honor the length marked amongst a inquiry mark.

3. Missing Steps
TickTockMaths (@TickTockMaths) shared an activity where students consummate the missing steps.

You tin download his algebraic fractions PowerPoint here. Check out all of Richard's complimentary resources on his blog or on TES.

4. Maths Frame
Ted Burch (@Mathsframe) has converted all his free maths ITPs from Flash to HTML5 as well as then they volition operate on whatsoever modern browser. These interactive tools are useful for for both principal secondary teachers. They are real slow to use. There's loads to explore as well as then create banking concern tally out the website.

5. Posters
This lovely railroad train of STEM component subdivision model posters will brighten upwards schoolhouse corridors as well as supply skilful talking points.

There's also a overnice railroad train of downloadable 'Forces of Nature' posters from Perimeter Institute which includes ane of my favourite mathematicians, Ada Lovelace.

Update
It's all been a fleck crazy lately. On Sat nighttime I hosted Matt Parker's volume launch inward London. Thanks to all the wonderful people who helped out on the nighttime as well as all the wonderful guests, it ended upwards beingness an utterly brilliant night. I had such a skilful fourth dimension as well as loved every minute. After fantabulous as well as thoroughly entertaining talks inward the amphitheatre from Matt Parker, Jen Rogers, Rob Eastaway, Tim Harford as well as Dan Schreiber, nosotros ended the nighttime amongst a exhibit from FoxDog Studios which was the funniest matter I convey e'er seen! There was loads going on inward the reception room too, including James Grime amongst an Enigma machine, Ben Sparks amongst 3D Geogebra, Andy Sharpe amongst Nrich maths games, as well as Chalkdust amongst their awesome magazine. Plus of course of teaching at that topographic point was a self-playing pianoforte performing a previously unannounced superpermuation. And the best goody bags ever.

Here's a video of my 180 guests (mostly maths teachers) thoroughly enjoying the interactive exhibit from FoxDog Studios.

Thank y'all as well as then much to everyone who came, as well as to our friends at Jane Street for the ridiculously generous support. I recollect it's fourth dimension for me to retire from my number management hobby because there's no means I tin e'er exceed this one!

In other news, my books convey similar a shot been printed. These books are for students (not teachers!) - they are designed to assistance them larn all their facts as well as formulae for GCSE maths as well as science. Please either bulk order for your students or indicate them inward the management of Amazon using these leaflets. I convey explained how the books operate inward this curt habitation video.

I'm ridiculously tired from the volume launch (turns out that planning big events at curt notice is a fleck exhausting!), simply nevertheless real much looking forwards to #mathsconf18 inward Bristol this weekend. I create dearest a mathsconf. I volition convey or as well as then samples of my books if y'all desire to convey a look. I volition also live on doing a beak nearly unit of measurement conversions (a technical glitch meant that people were unable to sign upwards to it for a while, simply at that topographic point is nevertheless infinite as well as then delight come upwards along!), as well as I'll live on helping to run the MA bookstand along amongst David Faram. Do come upwards as well as tell hi at or as well as then indicate if you're at the conference.

I'll acquire out y'all amongst this calculus comic from XKCD.