Similarity

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

Taken from Edexcel Higher Paper 1 Nov 2013

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

Two triangles are similar if they're 'equiangular' (a chip of a mouthful hence I learn 'AAA' instead). GCSE questions oft require us to kickoff jibe upward equal angles earlier nosotros start calculating unknown sides using ratio/proportional methods.  This 'matching up' usually involves using angle rules - encounter my postal service on FUN angles. The primal betoken to emphasise inward didactics is that it genuinely really helps to depict the 2 triangles separately, too inward the same orientation. Here's 3 examples to illustrate this:

Example 1 - Separate Triangles

Example 1 is straightforward - it's clear to encounter from the angle labels that the 8cm side inward the kickoff triangle is proportional to the side labelled ten inward the minute triangle.  I'd withal encourage my pupils to redraw the 2 triangles inward the same orientation though.

Example 2 - Joined Triangles

Example 2 is less obvious.  My pupils oft brand the error of thinking that side BC is proportional to side CE.  I learn them to label all equal angles inward the diagram, too hence depict triangles ABC too EDC separately. They'd too hence encounter that because <ABC = <CDE (alternate angles) too <ACB = <ECD (vertically reverse angles), the side BC is genuinely proportional to the side CD. 

Example 3 - Combined Triangles

In Example 3 we tin dismiss locomote the same approach equally inward Example 2. Label all the equal angles inward the diagram ie <ABD = <ECD (corresponding angles), too hence depict the triangles ABD too ECD separately. In this interrogation it's probable we'll live on asked to piece of occupation out the length BC, which simply requires a chip of thinking (ie calculate the length BD first, too hence subtract the length CD).  

Resources

• I honey these resources from the Mathematics Assessment Project. In particular, the sorting cards on pages fifteen - xviii render a challenging too engaging activity.  I asked my pupils to variety the cards into 3 categories (similar/not similar/can't tell), stick them onto A3 newspaper too annotate amongst reasons.  
• Similar pairs is a squeamish matching activeness from Don Steward.
• This blog post. 
• This is a great booklet of practise questions. There's also simply about 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 surface area too mass of similar figures, encounter my resource library.

5 Maths Gems #30

Hi in addition to welcome to my 30^th gems post. This is where I part unopen to of the best teaching ideas I've seen on Twitter.

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

One of Paul Collins' structure comic strips 

I haven't taught constructions this twelvemonth therefore I've non nonetheless had a peril to role these resources, or the awesome Gems 21).

I loved the function 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 ordinarily a fan of homeworks similar this because they're therefore fourth dimension consuming (both for students to attain in addition to teachers to mark) in addition to oftentimes they don't add together much value. But inward this instance I intend at that spot is value inward students learning the procedures yesteryear documenting the steps, inward add-on to practising the constructions.

2. Influenza A virus subtype H5N1 Level Resources

Thanks to @OxfordEdMaths for sharing a fix of excellent A degree assessments for C1 - C4, D1, D2, FP1, FP2, M1, M2, S1 in addition to S2. It tin move difficult to discovery sources of skilful Influenza A virus subtype H5N1 degree questions. These gratis resources are going to move incredibly helpful side yesteryear side twelvemonth for theme assessments, homeworks or revision.

Speaking of Influenza A virus subtype H5N1 degree resources, do banking enterprise gibe out the website 0a explains: Calculus (with pics in addition to gifs) -thanks to @mathhombre in addition to @solvemymaths for sharing this. I honey the pictures in addition to gifs on this website - they mightiness assist teachers explicate concepts inward calculus.

3. Homework Expectations
I've only discovered MathFour.com from Bon Crowder - it's total of creative ideas, unopen to of which I innovation to characteristic inward 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 inward September. I can't complain nearly my students' function 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 action inward detail. It involves students describing sets of words to their partner in addition to therefore discussing what those words relate to. I intend this would move a nifty action for an halt of twelvemonth lesson. Have a facial expression at Steve's post for resources. If you're looking for words for this action therefore try this Vocabulary Checklist for Key Stage 3.  

5. Activities

I've seen unopen to lovely activities in addition to questions on Twitter this week.

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

Gems 29.

@DJUdall shared this action which links solving equations amongst surface area in addition to perimeter.

@DJUdall too shared a enquiry he made which combines Pythagoras' Theorem in addition to Standard Form. 

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

Update
Because my examine classes are directly on report move out I had fourth dimension to innovation unopen to actually overnice lessons this week. With my Year 10s I did a lesson on similar triangles using resources from the Mathematics Assessment Project. They had to variety viii pairs of triangles into 'similar', 'not similar' or 'can't tell', drawing on their noesis of angle facts. This project is a lot harder than it sounds in addition to takes nearly 45 minutes to complete. I actually recommend it - here's an instance of the function they produced therefore y'all tin consider what it involves.

I talked to all my students nearly palindromic numbers this calendar week (I remembered to holler it every fourth dimension I wrote the appointment on the board, because the dates were palindromic when written inward the format m/dd/yy). Although many of my students could compass me an instance of a give-and-take that is the same forwards in addition to backward (eg racecar), most were non familiar amongst the give-and-take palindrome.

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

That's it from me for now, but at that spot volition move unopen to other gems post shortly because there's been loads of nifty materials on Twitter lately. Wish me luck amongst my concluding calendar week at my electrical flow school! My novel project starts later half-term.

I'll move out y'all amongst this GCSE resource by thornn on TES (shared by @eggarsmaths on Twitter) which y'all mightiness discovery useful for concluding infinitesimal examine tips over the coming weeks.

5 Maths Gems #105

Welcome to my 105^th gems post. This is where I percentage unopen to of the latest news, ideas in addition to resources for maths teachers.

1. MathsPad
As common James in addition to Nicola from MathsPad convey shared lots of first-class resources amongst subscribers inwards 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 yous tin access fifty-fifty if yous 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 cast a regular decagon. The chore is to honour the length marked amongst a enquiry 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 in addition to thus they volition function on whatsoever modern browser. These interactive tools are useful for for both main secondary teachers. They are really slow to use. There's loads to explore in addition to thus produce cheque out the website.

5. Posters
This lovely railroad train of STEM component subdivision model posters will brighten upwardly schoolhouse corridors in addition to supply proficient talking points.

There's also a prissy 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 flake crazy lately. On Sabbatum black I hosted Matt Parker's volume launch inwards London. Thanks to all the wonderful people who helped out on the black in addition to all the wonderful guests, it ended upwardly existence an utterly brilliant night. I had such a proficient fourth dimension in addition to loved every minute. After first-class in addition to thoroughly entertaining talks inwards the amphitheatre from Matt Parker, Jen Rogers, Rob Eastaway, Tim Harford in addition to Dan Schreiber, nosotros ended the black amongst a exhibit from FoxDog Studios which was the funniest matter I convey e'er seen! There was loads going on inwards the reception room too, including James Grime amongst an Enigma machine, Ben Sparks amongst 3D Geogebra, Andy Sharpe amongst Nrich maths games, in addition to 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 yous in addition to thus much to everyone who came, in addition to to our friends at Jane Street for the ridiculously generous support. I recall it's fourth dimension for me to retire from my final result administration hobby because there's no means I tin e'er travel past times 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 in addition to formulae for GCSE maths in addition to science. Please either bulk order for your students or signal them inwards the administration of Amazon using these leaflets. I convey explained how the books function inwards this brusk domicile video.

I'm ridiculously tired from the volume launch (turns out that planning big events at brusk notice is a flake exhausting!), precisely notwithstanding really much looking frontward to #mathsconf18 inwards Bristol this weekend. I produce dearest a mathsconf. I volition convey unopen to samples of my books if yous desire to convey a look. I volition also last doing a utter almost unit of measurement conversions (a technical glitch meant that people were unable to sign upwardly to it for a while, precisely at that topographic point is notwithstanding infinite in addition to thus delight come upwardly along!), in addition to I'll last helping to run the MA bookstand along amongst David Faram. Do come upwardly in addition to nation hullo at unopen to signal if you're at the conference.

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

Similarity

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

Taken from Edexcel Higher Paper 1 Nov 2013

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

Two triangles are similar if they're 'equiangular' (a chip of a mouthful hence I learn 'AAA' instead). GCSE questions oft require us to kickoff jibe upward equal angles earlier nosotros start calculating unknown sides using ratio/proportional methods.  This 'matching up' usually involves using angle rules - encounter my postal service on FUN angles. The primal betoken to emphasise inward didactics is that it genuinely really helps to depict the 2 triangles separately, too inward the same orientation. Here's 3 examples to illustrate this:

Example 1 - Separate Triangles

Example 1 is straightforward - it's clear to encounter from the angle labels that the 8cm side inward the kickoff triangle is proportional to the side labelled ten inward the minute triangle.  I'd withal encourage my pupils to redraw the 2 triangles inward the same orientation though.

Example 2 - Joined Triangles

Example 2 is less obvious.  My pupils oft brand the error of thinking that side BC is proportional to side CE.  I learn them to label all equal angles inward the diagram, too hence depict triangles ABC too EDC separately. They'd too hence encounter that because <ABC = <CDE (alternate angles) too <ACB = <ECD (vertically reverse angles), the side BC is genuinely proportional to the side CD. 

Example 3 - Combined Triangles

In Example 3 we tin dismiss locomote the same approach equally inward Example 2. Label all the equal angles inward the diagram ie <ABD = <ECD (corresponding angles), too hence depict the triangles ABD too ECD separately. In this interrogation it's probable we'll live on asked to piece of occupation out the length BC, which simply requires a chip of thinking (ie calculate the length BD first, too hence subtract the length CD).  

Resources

• I honey these resources from the Mathematics Assessment Project. In particular, the sorting cards on pages fifteen - xviii render a challenging too engaging activity.  I asked my pupils to variety the cards into 3 categories (similar/not similar/can't tell), stick them onto A3 newspaper too annotate amongst reasons.  
• Similar pairs is a squeamish matching activeness from Don Steward.
• This blog post. 
• This is a great booklet of practise questions. There's also simply about 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 surface area too mass of similar figures, encounter my resource library.

5 Maths Gems #30

Hi in addition to welcome to my 30^th gems post. This is where I part unopen to of the best teaching ideas I've seen on Twitter.

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

One of Paul Collins' structure comic strips 

I haven't taught constructions this twelvemonth therefore I've non nonetheless had a peril to role these resources, or the awesome Gems 21).

I loved the function 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 ordinarily a fan of homeworks similar this because they're therefore fourth dimension consuming (both for students to attain in addition to teachers to mark) in addition to oftentimes they don't add together much value. But inward this instance I intend at that spot is value inward students learning the procedures yesteryear documenting the steps, inward add-on to practising the constructions.

2. Influenza A virus subtype H5N1 Level Resources

Thanks to @OxfordEdMaths for sharing a fix of excellent A degree assessments for C1 - C4, D1, D2, FP1, FP2, M1, M2, S1 in addition to S2. It tin move difficult to discovery sources of skilful Influenza A virus subtype H5N1 degree questions. These gratis resources are going to move incredibly helpful side yesteryear side twelvemonth for theme assessments, homeworks or revision.

Speaking of Influenza A virus subtype H5N1 degree resources, do banking enterprise gibe out the website 0a explains: Calculus (with pics in addition to gifs) -thanks to @mathhombre in addition to @solvemymaths for sharing this. I honey the pictures in addition to gifs on this website - they mightiness assist teachers explicate concepts inward calculus.

3. Homework Expectations
I've only discovered MathFour.com from Bon Crowder - it's total of creative ideas, unopen to of which I innovation to characteristic inward 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 inward September. I can't complain nearly my students' function 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 action inward detail. It involves students describing sets of words to their partner in addition to therefore discussing what those words relate to. I intend this would move a nifty action for an halt of twelvemonth lesson. Have a facial expression at Steve's post for resources. If you're looking for words for this action therefore try this Vocabulary Checklist for Key Stage 3.  

5. Activities

I've seen unopen to lovely activities in addition to questions on Twitter this week.

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

Gems 29.

@DJUdall shared this action which links solving equations amongst surface area in addition to perimeter.

@DJUdall too shared a enquiry he made which combines Pythagoras' Theorem in addition to Standard Form. 

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

Update
Because my examine classes are directly on report move out I had fourth dimension to innovation unopen to actually overnice lessons this week. With my Year 10s I did a lesson on similar triangles using resources from the Mathematics Assessment Project. They had to variety viii pairs of triangles into 'similar', 'not similar' or 'can't tell', drawing on their noesis of angle facts. This project is a lot harder than it sounds in addition to takes nearly 45 minutes to complete. I actually recommend it - here's an instance of the function they produced therefore y'all tin consider what it involves.

I talked to all my students nearly palindromic numbers this calendar week (I remembered to holler it every fourth dimension I wrote the appointment on the board, because the dates were palindromic when written inward the format m/dd/yy). Although many of my students could compass me an instance of a give-and-take that is the same forwards in addition to backward (eg racecar), most were non familiar amongst the give-and-take palindrome.

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

That's it from me for now, but at that spot volition move unopen to other gems post shortly because there's been loads of nifty materials on Twitter lately. Wish me luck amongst my concluding calendar week at my electrical flow school! My novel project starts later half-term.

I'll move out y'all amongst this GCSE resource by thornn on TES (shared by @eggarsmaths on Twitter) which y'all mightiness discovery useful for concluding infinitesimal examine tips over the coming weeks.