5 Maths Gems #24

Hello as well as welcome to my 24th gems post - this is where I part five teaching ideas I've seen on Twitter. I'm going to live on brusk as well as sugariness today... I'm meant to live on marking!

1. Angles inwards Parallel Lines
I'm e'er on the expect out for practiced questions that I tin hand notice role inwards course of didactics as well as thus I was pleased when Cliff Pickover (@pickover) tweeted the occupation below. This volition do nicely for my Year 7s when they come upward to revise angles. I don't shout out upward they've seen the 'hatch mark' used for equal angles earlier (only equal sides) as well as thus it's a practiced exercise inwards interpreting musical note too. Answers are on page half dozen of this document. By the way, if you're non already next Cliff, I highly recommend his tweets.

2. Algebra Countdown
I was browsing @stephenbodman's lovely resources on his website secondarymaths.wikispaces.com when I spotted Algebra Countdown. This is an activity based on the TV programme Countdown, but instead of numbers students are given algebraic terms. Set upward the Countdown Clock as well as run the activity inwards Excel on your Interactive Whiteboard. It's a actually overnice activity for practising simplifying algebraic expressions.

3. Isometric Fractions
I was looking at the cool pads of sticky-backed graph newspaper on www.instagraphs.com (only available inwards USA as well as Canada) as well as spotted an interesting approach to teaching fraction add-on as well as equivalency using isometric grids (see film below). The grid only helps students to depict as well as combine equal sized parts, but anything that helps students sympathise the concept of a mutual denominator is worth considering.

4. Circle Theorems Badges
Cameron Fehr (@MrFehr_SVC) shared this film of the circle theorem badges he uses to vantage his students.

Cameron made these himself using a badge maker. His students tin hand notice earn them past times (for example) correctly reciting the quadratic formula. Cameron real helpfully shared his files here (where there's lots to a greater extent than award-related things to explore).

5. Artistic Mathematics
@MrMathsTeacher shared fantastic pictures of Piet Mondrian-inspired graphs of horizontal as well as vertical lines. I dearest this idea.

6. Imperial Measures

Influenza A virus subtype H5N1 bonus precious rock this week, peculiarly for my American readers. We don't role cups as well as quarts inwards the U.K. but if nosotros did, I'd uncovering a role for this fantastic diagram. It helps us visualise the relative sizes of each unit of measurement as well as respond questions similar 'how many teaspoons are inwards a gallon?'.

Reading!
I desire to recommend 3 posts this week... Craig Barton (@tesMaths) updated his 'Links to the Best Maths Websites inwards the World' - it's good worth a read, every bit is his extensive listing of maths resources - Essential Freebies.

Lucy Crehan (@lucy_crehan) shared this lovely post from the 'I am Malala' website. It features pictures of classrooms all over the footing - I actually enjoyed reading it.

That's it for this week. Thanks for reading. I'm utterly exhausted! My infant is 8 months quondam at ane time - volition she ever sleep? Roll on half-term! :)

5 Maths Gems #60

Welcome to my 60^th update from the basis of Maths EduTwitter. Here I summarise some of the latest ideas together with resources for teaching maths.

1. Perpendicular Gradient
I honey this gif demonstrating the human relationship betwixt gradients of perpendicular lines, shared past times Simon Pampena (@mathemaniac).

Geogebra fans volition endure pleased to run across that Tim Brzezinski ‏(@dynamic_math) made 'Slope Triangle Rotation' to explore this further.

2. Metric Units

Next fourth dimension I learn a lesson on units I'm going to demonstrate this 5 infinitesimal video on the history of the metric system. I intend it's actually interesting.

I discovered this on YouTube afterwards watching The mathematical secrets of Pascal’s triangle which was shared past times Cliff Pickover (@pickover).

3. Calculus Puzzles
H5N1 degree teachers volition similar this Chalkdust postal service 'Puzzles almost calculus' past times Matthew Scroggs (@mscroggs).

4. Displays

Twitter continues to endure a swell house to portion classroom display ideas. I saw 2 ideas final calendar week that I especially like. First, depository fiscal establishment gibe out Sarah Carter's (welcome sign. 

Second, Claire Mazurkiewicz (Gems 23. I straight off role it whenever I learn plans together with elevations.

Phil Bruce (@pbrucemaths) was inspired past times this icon to brand a PowerPoint of 5 to a greater extent than examples. You tin sack download it from his weblog here, nether "shadow shapes".

Update
My final twenty-four lx minutes catamenia of term was on Fri (hurrah!)... I know some of you lot are nevertheless at schoolhouse for a twain to a greater extent than days (nearly there!).

In instance you lot missed whatever of my recent posts, hither they are:

• Looking Ahead
• Mathsy Gifts: The Sequel
• 5 Maths Gems #59

I've used VideoScribe to brand a welcome video for Year seven together with an expectations video for Year eleven (you tin sack spotter both here) - I did something similar for my rootage lessons final yr together with it worked quite well.

If you lot didn't larn inward to researchED Maths together with Science dorsum inward June together with hence you lot mightiness similar to spotter some videos of the presentations here.

Please follow @Team_Maths1 if you lot haven't already - I role this trouble concern human relationship to tweet maths resources, together with my partner inward criminal offence Lucy tweets articles together with maths jokes. We also offering a resources hospital - inquire us for aid together with nosotros volition produce what nosotros tin sack to detect a suitable maths resources for your lesson.

Do depository fiscal establishment gibe out the hashtag #DonADay too.

If you're a fan of Don Steward's maths resources together with hence depository fiscal establishment gibe out the #DonADay hashtag. pic.twitter.com/FY73QVo4BX

— Jo Morgan (@mathsjem) 21 July 2016

I'll in all probability weblog a chip less often than commons over the summertime holidays (I've got lots of schoolhouse operate to do... I also promise to brand a start on organising #christmaths16... together with I desire to pass lots of fourth dimension amongst my daughters). But I volition endure using the hashtag #summerblogread to tweet links to posts that you lot mightiness convey missed over the years.

It looks similar La Salle are organising some other Pie together with Maths (see Gems 37 for my write upwards of the final one) hence - depending on the appointment - I mightiness endure at that topographic point for some summertime socialising.

I'll move out you lot amongst this query from brilliant.org. There are diverse approaches (it's pretty straightforward if you lot tin sack produce basic trigonometry) precisely the solution is interesting. Check out the replies to my tweet here to follow the discussion.

5 Maths Gems #80

Welcome to my 80^th gems post. This is where I percentage around of the latest news, ideas as well as resources for maths teachers.

1. Times Tables Tool
La Salle Education bring made a complimentary version of their Times Tables app available to everyone. It includes multiple representation of multiplication as well as partitioning facts. I expect frontwards to using this amongst my immature adult woman when she starts learning nigh multiplication.

2. Twinkl Taster Pack
I blogged nigh Twinkl's novel secondary maths resources dorsum inward Gems 65. They've straight off shared a free taster pack which includes a laid upward of revision mats suitable for Foundation GCSE students.

3. Quadratics Resources
Thanks to @TeacherBowTie for sharing around lovely quadratics resources including an A3 quadratics consolidation activity which would operate good for revision as well as a problem solving activity for practising factorising.

I've added both resources to my algebra resources library.

4. Times Table Facts
This times tables resource from Anthony Clohesy is good worth a expect - it shows the exclusively 28 times tabular array facts students demand to learn, arranged inward lodge from of import (at the bottom) to hard (at the top). While you're there, depository fiscal establishment agree out the residuum of his website thechalkface.net.

5. Universcale
Thanks to my lovely colleague Jane Zimmermann for telling me nigh Nikon's 'The Scale of the Universe' that I shared inward Gems 12, agency dorsum inward 2014.

Update
In illustration you lot missed it, my post 'The Top v Christmas Gifts for Maths Teachers This Year' was published yesteryear TeachWire. While you're thinking nigh your want list, bring a expect at Craig Barton's novel majority 'How I Wish I'd Taught Maths' which is straight off available to pre-order. I've been real lucky to bring a sneak preview of this majority - it's fantastic. Look out for my weblog post nigh it soon.

Did you lot choose handgrip of my post nigh MathsJam? If you're a maths enthusiast as well as so produce essay as well as choke involved inward your local MathsJam or come upward along to the annual gathering adjacent year.

In September I took purpose inward a researchED struggle called 'When the maths hits the fan: what produce the GCSE results actually mean?'. The recording of that session has straight off been published online - if you lot bring a spare xl minutes, produce bring a listen.

If you lot intend to come upward to BCME (the hugely exciting maths conference taking house at Easter that I wrote nigh here) delight recollect that you lot exclusively bring a brace of weeks left to use for a bursary. I've applied!

You also exclusively bring a brace of weeks left to percentage your thought nigh the proposed champaign of report association amalgamation - delight add together comments here.

Mock GCSE flavor is straight off upon us - expect out for my upcoming weblog post nigh the best revision resources as well as tools to back upward students inward their examine preparation.

I'll move out you lot amongst this nifty inquiry from Mark Chubb‏ (@MarkChubb3). Do these 2 bring the same area? Same perimeter? Will this ever live on truthful no affair how they are set together?

Map Scale

This inquiry on map scale inwards AQA's 2018 Foundation tier GCSE newspaper was answered actually badly:

Most students had no idea. In fact, they would withdraw maintain done improve if they'd but guessed. The most mutual reply given was 1:1000.

The inquiry requires students to sympathise ii things:

1. how to convert from cm to km. 
2. how to translate a map scale given every bit a ratio with no units (eg knowing that 1:100000 agency that 1cm on the map represents 100,000cm inwards existent life). 

I think that metric conversions are relatively tardily to memorise (most students know that at that spot are a hundred centimetres inwards a metre from their familiarity with a metre ruler together with the prefix cent, together with they should live on aware that kilo agency thousand). So this leads me to believe that the principal difficulty with this inquiry was a lack of familiarity with map scales given every bit a ratio. 

I withdraw maintain a feeling that this topic is sometimes skipped over past times maths teachers. Some students may solely meet i maths lesson on map scale inwards their entire fourth dimension at secondary school. It gets buried inwards alongside other topics on schemes of travel (it's usually inwards with either ratio or with bearings together with scale drawings, though I withdraw maintain seen it inwards with similarity too). I think it sometimes goes unnoticed together with doesn't acquire the fourth dimension it deserves. Perhaps this is because it rarely comes upwards inwards GCSE exams. 

Curriculum
You may live on wondering if the powerfulness to purpose a map scale of the shape 1:50000 comes upwards inwards geography. In the geography GCSE syllabus it says that students must "use together with translate OS maps at a gain of scales, including 1:50 000 together with 1:25 000 together with other maps appropriate to the topic". It doesn't specifically say that students withdraw maintain to mensurate together with convert distances, though this is implied. I institute this on a geography revision website:

"The scale set out on an OS map indicates how many centimetres on the soil are represented past times a centimetre on the map. On a 1:100,000 scale map, i centimetre on the map represents 100,000 cm on the ground, inwards other words, i centimetre on the map represents i kilometre inwards reality. H5N1 scale of 1:5,000 so agency that a centimetre on the map represents a distance inwards existent life of 5,000 centimetres (50 metres). This method of representing the scale of a map is called the fractional method, but yous volition also meet graphical representations or written representations similar 2 cm = 1 km."

I wasn't aware that the method of representing map scale inwards the shape 1:50000 is called the fractional method. I similar knowing proper names for things. Though I'm non certain whether this term is used consistently - I've seen other sites refer to it as a ratio scale or a fractional scale or a representative fraction.

Wikipedia lists dissimilar types of map scale including lexical (ie expressed inwards words - also known every bit verbal or stated scales), linear or graphical scales (represented every bit a bar), ratio scales, together with fractional scales. It points out that a lexical scale inwards a linguistic communication known to the user may live on easier to visualise than a ratio, but lexical scales may crusade problems if expressed inwards a linguistic communication that the user does non sympathise or inwards obsolete or ill-defined units (eg i inch to a furlong or i pouce to i league). So ratio scales withdraw maintain pros together with cons. When I read this I right away away sentiment that at that spot could live on roughly actually prissy opportunities for enrichment inwards this topic - I'd beloved to beak to my students virtually antiquated units of measurement!

Anyway, it looks similar 'map skills' inwards GCSE geography focuses mainly on recognising symbols together with using grid references. I haven't institute many geography resources on ratio scale, other than a brace of PowerPoints on TES that run through it real quickly. So it seems that measuring lengths on maps together with performing unit of measurement conversions using ratio scales isn't something they pass much fourth dimension on inwards the GCSE geography course.

We definitely create demand to pass roughly fourth dimension on it inwards maths lessons, together with it fits good at both Key Stage 3 together with 4. The maths GCSE specification says (in both the ratio together with geometry sections) that students should know how to purpose scale diagrams together with maps. AQA's Teaching Guidance helpfully provides additional clarification: "Scale could live on given every bit a ratio (for event 1:500 000) or every bit a commutation (for event 1cm represents v km)."  

Approach together with Resources

Without audio cognition of both place value and metric unit of measurement conversions nosotros can't fifty-fifty acquire started on this topic. So that's the start thing nosotros demand to check. I recollect i time giving my gain laid Year 10 a uncomplicated starter holler for them to set these lengths inwards ascending order:

It took way longer than expected.

If metric conversions demand teaching, at that spot are loads of practiced resources for this, including:

• Why the metric organization matters - first-class video past times Matt Anticole
• The Chalkface - Metric Units of Measurement and Units of Measurement
• CIMT Unit - KS3 Units of Measurement
• MathsPad - loads of dandy resources if yous subscribe including a converting metric lengths activity together with a laid of metric units of length exercises.
• BossMaths lesson - Converting betwixt metric units of measures of length together with mass

Students who scrap with uncomplicated unit of measurement conversions powerfulness honour it helpful to depict out a ratio tabular array each time, writing their known fact at the gain together with using multiplicative reasoning to fill upwards inwards the gap:

Once students are fluent inwards unit of measurement conversions, it would live on sensible to remind them of how ratios travel earlier moving onto map scale. There are lots of dandy resources available for this broad ranging topic (see my post on ratio), but the focus hither is simplifying ratios with mixed units (ie converting the antecedent together with consequent to the same units), together with on expressing ratios inwards the format 1:n. Useful resources include:

• Maths4Everyone - Simplifying Ratio
• Richard Tock - Pixel Picture: Equivalent Ratios
• Dave Taylor - Write Ratios inwards the Form 1:n

Now nosotros but demand to combine these ideas to sympathise map scale.

If a map has scale 1:50000, how create nosotros travel out what 6cm on the map represents inwards km on the ground? The ii steps involved (the unit of measurement conversion together with the criterion conversion) tin live on done inwards either order. I'd propose something similar this:

Here I've start past times writing the ratio scale with units - whatsoever units travel but cm is usually preferable. Instead of writing 1cm = 50,000cm (which is a horrible purpose of the equals sign!) I've used a table.

I did my unit of measurement conversion inwards ii steps, going via metres every bit the base of operations unit.

Using a similar approach to reply the question: "If 4cm on a map represents 100km on the ground, what's the ratio scale?", nosotros withdraw maintain the next process:

So the reply is 1:2500000.

Of course of written report at that spot are lots of dissimilar ways to laid the workings out hither - the tabular array is optional.

Most resources I've seen online for ratio scales skip through it real chop-chop - it's frequently covered inwards a brace of slides at the destination of a related lesson. Teaching it properly - inwards depth - should likely withdraw maintain ii or 3 dedicated lessons. The CIMT cloth 'KS3 Scale Drawing' is real useful, every bit are the Boss Maths lessons 'Using scale diagrams together with maps' and 'Scale drawings'. Corbett Maths has roughly examine manner questions on this topic.

I am eagerly awaiting something on variationtheory.com on all this!

Once students are fluent inwards metric unit of measurement conversions together with working with ratio scales, they powerfulness relish a flake of map travel to consolidate their learning. MathsPad withdraw maintain a free online map scale tool which is helpful for demonstrating map skills on the board. The Mapzone website shows what dissimilar OS map scales facial expression similar - this is non on the maths curriculum but powerfulness live on of involvement to students. This Reading Map Scales Activity from emtay on TES gives students the peril to practise using a ratio scale on a map of Europe.

No dubiety mortal volition tell me that when teaching this topic I *must* give my students total size OS maps together with ship them exterior on roughly big orienteering project! Hmm. I'm non certain that's practical on a principal route inwards Croydon... I also believe that although they may recollect the activity, it likely won't manage them either sympathise or recollect the maths. So I'll likely skip that.

Since we've all at nowadays got sat nav on our phones this topic isn't every bit much of a 'life skill' every bit it i time was. That's ok though. Thankfully nosotros don't instruct mathematics for its utility.

What's practiced virtually this topic is that every bit good every bit sewing together ii commutation areas of schoolhouse maths (ratio together with metric units), nosotros acquire the peril to come upwards dorsum to it when nosotros instruct bearings, together with i time again when nosotros create expanse together with book scale constituent with questions similar this:

A map has a scale of 1:50 000. H5N1 commons is shown on the map every bit a rectangle measuring 6cm past times 4.2cm . What is the actual expanse of the park?

The Boss Maths lesson 'Converting betwixt metric units of measures of expanse together with volume' covers this.

I'm involved inwards the London Thames Maths Hub workgroup on Challenging GCSE Topics inwards which I promise to facial expression at unit of measurement conversions together with ratio. Do arrive acquit on if yous desire to acquire involved inwards developing roughly resources for this topic.

In the meantime - let's all brand certain that map scale gets the fourth dimension it deserves inwards maths!

5 Maths Gems #24

Hello as well as welcome to my 24th gems post - this is where I part five teaching ideas I've seen on Twitter. I'm going to live on brusk as well as sugariness today... I'm meant to live on marking!

1. Angles inwards Parallel Lines
I'm e'er on the expect out for practiced questions that I tin hand notice role inwards course of didactics as well as thus I was pleased when Cliff Pickover (@pickover) tweeted the occupation below. This volition do nicely for my Year 7s when they come upward to revise angles. I don't shout out upward they've seen the 'hatch mark' used for equal angles earlier (only equal sides) as well as thus it's a practiced exercise inwards interpreting musical note too. Answers are on page half dozen of this document. By the way, if you're non already next Cliff, I highly recommend his tweets.

2. Algebra Countdown
I was browsing @stephenbodman's lovely resources on his website secondarymaths.wikispaces.com when I spotted Algebra Countdown. This is an activity based on the TV programme Countdown, but instead of numbers students are given algebraic terms. Set upward the Countdown Clock as well as run the activity inwards Excel on your Interactive Whiteboard. It's a actually overnice activity for practising simplifying algebraic expressions.

3. Isometric Fractions
I was looking at the cool pads of sticky-backed graph newspaper on www.instagraphs.com (only available inwards USA as well as Canada) as well as spotted an interesting approach to teaching fraction add-on as well as equivalency using isometric grids (see film below). The grid only helps students to depict as well as combine equal sized parts, but anything that helps students sympathise the concept of a mutual denominator is worth considering.

4. Circle Theorems Badges
Cameron Fehr (@MrFehr_SVC) shared this film of the circle theorem badges he uses to vantage his students.

Cameron made these himself using a badge maker. His students tin hand notice earn them past times (for example) correctly reciting the quadratic formula. Cameron real helpfully shared his files here (where there's lots to a greater extent than award-related things to explore).

5. Artistic Mathematics
@MrMathsTeacher shared fantastic pictures of Piet Mondrian-inspired graphs of horizontal as well as vertical lines. I dearest this idea.

6. Imperial Measures

Influenza A virus subtype H5N1 bonus precious rock this week, peculiarly for my American readers. We don't role cups as well as quarts inwards the U.K. but if nosotros did, I'd uncovering a role for this fantastic diagram. It helps us visualise the relative sizes of each unit of measurement as well as respond questions similar 'how many teaspoons are inwards a gallon?'.

Reading!
I desire to recommend 3 posts this week... Craig Barton (@tesMaths) updated his 'Links to the Best Maths Websites inwards the World' - it's good worth a read, every bit is his extensive listing of maths resources - Essential Freebies.

Lucy Crehan (@lucy_crehan) shared this lovely post from the 'I am Malala' website. It features pictures of classrooms all over the footing - I actually enjoyed reading it.

That's it for this week. Thanks for reading. I'm utterly exhausted! My infant is 8 months quondam at ane time - volition she ever sleep? Roll on half-term! :)

5 Maths Gems #60

Welcome to my 60^th update from the basis of Maths EduTwitter. Here I summarise some of the latest ideas together with resources for teaching maths.

1. Perpendicular Gradient
I honey this gif demonstrating the human relationship betwixt gradients of perpendicular lines, shared past times Simon Pampena (@mathemaniac).

Geogebra fans volition endure pleased to run across that Tim Brzezinski ‏(@dynamic_math) made 'Slope Triangle Rotation' to explore this further.

2. Metric Units

Next fourth dimension I learn a lesson on units I'm going to demonstrate this 5 infinitesimal video on the history of the metric system. I intend it's actually interesting.

I discovered this on YouTube afterwards watching The mathematical secrets of Pascal’s triangle which was shared past times Cliff Pickover (@pickover).

3. Calculus Puzzles
H5N1 degree teachers volition similar this Chalkdust postal service 'Puzzles almost calculus' past times Matthew Scroggs (@mscroggs).

4. Displays

Twitter continues to endure a swell house to portion classroom display ideas. I saw 2 ideas final calendar week that I especially like. First, depository fiscal establishment gibe out Sarah Carter's (welcome sign. 

Second, Claire Mazurkiewicz (Gems 23. I straight off role it whenever I learn plans together with elevations.

Phil Bruce (@pbrucemaths) was inspired past times this icon to brand a PowerPoint of 5 to a greater extent than examples. You tin sack download it from his weblog here, nether "shadow shapes".

Update
My final twenty-four lx minutes catamenia of term was on Fri (hurrah!)... I know some of you lot are nevertheless at schoolhouse for a twain to a greater extent than days (nearly there!).

In instance you lot missed whatever of my recent posts, hither they are:

• Looking Ahead
• Mathsy Gifts: The Sequel
• 5 Maths Gems #59

I've used VideoScribe to brand a welcome video for Year seven together with an expectations video for Year eleven (you tin sack spotter both here) - I did something similar for my rootage lessons final yr together with it worked quite well.

If you lot didn't larn inward to researchED Maths together with Science dorsum inward June together with hence you lot mightiness similar to spotter some videos of the presentations here.

Please follow @Team_Maths1 if you lot haven't already - I role this trouble concern human relationship to tweet maths resources, together with my partner inward criminal offence Lucy tweets articles together with maths jokes. We also offering a resources hospital - inquire us for aid together with nosotros volition produce what nosotros tin sack to detect a suitable maths resources for your lesson.

Do depository fiscal establishment gibe out the hashtag #DonADay too.

If you're a fan of Don Steward's maths resources together with hence depository fiscal establishment gibe out the #DonADay hashtag. pic.twitter.com/FY73QVo4BX

— Jo Morgan (@mathsjem) 21 July 2016

I'll in all probability weblog a chip less often than commons over the summertime holidays (I've got lots of schoolhouse operate to do... I also promise to brand a start on organising #christmaths16... together with I desire to pass lots of fourth dimension amongst my daughters). But I volition endure using the hashtag #summerblogread to tweet links to posts that you lot mightiness convey missed over the years.

It looks similar La Salle are organising some other Pie together with Maths (see Gems 37 for my write upwards of the final one) hence - depending on the appointment - I mightiness endure at that topographic point for some summertime socialising.

I'll move out you lot amongst this query from brilliant.org. There are diverse approaches (it's pretty straightforward if you lot tin sack produce basic trigonometry) precisely the solution is interesting. Check out the replies to my tweet here to follow the discussion.