5 Maths Gems #20

Hello. I'm pleased to introduce my 20th gems post today - a milestone! Twitter has been repose this calendar week because Christmas took our minds off travel for a span of days, but I've nevertheless got around nifty ideas for you. The Christmas holidays are curt in addition to busy therefore it won't live on long earlier you're dorsum to planning lessons - I promise this post gives you lot around inspiration for the Spring term.

1. Factorising Quadratics
You know questions like this:

In Question 1 above, you lot tin give notice run across that the travel past times left jail cellular telephone has to incorporate a iii because it's a element of both iii in addition to 6. The residual of the cells tin give notice live on completed speedily 1 time 1 mutual element has been established. This is a unproblematic instance but Don develops the questions to choke increasingly difficult, around having multiple solutions. 

The adjacent prepare of activities extend the same sentiment to algebra, starting amongst this:

There's lots of these to consummate - first-class practise of factorising linear expressions.

The adjacent phase of this exercise is factorising quadratics.

Conveniently I'm currently planning a Year 10 lesson on factorising quadratics. I desire my students to create a lot of practise therefore volition definitely live on using this activity. The questions construct upward to a suitably challenging degree of difficulty, ending amongst this one:

I desire to encourage my students to factorise 'harder' quadratics (ie a > 1) past times inspection. This is my preferred method (ie 'guess in addition to test') but my students ever need that I instruct them a to a greater extent than structured approach (eg 'the Grouping Method') which frustrates me. Their insistence on next an algorithm suggests a lack of confidence. I intend the inquiry inward a higher house turns factorising quadratics into a form of logic problem. Tackling this inquiry without an algorithm powerfulness aid my students educate the confidence to factorise harder quadratics past times inspection.

One final sentiment for a lesson on factorising quadratics - I similar the occupation below from openmiddle.com. There are a publish of possible solutions therefore you lot could challenge students to discovery a dissimilar solution to the someone adjacent to them. 

2. Angle Sense amongst the Interactive Whiteboard
I've been planning a Year vii lesson on angles inward which I'd similar my students to approximate angle sizes. If you lot were asked to to pull an angle of 210^o freehand, how would you lot create it? I'd intend of it equally a guide business addition a 3rd of a right-angle. If you lot choose proportional reasoning skills therefore it's pretty slowly to brand an educated guess. An angle estimation activity would travel perfectly good without applied scientific discipline (read out a serial of angle sizes in addition to enquire your students to pull their freehand estimates on paper. They therefore depository fiscal establishment jibe their estimates using a protractor - around other useful skill). But if you lot desire a similar activity for the interactive whiteboard therefore you lot powerfulness similar this fun here. Some of these angle games are quite funny - Banana Hunt in special made me chuckle.

If you lot similar these interactive whiteboard games therefore you'll discovery loads at Sheppard Software. It's amusing that there's an Absolute Value Number Balls game - this concept isn't covered until Year thirteen inward the United Kingdom of Great Britain in addition to Northern Ireland but I bet my students would honey to play this game - 5 minutes lite relief inward a C3 lesson!

FlashMaths.co.uk is around other nifty website for interactive whiteboard activities. Flash Maths was created past times Jonathan Hall (@studymaths) who brings us a plethora of fantastic tools on StudyMaths.co.uk. If you lot haven't seen it before, depository fiscal establishment jibe out MathsBot.com which is his unproblematic (but brilliant) worksheet generator.

3. Big Questions

Billy Adamson (@Billyads_47) shared a fantastic prepare of mathematical thinking prompts 'The Big Questions'. Here's a few examples: 

Lovely opened upward questions from Billy to generate intelligence in addition to educate understanding. There's around to a greater extent than expert examples of opened upward questions here:

4. Trigonometric Problem Solving

Our Year 13s' occupation solving skills are tested when they're asked to simplify expressions involving trigonometric identities inward C3 (like the example below).

I discovery that my students acquire frustrated when they can't topographic point a 'way in' guide away. They surrender quickly. There's genuinely a pretty criterion prepare of starting points, equally described on www.intmath.com (@intmath). 

I combat to aid my students experience confident inward tackling these problems, therefore I genuinely similar this activity from @mjfenton. Here's an extract:

The sentiment is that nosotros offset amongst a lot of construction in addition to gradually give fewer hints until students are able to solve the problems themselves. The steps powerfulness appear logical to us, but we're experienced occupation solvers. 

It's a expert sentiment for maths teachers to attempt to solve unfamiliar problems every at 1 time in addition to therefore (like the instance below from ‏@dannytybrown) to remind ourselves that mathematical occupation solving oftentimes requires patience, inventiveness in addition to multiple attempts. We all experience frustration inward occupation solving, merely similar our students do, but nosotros know that the satisfaction of eventually finding the solution is good worth it.

5. Dividing amongst Decimals

I've mentioned earlier that I honey MathsPad's resources - enough of them are complimentary in addition to the residual come upward at a terms of alone £3 per month. Whether your schoolhouse subscribes or not, it's worth registering for electronic mail updates inward companionship to proceed rail of all the novel resources. This month, the interactive resources on Decimal Calculations caught my eye. It ever surprises me how many students volition happily nation that forty divided past times ½ equals 20. Activities similar the 1 shown below volition aid tackle this misconception in addition to encourage students to intend earlier they answer.

That's it for this week. I'll travel out you lot amongst a video from 1977 - 'Congruent Triangles' past times Bruce in addition to Katharine Cornwell (another precious rock found on @MathMunch). Happy New Year!

5 Maths Gems #58

This is my 58^th update from the Blue Planet of Maths EduTwitter. Here I summarise about of the latest ideas as well as resources for didactics maths.

1. New GCSE Revision Resources

Thanks to @pixi_17 for sharing a fantastic develop of revision resources for novel GCSE students. This good designed develop of 9 - 1 revision booklets for 4 dissimilar degree levels (eg 'Aiming for a Grade 5') has come upward inwards handy for my Year 10s this week, equally they revise for their upcoming terminate of twelvemonth exams.

2. Whack a Prime 

I honey the Is This Prime? game simply about of my students learn disheartened past times depression scores. It's quite a stressful game to play! Slow it downwards with this choice 'Whack a Prime' game from @prehmet.

3. Polygons Angles

This novel tool from MathsPad is awesome. I've seen similar tools earlier simply this is the best yet. Click 'play' below for a demonstration.

#mathschat #mtbos Take a expect at our novel gratis interactive tool for exploring outside angles https://t.co/lPy5lvOUVf pic.twitter.com/nHrt19Ai56

— James Pearce (@MathsPadJames) 9 June 2016

4. Key Stage iii Scheme of Work

At this fourth dimension of twelvemonth many schools are thinking nearly their schemes of run for side past times side year. I actually similar the Year seven Scheme of Learning from the White Rose Maths Hub. Schools looking to alter their approach at Key Stage iii (less 'spiral', to a greater extent than 'mastery') volition uncovering this helpful. There's primary schemes hither too.

5. Interesting Exam Questions

Did you lot especially similar whatever of the questions inwards this year's GCSE papers? Share them on Twitter! For representative this inquiry was inwards the Edexcel Linked Pair Methods ii newspaper - it volition come upward inwards handy when teaching/revising recurring decimal proofs inwards hereafter years.

This circle theorems inquiry from Edexcel Methods 1 was a flake harder than commons - there's lots to produce here! Have a become at it.

For Influenza A virus subtype H5N1 flat teachers, this MEI inquiry is actually squeamish - it was sent to me past times a pupil who got stuck on it when revising.

Update
Did you lot grab my latest posts? One was nearly my twenty-four hours at researchED Maths as well as Science as well as the other was nearly maths schoolhouse trips.

On Mon I presented at LIME Oldham, focusing on mathematical methods. My slides are here.

Because I'm an Influenza A virus subtype H5N1 flat teacher, examination stream is nevertheless inwards total swing for me. The final examination is S2 side past times side Mon - phew! I'm looking frontward to Edexcel's conference inwards Warwick on s July, I should endure far less stressed past times then!

I've got a engagement inwards heed for here. This twelvemonth it volition belike accept a slightly dissimilar format - less CPD, to a greater extent than enrichment - simply I volition hold the 'Christmas political party for maths teachers' social element. Watch this space!

Finally, I'll locomote out with you lot with this squeamish action from James Tanton that I found, amongst other interesting tasks, inwards his 9th curriculum essay.

5 Maths Gems #20

Hello. I'm pleased to introduce my 20th gems post today - a milestone! Twitter has been repose this calendar week because Christmas took our minds off travel for a span of days, but I've nevertheless got around nifty ideas for you. The Christmas holidays are curt in addition to busy therefore it won't live on long earlier you're dorsum to planning lessons - I promise this post gives you lot around inspiration for the Spring term.

1. Factorising Quadratics
You know questions like this:

In Question 1 above, you lot tin give notice run across that the travel past times left jail cellular telephone has to incorporate a iii because it's a element of both iii in addition to 6. The residual of the cells tin give notice live on completed speedily 1 time 1 mutual element has been established. This is a unproblematic instance but Don develops the questions to choke increasingly difficult, around having multiple solutions. 

The adjacent prepare of activities extend the same sentiment to algebra, starting amongst this:

There's lots of these to consummate - first-class practise of factorising linear expressions.

The adjacent phase of this exercise is factorising quadratics.

Conveniently I'm currently planning a Year 10 lesson on factorising quadratics. I desire my students to create a lot of practise therefore volition definitely live on using this activity. The questions construct upward to a suitably challenging degree of difficulty, ending amongst this one:

I desire to encourage my students to factorise 'harder' quadratics (ie a > 1) past times inspection. This is my preferred method (ie 'guess in addition to test') but my students ever need that I instruct them a to a greater extent than structured approach (eg 'the Grouping Method') which frustrates me. Their insistence on next an algorithm suggests a lack of confidence. I intend the inquiry inward a higher house turns factorising quadratics into a form of logic problem. Tackling this inquiry without an algorithm powerfulness aid my students educate the confidence to factorise harder quadratics past times inspection.

One final sentiment for a lesson on factorising quadratics - I similar the occupation below from openmiddle.com. There are a publish of possible solutions therefore you lot could challenge students to discovery a dissimilar solution to the someone adjacent to them. 

2. Angle Sense amongst the Interactive Whiteboard
I've been planning a Year vii lesson on angles inward which I'd similar my students to approximate angle sizes. If you lot were asked to to pull an angle of 210^o freehand, how would you lot create it? I'd intend of it equally a guide business addition a 3rd of a right-angle. If you lot choose proportional reasoning skills therefore it's pretty slowly to brand an educated guess. An angle estimation activity would travel perfectly good without applied scientific discipline (read out a serial of angle sizes in addition to enquire your students to pull their freehand estimates on paper. They therefore depository fiscal establishment jibe their estimates using a protractor - around other useful skill). But if you lot desire a similar activity for the interactive whiteboard therefore you lot powerfulness similar this fun here. Some of these angle games are quite funny - Banana Hunt in special made me chuckle.

If you lot similar these interactive whiteboard games therefore you'll discovery loads at Sheppard Software. It's amusing that there's an Absolute Value Number Balls game - this concept isn't covered until Year thirteen inward the United Kingdom of Great Britain in addition to Northern Ireland but I bet my students would honey to play this game - 5 minutes lite relief inward a C3 lesson!

FlashMaths.co.uk is around other nifty website for interactive whiteboard activities. Flash Maths was created past times Jonathan Hall (@studymaths) who brings us a plethora of fantastic tools on StudyMaths.co.uk. If you lot haven't seen it before, depository fiscal establishment jibe out MathsBot.com which is his unproblematic (but brilliant) worksheet generator.

3. Big Questions

Billy Adamson (@Billyads_47) shared a fantastic prepare of mathematical thinking prompts 'The Big Questions'. Here's a few examples: 

Lovely opened upward questions from Billy to generate intelligence in addition to educate understanding. There's around to a greater extent than expert examples of opened upward questions here:

4. Trigonometric Problem Solving

Our Year 13s' occupation solving skills are tested when they're asked to simplify expressions involving trigonometric identities inward C3 (like the example below).

I discovery that my students acquire frustrated when they can't topographic point a 'way in' guide away. They surrender quickly. There's genuinely a pretty criterion prepare of starting points, equally described on www.intmath.com (@intmath). 

I combat to aid my students experience confident inward tackling these problems, therefore I genuinely similar this activity from @mjfenton. Here's an extract:

The sentiment is that nosotros offset amongst a lot of construction in addition to gradually give fewer hints until students are able to solve the problems themselves. The steps powerfulness appear logical to us, but we're experienced occupation solvers. 

It's a expert sentiment for maths teachers to attempt to solve unfamiliar problems every at 1 time in addition to therefore (like the instance below from ‏@dannytybrown) to remind ourselves that mathematical occupation solving oftentimes requires patience, inventiveness in addition to multiple attempts. We all experience frustration inward occupation solving, merely similar our students do, but nosotros know that the satisfaction of eventually finding the solution is good worth it.

5. Dividing amongst Decimals

I've mentioned earlier that I honey MathsPad's resources - enough of them are complimentary in addition to the residual come upward at a terms of alone £3 per month. Whether your schoolhouse subscribes or not, it's worth registering for electronic mail updates inward companionship to proceed rail of all the novel resources. This month, the interactive resources on Decimal Calculations caught my eye. It ever surprises me how many students volition happily nation that forty divided past times ½ equals 20. Activities similar the 1 shown below volition aid tackle this misconception in addition to encourage students to intend earlier they answer.

That's it for this week. I'll travel out you lot amongst a video from 1977 - 'Congruent Triangles' past times Bruce in addition to Katharine Cornwell (another precious rock found on @MathMunch). Happy New Year!

5 Maths Gems #58

This is my 58^th update from the Blue Planet of Maths EduTwitter. Here I summarise about of the latest ideas as well as resources for didactics maths.

1. New GCSE Revision Resources

Thanks to @pixi_17 for sharing a fantastic develop of revision resources for novel GCSE students. This good designed develop of 9 - 1 revision booklets for 4 dissimilar degree levels (eg 'Aiming for a Grade 5') has come upward inwards handy for my Year 10s this week, equally they revise for their upcoming terminate of twelvemonth exams.

2. Whack a Prime 

I honey the Is This Prime? game simply about of my students learn disheartened past times depression scores. It's quite a stressful game to play! Slow it downwards with this choice 'Whack a Prime' game from @prehmet.

3. Polygons Angles

This novel tool from MathsPad is awesome. I've seen similar tools earlier simply this is the best yet. Click 'play' below for a demonstration.

#mathschat #mtbos Take a expect at our novel gratis interactive tool for exploring outside angles https://t.co/lPy5lvOUVf pic.twitter.com/nHrt19Ai56

— James Pearce (@MathsPadJames) 9 June 2016

4. Key Stage iii Scheme of Work

At this fourth dimension of twelvemonth many schools are thinking nearly their schemes of run for side past times side year. I actually similar the Year seven Scheme of Learning from the White Rose Maths Hub. Schools looking to alter their approach at Key Stage iii (less 'spiral', to a greater extent than 'mastery') volition uncovering this helpful. There's primary schemes hither too.

5. Interesting Exam Questions

Did you lot especially similar whatever of the questions inwards this year's GCSE papers? Share them on Twitter! For representative this inquiry was inwards the Edexcel Linked Pair Methods ii newspaper - it volition come upward inwards handy when teaching/revising recurring decimal proofs inwards hereafter years.

This circle theorems inquiry from Edexcel Methods 1 was a flake harder than commons - there's lots to produce here! Have a become at it.

For Influenza A virus subtype H5N1 flat teachers, this MEI inquiry is actually squeamish - it was sent to me past times a pupil who got stuck on it when revising.

Update
Did you lot grab my latest posts? One was nearly my twenty-four hours at researchED Maths as well as Science as well as the other was nearly maths schoolhouse trips.

On Mon I presented at LIME Oldham, focusing on mathematical methods. My slides are here.

Because I'm an Influenza A virus subtype H5N1 flat teacher, examination stream is nevertheless inwards total swing for me. The final examination is S2 side past times side Mon - phew! I'm looking frontward to Edexcel's conference inwards Warwick on s July, I should endure far less stressed past times then!

I've got a engagement inwards heed for here. This twelvemonth it volition belike accept a slightly dissimilar format - less CPD, to a greater extent than enrichment - simply I volition hold the 'Christmas political party for maths teachers' social element. Watch this space!

Finally, I'll locomote out with you lot with this squeamish action from James Tanton that I found, amongst other interesting tasks, inwards his 9th curriculum essay.