easy way to learn mathematics: Estimation

Showing posts with label Estimation. Show all posts

5 Maths Gems #7

Common practise of successful departments' as well as 'What I learnt today' - both are good worth a read, especially for teachers of Influenza A virus subtype H5N1 degree maths.

Influenza A virus subtype H5N1 lot of the inspiration behind today's maths gems has come upward from teachers' blogs - I'm incredibly grateful to those who convey the fourth dimension to portion their ideas as well as experiences for the produce goodness of others.

1. Interactive Areas
Computer-based tools lead maintain made it easier to explicate some mathematical concepts as well as generate interesting questions. It's fantastic when applied scientific discipline enhances as well as enriches mathematics education.

I late tweeted this colourful instance which shows that nosotros tin cutting a circle into sectors as well as rearrange them to create upward one's involve heed the expanse (taken from @edfromo's Google+ post). @fmaths42 replied amongst this bright applet which illustrates the same matter inwards real clear interactive steps. Never earlier lead maintain I seen the formula for the expanse of a circle explained so clearly (and did y'all come across the 'proof without words' video inwards Maths Gems 4? That was skillful too).

Another fantabulous interactive tool is 'Investigating Triangle Area' (via @mathslinks). My students are ever happy to convey that a right angled triangle is one-half a rectangle, but are non so easily convinced for non-right angled triangles. The tool illustrates the fact past times allowing students to rearrange triangles into rectangles (click on subdivide as well as and then rotate as well as interpret the travel past times sections).

2. Estimation

Examples from estimation180.com

I've seen a lot of American teachers tweet close Common practise of successful departments' as well as 'What I learnt today' - both are good worth a read, especially for teachers of Influenza A virus subtype H5N1 degree maths.

Influenza A virus subtype H5N1 lot of the inspiration behind today's maths gems has come upward from teachers' blogs - I'm incredibly grateful to those who convey the fourth dimension to portion their ideas as well as experiences for the produce goodness of others.

1. Interactive Areas
Computer-based tools lead maintain made it easier to explicate some mathematical concepts as well as generate interesting questions. It's fantastic when applied scientific discipline enhances as well as enriches mathematics education.

I late tweeted this colourful instance which shows that nosotros tin cutting a circle into sectors as well as rearrange them to create upward one's involve heed the expanse (taken from @edfromo's Google+ post). @fmaths42 replied amongst this bright applet which illustrates the same matter inwards real clear interactive steps. Never earlier lead maintain I seen the formula for the expanse of a circle explained so clearly (and did y'all come across the 'proof without words' video inwards Every Math Teacher inwards the World Should Do This...Right Now!' by @nathankraft1 (shared amongst me past times @DianeMaths) y'all tin come across students working on whiteboards unopen to the classroom (I wishing my classroom was this big!).

Nathan enthusiastically says, 'When students are working on the whiteboards, I tin come across everything happening at once. It's similar I'm looking at the freaking Matrix. With a quick glance, I tin come across which students got it, which students are making fry mistakes, as well as which students lead maintain no sentiment what's going on. I tin chop-chop position errors for students. I tin inquire a stronger educatee to tending a struggling one. Once a educatee has the right answer, I yell, "Great! Erase it! Next problem!"'. His enthusiasm has rubbed off on me. I desire to sweat it! And earlier y'all disregard this sentiment because y'all don't lead maintain a room total of whiteboards, ship inwards involve heed that whatsoever vertical surface will produce - sweat writing on windows or using Common practise of successful departments' as well as 'What I learnt today' - both are good worth a read, especially for teachers of Influenza A virus subtype H5N1 degree maths.

Influenza A virus subtype H5N1 lot of the inspiration behind today's maths gems has come upward from teachers' blogs - I'm incredibly grateful to those who convey the fourth dimension to portion their ideas as well as experiences for the produce goodness of others.

1. Interactive Areas
Computer-based tools lead maintain made it easier to explicate some mathematical concepts as well as generate interesting questions. It's fantastic when applied scientific discipline enhances as well as enriches mathematics education.

Improves visibility.
Allows for transfer of cognition unopen to the room.
Non-Permanent removes fearfulness of writing.
Formative assessment past times instructor at all times.
Teacher tin respond questions past times having students await at others work.

Influenza A virus subtype H5N1 related sentiment comes from Common practise of successful departments' as well as 'What I learnt today' - both are good worth a read, especially for teachers of Influenza A virus subtype H5N1 degree maths.

Influenza A virus subtype H5N1 lot of the inspiration behind today's maths gems has come upward from teachers' blogs - I'm incredibly grateful to those who convey the fourth dimension to portion their ideas as well as experiences for the produce goodness of others.

1. Interactive Areas
Computer-based tools lead maintain made it easier to explicate some mathematical concepts as well as generate interesting questions. It's fantastic when applied scientific discipline enhances as well as enriches mathematics education.

I late tweeted this colourful instance which shows that nosotros tin cutting a circle into sectors as well as rearrange them to create upward one's involve heed the expanse (taken from @edfromo's Google+ post). @fmaths42 replied amongst this bright applet which illustrates the same matter inwards real clear interactive steps. Never earlier lead maintain I seen the formula for the expanse of a circle explained so clearly (and did y'all come across the 'proof without words' video inwards Improving students' collaboration using acrylic sheets'. Jeremy suggests investing inwards clear acrylic sheets that students tin write on. Diagrams, pictures, axes etc tin last pose underneath. Read his send service for to a greater extent than on this, it actually is a bright idea.

Next week

A lot of my readers volition last at La Salle Education's maths conference side past times side week. I’m actually looking forrad to it. Please come upward as well as tell how-do-you-do if y'all topographic point me. Bear inwards involve heed that I lead maintain a iii calendar month onetime babe who rarely sleeps, so if y'all come across me doze off at whatsoever betoken as well as then simply laissez passer on me a nudge.

I however promise to write a maths gems send service side past times side week, it volition last a twenty-four hours slow but hopefully total of ideas shared at the conference.

By the way, if y'all didn't grab my final send service 'Common practise of successful departments' as well as 'What I learnt today' - both are good worth a read, especially for teachers of Influenza A virus subtype H5N1 degree maths.

Influenza A virus subtype H5N1 lot of the inspiration behind today's maths gems has come upward from teachers' blogs - I'm incredibly grateful to those who convey the fourth dimension to portion their ideas as well as experiences for the produce goodness of others.

1. Interactive Areas
Computer-based tools lead maintain made it easier to explicate some mathematical concepts as well as generate interesting questions. It's fantastic when applied scientific discipline enhances as well as enriches mathematics education.

I late tweeted this colourful instance which shows that nosotros tin cutting a circle into sectors as well as rearrange them to create upward one's involve heed the expanse (taken from @edfromo's Google+ post). @fmaths42 replied amongst this bright applet which illustrates the same matter inwards real clear interactive steps. Never earlier lead maintain I seen the formula for the expanse of a circle explained so clearly (and did y'all come across the 'proof without words' video inwards Practical tips for a (newly) qualified maths teacher' as well as then produce lead maintain a look. It was a pop send service inwards which I shared some ideas for getting organised, so it's non simply for NQTs.

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 operate for a duet of days, but I've even therefore got around corking ideas for you. The Christmas holidays are brusk in addition to busy therefore it won't live on long earlier you're dorsum to planning lessons - I promise this post gives y'all around inspiration for the Spring term.

1. Factorising Quadratics
You know questions like this:

In Question 1 above, y'all tin come across that the move past times left jail mobile telephone has to comprise a three because it's a constituent of both three in addition to 6. The residue of the cells tin live on completed speedily i time i mutual constituent has been established. This is a uncomplicated instance but Don develops the questions to acquire increasingly difficult, around having multiple solutions.

The adjacent ready of activities extend the same see to algebra, starting alongside this:

There's lots of these to consummate - first-class exercise 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 exercise therefore volition definitely live on using this activity. The questions construct upwards to a suitably challenging marking of difficulty, ending alongside 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 mean value the enquiry higher upwards turns factorising quadratics into a sort of logic problem. Tackling this enquiry without an algorithm mightiness aid my students prepare the confidence to factorise harder quadratics past times inspection.

One final see for a lesson on factorising quadratics - I similar the work below from openmiddle.com. There are a unwrap of possible solutions therefore y'all could challenge students to discovery a dissimilar solution to the someone adjacent to them.

2. Angle Sense alongside the Interactive Whiteboard
I've been planning a Year vii lesson on angles inwards which I'd similar my students to approximate angle sizes. If y'all were asked to to clitoris an angle of 210^o freehand, how would y'all create it? I'd mean value of it every bit a direct delineate of piece of work addition a 3rd of a right-angle. If y'all choose proportional reasoning skills in addition to therefore it's pretty slow to brand an educated guess. An angle estimation activity would operate perfectly good without technology (read out a serial of angle sizes in addition to inquire your students to clitoris their freehand estimates on paper. They in addition to therefore banking firm represent their estimates using a protractor - around other useful skill). But if y'all desire a similar activity for the interactive whiteboard in addition to therefore y'all mightiness similar this fun here. Some of these angle games are quite funny - Banana Hunt in exceptional made me chuckle.

If y'all similar these interactive whiteboard games in addition to 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 inwards the U.K. but I bet my students would beloved to play this game - 5 minutes lite relief inwards a C3 lesson!

FlashMaths.co.uk is around other corking 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 y'all haven't seen it before, banking firm represent out MathsBot.com which is his uncomplicated (but brilliant) worksheet generator.

3. Big Questions

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

Lovely opened upwards questions from Billy to generate give-and-take in addition to prepare understanding. There's around to a greater extent than adept examples of opened upwards questions here:

4. Trigonometric Problem Solving

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

I discovery that my students acquire frustrated when they can't location a 'way in' direct away. They surrender quickly. There's genuinely a pretty criterion ready of starting points, every bit described on www.intmath.com (@intmath).

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

The see is that nosotros starting fourth dimension alongside a lot of construction in addition to gradually give fewer hints until students are able to solve the problems themselves. The steps mightiness appear logical to us, but we're experienced work solvers.

It's a adept see for maths teachers to seek to solve unfamiliar problems every instantly in addition to and therefore (like the instance below from ‏@dannytybrown) to remind ourselves that mathematical work solving oftentimes requires patience, inventiveness in addition to multiple attempts. We all experience frustration inwards work solving, only similar our students do, but nosotros know that the satisfaction of eventually finding the solution is good worth it.

5. Dividing alongside Decimals

I've mentioned earlier that I beloved MathsPad's resources - enough of them are costless in addition to the residue come upwards at a toll of exclusively £3 per month. Whether your schoolhouse subscribes or not, it's worth registering for e-mail updates inwards lodge to continue runway 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 tell that xl divided past times ½ equals 20. Activities similar the i shown below volition aid tackle this misconception in addition to encourage students to mean value earlier they answer.

That's it for this week. I'll exit y'all alongside a video from 1977 - 'Congruent Triangles' past times Bruce in addition to Katharine Cornwell (another jewel found on @MathMunch). Happy New Year!

5 Maths Gems #37

Hello too welcome to my 37^th gems post. This is where I portion about of the best maths teaching ideas I've seen on Twitter. If you lot bask reading these posts therefore you lot mightiness similar to explore my novel hashtag #mathsgems to reckon highlights from previous posts.

Last calendar week I attended #pieandmaths - this was an lawsuit organised yesteryear La Salle Education inwards which a grouping of maths teachers got together to verbalize over issues inwards maths education. It was a non bad solar daytime too I've included a brusk write-up at the terminate of this post.

I stimulate got a surplus of gems this calendar week therefore here's the kickoff five, amongst 5 to a greater extent than to follow afterwards this week.

1. Brilliant Indices Question
I kickoff wrote close Gems 21. I 'like' Brilliant's Facebook page which way I acquire regular maths problems inwards my Facebook feed. Since I joined Twitter I haven't used Facebook much, simply I've been on in that place quite a fleck this calendar week working on my novel Facebook page. Luckily that way that I spotted this awesome query from Brilliant:

My Year 12s volition live on treated to this inwards September!

2. 1001 Math Problems
Thanks to Denise Gaskins (@letsplaymath) for sharing the website 1001 Math Problems. This American website was created equally a rootage of problem-solving activities for simple too middle schoolhouse children. The problems are accessible too engaging. Solutions are included.

Here's a lovely example, taken from the pick of puzzles that explore factors/divisibility:

The problems are mainly suitable for Key Stage ii too 3. I honey 'The Spilled Juice Problem'.

3. Simulations
Last August I wrote a postal service Animations too Simulations, too since therefore I've occasionally featured animations inwards my gems posts, similar this lovely demonstration of the surface area of a circle from Gems 12.

One of my favourite simulation websites is PhET Interactive Simulations which I'm told is peculiarly useful for teaching Mechanics at Influenza A virus subtype H5N1 level. Some of the simulations on PhET are suitable for Key Stage three too 4, such equally this estimation activity. Do stimulate got a play amongst this activity, it's great.

Thanks to a tweet from @ChristinaGawlik I've also discovered the late revamped website www.explorelearning.com. This is the 'world's largest library of math too scientific discipline simulations'. These simulations (called Gizmos) are actually good. Unfortunately unless you lot pay a subscription, you lot tin dismiss entirely access each Gizmo for 5 minutes. Worth a expression though.

4. VideoScribe

Chris Smith (@aap03102) shared an impressive promotional video for his newsletters. He said it entirely took him fifteen minutes to brand this video too I didn't believe him! I ready a trial of VideoScribe and flora out he was correct - it's real quick to brand a video using this software. Here's my endeavor - a fun (but pointless!) promo video for resourceaholic.com:

I was wondering if in that place were whatever opportunities to work this software inwards the classroom when I coincidentally stumbled across this Classroom Expectations video from Cathy Yenca (@mathycathy):

Since starting at a novel schoolhouse too having to create 'proper' behavior administration for the kickoff time, I've realised the importance of setting expectations for students. I recollect this approach mightiness brand those expectations to a greater extent than memorable (and fifty-fifty if it doesn't, it's fun to brand the video!). Cathy says, "I innovation to demo this brief video I created using a free 7-day trial of VideoScribe too give students a difficult re-create of classroom expectations to fill upward inwards a few blanks equally they watch. I may demo this several times during the kickoff few weeks of school, postal service it on my website, too generate a QR code to link to it when individual needs a reminder".

I spotted Cathy's video inwards her first-class postal service Primary Maths page which links to blogs too resources. I updated my tangents too areas based on the novel GCSE specification.

Pie too Maths
La Salle Education is a fellowship dedicated to improving mathematics education. I honey La Salle's conferences too volition live on presenting at their adjacent conference inwards Sheffield inwards September. Last calendar week La Salle hosted an lawsuit called Pie too Maths which was attended yesteryear about of my Twitter buddies, therefore it was a skillful run a jeopardy to grab upward amongst people too verbalize close maths.

The lawsuit started amongst a demonstration of Complete Mathematics. This is a actually impressive organization too if you've non seen it earlier therefore it's worth exploring - La Salle tin dismiss come upward to your schoolhouse to demonstrate it. I actually back upward the underlying principles of Complete Mathematics - it has the potential to live on the ultimate collaboration tool for maths teachers. The content too functionality stimulate got developed good since I kickoff saw it concluding summer. The interface is actually user-friendly, allowing teachers to efficiently innovation lessons amongst access to well-written objectives, pedagogical notes, resources too assessment tools. Complete Mathematics currently covers Key Stage 1 through to GCSE. New content is beingness developed for Core Maths, providing much needed construction too resources for this novel post-16 qualification.

Can you lot advert the Twitter handles?

We enjoyed a lovely tiffin too therefore went to the pub for a debate, led yesteryear Mark McCourt (@EmathsUK). We discussed a number of issues including behaviour, parenting, teaching methods, instructor grooming too research.

Afterwards nosotros had lots of fourth dimension to chat too play maths games - I ended upward tied to Bruno Reddy (@MrReddyMaths). This video shows how nosotros got out of it (well done Bruno, I had no idea!).

Thanks to La Salle too Mark McCourt for organising a actually enjoyable event. I loved catching upward amongst Twitter friends too coming together novel people - here's the listing of attendees (sorry if I've missed anyone!): @getdiagnostics, @nishadealwis, @mrdrapermaths, @naveenfrizvi, @MissBsResources, @MissBaileyMaths, @kris_boulton, @DrTrapezio, @craigos87, @EJmaths, @tessmaths, @ColinTheTrainer, @MrMattock, @dannytybrown, @RJS2212, @mrreddymaths, @mathsatschool, @MrBenWard, @xanbritt, @CubbonSue too @mathsjem.

That's it for today's post. Good luck amongst GCSE results everyone! I'll acquire out you lot amongst this cute Nonagon video shared yesteryear @solvemymaths.