Chris McGrane
@ChrisMcGrane84
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Principal Teacher of Maths / Acting Depute Mathematical Tasks Book: …
Glasgow
Joined September 2013
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My number 1 bit of teaching advice:
Resist the urge to sit at your desk.
Talk to every pupil, in every lesson. Be interested in their work. Provide feedback and encouragement.
If you aren't doing this or using mini-whiteboards you are missing loads.
Teach between the desks.
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The best textbook series I know of is definitely the MEP.
It's free!
The quality of task design is incredible.
Look at this year 4 (primary 5) material, for instance:
Check out the whole of primary & secondary here
#MTBoS
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*Big Announcement*
I've been working with
@ShivMcKenna55
to develop our new early secondary mastery curriculum for
@HolyroodSec
and
@stninsmaths
We have uploaded the first 9 booklets:
More booklets will be added over the coming weeks.
#mtbos
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Tonight:
Drove to Supermarket.
Did shopping.
Arrived back at my front door with a heavy carrier bag.
Then remembered “I drove!!!”
Walked back to supermarket to get car.
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One of the challenges with area questions is setting them up and deciding upon initial steps.
Pupils don't get enough practice of this if they are doing full questions.
Here pupils are to write down the integrals required, without fully evaluating.
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35 Tasks on Fractions
Focused on developing understanding, fluency and problem solving.
Check them out here:
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*New Curriculum Booklet*
Algebra Book 2
The latest of our curriculum booklets has just been uploaded here:
#mtbos
@ShivMcKenna55
@garyl82
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Used this excellent
@mathsjem
task last week.
it always provokes a lot of discussions and brings misconceptions to the fore.
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Some carefully varied practice on substitution of negative numbers.
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My 5 year old twins started primary school this year. I've come to the conclusion that primary teaching looks much more complex than secondary. I've been blown away by the progress of both kids in maths and literacy over the past 3 months. Incredible respect for their teachers!
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*First upload of 2021*
A Pack of 58 Problem Solving Questions
From early secondary up to advanced levels...
Thanks to Dr. Matthews for sharing
@HolyroodsecM
#MTBoS
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Teaching Fractions?
Starting Points Maths now has 27 visual tasks to develop conceptual understanding and procedural fluency with fractions.
Suitable for primary and secondary.
Check them out here:
#MTBoS
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Backwards Volume Practice
Find the height, area, or radius given the volume.
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I've never been able to find a task which had a mix of:
- linear equations
- quadratic equations
- equations which look quadratic but are linear
- a sneaky cubic
Until now....
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How did I not know this? The distance between roots of a unitary x^2 quadratic is the square root of the discriminant!
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I don't normally teach BODMAS when doing order of operations.
My latest thinking is that order of operations isn't even a topic.
The key points will arise through tasks such as the two below, and in work on algebra.
#MTBoS
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*New Resource*
Our first Algebra Booklet is now uploaded!
A mix of our own tasks, some classics from old texts & others shared online.
-> The first of 3 Algebra booklets at this level
-> Also 2 equation booklets to come.
#MTBoS
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*New Task*
Fraction key skills
A single page run through of essential fraction work.
#mtbos
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Some of us started back school today!
A shameless plug for my website:
- Lots of different tasks, sorted by topic
- Curriculum booklets for early secondary
- A page dedicated to Higher Maths
- A page dedicated to upper primary
And much more...
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Our department meeting today was around planning of learning and teaching.
We focused on this tricky equations exercise.
@HolyroodsecM
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Teaching Negative Numbers?
Here are tasks on some of the big ideas...
Zero Pairs:
Addition:
Subtraction:
Multiplication:
Division:
#MTBoS
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Using the 'zero pairs' metaphor is such a powerful approach.
Nothing against the number line, but this approach has proven far more successful for me over the past 5 years.
My S2 class made tremendous progress on this today.
#mtbos
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The importance of not just asking “put your hand up if you got the correct answer”.
Vital to get round and look in jotters, or use mini whiteboards.
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*Another New Task* - Fraction Addition
( I've got a backlog of tasks to upload.)
This sequence of fraction addition questions worked really with one of my classes recently.
I think it's one the better sequences I've written.
#mtbos
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National 5 Fractions Exam Questions
Meant to post this during the week. Some practice on 'question number 1' in most N5 exams.
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Don't know why I never knew this before but...
Pressing 'Alt' and '/' produces a ÷ on a mac.
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I've got an obsession with writing quadratics tasks.
You might like some of them...
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*New Task*
Percentage Relationships
A use of variation theory to help pupils to see how to 'build' different percentage calculations.
#mtbos
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*New Task*
Scaffolded Factorisation: Using the 'ac' method.
An intervention sheet I used recently.
#mtbos
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I've always taught it like the approach on the right.
Suddenly, at the board today, it occurred to me that the approach on the left would be easier for pupils to grasp.
Subtle but I think it makes a difference.
Thoughts?
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Solving equations with variables on both sides.
A backwards faded task.
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Delighted to host this great task from
@McConvilleMaths
Prime factorisations, LCM, HCF
#MTBoS
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2.5 years ago I sat down to begin planning our new curriculum on a sheet of A3 paper. Here is the latest version of our Mastery Curriculum overview...
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A spot on late night editing for the book.
Excited to see a type-set version of it!
Looking like early October for release.
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A new blog: A Progression from Long Multiplication to Algebraic Long Division
Featuring:
Why Synthetic Division should go in the bin!
The Distributive law
Dabbling with Didactics
Grid Method for factorisation
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Check out my new website with a selection of prompts and tasks
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Teaching Indices?
@ShivMcKenna55
wrote this massive booklet with 51 pages of tasks and examples.
Download Here:
#MTBoS
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A thread:
"Factoring quadratics" is not just a mechanical process. We should teach it.
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We need to be passionate about mathematics.
We need to be even more passionate about teaching mathematics.
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All of us at
@HolyroodSec
Maths department are sad to say goodbye to the legendary Mr Cahill today.
Great teacher and great colleague who’s helped thousands of kids become better at maths in his 16odd years in the department.
Best of luck for the future!
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Having a look at some old SMP materials. I think this is a fascinating representation of the multiplication of negatives. I've done a bit of thinking in terms of algebra tiles or a vector approach but this is very nice...
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Doing some deeper thinking around algebra with second year this afternoon.
Love this SMP material we are using in the department booklets.
A proper challenge for them in their early formal algebra work.
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I keep coming back to SMILE as there are so many great little tasks, such as this.
These fraction tasks could be the basis of some great discussion.
#MTBoS
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*New Curriculum Booklet*
The latest curriculum booklet is now available to download:
Check out this and Solving Equations 1 from
@ShivMcKenna55
. Great resources.
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I used to struggle with Engelmann's assertion that 85% of a lesson should be review.
I'm beginning to change my mind after Implementing this approach with one of my classes this year. Seeing significant benefits so far.
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Finding axis intercepts
A practice task on finding where lines and quadratics intersect with the x and y axes.
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Some scaffolded work on differentiation for Higher tomorrow.
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Making use of an airport wait. What about this for an idea?
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I'm looking forward to trying this out with S1 tomorrow.
We will be looking at the additive structure of odd and even numbers.
Trying to arrive at the conclusions that:
odd + odd = even
even + even = even
odd + even = odd
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Trying to framework the assessment cycle for our department.
3 Stages:
-Teaching
-Reviewing
-Assessing and Improving
Thoughts?
Some of it is specific to my context. No mention of summative assessment in this. Feel that is separate from the normal pattern of classroom teaching.
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*New Curriculum Booklet*
Check out the ratio booklet created by
@ShivMcKenna55
Hosted
#mtbos
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A PDF of
@SegarRogers
wonderful task on the mean is now available to download on my site.
Another excellent use of the Pointon and Sangwin taxonomy for Task Design.
#mtbos
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SMILE is the home of some incredible task design.
This is so simple, yet incredibly effective.
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Asked S1 today (who haven't learned about powers yet) if we could write this in a shorter form:
2 x 2 x 2 x 2 x 2 x 2
"Two hexagon-ed"
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Zero pairs is such a powerful metaphor that helps pupils throughout their development of algebra.
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New Task:
*Scaffolded Practice of Differentiation*
Attention to technical details for procedural fluency
#MTBoS
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*New Task* - Areas of Sectors
This task is entirely pupil led, assuming they know how to find the area of a circle. Culminates in a general method for areas of any sector. Role of teacher is to observe and prompt individuals where needed.
#mtbos
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Into Task Design or want to learn more?
3 x 1 hour practical workshops on Mathematical Task Design, live broadcast online.
If this is of interest, comment below!
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I'm trialing a new layout for
The welcome screen is shown, or you can click at the top to filter tasks by topic.
Let me know what you think. I want to make it nice to look at, but usable. A lot of new tasks in coming weeks.
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Fraction Stories
A task on multiple interpretations of fractions:
Part whole
Mesure
Operation
Quotient
Ratio
A short blog accompanies the task:
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Delighted to host more of
@SegarRogers
excellent tasks on
These order of operations tasks are fantastic.
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First plug for my website in 2022!
Here are the ten most popular tasks, pages and posts of last year, in a thread.
1. The curriculum booklets for Third Level/KS3
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A little task on some essential indices skills for calculus.
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New Task:
Negative Powers & Fractions & Division
Collections of equivalent expressions!
#mtbos
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I'm doing a bit of work at First Level (KS1) this year with one of my classes. I'll be creating new tasks to support things as I go. First attempt is this one on place value:
The full task & mini blog are here:
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A wee warm up task.
Most of them didn’t spot the pattern.
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Today I gave my Higher this wee challenge I put together a few years back.
Always provokes good debates and pushed understanding of indices.
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*New Curriculum Booklet*
This latest one of our booklets from
@ShivMcKenna55
on solving equations is fantastic!
Really looking forward to using it
@HolyroodsecM
#MTBoS
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Division of Fractions
A Representations Task
Probably worth reading the notes first...
#MTBoS
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A reminder to anyone who needs it:
We all teach lessons that could have gone better.
The key is to address it next time.
Had one today. Used to beat myself up about it. Tomorrow will be better.
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I've uploaded a massive book of Indices tasks and examples compiled by
@ShivMcKenna55
at
51 pages of ideas, well worth a look!
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I *think* that's the final bit of work done on the book.
It includes:
-> Interviews with many world class educators
-> Pedagogy
-> The Curriculum
-> Task Design
-> Using and adapting tasks
-> Ideas for your own classroom
@EmathsUK
Order here:
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Sometimes kids want a way to remember stuff, without having to reason it all out.
Reminding S5 of fraction power rule…
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Over 1 million visitors to my site!
945k on Wordpress + 100k previously.
Curriculum Booklets
Hundreds of tasks by topic
N5/Higher and Primary tasks
Some interviews
And more...
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*New Task*
Rationalising the Denominator: A structured variation grid.
Inspired by
@mcnally_gerry
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It seems that pre-orders are now available for the forthcoming book.
@EmathsUK
will be pleased with Amazon's choice of language 🤣
The reviewers haven't hated it. Might be worth a read.
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What is a scheme of work?
Pinning my colours to the mast...
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Excited to be launching our new S1 curriculum this week
@HolyroodSec
All new resources and many new approaches- a big focus on conceptual understanding and problem solving.
First lesson is on clever multiplication strategies:
#MTBoS
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