- an answer that gives a probability greater than 1 or an acute angle greater than 90°
- getting one answer when the question said 'solutions' (or vice versa)
- a transformation/graph/chart going off the given axes
- getting a mean/median not within the range of the data
- a non-calc question requiring some rather involved calculations
- an answer not matching the form requested in the question (e.g. a+b√c)
- an answer that doesn't work when substituted back into the question
- an answer that doesn't use all the information given in the question
What warning signs could students pick up on that they might have gone wrong in an answer?
e.g.
- an unexpected negative/decimal answer,
- an answer requiring many more/fewer steps than the number of marks would suggest,
- an answer that would be weird in context (e.g. a taxi costing £3000)
...
@mr-man-maths.bsky.social's incredible video checklists are my go-to recommendation for curriculum-based videos:
mrmanmaths.wordpress.com/2023/11/20/p...
mrmanmaths.wordpress.com/2023/12/08/p...
A factor tree made from formula triangles
I'm having a very fun nostalgia trip
And these classics, of course
a formula triangle for median
I preferred this one
![An abomination.
[A formula triangle for Capture-Recapture]](https://cdn.bsky.app/img/feed_thumbnail/plain/did:plc:dgljohqg4oj6sgjc4pfoqpga/bafkreidiqhof66525rjd2tjvrnaeep4lvnjsibfajyit4du3zky5udafqa@jpeg)
An abomination. [A formula triangle for Capture-Recapture]
This is why I use a formula triangle for it.
To paraphrase my introductory probability lecture at university: Probability is merely the study of normalised countably-additive functions with a codomain of [0,1].
A selection of 4 questions involving the Harmonic Mean in different contexts.
A selection of 4 questions involving Product Rule for Counting in different contexts.
And a couple more...
A selection of 6 questions using proportional reasoning in different contexts with the same numbers. A prompt saying 'Which is the odd one out?'
A selection of 6 questions using linear relationships in different contexts with the same numbers. A prompt saying 'Change each question to make the answer 43.'
A selection of 6 questions involving reciprocals in different contexts with the same numbers.
A selection of 6 questions involving manipulating a given multiplication in different contexts.
I'd consider these to all be in the realm of Different Surface Same Deep, I reckon.
Some more available here:
interwovenmaths.com/daydream-int...
and here: interwovenmaths.com/making-conne...
Only the two I saw on the Chalkdust website! 🙂
'Christmaths Carols' has had a big upgrade for this year.
Now featuring 12 different songs, and recordings with my slightly dodgy piano and vocals!
interwovenmaths.com/christmaths
I'm looking forward to having a big sing-along with them in school later this week.
'Which of these numbers changes most when rounded to 4 decimal places?'
Thankfully not! We were in the grotto/fernery in the Swiss Garden at Shuttleworth.
A photo of me and Karen in a grotto/fernery.
Look who I happened to bump into...
If you don't know the history of zero, here's an explainer to get you up to speed with a fascinating story. Really there are two zeros: zero the digit and zero the number. So I start by exploring ancient number systems that had one or the other or both or neither.
youtu.be/7jQNTfe-5FM
The greatest hits of tasks by @nathanday.bsky.social 🎉
Unfortunately, for me, there was an even number in the class, so I had no-one to play against.
Fortunately, however, I had an online version of the game I made, which allowed me to play against the computer instead!
interwovenmaths.com/_DigitDisgui...
In #MathsToday*, I introduced Year 12 to the brilliant game Digit Disguises by @davidkbutler.bsky.social.
See here:
www.adelaide.edu.au/mathslearnin...
They really enjoyed it and immediately started coming up with lots of clever strategies.
*(Actually #Maths~16DaysAgo, but I've been a bit busy!)
Used @nathanday.bsky.social ’s sum-product(-difference-quotient) tables in an intervention session with Y10 in #MathsToday to support their factorisation of quadratics with negatives. Was really helpful to isolate the step of considering all the sign combos! 🤩
interwovenmaths.com/four-ops-tab...
To be fair, I already suggested it to you as a title in a conversation two years ago!
I'm not sure 'taught and shared' sounds quite enough like 'thought and said' for this title to work, but oh well.
📣 #MathsConf39: The Best That Has Been Taught and Shared with Nathan Day (@nathanday314)
Explore all-time great maths tasks, why they work, and how to adapt or design your own to enrich lessons & inspire learners.
completemaths.com/community/ma...
#UKMathsChat
In particular, the second row of the table (Finding an inequality with solution set 0 < x ≤ 1) prompted great discussions about whether it could be done with a quadratic, properties of asymptotes, etc.
A three-circle Venn diagram labelled A, B, and C inside a rectangle. Each region represents inequalities with certain properties: • A: the solution set is a subset of x \leq 1. • B: the solution set is of the form a \leq x \leq b. • C: the inequality is satisfied by x = 4. Below the diagram is a set of numbered inequalities in boxes. The task is to place each inequality into the correct region of the Venn diagram according to the properties of its solution set. https://undergroundmathematics.org/quadratics/inequalities-for-some-occasions
A table with three columns: “Solution set”, “Graph”, and “Inequality”. Each row must be completed so that it contains: • a solution set written in set notation, • a graph showing a function or curve to help solve the inequality, • the inequality itself. Some rows are partially filled with either a solution set, a graph, or an inequality, and the student must fill in the missing parts to match them consistently. https://undergroundmathematics.org/polynomials/inequalities
In #MathsToday, Year 12 tackled some Underground Maths tasks on inequalities.
Inequality sets: undergroundmathematics.org/polynomials/...
Inequalities for some occasions:
undergroundmathematics.org/quadratics/i...
I always find with their tasks there's more to them than initially meets the eye.
"Because here’s something else that’s weird but true: in the day-to-day trenches of adult life, there is actually no such thing as atheism. There is no such thing as not worshipping. Everybody worships. The only choice we get is what to worship. And the compelling reason for maybe choosing some sort of god or spiritual-type thing to worship–be it JC or Allah, be it YHWH or the Wiccan Mother Goddess, or the Four Noble Truths, or some inviolable set of ethical principles–is that pretty much anything else you worship will eat you alive. If you worship money and things, if they are where you tap real meaning in life, then you will never have enough, never feel you have enough. It’s the truth. Worship your body and beauty and sexual allure and you will always feel ugly. And when time and age start showing, you will die a million deaths before they finally grieve you. On one level, we all know this stuff already. It’s been codified as myths, proverbs, clichés, epigrams, parables; the skeleton of every great story. The whole trick is keeping the truth up front in daily consciousness. Worship power, you will end up feeling weak and afraid, and you will need ever more power over others to numb you to your own fear. Worship your intellect, being seen as smart, you will end up feeling stupid, a fraud, always on the verge of being found out. But the insidious thing about these forms of worship is not that they’re evil or sinful, it’s that they’re unconscious. They are default settings. They’re the kind of worship you just gradually slip into, day after day, getting more and more selective about what you see and how you measure value without ever being fully aware that that’s what you’re doing." https://fs.blog/david-foster-wallace-this-is-water/
Or, as David Foster Wallace put it, 'There is no such thing as not worshipping. Everybody worships.'
A maths worksheet titled “Simultaneous Equations & Points of Intersection.” It shows a grid where different pairs of equations intersect, and the task is to fill in the correct intersection points from a list of given coordinates. Some boxes are shaded and students must explain how many intersection points there are, without calculating the coordinates.
The previous task, but with answers.
An image of the graphs from the task.
In #MathsToday, Year 12 looked at some graph intersections and solving some simultaneous equations, and then sketching the graphs!
Lots more of Susan Wall's excellent tasks can be found at:
www.stem.org.uk/resources/re...
I'm finding a lot of them are great for generating interesting discussions and helping me work out which bits of the early chapters of AS Pure can be skipped.
Maths question titled ‘Suggest possible equations for the graphs on the diagram. Generalise your answer.’ The diagram shows two parabolas: one opening upwards and one opening downwards. They touch at a single point above the x-axis, forming a point of tangency. The task is to suggest equations for these parabolas and to generalise the form of such equations.
Maths problem saying ‘Identify the odd one out in each row. Fill the gap so that it is no longer odd.’ In each row there are three expressions with powers, with one that is not equal to the other two. There is a space on each row to fill with something equal to the odd one out.
Other ones we've done include:
1) another nice quadratics task with some lovely generalisinging
2) an odd one out indices task, with opportunities for some creativity when giving the odd ones out friends!
