Logarithmic Regression with Year 12 in #mathstoday
Finding that we are needing to scaffold things in #AlevelMaths more this year and we are enjoying putting together resources to help to students organise their thinking!
This is my favourite thing in further maths A Level - teaching hyperbolic functions starting with an area definition:
www.paddymacmahon.com/resources/a-...
(And what I'll be talking about at this year's @meimaths.bsky.social conference!)
#Mathstoday
Year 8 looked at Pie charts today. After some practice with just filling in the tables we drew some without needing a protractor.
(Then some with a protractor)
Awesome roots task by @dandraper.bsky.social
Also an excellent order of operations post here
mrdrapermaths.wordpress.com/2017/04/08/o...
A-level revision grid containing nine exam-style question on Year 2 sequences and series.
A-level revision grid containing eight exam-style question on Year 2 numerical methods.
More new A-level revision grids added today:
β¨Numerical Methods
β¨Sequences and Series
Available at www.draustinmaths.com/a-level-topics
Enjoy!
#ALevelMaths #UKMathsChat #MathsToday
Happy International Women's Day to all the wonderful Maths women - cis and trans - here on Bluesky π #MathsToday
Ooh yes, that was a good one!
5 years since you wrote us a puzzle @catrionaagg.bsky.social π
In #mathstoday I showed my students what a 95% confidence interval actually means by using Excel and taking 100 random samples and seeing that the population mean was only within the interval 95% of the time.
A clear cup filled almost to the brim with copper pennies. The pennies are stacked randomly, making it difficult to count visually and prompting an estimation challenge.
A list of five calculus clues to find the total number of pennies. Clue 1: Upper Bound. The total is strictly less than g prime of 1, where g(x) = (10x^2)(5x^5 + 5). Clue 2: Lower Bound. The total is strictly greater than h prime of 0, where h(x) = (250x) / (2x + 1). Clue 3: Tens Digit. The tens digit equals k prime of 2, where k(x) = (7/4)(2x - 3)^2. Clue 4: Shared Factor. The total is a perfect multiple of f prime of 1, where f(x) = x^3 - (1/2)x^2 + 3x - 10. Clue 5: Hundreds Digit. The hundreds digit equals m prime of 0, where m(x) = (2x + 1)^3 / (3x + 1).
Bringing the classic "esti-mystery" to my Calculus class. Students make an initial guess of how many pennies are in the cup, then use derivative rules (power, product, quotient, chain) to narrow down possible values one clue at a time. #ITeachMath #MathsToday docs.google.com/presentation...
Reminded by @xaqwg.bsky.social that I wanted to @geogebra.org this @catrionaagg.bsky.social puzzle. www.geogebra.org/m/fbfzkvhe
Yes I was surprised too! I guess because an angle problem already feels visualβ¦ but itβs not as familiar as the bar model, and you need the implicit knowledge of what the sum should be.
Iβve found bar models really help with angle problems. I like how it makes the 180 explicit too
Two straight lines, one with two angles at a point, the other with three. Underneath are two empty bar models with 180Β° written in the top bar of each.
I used another #BlankIsBest slide this week to introduce angles on the straight line.
The bar model underneath each diagram really helped some of my Y7's make sense of the problems I made up.
#MathsToday
Another bit of AI coding this morning. This one for visualising Normal approx of a Binomial distribution. I like being able to specify exactly how I want it to function rather than making do and clunking around with pre-existing stuff. I just don't have a convenient place for public sharing π«€
International Womens Day is this Sunday, so I thought I'd compile a list of books by and about Women in Mathematics.
The most important question I have for you is: What's missing?
uk.bookshop.org/lists/books-...
#Mathstoday
Year 8 did bar charts today and got to use the scaffolded worksheet I made 4 years ago when doing my teacher training.
Since then added some questions where they have to spot the mistake.
Is there a good source of homework style questions somewhere for mechanics and statistics that are split into year 1 and year 2? #AlevelMaths I have been using Jethwa maths a lot for homework for pure, wondered if there is something similar available for mechanics and statistics. #MathsToday
I like your isosceles triangle solution; I wouldnβt have thought of that approach.
An arrangement of seven squares. Six of the squares are identical and are arranged so that reading from left to right they form three stacks that abut and are of heights 2,3,1, with each base square aligned with the second square in the stack to its left. A tilted larger square overlays the six and shares a vertex with the lower right vertex of the bottom-most square. The top left vertex of the uppermost of the six squares lies on an edge of the larger square. A line is drawn from the left-hand vertex of the larger square to the lower right vertex of the rightmost small square. The angle formed by this line and the left-hand edge of the larger square is marked with a question mark.
notes.mathforge.org/notes/publis...
#geometrypuzzle #UKMathsChat #mathsky
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 Β£3000)
...
YES thanks. It's nice & concise, gets students going on problem-solving when they "don't know what to do". Good general framework for math & more.
I have a list of things I want my Ss to be thinking when they tackle problems, wrote about here:
karendcampe.wordpress.com/2017/05/10/t...
#iTeachMath
In #mathstoday, we are discussing u-sub vs guess and check when evaluating integrals #calculus #iteachmath
But I guess that element of doing things βin reverseβ is what makes it feel like a fun puzzle, rather than a procedural question
This kind of puzzle always makes me reflect on how one-directional my teaching of circle theorems is. Itβs always βhereβs a circle, so the angles follow this ruleβ, and never βthe angles follow this rule, so there must be a circle hereβ.
A grid of 16 practice questions involving generating difference types of sequences from their nth term.
A strip of practice questions involving recurrence relations - generating sequences, writing recurrence formulae and solving problems.
A strip of practice questions involving solving problems with quadratic sequences, including deciding whether numbers belong to sequences, finding nth term rules given some of the terms, and finding nth term rules for harder sequences.
A strip of practice questions involving solving problems with arithmetic sequences, including finding nth term rules given some of the terms, arithmetic sequences with algebra, and solving worded problems.
Lots of new sequences resources added to the site today:
β¨Problems with arithmetic sequences
β¨Problems with quadratic sequences
β¨Recurrence relations
β¨Generating different types of sequences
All freely available at www.draustinmaths.com/sequences
#MathsToday #UKMathsChat
Variation on a theme.
Two squares. Show that the red point bisects the green segment.
A blank parametric equations worksheet displayed as a table. Columns are titled: x = p(t), y = q(t), Cartesian Equation f(x,y), Intersection with axes, Constraint on t, Domain, Range, and Sketch. Five rows contain given parametric pairs such as x = 3 β t, y = β4 + 3t; x = 3tΒ², y = 6t; x = 4 cos t, y = 2 sin t; x = 1 + 2 cos t, y = 3 + 2 sin t; and x = eΒ²α΅, y = eΒ³α΅, with remaining columns left blank for students to complete
second blank parametric equations worksheet in table format. Columns match the first sheet: x = p(t), y = q(t), Cartesian Equation f(x,y), Intersection with axes, Constraint on t, Domain, Range, and Sketch. Five rows include parametric definitions such as x = tΒ² β 1, y = t(tΒ² β 1); x = 3 cos 2t, y = 2 cos t; x = 1 + 2tΒ², y = β3 + 4t; x = ln(t β 2), y = 1/(t + 1) with t > 3; and x = cot t, y = 3 sin t for 0 β€ t β€ Ο, with other columns empty for completion.
A new A level task.
Really enjoyed watching the students think about this one:
kshancock.co.uk/aleveltasks....
#MathsToday
A graph with three panels all with a shared x-axis. The x-axis is labelled "values" and ranges from 0 to 10. All three panels have a cloud of hundreds of black dots. The top panel is titled "chisquared" and has a cloud of dots more densely packed near 0 and becoming sparser and sparser towards 10. The middle panel is titled "normal" and the cloud of dots is sparse near 0 and 10 and more densely packed near 5. The bottom panel is titled "uniform" and the cloud of dots is more evenly dense across the whole range 0 to 10.
Just an idea I had to get out of my head about how we look at continuous numerical distributions.
There are six small pink squares, and a larger tilted purple square which shares ones vertex with the bottom pink square. One vertex of the top pink square lies on the top edge of the purple square. A line from the bottom right vertex of the rightmost pink square makes an unknown angle with the left side of the purple square.
Seven squares. Whatβs the angle?
#geometrypuzzle
