I proved the product rule at the board using logs and implicit differentiation in #MathsToday. One student described the performance as “like when Maradona went round all those players”. I guess they mean Mexico ‘86 vs England. I’ll take the compliment.

Y12 learned about Argand diagrams in #MathsToday. I’ve been trying to bring a bit of history to my teaching this year, so I gave a mini biography of Jean-Robert Argand. My group appear to be enjoying these little diversions. And I like that it makes the maths a bit more human.

In #MathsToday a pupil asked me “What is a complex conjugate pair?” They had been using the properties of conjugate pairs for a number of lessons, the class had been using the language in discussions, and, if asked, I would have said they all knew what the words meant. At least one didn’t.

Students needed to integrate the square of sin(𝔁) today. Reminded me to show them this neat way to derive forms that are easier to integrate. #MathsToday

Wow, thanks calculator, this is helpful 😁 #MathsToday

Intermediate Maths Challenge (IMC) in #MathsToday. What tips did you give pupils sitting IMC this year before you saw the questions? I suggested they memorise 2025 = 3⁴ x 5². I’m looking forward to seeing the questions to find out if that was useful advice.

A nice extension I made up while working on nth terms. #MathsToday

In #MathsToday we tried to write the equation in the image below in the form 𝔂 = f(𝔁). We were asked to find the gradient function so we explored 2 approaches; implicit differentiation and quotient rule.

Today we tackled a question that boiled down to the image below. How would you guide students with generally helpful approaches/principles rather than giving specific steps? #MathsToday

In #MathsToday we tackled a traditional hand written worksheet to build skills in deciding which method of differentiation to choose. Mainly product, quotient and chain rules. Answers to follow.

In #MathsToday we looked at collisions of 2 spheres. My choice of how to display the Restitution equation led to some confusion. I think it’s because, in the second image, I had a numerator where I thought about direction and a denominator where I just applied the “different of velocity” rule.

Unexpected misconception in #MathsToday. My class had found the derivative of tan(𝔁) using the product rule [by setting v = (cos(𝔁))^(-1)], then 3 of them tried to find the derivative of tan(𝔁) using the quotient rule and still set v = (cos(𝔁))^(-1) rather than just cos(𝔁).

Today Y13 were studying collisions of spheres and wanted to know “why, in the spec, do spheres need to be of equal radius?” A good occasion to teach the general lesson that sometimes, by simplifying problems, you lose important features. Here the Impulse isn’t parallel to the plane. #MathsToday

Today’s work on the chain rule led to finding this derivative. I enjoyed one student’s suggestion that we “times both sides by dy/dx to get 1 on the left.” I was expecting them to say find the reciprocal directly. #MathsToday

I've been thinking about this a lot over the last few days. In your opinion, what is the optimum number of records required to have a comprehensive record collection? Assuming that money & space aren't an issue, but your time left on earth, very much is. #VinylExistentialism

Finding a good reason to study limits with Y12. “It would be a real shame to have this whole pattern and just have to shrug when 𝔁 = 0.” #MathsToday

Today I was teaching about collisions with slopes. I was quite pleased with how this example turned out when I used colours to help eyes track the right elements. #MathsToday

I wrote 16 up as “a number that’s easy to find the square root of” and asked pupils to give me numbers that are harder to find the sqr root of. I got loads of answers before anyone gave me a non-square. I got 144, kept asking “even more difficult” and was given larger and larger squares. #MathsToday

A pupil asked me, “What form should I leave my answer in?” I answered, “It depends what you want to do with that answer next.” I think this is a good response, even though they might prefer that I answer along the lines of, “As a fraction always.” #MathsToday

I have a middle school class this year that watch quietly while I speak, only answer questions if I call them by name (bar a few “hands up every time” types), and work in near silence unless I explicitly tell them to talk. The origins of this behaviour are a mystery to me.

That’s it, no more teaching “same sign subtract” or similar for elimination with simultaneous eqns for me. This year I’ll teach change the subject and substitute as the go to method. I’m expecting this will help students with solving tricky equations too. #iTeachMath

A student asked me today how they are supposed to know whether there is a part of the function on the x-axis (I’ve added it in purple). The mark scheme required that they assume there is no line segment on the x-axis. I think I now know why but didn’t spot it in the lesson. #iTeachMath #Mathematics

Today students worked on identifying methods for finding a value of N that works. Their responses were mostly variations of the same equation. This prompted some good discussion on algebraic equivalence.

A student in today’s lesson said: “I’m not sure I get the difference between reciprocal and negative reciprocal when we’re doing perpendicular lines.” I thought if they saw both represented by line graphs they might find it easier to see why we need the negative reciprocal for perpendicular lines.

Reflecting now on why, in today’s lesson, Y9 had more difficulty factorising -𝔁² + 9 than 64 - 𝔂². I think lots of them at can spot a difference of 2 squares in a very specific format only at present. #iTeachMath

This is a recreation of the working a pupil used to find the nth term of the quadratic sequence. The use of a table is standard but the explicit use of 𝔁 as a label for the sequence is their idea. I thought it might help students grasp the last step more easily. #iTeachMath #Mathematics

I used this question in class today. The answer is 0.16 but a few students needed persuading that P(X < 60) + P(X > 60) = 1. They had previously met only discrete distributions and were worried because similar reasoning doesn’t work there.

A lesson on the difference of 2 squares today…show how the prime factors of 3599 can be found without a calculator.

Key point from a maths class today…R = mgcos(θ) only when F = 0. Several students needed help seeing that F has an impact on R. Considering very steep slopes helped with this.