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.

We did look at that, which led to us looking at the question “When does green become red?”

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

Ah, we allowed ourselves the use of the plus/minus symbol and defined more of a mapping than a function.

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.

I agree that it’s demanding. The list of 3 things I wrote earlier is actually a list of the things I had to do to complete the rearrangement. TheMathsBazaar is right that the context was iterative methods.

We had, in no particular order…
1) Remove decimal coefficients.
2) Identify what the last few steps in the rearrangement must be.
3) Work towards a middle with both forms then rewrite the process start to finish afterwards.

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

Answers below.

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.

Recently I’ve been going with “Two sinh sinh, hush hush, minus sign” to the tune of Kajagoogoo’s Too Shy.

This led to good discussion, partly because, with v = 0 there is no way to reverse engineer the right numerator. I think v has to be v or -v throughout. Ordinarily I’d take my own advice and have the “after” arrows pointing in the same direction. I find pupils make sign errors less often that way.

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).

I also showed them the classic puzzle, “how do you slice a cake into 8 equal pieces with only 3 cuts?” Here the natural model for the cake, a circle, makes the problem impossible.

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

One student did ask about the reason for taking the +ve square root. We looked at the graphs below to help us decide.

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

Yes, that’s what I’ve got planned next. Using projections and the scalar product to calculate e directly. Also using matrices to rotate the problem so the wall is parallel to the 𝔁-axis.

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

If the 13.3 wasn’t a guess, I’d love to know the thought process behind it. The other answers make sense to me as slightly wrong shuffling of digits. But the extra 3 is a real head scratcher.

They were doing some drill on the chain rule. We followed up my response by talking about what they might be likely to need to do next. Which led neatly into some examples I had prepared about finding turning points. We also discussed sensible forms for final answers in the absence of next steps.