Christian Lawson-Perfect

Christian Lawson-Perfect on Rounding and estimating calculations 2 8 years, 5 months ago

Gave some feedback: Has some problems

Christian Lawson-Perfect on Rounding and estimating calculations 2 8 years, 5 months ago

Saved a checkpoint:

There are too many items in part a - I can't add them all up in my head. Just two or three items, plus the ice cream, would be enough to get the idea across.

Both parts a and b have this problem - even after rounding, I can't do these calculations in my head, so I might as well use a calculator. 

"The dimensions of the room are 6.49m×2.88m×3.39m where 3.39m is the height." is oddly worded. I'd say "The room measures 6.49m×2.88m, and 3.39m high."

In part b, I'd round to the nearest metre and do the calculation in my head. My maximum error when rounding to the nearest metre is $4 \times \left(\frac{1}{2}(\text{width}+\text{depth}+\text{height})+\frac{1}{4} \right)\text{m}^2$, which will be around one bucket's worth.

By the way, the height I got, 3.39m, is completely unrealistic! In the UK the minimum ceiling height is 2.1m and the standard is around 2.4m. 

The thesis of this question is that sometimes rounding to 1 sig fig is too blunt, but I don't think the given scenarios make a great case for it: they're all 'mental maths' scenarios. If I'm going to use a calculator, I might as well type in 2 decimal places rather than rounding to 1. Can you think of scenarios where you've got some very precise measurements, but only want a moderately precise answer? 

You could use the separate minimum and maximum accepted value settings for number entry parts in a question like this - accept anything within a generous bound of the true answer, and let the student perform whatever estimation they like, maybe guiding them towards one.

Christian Lawson-Perfect on Factorising Quadratic Equations with $x^2$ Coefficients of 1 8 years, 5 months ago

Gave some feedback: Has some problems

Christian Lawson-Perfect on Factorising Quadratic Equations with $x^2$ Coefficients of 1 8 years, 5 months ago

Saved a checkpoint:

You need to write a feedback message to show when the student doesn't use brackets.

I got $x^2-16$ for part b, which I'd solve by noticing it's the difference of two squares. Can you make sure the coefficient $x$ is non-zero?

I'd spin part b into its own question: first factorise, then write down the roots.

Christian Lawson-Perfect on Simple interest 8 years, 5 months ago

Gave some feedback: Ready to use

Christian Lawson-Perfect on Simple interest 8 years, 5 months ago

Saved a checkpoint:

I've changed some of the wording, and used dpformat to make sure currency amounts are always shown to two decimal places. A good, simple question.

Christian Lawson-Perfect on Expand brackets and collect like terms 8 years, 5 months ago

Saved a checkpoint:

The string restrictions aren't doing a great job here. I don't think you should require the asterisk.

Talk to Elliott about adding pattern matching.

This should be two questions - a question with each of the items from part a as a separate part, and part b on its own.

Christian Lawson-Perfect on Expand brackets and collect like terms 8 years, 5 months ago

Gave some feedback: Has some problems

Christian Lawson-Perfect on Identifying different types of sequences 8 years, 5 months ago

Gave some feedback: Has some problems

Christian Lawson-Perfect on Identifying different types of sequences 8 years, 5 months ago

Saved a checkpoint:

Advice for part a could show each sequence with the common differences underneath, so it's easy to see which are linear. That's how I'd work it out.

Similarly with common ratios for part b.

For part c, I just use the fact that the difference between consecutive triangle numbers increases by 1 at each step. A drawing of the first few triangle numbers would help show this. While you can use the formula, it's not obvious, and you'd look at common differences first.

In part d, rather than using the triangle sequence in particular, I'd give a formula of the form $\frac{an(n+b)}{c}$ (what constraints are there on randomising this?) - you want to see that the student's comfortable with using a formula to get the nth term of a sequence without working out all the previous terms.

Part e relies on noticing that the sequences are the squares and cubes, respectively. How would you work this out? It's not enough to just state it in the advice. You might look at common differences, then make a guess that it's $n^2$ or $n^3$. The advice should show this experimental thinking - is it really $n^2$? How do we check? Draw a table of $n$ against $a_n$?