Christian Lawson-Perfect

Christian Lawson-Perfect on Inverse and composite functions 8 years, 8 months ago

Gave some feedback: Has some problems

Christian Lawson-Perfect commented on Inverse and composite functions 8 years, 8 months ago

Use \left( and \right) around fractions to make sure the brackets stretch to the correct height.

In the advice for the final part, I would use an identity symbol ($\equiv$), and maybe preface the identity with "it is always true that"

Christian Lawson-Perfect on Square and cube numbers 8 years, 8 months ago

Gave some feedback: Has some problems

Christian Lawson-Perfect commented on Square and cube numbers 8 years, 8 months ago

I don't think part a is a well-conceived question. First of all, I don't like telling students not to use calculators. You can sometimes hint that a calculator won't be useful, but don't give them the idea that using calculator is ever bad.

When you're told $x$ and $x^3$ but not $x^2$ - why would you ever calculate $(x^3)^{2/3}$ instead of just squaring $x$?

Similarly, when you're given $x^3$ and $x^3$ but not $x$, I don't think anyone would take the cube root instead of the square root. So why show both?

Some ideas for different questions on the same topic:

• Calculate $x^2$ for $x$ from 1 to 10.
• Calculate $x^3$ for $x$ from 1 to 10.
• Find a number such that $x^2 \gt 100$ and $x^2 \lt 120$.
• An "always/sometimes/never" question for some statements. The student has to say if each of the statements is always true, sometimes true, or never true.
  • $x^3$ is greater than $x^2$. (sometimes)
  • If $x$ is negative, $x^2$ is negative (never)
  • If $x$ is negative, $x^3$ is negative (always)
  • $x^2 = x$ (sometimes)
  • $(x+1)^2 \gt x$ (sometimes)
  • $(x+1)^3 \gt x$ (always)
  • When $x$ is a whole number, $x^2$ divides $x^3$ (always)
  • $x^3$ has the opposite sign to $x$ (never)

Part b is good - it could be a separate question, called "calculate powers of ten"

Christian Lawson-Perfect on Using the Quadratic Formula to Solve Equations of the Form $ax^2 +bx+c=0$ 8 years, 8 months ago

Gave some feedback: Has some problems

Christian Lawson-Perfect commented on Using the Quadratic Formula to Solve Equations of the Form $ax^2 +bx+c=0$ 8 years, 8 months ago

The non-zero right-hand sides in part a are gotchas: I'd like to have a nice part first, where the right-hand side is zero.

Could you make the coefficients in part b work so that you get integers out? You want to see if the student can work out how to deal with getting an algebraic answer, and rounding errors would be a distraction.

In part b it looks like the roots are the wrong way round - the lowest root is second.

You could split this into two questions: "use the quadratic formula to solve an equation with non-zero RHS", and "use the quadratic formula to solve an equation in terms of another variable".

Christian Lawson-Perfect on Expansion of brackets 8 years, 8 months ago

Gave some feedback: Has some problems

Christian Lawson-Perfect commented on Expansion of brackets 8 years, 8 months ago

In part a, when a[1]=1, I didn't get any brackets. Either make sure it's greater than 1, or turn off the unitFactor rule.

You need to give feedback messages for the string restrictions. "It doesn't look like you've expanded - make sure you don't use any brackets in your answer" would do.

Did you try adding expected variable names to the parts?

Christian Lawson-Perfect on Percentages and ratios - box of chocolates 8 years, 8 months ago

Gave some feedback: Has some problems

Christian Lawson-Perfect commented on Percentages and ratios - box of chocolates 8 years, 8 months ago

When ratio_dark is 1, the advice says "there are 1 dark chocolates". You could either write two versions for the singular and plural cases, or make sure ratio_dark is always greater than 1.