Transition to university

Bradley Bush on Expansion of brackets 8 years, 6 months ago

Saved a checkpoint:

before removing the gap fill

Christian Lawson-Perfect on Surds simplification 8 years, 6 months ago

Gave some feedback: Has some problems

Christian Lawson-Perfect commented on Surds simplification 8 years, 6 months ago

The prompt for part b is hopelessly generic! "Match each product with the equivalent surd" might do, but that's not quite right either. Also think about how the numbers are laid out - would it be better to put the products down the side and collected surds on top? As it is, I can rule out a few combinations without thinking, like $\sqrt{44}$ is obviously not equal to $\sqrt{30}$.

Part c: I would repeat $\sqrt{n} = $ before the gap-fill. As stated, how is "$\sqrt{300} = \sqrt{100} \times \sqrt{3}$, so $\sqrt{300} = ?? \times \sqrt{3}$" different to $\sqrt{100} = ??$". Maybe just $\sqrt{300} = \text{[gapfill]} \times \sqrt{3}$ would do.

Part d: for "simplify" to make sense here, I think you need to give the hint that they can be simplified to whole numbers.

Part e: instead of [1] and [2], write $a$ and $b$. I got $\frac{\sqrt{6}}{\sqrt{3}}$, which it expected me to write as $\frac{\sqrt{18}}{3}$. I'd write that as just $\sqrt{2}$. Can you set it up so there's only one way of writing it? Making sure the top and bottom of the original fraction are coprime might do it.

Part f: I had to reduce the fraction - you should say that in the prompt. "Rationalise the denominator of this expression and reduce to lowest terms".

In parts g, h and i, the big expression is REALLY big - have you formatted it as a header? I don't think you need the "= ?" bit, or "and select the correct answer from the list of options". 

None of the parts of this question really lead on from each other - you could split this into several smaller questions.

Advice

Some numbers not in LaTeX in part a. "Roots are necessary but not sufficient conditions for surds" isn't completely clear - I'd say "all surds are roots, but not all roots are surds".

Part e: this might be incredibly pedantic, but does "the denominator is $\sqrt{6}$" sound better than "\sqrt{6} is the denominator" to you?

A few sentence of a similar form to "This gives the final answer as:"; I would say "So the final answer is:". 

Some wordy explanation of what's happening at each step, or a description of the plan of attack, in part f wouldn't go amiss.

Part g: It's not true that you can't multiply by those things, it just doesn't help. Get someone else to read that paragraph and have a go at rewriting it: it's a bit long and easy to get lost in. There's an unhelpful "simply" in there, too.

I have a few problems with this sentence: "To be able to do a question like $\frac{2}{\sqrt2+\sqrt8}+\frac{1}{3}$ which requires you to add fractions, you need to have the same denominator." 

• $\frac{2}{\sqrt2+\sqrt8}+\frac{1}{3}$ isn't a question, it's an expression.
• "you need to have the same denominator" isn't a complete phrase - the same as what? 

Try:

To add $\frac{2}{\sqrt2+\sqrt8}$ to $\frac{1}{3}$, you must put write both terms with the same denominator."

Likewise, "the question is now $\frac{2}{3\sqrt2}+\frac{1}{3}$" isn't right. You could say "the expression is now ...".

Aiden McCall on Algebra vocabulary 8 years, 6 months ago

Gave some feedback: Needs to be tested

Christian Lawson-Perfect on Surds simplification 8 years, 6 months ago

Saved a checkpoint:

I've reworded the statement slightly.

Hannah Aldous on Completing the square 8 years, 6 months ago

Gave some feedback: Needs to be tested

Christian Lawson-Perfect on Expansion of brackets 8 years, 6 months ago

Gave some feedback: Has some problems

Christian Lawson-Perfect commented on Expansion of brackets 8 years, 6 months ago

The question statement is a bit of a run-on sentence. Try something like:

Expand each of the expressions below. 

Multiply each of the terms inside the brackets by the term outside the brackets.

One of the GCSE textbooks might have a good formulation of this prompt that you can use for inspiration.

Why have you made your own part headers instead of splitting each expression into its own part?

Think about the difficulty curve for these problems: you should start with a very simple example, and slowly add more complicated elements, one at a time. So you might start with $2(x+1)$, then follow that with $x(x+1)$, which requires multiplying $x \times x = x^2$. Think about how games do this: you begin with very simple challenges while you get used to the controls, then more elements are added in as you become more secure in those.

While randomised numbers are good, this question is about algebra so maybe restrict coefficients to single digits. I don't know my 17 times table! Don't let students fail for the wrong reason: a mental arithmetic error is a distraction here.

The advice is written in the passive voice: "Brackets are expanded by..." Give a concise explanation of what "expanding brackets" means - you multiply terms so that no brackets are left - and then give a few generic examples, such as $a(x+2) = ax + 2a$.

Christian Lawson-Perfect on Percentages and ratios - box of chocolates 8 years, 6 months ago

Gave some feedback: Has some problems

Christian Lawson-Perfect commented on Percentages and ratios - box of chocolates 8 years, 6 months ago

Statement

"There is an equal distribution of chocolates throughout the box." seems either clunky or ambiguous to me. Maybe "The box contains equal numbers of each kind of chocolate."

Parts

In part c, you want each kind as a proportion of the remaining chocolates. You could say "what percentage of the remaining chocolates are plain?"

In part d, put the i) and ii) in italic or bold to make them stand out.

In part e, I would prefer "$\Pr(\text{Nutty chocolate picked}) = $" to "Probability = ". Set precision restrictions on the gaps - 2 decimal places for the first one, and 0 decimal places for the second one.

Advice

"Whole complete" is a tautology. You could say "100% represents the whole box of chocolates".

In the advice for part b, rather than "You know that each type of chocolate is represented equally in the box, so you need to find 20% of the original number of chocolates." you could say "We worked out above that each type of chocolate makes up 20% of the box, so we need to work out 20% of {chocs}".

In part c, I'd replace the first sentence with "There are now {type} fewer chocolates in the box, leaving {chocs}-{type} = {minusc}."

Part d: NEVER use the word "simply"! No matter what you're talking about, there will always be a student for whom it isn't simple, and saying so won't make them feel great. Cutting out the word "simply" leaves a perfectly acceptable sentence. And again you've got "amount" where it should be "number". "Amount" is used for continuous measurements, while "number" is used for discrete numbers of objects.

Part e: "The amount of chocolates in the box is equal to {a}" is a clunky way of saying "There are {a} chocolates left in the box". You might want to put "(to 2 decimal places)" after the calculation.

You've got some stray bits formatted as headers instead of paragraphs.

Christian Lawson-Perfect commented on Basic arithmetic operations: addition and subtraction 8 years, 6 months ago

Did you do something to make the revealed answers for part c work? It looks OK on my PC now.

Elliott Fletcher on Laws of Indices 8 years, 6 months ago

Gave some feedback: Needs to be tested

Lauren Richards on Surds simplification 8 years, 6 months ago

Gave some feedback: Needs to be tested

Bradley Bush on Expansion of brackets 8 years, 6 months ago

Gave some feedback: Needs to be tested

Stanislav Duris on Basic arithmetic operations: addition and subtraction 8 years, 6 months ago

Gave some feedback: Needs to be tested