We have added two new topics to our TopTopics question generators. One is on vectors, and the other is titled If I know…, then I know…:
Most of the question generators on the site are focussed on procedural bread-and-butter. In order to better cater for students aiming at higher grades, we have started creating generators for longer form questions. We are using compilations of these to create printable topic-focused mini exams, with worked solutions. See the Teacher Resources at G25c on Vectors for the first topic for the first mini exams we’ve made available. There are two printable “fixed” mini exams in PDF, but you can also generate further versions with dynamically generated questions. Note that these dynamic versions are also printable. The idea with the longer form generators is to do more than just randomly generate new numbers within the questions. For example, notice the difference between the following pair of questions from the same generator. Not only do the numbers change, but the vectors given and their directions are also changeable.
In this next pair, again notice how it is not just the numbers in the question that update. The question itself changes somewhat: the second involves a midpoint where the first does not, and the ratio stated in the first is 1 : k whereas it is k : 1 in the second.
A stepping-stone to factorising by inspection
Ideally, I’d like all of my students to factorise quadratic expressions by inspection, rather by using a more formal method. Before attempting to factorise by inspection, fluency in expanding brackets is essential. In particular, it is helpful if students can effortlessly expand mentally. A key hurdle in this process is finding the coefficient of the linear term, since it involves a bit more than the coefficients of the quadratic and constant terms. This applet allows students to ignore those terms and just focus on the mental arithmetic required to find the coefficients of the linear terms. Note that there are also some non-quadratic expressions here to force the students to think and prevent them from answering all of these by some kind of mindless algorithm:
We have continued to add Delta exercises to a few topics, to follow on from the Alpha, Beta and Gamma exercises. We will keep adding more over the coming months.
LOTS of behind-the-scenes work…
We have created over 100 longer-form question generators, which we’ll be able to use to create more topic-based mini exams like the one on vectors described above, but we have bigger plans for these question generators, which we’ll be able to announce in the New Year. Watch this space.