#### Enrichment session 11

We have added a set of 25 slides and an associated GeoGebra applet for Enrichment session 11, titled*Imaginary numbers*, which looks at the need for imaginary and complex numbers, the Argand diagram, properties of the modulus and argument, and how these fit in with students’ existing understanding of multiplying directed numbers.

#### Updates to R5a – Dividing a quantity in a given ratio, and expressing the division of a quantity as a ratio

We have updated this GeoGebra applet included with topic R5a to include a couple of extra question variants. I typically prefer to handwrite worked examples on a whiteboard/chalkboard live in class, rather than use a pre-made step-by-step worked example on an interactive whiteboard. With live-handwritten worked examples, however, it is impractical to demonstrate extra examples if needed or to produce **faded examples** (examples where the working is only partially complete, with students needing to do the rest). This style of applet is great for guidance fading, as you can generate new examples at the click of a button, and then drag the slider down to adjust how much working to show in the faded example.

This applet is also great for fans of **variation theory** (and **minimally different questions** in particular). You can easily investigate how the working is affected when you either fix the amount of money and adjust the ratio, or keep the ratio fixed and adjust the amount of money.

We have also created the following GeoGebra applet that generates a particular style of question on ratio and distance. Again, guidance fading with this applet is easy—simply drag down the slider to reveal steps of working:

#### TopTopics, Random Question Generators, and Skills Drills worksheets

Questions on **percentages** and **simultaneous equations** have been added to TopTopics:

We have included quick-access sets of **random question generators** under the Teacher Resources for the following related topics: R9a, R9b, R9c, R9d, R9e, A19a (three levels of difficulty), A19b, and A19c.

We have also added **skills drill worksheets** for some of those topics

#### Mixed-topic problem-solving

We have begun creating what we’re calling *Shortcut* problems such as that shown below, and linked to these from within the Teacher resources for the relevant topics. These can be solved with very little working if students understand how to use the information given at the start of the problem. It is possible to solve these *without* using the given information, but this will generally be far more laborious.

The purpose of the question sets is to encourage students to consider the information available to them rather than jump to a procedure they are familiar with. For example, in the following case, many students “auto-pilot” their way through a method that involves them calculating the value of *c*. This can in fact be avoided by considering what is meant by *gradient*.