IGCSE Booklets Part 2: How I Make Them

In part 1 of this series I discussed why I have been won over by the humble booklet. In this post I am going to expand on how I design my booklets and what I include in them. I will include images from some of the booklets in the post, but I am not able to share whole booklets as I use some material that I do not have permission to share. I will reference to the main sources I use for each section of the booklet, and give some images of the types of resources used. You can find one full example on Coordinate Geometry here.

The front page is fairly simple, with the unit number and title, a space for students to write their name, and the video numbers linked to the topic on www.corbettmaths.com. I also have a back page to all the booklets which has references to websites I use to put them together.

The front page of the Advanced Trigonometry booklet.

The back page of a booklet contains references to commonly used materials. Not all will be used to create this booklet, but they are sites I use regularly.

Within the unit I start by breaking down the objectives into individual skills that students will need to master. So, for example, in the advanced trigonometry unit there is a skill for sine rule, one for cosine rule and one for identifying which one to use. Within each skill I will break them down into smaller sub skills if necessary. So sine rule is broken down into finding missing lengths and finding missing angles.

So the final break down of skills and sub skills for the advanced trigonometry unit is:

• Right Angled Trigonometry (recap of prior knowledge)
• Angles bigger than 90 (includes labelling triangles and calculator skills)
• Sine Rule (split into lengths then angles)
• Cosine Rule (split into lengths then angles)
• Area of a Triangle (finding area then finding other missing information)
• Choosing the Rule
• Bearings
• Trigonometric Graphs
• Exact Values (the standard results)
• Other Exact Values (given value of sin x find cos x)

With each skill identified, I go about planning them following the same format.

Required Prior Knowledge
The skill starts with a short item on the required prior knowledge for that particular skill. Sometimes this is a recap of a prior skill from the current unit (eg factorising quadratics before solving them). Sometimes it is something from an earlier unit (eg solving equations before sine rule).

As can be seen in the examples below, these take a variety of forms. Some are simply questions on processes that need to be secure. Some are ideas that will lead into the current skill. One of the things I need to work on is developing these to cover ALL the prerequisite knowledge and skills that have not been covered already in the current unit. 

The point of this section is to help me and students identify if they can do the necessary skills required to do the new skill. If they can't do them, then the lesson will adapt to address those issues first, before moving on with the new skill. There is little point in teaching students to solve the Sine Rule, if they cannot solve equations with the unknown as part of a fraction.

It is worth noting here that these are not meant to be lesson starters. I use a retrieval starter of Last Lesson, Last Unit, Further Back as the 'Do Now'. In single periods I have started doing a single retrieval question rather than four, usually from last lesson. I do sometimes plan the Further Back question to address any required prior knowledge too, but this might be a couple of lessons ahead of teaching what requires it. 

Notes
Next there is a section for notes. In terms of teaching, this is when I will explain the new skill, and give any definitions, etc. 

The notes section is structured as a fill in the gaps exercise, usually with a sentence starter given, and then some space. I also have prepared powerpoint files to go alongside the booklets (though I have stopped using them as much) which line up with the notes section. I now prefer to say and explain the idea and give students time to fill in the gaps themselves. 

I have been thinking a lot about the use of non-examples at this point of the booklet, and although they are not embedded in them at the moment, I will be adding space for these in the next iteration of them. I am thinking of adding Frayer Diagram templates as well as a way to structure students notes on the definition, characteristics and examples and non-examples of concepts. I have used these a little at the end of units as a reflection activity, but I think they have potential to form part of the actual notes students produce as well, and would push me to think more deeply about non-examples.

Example Problem Pairs
The notes section is followed by sets of Example Problem Pairs. These largely follow the idea set out by Craig Barton here, though I have not been so careful with making them minimally different yet. Perhaps I will adjust these moving forward.

Printed are both the example and the your turn problem, as you can see below. This allows me to give students the questions (no time spent copying out questions), and include any images so they don't need to draw them. It also allows me to include graph paper when necessary, along with any other diagrams (for example they can write straight on transformation examples).

Of course this does introduce the potential issue of students rushing ahead and not paying attention to the example (I will discuss how I deal with this in Part 3).

The biggest issue I have found with this layout is that I need to make sure I include enough space for students to write their answers! They tend to require a lot more space than I do to answer a question (bigger handwriting is one problem, but also the fact they are novices so can't "see" the way forward as easily and so jot things around a bit more). This is one of the things I take note of when annotating my copy of the booklet for adapting the following year.

I have also just finished reading the excellent Making Every Maths Lesson Count by Emma McCrea, and recently listened to the Mr Barton Maths Podcast with Michael Pershan, both of which mention Algebra by Example. In particular they mention the use of incorrect examples, and this is something I want to explore further within the booklets. Getting students to review an incorrect example, or compare an incorrect with a correct example, sounds like a great way to get them thinking about the details a little more.

There is also incomplete examples, where students have to fill in the missing bits, as you gradually reduce the amount that is given to them. Booklets would be great for this as you can have them all printed a ready for students to write on.

The number of example problem pairs will vary depending on the skill. For example, in using the sine rule to find lengths, there is a single example problem pair. But in graphing regions using inequalities there are a total of 8 example problem pairs. These are included to go through the different variations of the types of questions that can occur. If a class is moving on fine though, I might push them to do the remaining examples themselves, rather than working through them.

Exercise
After the example problem pairs, there will be an exercise. This will probably be a fairly classic set of questions to practice the new skill they have just learned. I do sometimes make use of the sets of questions from Variation Theory, but also use CorbettMaths, Dr Frost Maths, 10 Ticks, exercises from our ebooks, Pixi Maths and my own site Interactive Maths. These are not the only ones I use, as I also get stuff from TES and Resourceaholic, and have found the old textbooks great for some of these too.

I like to include more than enough practice in here for students to do, so will generally have much more than I need. This is also the bit of the booklet where students write in their own exercise books to save space, so I can bunch questions up as much as possible. This allows me to choose what I want them to do based on how they are understanding the material.

For each skill there is also an accompanying powerpoint that has the answers to most of the exercises.

Further Practice
Sometimes I will also include links to even further practice for students. Usually this is to a page in their textbook or CorbettMaths, but also CIMT. We very rarely use these in class, and they are provided as extra for students to do in their revision outside of class.

Test Your Understanding?
These are not always included in the skill, but when they are I use them as a quick way to check before moving on to another subskill, or before more independent practice. These will usually be answered on mini-whiteboards, and are there in case students struggled with the your turn and need a little more guided practice before moving on to the exercise. They normally include 4 questions similar in style to the example problem pair.

Sometimes instead of including these in the booklets, I have used diagnostic questions as part of the powerpoint, which I project and students answer by raising the number of fingers that correspond to the answer they think is correct.

Another sub-skill?
Sometimes a skill is broken into smaller sub-skills. Rather than creating booklets with 20 skills for a unit (which I feel can be a bit overwhelming) I will not relabel these sub-skills, but rather incorporate them into the bigger skill. For example, in the skill of Sine Rule, there is a section on finding lengths and then on finding angles.

I also make a lot of use of these in the first skill of a unit when that is largely prior knowledge. For example, in the unit on Quadratic Equations the first skill covers expanding, factorising and use of the graphical calculator. I do not want to dedicate a whole skill to each, but this does mean there is some material on these if I discover I need to reteach some bits of it.

Each new sub-skill will follow largely the same layout as above. I am more likely to use Test for Understanding instead of an exercise if there are lots of sub-skills that build up, and then include the exercise at the end of the whole skill.

Activities
I sometimes include activities like matching activities, or odd one outs. These will often cover the whole skill and so will be included at the end of the skill. Sometimes this is just a blank space with a title to stick in the cards. Other times there is more structure. It depends on the activity. This is where I still get to include some of the great activities you find on TES.

Challenge
At the end of the skill there is usually a challenge section. What I mean by challenge is that it is not your "ordinary" style questions. This is where I include things like Maths Venns, stuff from Don Steward, Clumsy Clives, Arithmagons, stuff from nrich, UKMT questions. This is not something I included from the beginning so not all booklets have them yet, but I will be adding as I find new things and adapt them the next time I teach the unit.

More so than other sections, this is the one I find most useful to have available at any time, as I can push students who have demonstrated a basic understanding on to these tasks to develop their understanding further. 

Unit Review
At the end of the booklet I like to include a unit review section. This will always include a Unit Review Worksheet which basically has a two questions on each of the sub-skills from the unit. It is meant to be used by students to assess themselves on what they can and cannot do.

There are also sometimes activities that cover the whole unit, though these really do depend on the unit in questions.

Exam Questions
For some units I also included a section of exam questions on the topic at the end of the booklet. We already have a set of documents of exam questions by topic, so this is not something I have done religiously as they already existed. However, I am starting to think that including them at the end would remind me to make use of them more often, and would truly enable students to have everything in one place. 

Concluding Remarks
In part 1 I discussed 10 reasons why I have been won over by the use of booklets. Some of these are determined by the way I make the booklets (e.g. having everything in one place). Although there is definitely an initial time commitment to putting these booklets together in the first place, in following years you only have minor tinkering to do for a whole unit, which allows you to focus on how you can best use the booklet in your teaching, and how you can use that extra time made available to teach better. In part 3 of this series I will be exploring how I go about using the booklets I produce, both in planning and in class.

Do you use booklets in your teaching? What do you include in them? Do you do things differently to me? If you don't currently use booklets, could you see any benefits in having a resource like this?