12 September 2014

Starters and Inequalities

I recently participated in a Twitter chat about lesson starters. Initially a forum for sharing ideas, it turned into a debate about whether starters are necessary in maths lessons. In my opinion there is no right or wrong lesson structure - every teacher does what works best for them and their students. For me and my students, starters work well. I use them in the vast majority of my lessons.

What is a starter?
Presumably in a lesson without a starter, students enter the classroom, sit down and immediately listen to an exposition. In a lesson with a starter, students do some maths immediately on arrival, before the main teaching element begins. Lesson starters (or 'bell work') take many forms. Every teacher has a different approach.

My starters have one of three purposes:
(a) recap and practice of what students learnt in the previous lesson.
(b) prerequisite skills check to assess a starting point.
(c) a hook to engage and intrigue.

Starters also help to awaken my students' brains - they get into a mathematical way of thinking before I start teaching them something new. 

When students arrive I greet them at the door with their starter, usually a printed question. They're used to this format so they sit down and start immediately. They do the starter independently while their peers arrive and I set up.

My starters are normally very short - no more than 5 minutes - because this minimises the variation in how long students take to complete them. A starter that takes anywhere between 10 and 20 minutes to complete could be problematic (early finishers are left waiting) but in a starter that takes 3 - 5 minutes this is less of an issue. The early finishers stick their completed starter in their books and by the time they've done that, the rest are ready so we then review it as a class. There's rarely a point at which students are not occupied.

Sometimes starters lead to interesting questions. Sometimes they result in me changing my lesson plan on the spot. This is a challenge for me, but I'm getting better at thinking on my feet as I get more experienced.

Typical Examples
I'll give you an idea of what my typical starters look like. Bear in mind, as I said earlier, every teacher does this differently. I've picked a topic at random: in three lessons on inequalities with Year 10 last year, these were my three starters.

In lesson 1 we're solving linear inequalities and representing solutions on number lines. They've done this before so I start with a skills check to make sure they remember the basics:

Inequalities starter - lesson 1

In lesson 2 we're going to start looking at graphical inequalities - for this they need to know how to plot straight lines so I give them another skills check starter to see if I need to go through this:

Inequalities starter - lesson 2

In lesson 3 we're looking at some harder graphical inequalities so I want to remind them of what they did in the previous lesson and give them a taste of the sort of question they will be seeing today:

Inequalities starter - lesson 3

The 'list the integer coordinates' part of this question is new to them so requires some thinking. I expect it to generate questions which link smoothly into my exposition. I like my students to think that the direction of the lesson is prompted by the questions that arise during the starter, when in reality I've normally pre-empted their questions and planned accordingly.

So you can see that my starters are nothing special but to me they are an essential part of the lesson.

Exam Questions
Sometimes, particularly at A level, I use the starter as an opportunity to do an exam style question. For example if I teach a Year 12 lesson on finding the equation of a circle using these excellent activities from Mathematics Assessment Project, then the next lesson I would give students an equation of a circle past exam question on arrival. This gets them used to the format and wording of exam questions and recaps what they learnt in the previous lesson. A single 4 or 5 mark exam question is the perfect length for an A level starter.

With GCSE classes, I sometimes give a QWC exam question (a 'star' question) as a starter.

More Inequalities Starters
So now I've described my typical starters, let's look some alternative activities. I've featured three starters here, again focusing on inequalities.

Most maths teachers are familiar with Transum's 'starter of the day'. What I like about the Transum website is that starters are also listed by topic. Here's an example of an inequalities starter.

'Less than' by Transum

Short card sorts can work well as starters. This number line card matching activity is suitable for an inequalities lesson.

There's also a great card match (and other excellent activities) in Evaluating Statements about Number Operations from Mathematics Assessment Project. Some of these might be too long for a starter but would be suitable for a main lesson activity.

When is the statement true? - Mathematics Assessment Project

If you're looking for more main lesson activities on inequalities then these two resources are superb: Introduction to inequalities by Project Maths (activities towards the back of the pdf) and Defining Regions Using Inequalities by Mathematics Assessment Project. There are lots more resources in my algebra resources library.
Project Maths

Sources of Starters
These ideas are just the tip of the iceberg. There are loads more sources of starters - a classic is 30 Maths Starters from Subtangent. MathsPad has some great interactives like this Simplifying Magic Square. FlashMaths has good interactives too. I could go on but there's no point reinventing the wheel. Colleen Young has an amazing website 'Mathematics Starters and Plenaries' which I highly recommend.

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