The BestEver Mathematics Extension Activity Explained.
(Help! Some Students Are About To Finish Two Lessons Early  What Do I Do?)
‘What do I do with the early finishers?’I am often asked this question by the teachers I work with. The question most often arises when teachers are implementing studentcentred units of work, units that tend to invite early finishers.
So  great question  what do we do with the early finishers? We need some early finisher activities! Teachercentric, procedurallybased teachers may rarely face the situation where a student completes a unit more than a lesson early, and when they do will usually direct the student to challenging textbook questions. This can be OK. However, some students see textbased ‘extension’ work as simply ‘extra work’ and not particularly engaging, perceiving such extension work to be an imposition for finishing early. Another option is to compile a bank of engaging problemsolving problems which students access when required over the course of the year. This is a great option. However, the initial effort required to set up such a bank can be considerable. Also, such a system can be challenging for ‘mobile’ teachers  those who do not have one designated classroom. The bestever, youbeaut, wowee extension activity!The best extension activity I have ever used is exceptional for four reasons:

1) It is highly engaging because it is creative and openended
2) It is very mathematical
3) It has the potential to involve all students, even those not directly undertaking the activity.
4) It requires minimal preparation.
Sound interesting?
But first, a warning!
After I announce the name of this ‘bestever’ extension activity, you will need to keep reading. This is because, on first glance, you’ll likely think “How can THIS activity be THAT good?”
Drum roll …
2) It is very mathematical
3) It has the potential to involve all students, even those not directly undertaking the activity.
4) It requires minimal preparation.
Sound interesting?
But first, a warning!
After I announce the name of this ‘bestever’ extension activity, you will need to keep reading. This is because, on first glance, you’ll likely think “How can THIS activity be THAT good?”
Drum roll …
“Make up your own worded problem.”
There! I warned you! It doesn’t sound that impressive, does it?
Believe me; the Make Up Your Own worded problem extension activity is brilliant, so please read on …
Believe me; the Make Up Your Own worded problem extension activity is brilliant, so please read on …
Worded Problem?
By ‘worded problem’, I mean a problem or question that requires a few steps, some mathematical thinking and more than a few minutes to answer; a problem that cannot be answered by a learned, mathematical procedure.
Have you ever made up your own maths worded problem for your students? (If you are a maths teacher then, yes, of course you have!) And when you are in the middle of making up a great worded problem, have you ever thought (in addition to “Gee I’m brilliant!”) … “Wow, there’s a lot of maths involved in making up these problems!” And “This is a lot of fun!!” Correct? Well, herein lies the extension activity  have students make up their maths word problem.
Have you ever made up your own maths worded problem for your students? (If you are a maths teacher then, yes, of course you have!) And when you are in the middle of making up a great worded problem, have you ever thought (in addition to “Gee I’m brilliant!”) … “Wow, there’s a lot of maths involved in making up these problems!” And “This is a lot of fun!!” Correct? Well, herein lies the extension activity  have students make up their maths word problem.
Suggested steps
The success of this extension activity is dependent on the setup. Below are some recommended steps to helping your students create their own math word problem. .
One: Guide the student into the type of worded problem to create.
 To maximise student engagement, students need to be able to choose the type of problem they create. However, the activity will fail if students choose one that is too difficult. Therefore:
 Give the student a few choices of problems (show them several text examples) but limit the level of difficulty to ‘one or two levels’ below the maximum difficulty to which the student can cope. This is critically important.
 Ask the student to create a worded problem that most class members will be able to answer’.
 Alternatively, you can point out a specific textbook example and say “Create a problem roughly to this level of difficulty”.
Note that If you don’t scaffold their choice, many students (especially boys) will attempt to create a problem more difficult than they can cope with and the mathematical benefits of the activity will be lost.
Note also that in each case it is important to explain WHY you are limiting the difficulty of their tobecreated worded problem, so they understand you want them to maximise the amount of mathematical benefit they can receive from the activity.
Two: Create a rough copy with a valid solution.
 Creating the worded problem and its valid solution is the main task.
 You will need to check the solution to ensure its validity prior to Step Three.
Three: Create a neat copy of both the problem and solution.
 The student now needs to create a neat copy. This is extremely important and paves the way for the highly engaging and mathematically valid, socialengagement aspect!
Four: Photocopy the worded problem and solution and add to your bank of extension questions.
 Once the neat copies have been submitted, photocopy both the problem and the solution.
 You may want to make several copies of the worded problem.
 Add the copies to your worded problem bank.
Five: Have other students answer the problem.
 This is where the activity really takes on a life of its own!
 If you’ve been running this activity in previous years for the same unit, then you’ll have a bank of excellent worded problems and solutions from past students.
 These problems can now be incorporated into the unit of work.
 This means that during the final few lessons of the unit, most students will work through problems that have just been created by students  current or past  who have engaged in the extension activity.
 However, to take advantage of student engagement, it is ideal that any newlycreated problems by current students are given priority when being handed to other students to work through.
Time requirement
Note that the activity will require, ideally, a couple of lessons plus homework as a minimum, assuming you want to reap the benefits of both problemmaking and social engagement. However, one lesson plus homework will be sufficient for a neat copy of the worded problem and solution to be produced ready for use at a later time.
Alternatively, the Make Up Your Own Worded Problem could be used over a threefive lesson timeframe  the first couple of lessons for students making up their own worded problems and the last couple of lessons involving all students, many creating worded problems, others answering problems, some doing both. 
For a quick explanation, watch this ...

In summary
The Make Up Your Own Worded Problem extension activity is ideal because it:
 Requires minimal preparation.
 Is portable.
 Is an engaging activity for students creating worded problems.
 Actively builds out a bank of problems which the class find engaging to work through.
 Creates social engagement with the entire class.
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Call to Action
What do you think? Is this an extension activity you already use? If not, are you tempted to try it or do you already use an extension activity that is highly engaging, requires minimal prep and is super easy to run? Whatever your situation, we’d love to hear from you.