Recently I have been developing a series of activities that produce quick puzzle questions that are ideal for using as a starter to any lesson. At the moment there are 3 activities, and they are all loosely based on ideas from 7puzzleblog.com.
The first is the Mathematically Possible (QQI). This activity has students find all the possible numbers that can be made using three numbers and any operations. There is a handy hint button, which reveals how many different answers there are, and a answer button that shows all the numbers that can be made. You can generate as many as you like, change the range that the answers must belong to, and even use your own values.
This has proven very popular with my classes, and really gets them thinking. They have to be very systematic to make sure they find all the possible answers. It really gets them thinking about the order of operations as well as the different ways to combine numbers. This is probably my favourite of the activities, as it is great at an age range, and across the ability range.
The second starter activity is the Adding Challenge (QQI). In this one, students are asked to use the digits 1-9 and add them together to make a target number. The challenge is to find all the different ways to do this, using unique digits in each sum. Again, there is a hint button revealing how many different ways there are to make the target number, and an answer button that shows them all. You can choose what range you want the target number to be in, as well as whether they can use 3, 4 or 5 numbers. You can also use your own target number.
To ensure they find all the possible ways to add together numbers to get the target number, students must work systematically. It is advised that you only give them the hint after they have had a decent amount of time to try and convince themselves they have found them all first. Students enjoy this task, as it seems trivial (it only involves adding after all), but actual gets them thinking about the best process.
The third and final activity is Missing Signs (QQI). In this one, students are given a sum of numbers and the answer. However, all the signs are missing, and they must input the correct symbol between each digit to get the answer. There is a hint which gives them the first sign that is missing, and the answer is also revealable (though the answer may not be unique, this can generate a nice discussion). You can choose the range of the numbers in the sum, as well as whether you want 3, 4 or 5 numbers. There is also the choice to work from left to right one step at a time, or to use BIDMAS (or the correct order of operations).
This is probably the easiest of the activities here, as students are not challenged to find all the possibilites, thus eliminating the need for systematic work (though it might help). Some students are very good at spotting these straight away, whilst others will struggle to work it out.
All three of these activities have been well received in my classroom with my Key Stage 3 classes. After a few goes, they start to get the hang of working systematically, and the fact they need to find all the solutions definitely makes this necessary. It is a very important part of maths, that sometimes gets left by the wayside. They are also all really good for getting their mental arithmetic better, as they are working with numbers all the time.
I am a maths teacher looking to share good ideas for use in the classroom, with a current interest in integrating educational research into my practice.