This three-book series contains a range of open-ended maths problems based on fun and engaging stories. The problems are placed into real-life everyday contexts in which the students are likely to find themselves. It’s important for students to know that open-ended maths problems have more than one answer and that students often need to add to the information to be able to solve them. For example, if the problem is: ‘If I have 30 tablets, how many days will it take me to finish them all? – students need to decide how many tablets the patient is required to take each day, to work out how many days it would take to finish the course. They could work out answers for 1 a day, 2 a day, 3 a day, etc.
A benefit of using open-ended problems is that all students in one class, with their range of experiences and mathematical knowledge and skills, can be working on the same problem. This is because these problems can be solved using a variety of strategies, which means students can tackle them at their own level.
You will notice that the problems based on the stories have accompanying support and extension questions. This allows for further differentiation. If there are students who seem to be struggling with the main problem (this will often happen when you are first introducing these kinds of problems) it is a good idea to have a support question on hand for them to attempt first. In my experience usually, once students have worked through the support question they are then ready to move on to the main question. The extension questions are there for the students who solve the main problems quickly to challenge them further.
Reflection time is important when implementing these lessons, not just at the end of a lesson, but also during it. It is important to stop at regular intervals and share how students are tackling the problems. This allows students to share successes and to learn about a range of different strategies. It also helps those students who may be struggling or are using a strategy that isn’t working for them.
The questions that you pose during these lessons are also important. These questions can help students delve deeper or think more critically. For example:
- What would happen if…?
- Can you do it a different way?
- How do you know….?
- Have you found all the answers?
- How could you make this problem more challenging/easier? (This question encourages them to take responsibility for their own learning.)
- Prove it! Convince me!
- Can you show me/explain to me how you got your answer?
- Can you find a pattern?