A common misconception around maths is that there is always a single ‘right’ or ‘wrong’ answer. Yet the richest mathematical experiences give teachers and students opportunities to explore concepts and deepen their knowledge. In maths, problem-solving questions are a great way to bring about these experiences. But with so many resources now available, how do you know if you’ve picked out a good problem?
To help you on your way, we have identified five factors that make a good maths problem-solving question.
1. A good maths problem-solving question is open
Some of the best maths problems are open questions that teach students that there are many different ways to tackle a challenge. A good example of an open maths question is “How many pennies can fit into a classroom?” Students can start by measuring the size of the classroom and measuring the volume of the pennies before using that information to make an estimate. When working through an open question like this, it is important to emphasise to students that understanding the process of solving the problem is far more important than getting the ‘right’ answer.
2. It’s exploratory
Exploratory questions encourage students to solve problems by developing and testing their ideas. A good exploratory problem will encourage students to sniff out patterns early on. The best problems may even surprise them. A particularly devilish example of this involves plotting points on the circumference of a circle. Based on the pattern below, how many regions would a circle with six points have?
After noticing the initial pattern, which suggests that each new point doubles the number of regions, many students are likely to guess 32 regions for the next circle along. And yet, when you plot six points you somehow get 31 regions! (Count them if you don’t believe us!)
3. It’s playful
The most addictive maths problems feel like play rather than work. They have carefully designed rules that embed mathematical concepts in an engaging way. Playful problems may have elements of randomness, strategy and healthy competition. One way to introduce playful problems to the classroom is through board games. If you are hunting for maths-based board games to try with your students, look no further than our recent blog post on Five Fun Maths Board Games.
4. It has a low-floor but also a high ceiling
Problem-solving should be accessible to all students while taking their individual levels of knowledge into account. A low-floor, high ceiling problem is one that possesses low-barriers to entry, so that every child can attempt it but also has several layers of depth that challenge higher attaining students. A myriad of websites offer ‘low-floor, high ceiling’ problems – we are especially fond of NRich. You will also find several extension problems that are based on the same principles in Maths-Whizz’s Teachers’ Resource.
5. It’s hands-on
Cast your mind back to those interactive museums you used to visit as a child which let you touch the exhibits. Remember how engaging they were because you got to use all your senses? In the same way, good problems allow students to experience mathematics with all their senses – to touch, see and feel mathematical concepts. YouCubed’s paper folding exercise is a great example of how to bring concepts like shape and area to life using physical materials.
Want to super-charge your lessons?
Then look no further than the Maths-Whizz Teachers’ Resource. We have over 1240 interactive exercises and worksheets that will challenge your high-performing students, while also giving your struggling students the attention they need. For more information, click here.