5 ways to deal with questions that have multiple correct answers

If you are not careful, they can trip you up!

This newsletter is made possible by Eedi. Check out our brand-new set of diagnostic quizzes, videos, and practice questions for every single maths topic, ready to use in the classroom, and all for free, here.

Recently I observed a lesson where the teacher asked her students the following question:

This is a good question, allowing students to generate their own examples. But there is an issue: how do you assess students’ understanding?

In this case, the teacher opted to Cold Call one or two students to find out what they got, and promptly wrote their answers up on the board. But she was then met with a sea of hands from the other students desperate to know if their choices of answers were also correct.

In a different school, I observed a teacher give her students the following slide and ask them to use the numbers to generate an improper fraction:

This teacher chose to ask students to show their answers on their mini-whiteboards. But with 30 students in the class and at least 8 different answers visible around the room (some of which were correct, some of which were not), it wasn't easy to check the understanding of all students accurately without spending time looking at every board, and indeed some wrong answers were not picked up on.

Both of these questions share the feature that there are multiple (sometimes an infinite) number of possible correct and incorrect responses. So, how can teachers accurately assess students’ understanding of questions like these in a reasonable timeframe?

Here are 5 ideas:

1. Think carefully when you ask them

I like questions like this where students need to generate their own examples. I think it is a fantastic check for understanding and can provide the catalyst for good discussions, either at a whole-class level or between pairs of students. But I also think there is a time and a place for them. For example, I don’t think including them in the Do Now is a good idea. You want the start of the lesson to be short and snappy, and if you find you need to take a relatively long time checking the understanding of a certain question because it has multiple possible correct answers, then you may find that portion of the lesson begins to unravel.

2. Adapt the question

Most questions with multiple answers can be adapted so there is only one correct answer. In the equivalent fractions example, students could be tasked with finding equivalent fractions with specific numerators or denominators. In the improper fractions example, the constraints could be tightened so that the improper fraction has to have a specific numerator, or must lie between two values. This makes checking for understanding much easier.

3. Use Adam Boxer’s approach

When Science teacher, Adam Boxer, came on my Mr Barton Maths podcast, he described how he approaches assessing questions with multiple answers. Adam begins by collecting a series of correct answers from his students, either via Cold Call or mini-whiteboards, and writing them up on the board. He then quickly adds any other common correct answers that he predicts students might have put, alongside any incorrect ones, carefully explaining why the first group are correct and the second group are wrong. He then tells his students that if they have a different answer and they are not sure whether it is right or wrong to put a star by it and ask him whilst he is circulating during the lesson. This stops Adam from having to deal with a load of questions in the moment.

4. Peer assessment

Students can be great at checking each other’s work when there are multiple correct answers. I give them the following instructions:

• Swap your book/board with your partner and check their answers

• Any that you are sure are correct, give a tick

• Any that you think might be wrong, put a star

• When both of you are ready, discuss any answers marked with a star and see if you can reach an agreement

• If you can’t, put your hands up and we will discuss these as a class

Of course, this approach does not guarantee a wrong answer will not slip through the net - after all, both students might share the same misconceptions - but I find it does catch most issues, and those starred questions always provide a fertile catalyst for whole-class discussions.

5. Use Give an example of...

Give an example is a framework for learner-generated examples that I love. For the first question in this post, it would look like this:

Give an example of…

Here students are challenged to come up with:

• Multiple examples

• A boundary example

• A plausible non-example

Students would then assess each other’s work using the strategy discussed in point 4 above.

What do you agree with, and what have I got wrong?

Let me know in the comments below!

🏃🏻‍♂️ Before you go, have you…🏃🏻‍♂️

1. … checked out our incredible, brand-new, free resources from Eedi?

2. … read my latest Tips for Teachers newsletter about challenging students to think of a peculiar example?

3. … listened to my most recent podcast with Kris Boulton about Atomisation?

4. … considered booking some CPD, coaching, or maths departmental support?

5. … read my Tips for Teachers book?

Thanks so much for reading and have a great week!

Craig