Since White Rose Maths began creating questions for Diagnostic Questions last year, there have been 2,721,752 answers to White Rose Maths questions given by students all over the country. Perhaps more importantly, 1,012,072 of these answers have been incorrect.

So, with SATs on the horizon, I thought it would be a perfect time to reflect on five areas of mathematics that have proved particularly troubling to Key Stage 1 students answering our daily SATs questions – and in another blog I will do the same for Key Stage 2. For each of these areas I have selected a poorly answered question, provided some insight as to where the confusion may lie, and shared a real-life student explanation taken from the site.

A good approach might be to show one of the questions to your students in class, get them to vote with their fingers for the correct answer, have a discussion about both the correct and incorrect answers as described in this blog post here, and then set the accompanying mini 5 question quiz for homework to see if their misconceptions have been resolved. Then repeat for the other four areas.

You can find the complete White Rose Maths collection here, which contains all the Key Stage 1 and 2 daily revision questions and topic-specific quizzes at the bottom of the page. Here you will also find information about our completely free schemes of work that allow you to automate the setting of top-quality quizzes throughout the year.

I really hope you and your students find this useful.

Craig Barton – @mrbartonmaths

## Topic 1: Money

Results:

 A B C D 1% 35% 4% 60%

Discussion:

Looking at the most common choice of incorrect answer, it is quite clear where students go wrong on this question. Perhaps they have not read the question correctly, or maybe they are not aware of the possible denominations of coins. Alternatively, the complexity of the calculation involved in getting the correct answer may prove too much.

Example student explanation:

B – “because when you add 17 and 3 together it gives you a total of 20p”

Follow-up Quiz: https://diagnosticquestions.com/Quizzes/Go#/80144

## Topic 2: Representing addition and subtraction

Results:

 A B C D 10% 14% 13% 63%

Discussion:

This time the choice of incorrect answers is more spread over the three options. This may suggest students are not familiar with what this diagram represents, or have made an arithmetic slip when calculating the answers. However, I feel it is far more likely that students have failed to read the question properly – after all, if they do not spot that “not”, then all of a sudden A, B and C look very appealing.

Example student explanation:

B – “I think it’s B because 5 and 7 equals twelve and it goes in order”

Follow-up Quiz: https://diagnosticquestions.com/Quizzes/Go#/80145

## Topic 3: Fractions

Results:

 A B C D 62% 8% 26% 4%

Discussion:

Fractions are a minefield of misconceptions for students of all ages, and so it is of little surprise that Key Stage 1 students struggle here. The most common choice of wrong answer leaves us in little doubt as to the root cause of this misconception – students are unaware that the three regions must be equal in area for one-third to be a valid answer.

Example student explanation:

C – “it is because the shape is split into 3 so you instantly know that’s correct when the denominator is over 3 and the numerator is 1”

Follow-up Quiz: https://diagnosticquestions.com/Quizzes/Go#/80146

## Topic 4: Measuring

Results:

 A B C D 72% 12% 3% 13%

Discussion:

I really like this question, and it is caused my Year 7s a few issues this year. Looking at the spread of the answers there seems to be two distinct reasons why students would get it wrong. The first is simply reading the mark at the end of the car and thus failing to notice that the car does not start at zero. The second is a confusion with the units used. With the ability to accurately measure something so important across lots of different topics, this is a great question to ask students.

Example student explanation:

B – “I think it’s 8 cm because the car finishes on number 8.”

Follow-up Quiz: https://diagnosticquestions.com/Quizzes/Go#/80147

## Topic 5: Mental arithmetic

Results:

 A B C D 8% 69% 15% 8%

Discussion:

This is a really interesting question which on the surface test two separate skills – students’ ability to work out the answers to the calculations, and their knowledge of what the signs mean. However, reading through students explanations suggests the issue lies more with the tendency of students to write calculations as they would write sentences. So, 30 – 1 = 29, and then continue on the same line by adding 1. It used to infuriate me when I saw Carol Vorderman doing something similar on Countdown back in the day, and it seems the issue lingers on.

Example student explanation:

C – “It is C because 30-1= 29 29+1= 30 and that is why I think it is C”

Follow-up Quiz: https://diagnosticquestions.com/Quizzes/Go#/80148