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 2 students answering our daily SATs questions – and in another blog I will do the same for Key Stage 1. 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: Factors and Multiples Question link: https://diagnosticquestions.com/Questions/Go#/32836

Results:

 A B C D 21% 13% 60% 6%

Discussion:

The confusion between factors and multiples is a common one. Both answers A and B suggest students are muddling up these two related concepts. This question is made all the more challenging by the fact the correct answer is one of the numbers given in the question. Students’ knowledge of multiples needs to be very secure to get this lovely question right.

Example student explanation:

A – “I think that 2 goes into both 4 and 12 as 4 and 12 are both even meaning they are in the twos.We can check this by doing 2×2 and 2×6 as they both get you twelve.

Follow-up Quiz: https://diagnosticquestions.com/Quizzes/Go#/50500

## Topic 2: Percentages Question link: https://diagnosticquestions.com/Questions/Go#/33473

Results:

 A B C D 23% 59% 7% 11%

Discussion:

This question catches out any student who does not pause to think. Answer A suggests students have seen 20%, seen 60, and just assumed they are being asked to work out 20% of 60. Answers C and D are also interesting, implying students may have spotted the correct method to use, but were then let down by their arithmetic skills.

Example student explanation:

A – “Finding 20% of a number is the equivalent to dividing a number by 10 then multiplying it by 2. So, I did this with 60. 60 divided by 10 = 6 and 6 x 2= 12 and that is how I got the answer of 12.”

Follow-up Quiz: https://diagnosticquestions.com/Quizzes/Go#/50503

## Topic 3: Area and Perimeter Question link: https://diagnosticquestions.com/Questions/Go#/32828

Results:

 A B C D 19% 11% 58% 12%

Discussion:

Here we have another example of students confusing two related concepts, this time area and perimeter. Answer A has lured in any students who failed to make that distinction. Interestingly, students answering B may have a sense that perimeter is to do with adding, but have failed to account for the other two sides. Students answering D may be guessing based on the diagram, or made an arithmetic error during the division.

Example student explanation:

A – “I know to find the perimeter you need to times length by width I also know that the perimeter of the rectangle is 24 cm ; 3 is in my multiple choice and I know that 8 x 3 = 24 so I now know what the width is.”

Follow-up Quiz: https://diagnosticquestions.com/Quizzes/Go#/50504

## Topic 4: Fractions Question link: https://diagnosticquestions.com/Questions/Go#/33470

Results:

 A B C D 14% 10% 38% 38%

Discussion:

This is one of my all time favourite questions, because each answer clearly reveals a different misconception, and to get this question correct students must be secure in more than one area of mathematics. Answer C suggests students have ignored the inequality sign and just made the two fractions equivalent. Answer A implies students have spotted that a multiplying factor of 5 has been used on the numerators, whereas students choosing answer B may understand the inequality sign but not know how to order fractions. A great question!

Example student explanation:

C – “I think it is this answer because you work out how many 4’s go into twenty and that is 5. So with fractions whatever you do to the top you do to the bottom. Now you divide 5 by 35 because it is the same as saying ?×5=35. Once you have got your answer I can assure you it will be the right one.”

Follow-up Quiz: https://diagnosticquestions.com/Quizzes/Go#/50508

## Topic 5: Angles Question link: https://diagnosticquestions.com/Questions/Go#/34576

Results:

 A B C D 51% 15% 18% 16%

Discussion:

Another fantastic question for highlighting specific misconceptions that students have. Answer C suggests that students understand that angles on a straight line add up to 180, but have not read the question carefully enough. Answer B implies students have correctly worked out the size of each angle, but have chosen the wrong one. Finally, students who chose D may well be simply going off inspection. Once again, to get this question right, you really need to know your stuff!

Example student explanation:

C – “I know the answer is 140° because angles on a straight line total 180°. I need to find out how much the larger angle is and I know it is 40° larger than the smaller angle of B so if I take 40° away from 180°(the total) I will get my answer of 140° (C)”

Follow-up Quiz: https://diagnosticquestions.com/Quizzes/Go#/50509

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 Question link: https://diagnosticquestions.com/Questions/Go#/33364

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 Question link: https://diagnosticquestions.com/Questions/Go#/32989

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 Question link: https://diagnosticquestions.com/Questions/Go#/31758

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 Question link: https://diagnosticquestions.com/Questions/Go#/33374

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 Question link: https://diagnosticquestions.com/Questions/Go#/32997

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