Year 6 Fractions Quiz: 15 Items on Unlike Denominators, Built Around the "Add the Denominators" Error (Draft)

Interpretation. I aligned this draft to the National curriculum in England: mathematics programmes of study (GOV.UK), Year 6, Number - fractions. This is inferred from "Year 6 maths (UK National Curriculum)"; I assumed England. The quiz has 15 items (8 multiple choice, 5 short answer, 2 extended response) worth 25 marks, for 30 minutes. It is a draft for you to review and trial. All contexts and names are invented, and no exam questions were copied.

Objectives and weighting

The official wording for Year 6 is: "use common factors to simplify fractions; use common multiples to express fractions in the same denomination", "compare and order fractions, including fractions >1", and "add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions". The non-statutory guidance says pupils should start with fractions where one denominator is a multiple of the other and progress to varied and increasingly complex problems. I used that to order difficulty.

Code	Objective (my split of the wording above)
O1	Compare and order fractions using common multiples as a common denominator
O2	Add fractions with different denominators, including mixed numbers
O3	Subtract fractions with different denominators, including mixed numbers
O4	Solve word problems that need O2 or O3 (inferred from "varied and increasingly complex problems" in the guidance)

Weak-area weighting. Nine of 15 items (60%) are built on your two reported gaps: direct adding of denominators (items 1, 3, 5, 9, 10) and word problems (items 6, 7, 14, 15). That is the top of the 40 to 60% range. The other six items check comparison, regrouping and equivalence, so a pupil who fixes the headline error is not given easy marks.

Item table

Difficulty is my judgment (inferred), aiming for about 30/50/20. The actual split by item is 3 foundation (items 1, 2, 9), 7 core (3, 4, 5, 6, 10, 11, 13), 4 stretch (7, 8, 12, 15), and item 14 spans core to stretch, so it runs slightly harder than planned. Marks follow the convention that a correct final answer earns the mark even if the working shown is wrong, and a mixed-number answer must pair the integer with a proper fraction (2019 KS2 mark scheme general principles). Every key was recomputed with exact fraction arithmetic in data/verify_keys.py; no distractor equals the correct answer.

#	Objective	Item text	Type	Difficulty	Correct answer	Rubric (marks)	Misconception targeted and distractors
1	O2 add	What is 1/3 + 1/4? A 2/7 B 7/12 C 2/12 D 1/12	MC	Foundation, recall/procedure	B 7/12 (4/12 + 3/12)	1 mark for B	Adding numerators and denominators, described as a tendency to "add the numerators and add the denominators". A 2/7 adds both; C 2/12 adds numerators over the product of denominators; D 1/12 multiplies.
2	O1 compare	Which is the largest fraction? A 2/3 B 3/4 C 5/6 D 7/12	MC	Foundation, recall	C 5/6 (10/12 vs 8/12, 9/12, 7/12)	1 mark for C	Whole-number reasoning on fraction size (my inference; whole number bias appears in a 2026 study of 1,055 pupils). D 7/12 has the biggest numbers; A 2/3 and B 3/4 are plausible guesses with no single named error.
3	O3 subtract	What is 7/8 - 1/4? A 6/4 B 5/8 C 6/8 D 3/8	MC	Core, procedure	B 5/8 (7/8 - 2/8)	1 mark for B	Subtracting across, the mirror of the target error. A 6/4 subtracts both numbers; C 6/8 subtracts numerators only; D 3/8 uses a wrong equivalent (1/4 = 4/8).
4	O1 compare	Which list is in order, smallest first? A 1/2, 3/4, 5/8 B 1/2, 5/8, 3/4 C 3/4, 5/8, 1/2 D 5/8, 3/4, 1/2	MC	Core, procedure	B (4/8, 5/8, 6/8)	1 mark for B	A orders by denominator size; C is the reverse order; D orders by numerator, largest first (distractor logic is my inference).
5	O2 add	What is 1 1/2 + 2 1/3? A 3 2/5 B 3 5/6 C 3 2/6 D 3 1/6	MC	Core, procedure	B 3 5/6 (3 + 3/6 + 2/6)	1 mark for B	Direct adding of denominators in the fraction part. A 3 2/5 adds both; C 3 2/6 adds numerators over the product; D 3 1/6 subtracts by slip.
6	O4 word	Mina eats 1/4 of a pizza. Jo eats 1/6 of the same pizza. What fraction did they eat altogether? A 2/10 B 5/12 C 2/12 D 7/12	MC	Core, application	B 5/12 (3/12 + 2/12)	1 mark for B	Same error inside a context. A 2/10 adds both; C 2/12 finds the common denominator but adds numerators 1 + 1; D 7/12 uses a wrong conversion (1/6 = 4/12).
7	O4 word	A recipe needs 3/4 litre of milk. Sam has 2/3 litre. How much more milk does he need? A 1/1 B 1/12 C 1/7 D 17/12	MC	Stretch, application	B 1/12 (9/12 - 8/12)	1 mark for B	Operation choice and the direct-subtract error. A 1/1 subtracts both numbers; C 1/7 subtracts numerators and adds denominators (inference); D 17/12 adds instead of subtracting.
8	O1 compare	Which comparison is true? A 3/7 > 1/2 B 5/8 > 3/5 C 4/9 > 1/2 D 2/3 < 5/8	MC	Stretch, reasoning	B (25/40 > 24/40)	1 mark for B	Judging size from the numerator-denominator gap or gut feel (inference). A, C and D are false (6/14 < 7/14; 8/18 < 9/18; 16/24 > 15/24).
9	O2 add	Work out 2/5 + 1/10. Give your answer in its simplest form.	SA	Foundation	1/2 (accept 5/10 for no mark if not simplified)	1 mark: 1/2 only	Common wrong response: 3/15 (adds both). Tests that one denominator is a multiple of the other, the stated starting point.
10	O3 subtract	Work out 5/6 - 1/4.	SA	Core	7/12	1 mark: 7/12	Common wrong response: 4/2 (subtracts both).
11	O2 add	Work out 2 1/4 + 1 5/6. Give your answer as a mixed number.	SA	Core	4 1/12 (3/12 + 10/12 = 13/12)	2 marks: 4 1/12. 1 mark for 3 13/12 or 49/12 (correct unsimplified). Mixed-number answer needs a proper fraction.	Common wrong responses: 3 6/10 (adds both) and 3 13/12 left unconverted (regrouping gap).
12	O3 subtract	Work out 3 1/5 - 1 3/4.	SA	Stretch	1 9/20 (3 4/20 = 2 24/20, minus 1 15/20)	2 marks: 1 9/20. 1 mark for correct common denominator (4/20 and 15/20) with an arithmetic slip.	Likely wrong response (my prediction): 2 11/20 (subtracts the smaller fraction from the larger without regrouping: 3 - 1 and 15/20 - 4/20).
13	O1 compare	Write 3/4 and 5/6 with the same denominator. Which is greater?	SA	Core	9/12 and 10/12; 5/6 is greater	2 marks: both equivalents correct and conclusion. 1 mark for one correct step.	Common wrong response: 3/4 greater because 3 and 4 are "closer together" or comparing numerators only (inference).
14	O4, O1	Tia reads 2/5 of her book on Saturday and 1/4 on Sunday. (a) What fraction of the book has she read in total? (b) What fraction is left? (c) Tia says, "I have read more than half." Is she right? Explain.	ER	Core to stretch	(a) 13/20 (b) 7/20 (c) Yes, 13/20 > 10/20	4 marks: (a) 2 marks (1 for 8/20 and 5/20); (b) 1 mark (follow through from (a) if 1 - their total is correct); (c) 1 mark for a comparison using a common denominator (not just "13 is more than 10").	(a) common wrong response 3/9 (adds both); (b) part-whole slip, 1 - 13/20 treated as 12/20; (c) comparing 13 with 20 or with "half of 13".
15	O4, O1	Lena has 2 1/2 metres of ribbon. She uses 3/4 m for a bow and 1 1/3 m for a banner. (a) How much ribbon does she use altogether? (b) How much is left? (c) She needs a piece 1/2 m long. Does she have enough left? Show how you know.	ER	Stretch	(a) 2 1/12 m (b) 5/12 m (c) No, 5/12 < 6/12	5 marks: (a) 2 marks (1 for 9/12 and 4/12 with a slip); (b) 2 marks (1 for 2 6/12 and 2 1/12 with a slip, or follow through); (c) 1 mark for a common-denominator comparison with a "no" conclusion.	(a) 1 4/7 (adds numerators and denominators: 3+1 over 4+3); (b) subtracts the wrong way or ignores the whole-number part; (c) says yes because 5 and 12 are "big".

Why these errors, and what the evidence does and does not say

Adding numerators and denominators: A teacher-facing article in the ERIC record of Howard (1991), Mathematics Teacher discusses why students tend to "add the numerators and add the denominators", and suggests ratio, concentration and distance examples to show when that approach does apply. That supports distractors A in items 1 and 5 and the common wrong response in item 9. Your own data (60% on the last quiz) outranks this general research.
Many error types, often used inconsistently: A 1984 error analysis of about 600 junior-high pupils found many erroneous rules, often used only sporadically by a pupil, and that some errors appear among high scorers. This is why each item has one identifiable error per distractor, and why I would not read one wrong answer as a fixed belief.
Why errors persist: A 2017 computational model found that the mix of problems in textbooks can bias learning of fraction arithmetic. This is a reason to include items 3 and 8, where the pattern is not "same denominator, add across".
Instability across tasks: The 2026 study of 1,055 pupils in Grades 4 and 5 found students often reverted to whole number bias when new topics appeared, and that a correct answer at one time point does not always mean stable understanding. Hence the repeated target across item types (multiple choice, short answer, context).
Word problems: I did not find a fetched source specific to Year 6 fraction word problems, so the word-problem items (6, 7, 14, 15) rest on your report of the gap and on the curriculum's guidance on varied problems. Their distractors for operation choice are my inference.

Objective coverage summary

Objective	Items (marks)	Marks	% of 25	Difficulty spread
O1 Compare	2, 4, 8 (1 each); 13 (2); 14c, 15c (1 each)	7	28%	items 2 (foundation), 4 and 13 (core), 8 (stretch); 14c and 15c sit inside the extended items
O2 Add	1, 5 (1 each); 9 (1); 11 (2)	5	20%	items: 2 foundation (1, 9), 2 core (5, 11)
O3 Subtract	3 (1); 10 (1); 12 (2)	4	16%	items: 2 core (3, 10), 1 stretch (12). Thin.
O4 Word problems	6, 7 (1 each); 14a-b (3); 15a-b (4)	9	36%	items: 1 core (6), 2 stretch (7, 15), 1 core to stretch (14)

Total 25 marks. Subtraction is the thinnest objective; if you want it stronger, swap item 4 for a second subtraction item.

Suggested timing

Section	Marks	Minutes
Items 1 to 8 (multiple choice)	8	7
Items 9 to 13 (short answer)	8	9
Items 14 and 15 (extended)	9	11
Reading and checking		3
Total	25	30

This is tight, at roughly one minute per mark. Trial it first with a few pupils. If it overruns, drop item 4 or 10.

Do next

Trial items 1, 5 and 9 first: they show quickly whether the denominator-adding error has fallen from the 60% baseline.
Reword items 14 and 15 for EAL learners if needed (for example, shorten "altogether"), then check that the maths is unchanged.
Mark item 14(c) and 15(c) by the comparison method, not just yes/no.
Mark with a correct-answer-earns-the-mark rule for multiple choice, and use the common wrong responses to sort pupils for re-teaching.

Near misses and open items

Dropped: a 3-denominator ordering item and a "simplify fractions" item. Both would test objectives outside your two stated topics.
Assumption to confirm: the curriculum is the England national curriculum, and the 30-minute limit covers all 25 marks.
Calibration: I used the general marking principles of the 2019 KS2 mark scheme for mark conventions only. I did not extract specific fraction items or their command words from it, so item difficulty is my own judgment.

Coverage note

I could not extract the full text of the Braithwaite paper PDF or the sats-papers question paper in readable form, so I used the ERIC abstract and the mark-scheme extract. The Year 6 fractions wording above is from the same GOV.UK page; the Year 6 section sat near the end of a long page, so I checked it with a targeted text extraction.