“There is more than one correct answer.” Illustrative Mathematics suggests teachers say that line, if a class needs it, to close one of its Which One Doesn’t Belong warm-ups.
Sunday, 8 p.m. Tomorrow is equivalent expressions, and you’d like a which one doesn’t belong math warm-up that walks the class straight into it. The search hands you four shapes, a number set for a younger grade and a worksheet with a single answer key. None of it is about expressions, so you start writing one yourself. The hard part is making that IM line true for your set.
A set is ready when you can write down a reason each of the four items doesn’t belong. With a sticky note, that check takes about ten minutes on any topic, and six sets for grades 3–8 that already pass it are further down.
Key Takeaways
- What a good set needs: each of the four items can be the one that doesn’t belong, for a reason students can say out loud.
- How to write one: start from this week’s idea, give every item its own “only one that…” reason and check all four on a sticky note.
- Sets for this week: six original sets, one per grade from 3 to 8, from whole numbers up to scientific notation.
Why Does the Set You Found Fall Flat?
There are two usual ways a Sunday-night set goes wrong.
The first is borrowing a good set on the wrong topic. Four shapes make for a lively ten minutes, but if Monday is about fractions, the class spends those minutes on sides and angles and then has to switch topics. The warm-up and the lesson stay two separate things, and the class never hears you say “hold on to that idea, we need it now.”
The second is the quick home-made set. You pick three fractions in quarters and one in thirds, and the odd one is obvious. That’s an odd-one-out question with one right answer, even though it sits in a four-square grid.
When only one item really differs, the first student to spot it says it, and everyone else stops looking. Illustrative Mathematics runs its version as a 10-minute warm-up, and with one real answer those ten minutes turn into a race the fastest student wins. The students who needed the extra thinking time hear the answer before they’ve finished reading the grid.
What Makes a Set Worth Ten Minutes?
Which One Doesn’t Belong is a math warm-up built on four items, usually in a two-by-two grid, and one question: which one doesn’t belong? Every item can be the answer if you give a reason. Students think quietly, talk with a partner, then share their reasons, and the class ends up with more than one right answer.
The routine is closely linked to Christopher Danielson, whose book Which One Doesn’t Belong? is a shapes book with a teacher’s guide. Mary Bourassa built a website of sets inspired by his idea. In 2024 that collection moved to Danielson’s site, Talking Math with Your Kids, when she retired from running it. Its about page puts the rule plainly: a set is “chosen so that any one of the four can be the one that doesn’t belong.”
Amplify Desmos Math’s routine notes give a timing that fits a middle school period: one minute of quiet think time, then two minutes with a partner to find at least one reason each item doesn’t belong. Students then share with the stem “The top left is the only one that ___”. The same notes credit the routine to the work of Christopher Danielson, Megan Franke and Sesame Street, among others.
For shapes, graphs and photos, the free Which One Doesn’t Belong collection is the place to go. Its categories run from shapes and numbers to graphs and expressions, plus photos and incomplete sets. Rights to each set stay with its named author, so use them from the site and credit them. The sets on this page are our own, written in text so they paste straight into a slide. If you teach first grade, our odd-one-out worksheets for first graders suit that age better.
How Do You Write One for This Week’s Topic?
Illustrative Mathematics writes every set in its curriculum to one rule: any three of the four share a feature the fourth doesn’t. Students aren’t expected to follow it. They’re invited to find a reason each item belongs and a reason each one doesn’t. That rule turns into a ten-minute method you can run on any topic.
- Name this week’s idea (1 minute). “Negative”, “equivalent”, “greater than 1”, “not in scientific notation”.
- Pick the item that’s the only one with that idea (2 minutes).
- Add three more items, each with its own “only one that…” reason (4 minutes). Use features the whole class can see. Size and sign work. So do even or odd, whole number or not and the number of digits or terms.
- Write the four reasons on a sticky note (2 minutes). For each reason, check the other three items. If a reason also fits another item, or an item has no reason, swap an item.
- Check the floor and the ceiling (1 minute). At least one reason a student who’s behind can spot, and at least one that needs this week’s idea.
Worked example
Here’s how that runs for a grade 6 lesson on negative numbers and distance from zero. The idea is “negative”, so the first item is −8, the only number below zero. Then we add 12, 3.5 and −15. On the sticky note, 12 gets “the only one more than 10 away from zero”, 3.5 gets “the only one that isn’t an integer” and −15 gets “the only odd integer.”
Then the check catches the problem. Run each reason past the other three items and two of them break. −15 is below zero too, so −8 is no longer the only negative number. It’s also 15 away from zero, so 12 is no longer the only one more than 10 away.
Swap −15 for 5 and all four reasons hold again: 5 is now the only odd integer, and also the only prime. Now the floor is “3.5 is the only one that isn’t an integer”, which a student can spot from the decimal point. The ceiling is “12 is the only one more than 10 from zero”, the distance idea the lesson is about. That’s the whole method, start to finish.
Six Which One Doesn’t Belong Math Sets You Can Use This Week
Each set below is a two-by-two grid: A is top left, B top right, C bottom left and D bottom right. We wrote all six for this page and checked every reason against the other three items twice, once by hand and once with a short script that tested each property. Open the reasons only after the class has had its turn.
Grade 3: Whole Numbers
| Top left | Top right |
|---|---|
| A: 36 | B: 50 |
| C: 27 | D: 128 |
Floor: C is the only odd number. Ceiling: A is the only one you can arrange as a square array.
Show the four reasons
- A (36) is the only one you can arrange in a square array, 6 rows of 6.
- B (50) is the only one in the 5 times table.
- C (27) is the only odd number.
- D (128) is the only number with three digits.
Grade 4: Fractions
| Top left | Top right |
|---|---|
| A: 3/6 | B: 5/4 |
| C: 1/3 | D: 2/10 |
Floor: B is the only one with a numerator bigger than its denominator. Ceiling: A is the only one equal to 1/2.
Show the four reasons
- A (3/6) is the only one equal to 1/2.
- B (5/4) is the only one greater than 1.
- C (1/3) is the only one written with a numerator of 1.
- D (2/10) is the only one less than 1/4. It’s also the only one with an even numerator.
Grade 5: Decimals
| Top left | Top right |
|---|---|
| A: 0.6 | B: 0.45 |
| C: 1.2 | D: 0.08 |
Floor: C is the only one greater than 1. Ceiling: D is the only one less than one tenth.
Show the four reasons
- A (0.6) is the only one between one half and 1.
- B (0.45) is the only one with a digit other than zero in both the tenths and the hundredths place.
- C (1.2) is the only one greater than 1.
- D (0.08) is the only one less than one tenth: the 8 is in the hundredths place.
Grade 6: Expressions
| Top left | Top right |
|---|---|
| A: 4(x + 3) | B: 4x + 3 |
| C: 4x · 3 | D: x + 12 |
Floor: A is the only one with parentheses. Ceiling: A is also the only one equivalent to 4x + 12.
Show the four reasons
- A, 4(x + 3), is the only one with parentheses and the only one equivalent to 4x + 12.
- B, 4x + 3, is the only one that’s odd for every whole number x.
- C, 4x · 3, is the only one that simplifies to a single term (12x) with no constant.
- D, x + 12, is the only one where x has a coefficient of 1.
Grade 7: Equations and Inequalities
| Top left | Top right |
|---|---|
| A: 2x + 5 = 11 | B: x − 4 = −7 |
| C: 3x = 9 | D: 2x + 1 > 7 |
Floor: D is the only one without an equals sign. Ceiling: B is the only one with a negative solution.
Show the four reasons
- A is the only equation that takes two steps (subtract 5, divide by 2; x = 3).
- B is the only one with a negative solution, x = −3.
- C is the only one with nothing added to or subtracted from the x term (x = 3).
- D is the only inequality, with infinitely many solutions (any x greater than 3).
Grade 8: Exponents and Scientific Notation
| Top left | Top right |
|---|---|
| A: 4³ | B: 6.4 × 10⁻² |
| C: 64 × 10² | D: 6.4 × 10⁵ |
Floor: A is the only one with no power of ten. Ceiling: C is the only one that looks like scientific notation but breaks its rule.
Show the four reasons
- A (4³ = 64) is the only one whose base isn’t 10.
- B (0.064) is the only one with a negative exponent and the only one less than 1.
- C (6,400) uses a power of ten but isn’t in scientific notation, because 64 isn’t between 1 and 10.
- D (640,000) is the only one greater than 10,000.
What If a Student Says There’s Only One Right Answer?
Someone usually will, often the student who spotted the first reason fastest. Ask for a reason for every item before anyone is allowed to defend a favorite. Then try the move from Amplify Desmos Math’s notes: a student shares why they chose an item but not which one, and the class works out which item they meant. Now the whole class is testing that reason against all four items.
If the room still wants a single winner, go back to that line from Illustrative Mathematics: “There is more than one correct answer.” Say it once, then point at the item nobody has defended yet.
Sentence stems help the quieter half of the room. Edutopia’s article on the routine uses “A doesn’t belong because…”, labels the four images A to D and gives students about five minutes to think and write. The author notes that the letters make it easier for multilingual learners to join in, since “B doesn’t belong because” is easier to say than describing a position.
Fast finishers need a harder job. Once they’ve found a reason for all four, ask them to write a fifth item that would break the set: something that shares a reason with one of the four, so that item loses its “only one”. If they want more, our guide to solving math olympiad problems covers strategies for harder problems, such as working backwards and trying small cases. Grade 6–8 students who enjoy this kind of argument may also like a guide to math competitions for middle school.
How Will You Know It’s Working?
You won’t get a score, and you don’t need one. Watch for four things over the first few weeks.
- Who spoke. Count the students who gave a reason, aloud or to a partner, and see whether it’s more than the usual three.
- Reasons per item. If every item in the grid ends the ten minutes with at least one reason, the set did its job.
- This week’s idea. Did at least one reason use it? That’s the reason to write on the board and come back to in the lesson.
- The one-answer student. Did they offer a second reason without being asked?
If an item gets no reasons at all, that’s information about the set more than the class. Check it against your sticky note before next time.
So next Sunday goes differently. You name the idea, pick the item that owns it and give the other three a reason each. Then you check the sticky note, and the set is done in about ten minutes. Six sets are already written for this week, and you have a plan for the student who wants a single winner.
The routine and Gonit do different jobs. A WODB set is for talk, with four defensible answers on the board. Gonit is multiple-choice practice by grade and topic for grades 1–12, with 10,000+ original questions students work through on their own between lessons. Its topics include arithmetic and number sense, algebra and geometry. They also cover logical reasoning and probability, so the idea your warm-up opened can get some quiet practice later in the week.
Make Preparing for Math Olympiad Simple!
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- A Mu Alpha Theta practice test you can run in one club meeting
- MOEMS practice problems by division
Louise R. Fox holds a Ph.D. in Mathematics and brings a researcher's perspective to how students actually learn the subject. Based in the United States, she writes about olympiad-level problem solving and the deeper thinking skills that carry students well beyond the classroom.
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