Who Came First? Ordering and Position Puzzles
- Grade band
- 5-6
- Duration
- 40 minutes
- Skill
- Reasoning with order and position clues
- Standards
- MP.1 — Make sense of problems and persevere in solving them.
- MP.2 — Reason abstractly and quantitatively.
- Materials
- Student worksheet with number-line slots (printable, included)
- Name tiles (printable, included)
- Scissors
Learning objectives
- Students will be able to translate order clues (“directly behind,” “exactly two places behind,” “somewhere between”) into position statements such as Ivy = Fay + 1.
- Students will be able to identify which possible placements a pair clue allows and eliminate the ones that break another clue.
- Students will be able to justify a final order by showing that every alternative placement fails at least one clue.
Lesson procedure
- Line up (5 minutes) — I Do. Call up five volunteers and say: “Sam is directly behind Ana.” Have them try several positions. Point out that “directly behind” doesn't say where the pair stands — only that they're glued together. Write it as a math sentence: Sam = Ana + 1.
- Clue translation (8 minutes) — We Do. Complete Part 1 together. Build a class anchor chart: ahead of / before = smaller number (closer to 1st), behind / after = bigger number, directly = exactly 1 apart, between = strictly in the middle.
- Lunch-line puzzle (10 minutes) — We Do. Use the cut-apart name tiles on the Part 2 number line. Place Gus first (Clue 1 is a fixed spot). Then ask: “Where could the Eli–Hana pair go? Where could the Fay–Ivy pair go?” List the options and use Clue 4 to eliminate one.
- Race puzzle (12 minutes) — You Do. Students solve Part 3 with their tiles. Require them to complete the “try every spot” table for the Lu–Jo pair, showing why two of the three placements fail.
- Exit ticket (5 minutes) — Closure. Students write one clue that would make a different runner win the race, and check that it still leads to just one order.
Printable worksheet
Part 1: Turn words into math. Position 1 is the front of the line (or 1st place). Write each clue as a position statement.
| Clue | Position statement |
|---|---|
| Max finished directly ahead of Ben. | Example: Max = Ben − 1 |
| Rio finished exactly three places behind Zoe. | |
| Kira was somewhere ahead of Tom. | |
| Paz was last. | |
| Lee finished somewhere between Ana and Cole. |
Part 2: The lunch line. Five friends stand in line. Spot 1 is the front.
- Gus was last in line.
- Eli was directly in front of Hana.
- Ivy was directly behind Fay.
- Hana was not second in line.
| 1st (front) | 2nd | 3rd | 4th | 5th |
|---|---|---|---|---|
Part 3: The race. Five runners finished a race. There were no ties.
- Kai did not finish first or second.
- Jo finished exactly two places behind Lu.
- Max finished somewhere between Jo and Kai.
| 1st | 2nd | 3rd | 4th | 5th |
|---|---|---|---|---|
Try every spot. Clue 2 means Lu and Jo can only be in three places. Test each one.
| Lu | Jo | Does it work? Which clue breaks it? |
|---|---|---|
| 1st | 3rd | |
| 2nd | 4th | |
| 3rd | 5th |
Part 4: Name tiles. Cut these apart and slide them along the number lines while you solve.
Background for the teacher
Ordering puzzles use a different structure from matching grids: instead of “who has what,” every clue is about relative position. The most useful habit is translating each clue into a precise statement about numbers. “Directly behind” is a difference of exactly one; “somewhere ahead” is only an inequality; “between” means strictly in the middle, in either direction. Abstracting the words into numbers and then returning to the context to check an answer is exactly what the “reason abstractly and quantitatively” practice describes.
Students often place a pair clue in the first spot that fits and move on. The “try every spot” table builds the stronger habit of listing all possible placements of a pair and eliminating them one by one — that's how they can be sure an answer is the only one, not just a possible one. Watch the direction words: students regularly flip “ahead” and “behind,” so the anchor chart (front = 1) is worth keeping visible. In the race, note that Nell is never mentioned; she ends up in the only open spot.
Differentiation
Support: Tape the two pair clues together as physical “double tiles” (Eli+Hana, Fay+Ivy) so students slide one pair at a time. Solve the lunch line in a small group before the race.
Extension: Add a sixth runner and one new clue to the race so it still has exactly one finish order. Have a partner verify it with the “try every spot” method.
ELL support: Act out “ahead of,” “behind,” “directly,” and “between” with students in a line, and label the anchor chart with arrows and position numbers rather than words alone.
IEP/504 support: Provide the number lines on a larger card with spaces sized for the name tiles, and reduce Part 1 to three clues. Allow students to show the “try every spot” work with tiles and explain it orally.
Answer key (for teachers)
Part 1. Rio = Zoe + 3 · Kira < Tom · Paz = 5 (or the last position) · Lee is between Ana and Cole: Ana < Lee < Cole or Cole < Lee < Ana.
Part 2 — Lunch line. 1st Fay, 2nd Ivy, 3rd Eli, 4th Hana, 5th Gus. (Gus is 5th, so the two pairs fill spots 1–4. Either Fay–Ivy–Eli–Hana or Eli–Hana–Fay–Ivy; the second puts Hana 2nd, which Clue 4 forbids.)
Part 3 — Race. 1st Lu, 2nd Nell, 3rd Jo, 4th Max, 5th Kai.
Lu 1st / Jo 3rd: works — Kai must be 4th or 5th (Clue 1), and Max must be strictly between Jo and Kai, so Kai 5th and Max 4th; Nell takes 2nd.
Lu 2nd / Jo 4th: fails — Kai would be 3rd or 5th (Clue 1), and either way no spot is strictly between Jo and Kai (Clue 3).
Lu 3rd / Jo 5th: fails — Kai would have to be 4th (Clue 1), leaving no spot between Jo and Kai (Clue 3).
Exit ticket. Open-ended; accept any clue that produces a single, verified order.
Digital extension (optional)
For grid-style deduction practice, try a case in Sleuth Scouts. Cases use matching grids rather than lineups, so they're a good way to compare the two puzzle structures students saw this week.