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Grades 6–7MathProbabilityLesson 3 of 4Ages 11–13

Years 7–8 in England and Wales · Cambridge Lower Secondary Stages 7–8 · IB MYP 1 to MYP 2, ages 11–13

Why does horse 7 always win?

Teams play a horse race where horses numbered 2 to 12 move when the sum of two dice matches their number. Horse 7 wins again and again, and horse 2 and horse 12 hardly move. Students build the 36-outcome sample space in a table, find probabilities of compound events, and explain why sums in the middle are more likely.

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First page of the Why does horse 7 always win? teacher guide
A green felt race board with eleven lanes and coloured markers at different distances, the marker in the middle lane furthest ahead, and two dice beside the board.Preview · the opening mission

Read this to the class:

A games club has a horse-race game. There are eleven horses, numbered 2 to 12. Each turn you roll two dice and add them, and the horse with that number moves one step. The first horse to reach the finish, 8 steps away, wins. New players always pick their favourite number. "It's fair," the club leader says. "Every horse has a number." Your team's job: race the horses, work out whether the game is fair, and explain to the club why some horses win far more often.

Teams of three, with jobs that rotate after each race: Roller (rolls both dice), Adder (calls out the sum), Jockey (moves the horse and records the winner).

Look inside the PDF

Sample pages, stamped “preview”. The download is the clean, full lesson.

Teacher guide, page 1
Inside: the lesson steps
Student sheet, ready to copy

In the full lesson PDF

8 printable pages

  • Predict (5–10 min)
  • Hunt (20 min)
  • Reveal (10–15 min)
  • Act (10 min)
  • Background for the teacher
  • Assessment
  • Student sheet
  • Worksheet: Race track
  • Worksheet: Label it
  • Worksheet: Try it at home

On the student sheet

  • My prediction
  • Sums rolled in our races
  • The sample space
  • Our advice for the club
  • Exit ticket
  • Race track
  • Label it
  • Try it at home

US Letter, prints cleanly in black and white. The student sheet is on its own page, ready to photocopy.

Free with an account (any 3 lessons), or US$19 for all 4 lessons in this unit.

What students show by the end

  • Builds the sample space
  • Finds compound probabilities
  • Explains fairness

From the lesson’s rubric, which scores each one as not yet, getting there or got it.

Questions teachers ask

How long does “Why does horse 7 always win?” take?

50–60 min. Group size: teams of 3.

How much prep does it need?

10 minutes: each team needs two dice, a cup to roll into and the Race track from the Worksheet, plus 11 small markers (counters, paper clips or scraps of paper) for the horses.

What materials do I need?

Six-sided dice; race track (from the Worksheet) and 11 small markers; paper cup or tray to roll into. Cost: about $5 for dice if you have none.

Which curriculum standards does it cover?

Common Core Math (US): 7.SP.C.7 (partly) and 7.SP.C.8.

What’s in the lesson PDF?

A teacher guide that walks you through predict, hunt, reveal, act, background for the teacher and assessment, then a student sheet (“My prediction”, “Sums rolled in our races”, “The sample space”, “Our advice for the club”, “Exit ticket”, “Race track”, “Label it” and “Try it at home”) on its own page, ready to photocopy. It’s US Letter and prints cleanly in black and white.

Can I try it for free?

Yes. A free account includes any 3 full lessons of your choice, and this can be one of them. After that, this unit is US$19 for all 4 lessons, yours to keep, or every lesson is US$199 a year.