W. Pa Ffordd i Fyny

Aims
  • To explore probability, listing all possible outcomes and testing intuitive theories systematically.
  • To handle multiplicative relations, ratio and inverse proportionality in a familiar context.
  • Resources Vocabulary
  • Centimetre Which Way Up? Notesheet – one per group
  • Calculators
  • Pass the Pigs game, one pig between three or four children; or an alternative to ‘Pigs’: – rectangular blocks of an eraser rubber, 15mm x 15mm x 10mm, with a single cut-out piece as shown. Accuracy is important. Children should make drawings on each face.
  • fair, evens, 50%, equal chance, 0.5, less than half as likely, unlikely, impossible
    Organisation
  • Near achievement threes or fours
  • Children should start the lesson describing the faces of the piece from above. The class must agree on a term to describe each position. If working with alternatives to pigs, they choose terms to describe each of the different faces. Note that the blocks must all feature the same design on the same face.
  • Whole class Preparation: (about 15 mins)
  • The aim of this lesson is to explore chance in games.
  • Who has played this game before? What ways can the pig fall? Allow children to test out
    the ways that a pig could fall. If an alternative is used then see above.
  • Agree of a list of different positions and names and record these on the board (if the
    pig is used, this may or may not include the right ear position, which is actually
    impossible on a level surface; if an alternative is used, then collect alternative
    descriptions, and agree on appropriate ones).
  • Which positions do you think are the most likely? Which do you think are the least likely?
    Record the two most popular responses to each question on the board.
  • Group work : (about 10 mins)
  • Working in threes or fours, collect the data of the position the pig/block falls
    into for 20 (or 50) throws. Take turns to throw the pig/block and keep a tally
    of the number of times it falls into each of the positions.
  • Rubber blocks are best dropped from a nearly standard height of a pencil
    length. Use sheets of paper with the edges folded up to confine the roll
    of a block.
  • What do you notice about the results for the different positions?
  • Ask each group to add their results to the tally chart on the board.
  • Class sharing : (about 10 mins)
  • Allow discussion of the results. Are the results from the different groups for each position similar or completely different? What is similar, what is different?
  • How should we represent the results? Collate the tally chart results from the groups onto a large table, using small circles to represent ten outcomes and semi-circles for something around five.
  • Use the visual representation and the numeric totals for each position to compare pairs of positions. Start with extremes, or nearly double. How many times more likely are you to get this position than that one?
  • Group work: (about 15 mins)
  • We want to design a scoring system for the game, using the scores 1–10.
  • Decide with your group what a fair scoring system would be for the different
    positions. Which should have the lowest score and which the highest? How
    would you allocate scores to the positions that are neither common nor
    rare?
  • Use the space on the notesheet for making notes about your system.
  • Class sharing: (about 10mins)
  • Compare the different scoring systems devised. Ask one or more groups to explain their system to the class. Encourage rounding and use of ratio.
  • Play a game with your group, taking turns to throw the pig/block. Record all your scores. Take 10 throws each.
  • Do you still think that your scoring system is fair? Is there anything that you need to change?
  • Pick a pair who changed their scoring system after they had played the game and get them to explain what they changed and why.
  • How did you go about working on this problem?
  • What other games of chance do you know? What is similar or different?
  • License

    Gwersi PCAME a Dewch i Feddwl Mathemateg (9 i 11 oed) Copyright © by Ann Longfield, David Johnson, Jean Hindshaw, Linda Harvey, Jeremy Hodgen, Michael Shayer, Mundher Adhami, Rosemary Hafeez, Matt Davidson, Sally Dubben, Lynda Maple, and Sarah Seleznyov. All Rights Reserved.

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