R. Pwy Dunnit

Aims
  • To explore ratio and proportion through the context of personal measurements.
  • Integrating different strands of children’s mathematical knowledge.
  • Resources Vocabulary
  • Centimetre Calculators
  • Hat and glove (optional but if using real objects,take from two different people of different heights)
  • Tape measures
  • Small toy people for the Left/Right Robots
  • mean, median, mode, range, divide, multiply, fraction, ratio, proportion
    Organisation
  • Groups of three of four children on mixed achieving tables
  • Whole Class Preparation: (about 10 mins)
  • Imagine the scene. Your furniture is scattered all over the floor, the safe is open and all your
    valuables are gone. You look around the room for clues as to who has done this... (embellish
    the story). The police cannot find any fingers or footprints – they are baffled. Finally, you
    come across some crucial evidence. You find a glove underneath the desk. Nearer the
    window you find a hat. Could you use this information to find out more about the
    intruder(s)? How?
  • Measure the circumference of the hat and the length of the glove. Do you think this
    information might be important? Why? Might it lead you to any other information about
    the intruder(s)?
  • As a class, look at one person (chosen sensitively). Can you make any judgements about
    the proportions of their body based on their head or hand?
  • Roughly how many times does the length of their hand go into their height? Guess.
  • Do you think there might be a relationship to discover? How could we do this?
  • What about the circumference of their head? Could finding out more about this help us to form an idea of what the intruder(s) look like?
  • Group Work: (about 10 mins)
  • Agree Record the height of each person in your group, as well as the length of their hand and the circumference of their head.
  • Record all results in a table.
  • Use your calculator to find these ratios: height:hand and height:head. Tell the children about calculating ratios if you need to. Record these results in the table.
  • Class Sharing: (about 20 mins)
  • Did anyone find any surprises or similarities?
  • How did you use your results to find the ratio or proportion of our hands to our overall height? Height
  • hand length.
  • Discuss the problem of the many decimal places in the results. Recap quickly on rounding or consider truncating to two decimal places – do not spend a lot of time on this.
  • Look at the new values for two or three examples. Are the answers very different? Do you think they will be different for your group? Accept ‘yes’.
  • Repeat for the circumference of the head.
  • Order the data from the groups in a table (see stem and leaf diagram in the background notes) so as to obtain a median or mode and range, for each of the two ratios.
  • Group Work: (about 10 mins)
  • Now look at the table for the values of the two ratios. What do you think you might be able to say given we know the length of the glove (either measure the one you have or use about 19 cm) and the circumference of the hat (again, a real measurement or use 55 cm)? Discuss this with the others in your group.
  • Help groups reach a decision to multiply to obtain a representative height or even the representative height and range of heights for using each of the two ratios.
  • Class Sharing: (about 10 mins)
  • How did you get estimates for the height of the intruder(s)? For example, multiply the glove length by 9, multiply the hat circumference by 3.
  • Was there more than one intruder? Heights should be similar, but it may be that the hat size suggests a shorter person.
  • Can we decide on a good range for the height for each of the ratios?
  • How many people do you now think might have burgled the house? How accurate is our estimate? What can we tell the police?
  • Think back – how did you go about solving the problem? What else might we do with our information? What if there was a footprint?
  • 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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