Smarties

Years 1 - 6

Summary

Taken from page 16, Calculators, Children and Mathematics, the report of the Calculator Aware Number project, this activity involves many aspects of number, chance and data collection. It refers to a sugar-coated chocolate called Smarties, similar to M & Ms in the USA, but is easily modified to coloured counters in a box or bag (with no risk of the maths materials being eaten before the activity is completed!). In part Smarties is an investigation and in part an activity suitable for threading as described in Variations & Extensions below.

Materials

  • One packet of Smarties per pair
  • Recording paper
  • One calculator per person
Smarties
Figure 3.6, page 17, Calculators, Children and Mathematics

Procedure

One teacher invented a game in which negative numbers were likely to turn up naturally, The game was called 'Smarties', and the rules were as follows:
  • Before starting this game, children count and sort a tube of Smarties, and make a block graph of the colours of the Smarties. Suppose there are 31 Smarties in the tube. Each child receives 31 points to start the game.
  • The Smarties are returned to the tube at the beginning of the game. They are taken out one by one, and each child records a guess as to which colour will come out next.
  • Correct guesses score 2 points.
    Incorrect guesses lose 2 points.
The teacher wrote about what happened:
Number-lines and calculators are available for this game. Children are encouraged to consult the graph and to work out a probable colour to appear next. They often record when all the Smarties of one colour are out. A tube containing 31 Smarties is useful; it gives experience of moving up and down the number-line on odd numbers. Negative numbers appear naturally, so the number-line should stretch below zero. Much of the calculation of scores will be mental, but calculators and number-lines are available for checking.
 

Content

  • addition facts beyond 10
  • addition facts to 10
  • data: collecting, recording, displaying
  • data: interpretation
  • estimating number
  • likely, less likely and unlikely events
  • negative numbers
  • number line - ordering, operations
  • operations - whole number
  • problem solving
  • properties of number
  • properties of zero
  • recording - calculator
  • subtraction
  • tallying

Variations & Extensions

  1. The game need not be a competition between two players. If two students are playing they can make an agreed guess about the colour and keep a joint record of their on-going score.
    If an objective is needed it can simply be to finish with a positive score.

  2. If you find children enjoy and learn a lot from this experience it can be turned into something of a threaded activity by asking each group to make a small container of various colour counters. (Film canisters work well if you can still get them.) You want all the containers to be different in total and colour ratios. Then you have a class set of pretend Smarties that children can revisit for a new challenge within a familiar structure.

  3. See the activity Take A Score for another game in which negative numbers occur naturally.

  4. Task 218, Guessing Colours Game, from Mathematics Task Centre, simulates the Smarties packet with discs in a bag and adds a competive element and a hint of chance and probability.

  5. Task 47, Red & Black Card Game, from Mathematics Task Centre, and the extended form of it in Lesson 89 Maths300 also provides situations where negative numbers come up naturally.

  6. See Children's Methods of Calculation to develop a sense of how working with negative numbers can lead to a powerful alternative approach to subtraction. One Calculating Changes teacher commented some years later after becoming a dedicated user of calculators:
    Negative numbers are no problem to my Year 1. They just call them underground numbers.
  7. If a calculator has a +/- button it will probably correctly evaluate the arithmetic of positive and negative numbers. With this feature available, children can be asked to find out for themselves how these numbers behave in combination. What does happen on your calculator when:
    • a positive is added to a positive?
    • a positive is added to a negative?
    • a positive is subtracted from a negative?
    • ...
    • a negative is multiplied by a negative?
    • and so on
    However, discovering these behaviours doesn't explain why they happen.

  8. Visit Integers to see how Poly Plug can be used as a concrete model of the arithmetic of positive and negative numbers (integers). This exploration with Poly Plug derives from Task 130, Protons & Anti-Protons from the Mathematics Task Centre, and is extended in Lesson 76 Maths300.
These photos from Bill's class at MacKillop College, Swan Hill,
suggest how the activity has been used in Year 7
using similar 'chocolate beanies' available in packets of around 200.


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