MicroSMILE Mathematics Software: Probability
I was delighted to have the chance to try out this SMILE program, as fellow teachers have always spoken highly of them and I had never seen them!
There are five programs on the Probability Disk. The programmes are: Hidden Contents, Loaded Dice, Pinball, Probability Match and Routes. The programs are suitable for Key stages 2, 3 and 4. Pinball and Routes are resource programs which allow students to model an experiment and to explore the distribution of the results. Hidden Contents and Loaded Dice encourage students to consider the number of trials of an experiment that would be appropriate before they are able to deduce a reasonable approximation for the theoretical probability. Probability Match is a game which consolidates understanding of the probability of an event based upon equally likely outcomes.
Accompanying the CD is a comprehensive set of teachers notes. For each program there is a mathematical content summary, a description of the software, a sample lesson plane for key stage 2 and lesson notes for key stage 3 and assessment material. There is also a copy of the instructions for each program.
Hidden Contents
The program challenges you to identify the contents of a bag containing coloured balls using experimental probability. In puzzle mode, the students decide the number of balls and the number of colours and the computer will then choose the balls one at a time at random. The colours of the balls are recorded in a frequency table and in a pie chart. The students then need to predict the contents of the bag. This is similar in the challenge mode, although the challenge is to identify the contents of 5 bags in the shortest time.
The students enjoyed using this programme and soon came to the conclusion that you need to pick “enough” balls before a decision could be made and there was an interesting decision on what enough meant.
Loaded Dice
This program is very similar to Hidden Contents. It challenges you to identify which of the two dice has been loaded to make it biased. The dice can be loaded in three ways, at a vertex, at the centre of a face or at the centre of the edge. When using this program with students, we spent time discussing what the results would look like if the die had been loaded in a certain way. I encouraged the students to predict not only which die was loaded, but also how. It helped to have dice in the room, so that they could justify their predictions and reasons.
Pinball
Pinball simulates an experiment where a number of balls are dropped onto hexagonal blocks it explores how the probability of going left affects the distribution of the balls. The probability of going left once set, is fixed at each junction. When the experiment is complete, the number of balls in each box, together with the inputs for the experiment is displayed. A graph of the results can also be displayed.
The resource material offered by Smile to accompany this programme is comprehensive. In class, we used this as an introduction to tree diagrams and the Binomial Distribution.
Routes
Routes simulates an experiment where a number of balls are dropped onto hexagonal blocks it explores how the probability of going left affects the distribution of the balls. The probability of going left can be changed at each junction. When the experiment is complete, the number of balls in each box, together with the inputs for the experiment is displayed. A graph of the results can also be displayed.
The resource material offered by Smile to accompany this programme is comprehensive. The support material, suggesting fair games and traffic flow and river delta are all excellent modelling activities. In class, we used this as an introduction to tree diagrams and the Binomial Distribution.
Probability Match
Probability match is a game for one or two teams in which students attempt to match cards to a given probability. There are 2 levels and feedback is given, which is especially helpful when the answer is incorrect. This is an excellent programme that consolidates and develops the students understanding of probability, the students liked playing this game and when working together the year 7 students managed to cope with the demands of level 2, where they had to select for example counters that were square or blue etc.
Overall, I think the variety of programs is good. There are those that review basic probability understanding as well as these that are a starting point for further discussion within the classroom. The girls found the programs easy to understand, provided they read the instructions, but did get a little frustrated at the slow paced that the counters were picked in some of the programmes.
Kersten Watkins
Mathematics Teacher, Jersey College for Girls, Channel Islands
MicroSMILE Mathematics Software
Isaac Newton Centre
108A Lancaster Road
London
W11 1QS
Tel: 020 7598 4841
Fax: 020 7598 4838
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