Matching FacesTask 223 ... Years 4  10SummaryThe task is constructed around the story shell of a student tricking a new teacher by randomly placing name cards in front of a group of classmates. Given the placement is random, how many correct matches of name card to person would you expect. Students at almost any level can design an experiment to gather data about the focus question. Given the guidance on the card, more experienced students might break the problem into parts, collect and organise data and discover a pattern or two. 
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IcebergA task is the tip of a learning iceberg. There is always more to a task than is recorded on the card. 
In this task our student mathematicians are faced with the question of the number of matches (name to person) to expect for different size groups. The suggested approach is to predict an answer and then carry out experiments to get an idea of what might be expected. Four students and four names is the first experiment because it is just enough to provide a response that might not be expected. It is not unusual for students to reason that if there are more faces receiving names there will be more matches. If four faces are involved then initial reasoning suggests that for any trial there could be 4, 3, 2, 1 or 0 matches. Here is a partial record of one set of student results:

Whole Class InvestigationTasks are an invitation for two students to work like a mathematician. Tasks can also be modified to become whole class investigations which model how a mathematician works. 
As a whole class investigation, this problem cries out to be acted as an introduction. You will also need 5 blocks or counters in different colours for each pair to be the 'faces'. Choose four students to be 'the class' and one to be the monitor. Write the students' names on pieces of paper and tell the story as the monitor acts it out, randomly placing the names face down in front of the students. Dramatically pause and take a straw vote of the expected number of matches. Record on the board. Carry out the experiment and record the result of this first trial. Repeat the experiment another two or three times, modelling recording of the outcomes. Invite students to begin their journal entry for the problem by describing the experiment, copying the results so far and including their prediction of the expected number of matches. As students complete their entry they collect a set of 'faces' and carry out their own five experiments. Results are added to the class data. The evidence will point to one match as the expected number.
Round off by discussing the evidence which suggests that even for 100 students and names the expected number of matches is just one.
At this stage, Matching Faces does not have a matching lesson on Maths300. 
Is it in Maths With Attitude?Maths With Attitude is a set of handson learning kits available from Years 310 which structure the use of tasks and whole class investigations into a week by week planner. 
The Matching Faces task is an integral part of:
