ALG 13

Week 13: Here we look at how information (about the times at which goals were scored in a football match) can be represented in an ordered way in a table, and as points (or 'dots') on a Cartesian graph. The tasks give pupils the opportunity to make sense of such graphs by thinking about how the dots are linked and how this tells the story of how the score changed during the match.
You can of course choose your own football matches, perhaps involving a local team, or women's teams - or choose a different sport. But try to include 'interesting' scorelines, eg where the lead fluctuates.
You could also simulate scores by tossing a coin several times - with Heads representing a home goal, Tails an away goal - or forget scores and simply plot Heads and Tails cumulatively, ie as they arise. What sort of path will be formed by the dots?
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Monday: This task introduces pupils to the context of football 'score cards' and how we can use the information about when goals were scored to record how the score changed. Pupils need to work in a methodical way and it might be helpful for some pupils to have a copy of the score card so that they can cross through the times as they record each change in score.

You might want to ask pupils to describe the information contained in the completed table. How does it show the fluctuating fortunes of the two teams?
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Tuesday: Here we are using the standard coordinate system to represent the information in the table on a Cartesian graph. Where will the next dot be? - one unit up or one unit to the right?

It might help some pupils to join each new dot to its predecessor. Notice that each new dot is one unit above or to the right of the previous dot (why?) and that we start, inevitably, at the origin (0, 0) (why?).
This is what the final graph looks like:

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Wednesday: Here pupils have a chance to consolidate what they have met so far. Some pupils might want to draw an ordered table of the scores before completing the graph.

You might want to ask pupils to describe the characteristics of their completed graph and how this tells us about the changing scoreline. We look at the graph in more detail in Thursday's task.
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Thursday: Here we look at the completed graph from Wednesday's task. Note that we have added a red line to the graph - what is special about any of our dots that lie on the line?

Part b) is quite challenging, but also quite fun. The effect of the extra goal for the home team would be to move all the 'later' dots (goals) one unit to the right, as shown below.
You might want to ask other questions that 'transform' the graph in some way. For example, what if Ngadeu-Ngadjui hadn't scored at all? Or what if we'd had the same goals, at the same times, but that Sevilla had been the home team?

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Friday: This task should help pupils get a better feel for what the table and graph are telling us. It turns out that there is only one possible answer for some of the missing scores, but for others there are two answers that would fit the run of scores.

There is only one way to get from 3,1 to 5,1, namely 4,1. But we can get from 5,1 to 6,2 via 6,1 or 5,2.
The graph is illuminating here. We know that if we join consecutive scores (dots), we get a path composed only of horizontal and vertical segments and where the 'journey' from the origin only ever moves upwards or to the right. This means there is only one way to fill the 'gap' between the 2nd and 4th dots, but two possible ways to get from the 4th to the 6th dot, ie two possible positions for the 5th dot:

The actual times of the goals in these two matches are listed below. If they so wish, pupils can use this information to find the actual order in which the scores changed.

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We take a further look at ways of representing football scores in Week 14.