A new appreciation for Problem Solving and for Algebra

I am so proud of the kids I teach today.  Since the start of the year we have had a much stronger focus on patient problem solving than they might have been used to in the past and until today there has been a lot of resistance to attempt some of the tasks.  But today they were superstars, it is the first time where almost all of them had persisted in solving a problem, even when they found it difficult.  There had been pockets of this in the past, but to see most of the class doing it today was fantastic.

Over the last few days I have been speaking to another teacher about algebra and some of the ways we can make it more interesting to students whilst also focusing on some very collaborative problem solving.  He mentioned previously that he had worked on taxi fares as a way of introducing a real life context for linear equations including substitution and solving equations.  So we sat and developed the idea.

The lesson that we decided to look at was based on an ad produced by the motor accident commission in South Australia.  The idea behind the lesson, which they came up with at the start, was to find out how long they were actually in the back of that taxi.  For the sake of trying something a bit different we combined three maths classes with three maths teachers to see how it would go.

Students were then asked to generate some ideas about what is the sort of information that they might need to know to answer the question and they came up with

• Cost per minute
  
• Cost every 5 minutes
  
• Where they took the taxi from
  
• What their destination is
  
• Time taken to the arrive to the destination
  

From here they need to have some information in order to be able to progress forward firstly was how they calculate the taxi fares.  Students were given the formula below, but were not shown how to use it at all.

Cost of the fare = Distance cost + Waiting Time Cost + Flagfall

Next they were given the following images that show the taxi meter, the map of the route and the prices and were asked to use only the information provided to determine how long they were in the taxi.  This was enough to create a hive of activity in those three classes.

It was great to see how students had made the decision that they needed to compile information from several sources realising that they needed to use the time of departure to find out what tariff they would use and then using the tariff information to relate back to the distance traveled.  This continuous movement between different sources of information was really great to see.  The path they took from this point was pretty different with each group. some were able to work through it themselves and some needed some further prompts, but very few actually gave up on the problem. Even when they did not have much success initially they really took on the prompt and tried to incorporate it into their thinking and that is why I am so proud of them today.