Lesson 83

Temperature Graphs

Overview | Lesson Plan | Classroom Contributions

Lesson Plan

Summary

At first glance, this lesson doesn't seem dramatically different from traditional practice. However, it does contain several elegant and significant features which contrast somewhat with that traditional approach.

Students in small groups are given a number of graphs representing the average temperatures of various cities over a one-year period. They are challenged as a group to match each graph to a city and to justify their choice. The lesson actively uses a relevant context (regional geography), problem solving and cooperative group work to develop graph reading skills. This approach directly contrasts with a traditional 'text-book' approach.

Extensions using computer support allow the teacher and student to explore a range of similar challenges.

Charles Lovitt Comments:

I was surprised how the same resource - a piece of paper with graphs - could be used by two different teachers in two utterly different ways. One chose an open problem solving approach; the other the closed question approach!

Resources required

• Investigation sheets (supplied):
    Australia's Capitals
    Asia Pacific Cities
• software is available from the Software Sample Library.

Lesson stages

1. Getting started
2. Solving the problem: in groups
3. Discussing results: as a class
4. Finishing the problem: conclusion

Lesson notes

1. Getting started

This lesson is as presented by a particular teacher. The commentary has been added by the observer who was alert to the importance of the teaching craft being displayed. Key features of that craft are collected at the end of the lesson.

Preparing for the lesson

To prepare for the lesson, print copies of one of these worksheets:

Australia's Capitals
Answers: Reading from left to right across the rows the answers are Darwin, Perth, Adelaide, Canberra, Hobart, Sydney, Melbourne, Brisbane

Asia Pacific Cities
Answers: Reading from left to right across the rows the answers are Honiara, Suva, Kuala Lumpur, Jakarta, Auckland, Adelaide.

Introducing the challenge

The teacher handed out the worksheet to students sitting in small groups of 3 or 4.

I have a puzzle for you. These graphs are temperature graphs. There is one for each of the eight capital cities of Australia that are written on the sheet.

The top line on each graph is ...(pause for response)... the average daily maximum temperature for each of the months of the year,
and the bottom line is ...(pause for response)... the average daily minimum temperature for each month of the year.

Can you guess the challenge I have for you?

Students easily guessed and stated the challenge of matching each city to its graph.

2. Solving the problem: in groups

Are you willing to have a big fight (I mean discussion) in each group and see if you can agree on which city goes with which graph?

Pause...

Can I give you about 6 or 7 minutes? Then we'll see if we can all agree!

The students then argued (sometimes strenuously) until they had reached agreement about the matching. Much incidental knowledge emerged. One student said:

Look at this graph - it's always hot - it must be in the tropical area!

3. Discussing results: as a class

The teacher had to find a moment of intervention, which was when most groups were nearing completion.

Let's see if we can agree on which goes with which. Don't worry if you have not finished yet, or if you want to change your mind as you hear other groups report. That's okay. Which graph 'attracted' you first?

The graphs were argued for one by one. The teacher, rather than give a signal about whether any 'guess' was correct or not, looked to the rest of the class for approval or disagreement.

I'm looking around for nods of approval - or say so if you disagree.

The extreme graphs were easy to get and all groups seemed to agree, but for the last few there was significant discussion as different opinions emerged.

If the discussion did not generate the 'right' answer, the teacher calmly said:

and in so doing brought the discussion to a nice close.

4. Finishing the problem: conclusion

The teacher wanted the class to reflect on their own learning journey and led the class into a discussion with the question:

Well done, we've got all the graphs correct. I'd like to ask you Is this a good way to learn your mathematics? What did you like about the lesson? Or perhaps, what was not so good about it?

With this question, the teacher was acknowledging that there are differences between this lesson and traditional practice and wanted the students' opinions about these. Such opinions can sometimes be very illuminating. One student said:

It was much better than the boring text book!

Not content with this superficial response, the teacher probed further:

What do you think it was that made it less boring?

Extensions

The computer support for the lesson is provided by a database of various cities, and an interactive page that lets the teacher (or the student) click on a range of cities. Six cities make up a worksheet. For example, selecting Asia Pacific cities produces the on screen layout shown.

This worksheet can be done interactively on screen or printed as a handout for students.

Each option performs as follows:

• Asia Pacific:

  The program randomly selects six cities from this region and constructs a worksheet as shown.

• North America:

  Similarly, selecting this option randomly generates a worksheet of six cities from this region.

• Any 6 cities:

  If this option is selected, a data base of cities is offered. In this picture, four cities have been selected so far.

  

  After six cities have been selected, they appear as an electronic worksheet, as in the other options, that can then be solved on screen or printed and copied.

  The software therefore allows worksheets to be crafted to fit the interests of the group. They can be made simple or quite difficult, depending on the prior knowledge of the group. They can be regional or global, depending on the geography being studied.

• Edit or add to city data:

  This option allows the student or teacher to use the data base to insert data for any cities for which it is known. Here the new city has been called TEST and the entry of data has begun.

  

  When all months have been entered and a category selected, the Add entry button adds TEST CITY to the alphabetical list, and it becomes available to the other options. In this case it was added to the Asia Pacific category.