Laying it on the line
The key stage 3 framework of the National Numeracy Strategy is littered with the words "explore with a graphic calculator", but for teachers who have had little experience of using them with a class of 30 students, it isn't always that easy to see how to go about doing this.
If you are considering buying a class set, or maybe you already have and are considering getting them out of the cupboard for the first time, then here is a description of a lesson that I taught with Annie Botfield, a teacher from Parkfields Middle School, Toddington. Hopefully it will give you some ideas on how you can use graphic calculators to enhance some of your lessons.
The guinea pigs were a top set Year 7 class and the main learning objective was to "Recognise that equations of the form y=mx+c correspond to straight-line graphs".
Their teacher started the lesson with a quick mental and oral activity using a counting stick. The pupils counted aloud, two sequences at the same time: 1, 6, 2, 12, 3, 18...
She then asked them questions such as: "what would term 10 be for each sequence?" and "Is there a rule that maps one sequence on to the other?"
She then extended the activity by looking at other sequences and finally square numbers.
I took over at this point and handed out an envelope to each pair of students. Inside the envelopes were 24 cards, on to which were printed different equations (see table). We asked the students to classify the equations into different groups. We gave them a few minutes to discuss in pairs and then asked for some feedback. There was a whole range of different solutions and their responses ranged from one pair who had only two groups, to another which had 10.
Next we asked them to split their largest group into further sub-groups.
Once again we took feedback from as many students as possible.
At this point the graphic calculators came out of their boxes to the great excitement of the class. Using an overhead projector I gave them a quick tour of the calculator. We then asked the students to draw one of their groups, containing around four equations, and to describe to the class what they saw on the screen. As the graphs started to appear, you could tell they were impressed by the strange noises that could be heard around the room. Several students provided feedback and we encouraged them to discuss and explain their thinking as much as possible.
Next we asked them to come up with a new member for their group that would satisfy the criteria, which they then tested with the graphic calculator.
Finally, we asked them to come up with a counter example that would not fit the group and would look out of place on the screen. We took a considerable amount of feedback at the end of this section to try and maximise the learning.
For the plenary I drew three graphs on the overhead projector and put three equations on the board and asked everyone to match the graph with the equation. We stressed to everyone that they needed to be ready to justify their answers. The responses from the plenary showed that the lesson had met its objectives and the comments from the students showed that they thoroughly enjoyed the lesson.
The teacher was also positive and said that: "Seeing the different groupings of equations and graphs consolidated the children's understanding of the components of the equation y=mx+c and gave them the chance to see many more examples of straight-line graphs and how they were related to each other."
The idea for this lesson came from the Bedfordshire Thinking Maths Group, which is a team of about 20 teachers from primary, middle, upper and special schools. This group is part of the Bedfordshire Schools Improvement Project (BSIP) - a network of 56 schools working on a range of development activities to improve teaching and learning.