UK Video clip Fact Sheet: Exploring equivalent algebraic expressions
General information
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2006
UK
English
11-12 years
A middle achieving class in a state comprehensive school.
Exploring equivalent algebraic expressions
Flash applet and interactive whiteboard
(version 2.0 - used in video)
http://www.skoool.co.za/ToolKit/files/Vs1.8_numberline_za_setup.exe
(version 3.0)
http://lgfl.skoool.co.uk/content/toolkits/numberline/index.html
Students working both individually and as a whole class using the interactive
whiteboard in the mathematics classroom
Male teacher new to mathematics teaching and in the use of a flash
interactive number line
Lesson outline.
Student worksheet developed by the teacher.
Qualifications and Curriculum Authority (2004)
Starting situation
The video is an extract from a television documentary that features a mathematics department in an
English state secondary school who are working together to develop the way that they use
technology in their mathematics lessons. They are being supported by an external consultant who
introduces them to a Flash applet, which features a dynamic number line designed for use on an
interactive whiteboard. Having been introduced to this new resource, one of the teachers develops
a lesson for his class of middle achieving 11-12 year olds to support the students to develop a deeper
understanding about a given set of equivalent algebraic expressions.
Task description
The students have been given a worksheet, prepared by the teacher, on which a number of
expressions are given and the students are asked to try choosing difference values for ‘n’ and
through substitution, identify the expressions that are sometimes or always equal. During the final
lesson plenary, the teacher invites selected students to test their conjectures by inputting two
expressions and exploring whether they are sometimes or always equal by dragging ‘n’ along the
number line.
Clip description
The video clip begins with a group of teachers, who have just been introduced to a dynamic number
line tool, discussing how they might use the resource in their mathematics classrooms with their
students. The clip follows one of these teachers into his classroom as he uses the resource for the
first time. We watch him introduce the students to the notion of dragging a number flag marked ‘n’
along the line and hiding and revealing its value. Later in the lesson, the teacher defines two new
number flags as a= n2 and b = 2n, to enable the students to discuss for which values of n, the values
of a and b would be equal. During the final plenary, he invites a student to the board to drag the
position of n and identify that, when n=2, the values of a and b are also equal.
Transcript
Narrator: As they experiment with the new software the teachers discuss the impact it might have
on their teaching.
Teacher: And then I’d get a student up [to the front of the class] and then they press the on button
and show the true value.
Teacher: They are not sitting waiting while you are writing. They are with it all the time and in the
lesson you should get much much more covered- and hopefully they would learn a lot more.
Teacher: It gives you the opportunity to be able to think of more questions that might mean us
having a departmental meeting where we can think of various questions that go with different levels
of students abilities.
Narrator: So, straight away maths teacher Barry Miles tries out the new interactive number line for
the first time with his class of middle ability year 7 pupils (11-12 years).
Teacher: [to the student] Thank you very much – and what would you hazard a guess at
Student: Errr ten point seven.
Teacher: ten point seven? Well let’s see what it actually is… ten point seven.
Narrator: The purpose of the lesson is to look at expressions involving the letter ‘n’, including some
which are often the source of confusion such as 2n and n2. In the plenary session they discuss these
expressions.
Teacher: When might n2 be the same as 2n?
Student: Two?
Teacher: Two? Do you want to have a quick try? It’s your answer, you show it… We’re looking for any
places where they may have the same answer, although they (the expressions) are not equivalent.
Teacher: Look at that, on two, one under the other because two times two is four and that is two
squared, isn’t it? Anywhere else where they might be the same?
Narrator: Barry realizes that he can involve the pupils more by letting them explore the number
relationships for themselves on the number line, leaving him to ask more questions.
Teacher: What is happening to a as you move (n) to the right?
Student: It’s going ten more than it should.
Teacher: well, it’s going a lot further isn’t it? You are losing it off the scale. So going that way, you
would expect a to go further and further away from you, wouldn’t you? Would you try the other way
then? It’s coming back, it’s getting closer.
Teacher: That’s the one we had, go on, keep going… because ‘a’ is under there but… Look at that, on
zero.
Teacher: The package is quite easy to use and the children can find out how to use it quite easily
themselves. So, from my point of view it’s revising my questioning techniques so that I can actually
get the misconceptions out of them (the students) and hopefully it will just breed their interest in the
maths’ concepts.
Additional information
The teacher’s complete lesson plan and the worksheet used by the students in this lesson can be
downloaded from the EdUmatics website.