How can I get my Year 7s to understand how enlargement links to ratios?

Context

• A coastal Technology College in the south of England,  Year 7 lower ability group.
• Level 3 and 4 students, with quite a wide ability range.
• Six boys, six girls.

Teaching and learning objectives

– Ratios and simplifying ratios
– Similar shapes
– Unit and aspect ratio
– Gradient
– Dimensionality

ICT resources and context

Children are familiar with the rudiments of GSP, a form of dynamic geometry software.   Each child had access to their own machine, which they could use to create and manipulate their drawing.

In this lesson the teacher allows the children to build up their own drawing, rather than providing one.

Explanation of the lesson

Students develop a sketch in GSP that illustrates similar rectangles, their unit rectangle equivalent and the gradient of their unit ratio. They recorded patterns for each ‘family of rectangles’ in a spreadsheet; the gradient graphs were then created using XY-scatter graphs.

Each stage of the process was carefully discussed and debated. The students were encouraged to articulate the patterns for themselves prior to be being told the correct language and notation. The students were encouraged to recognise when rectangles belong in the same family (similar) and when not, later in the lesson this was related to simplifying ratios.

For an extension activity some students investigated simplifying.

Evaluation of the impact of ICT on learning

Students gained a good understanding of similar rectangles and how this relates to simplifying ratios, they related each ‘family’ of similar rectangles to a family of similar ratios.
Some students extended this idea to unit ratio and related this to gradient.

One student produced a graph in a spreadsheet that plotted the unit ratio of each rectangle ‘family’ as a separate line.

The use of ICT meant that not only did children have their own dynamic investigation tool, they also completed their investigation in a fraction of the time that scale drawings would have taken.   Because they each had access to a machine they were actively involved in the lesson rather than being passive viewers of it.

Further development

I want to continue to develop this sketch with some older and more capable students. There are many possible extensions, some are suggested here along with the development needed to put this in a lesson.
Enlargement – movable centre for the enlargement diagrams.

y=mx+c – including relationship which are not directly proportional as dissimilar shapes.

Dimensionality and its effect upon area and volume under enlargement.


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