Recreating Ratios TN
One of the challenges of mathematics is to provide opportunities for students to be creative with their mathematics, and to find activities that allow students of differing abilities to obtain satisfaction in this process. The more creative students are with this “Recreating Ratios” activity, the more it will help to draw out the concept of proportion. They will see for themselves that despite the myriad forms and size of each others patterns, the proportions remain the same.
Students can struggle to see the relationship between the ratio 1 : 3 and a picture with 3 red and 9 blue counters in it, or 15 red and 45 blue, especially when one ratio patten is in the shape of a boat and the other is in the form of a giant. However, in having to construct the pictures for the different ratios themselves, the link between the simplified ratio and their more complex design is made concrete. This ratio concept is given a kinesthetic, experiential anchor.
Designing their Creations
The following slideshow demonstrates the variety of designs that a handful of groups produced in 5 minutes for the ratio 2:5. In one class, no two pairs of students had produced the same design!
Anything can act as a counter, the only real requirement is that you have sets of things that are all the same: two different shapes of pasta, two different coloured sets of stones, or shells, collected from the beach, collage equipment/media from the art block. The display possibilities for this activity are wide ranging, visually very appealing and hugely help to reinforce that proportion is a comparison of quantities not an absolute quantity.
The activity does require a full hour, and longer, if you want to use the pictures taken, or artwork designed during the lesson, to make a display for the classroom.
Cross topic links
I used this activity, at the end of a module on ratio and rounding, as a lead in to the next module on sequences and graphs. Students can take one of their patterns and “grow” it through several (‘n’) stages of evolution, then find the term-to-term and position-to-term rule to generate the red beads, and the same for the blue! Why not then plot these sequences on a graph and make the link to equations of graphs and the gradient as a simplified ratio: change in y, for a corresponding change in x. The options are many, varied and creative.
The worksheet, complete with sketches, can serve as a revision record of their work, as well as the photos downloaded onto their mobile phones or other electronic devices and/or a completed classroom display. They could use the pictures as the screensaver on their home computer for the week!