# Four Ways to Use Your Learners as Equipment in Maths Lessons

I cannot take the credit for these ideas; I got them from an excellent session run by John Suffolk at the Association of Teachers of Mathematics conference. John explained that it is a good idea to use your students as equipment because then you don’t have to carry the equipment around from one classroom to another. Another advantage of this kind of teaching method is that taking an active part in the lesson, rather than just listening passively, helps students to learn.

1. Learning about multiplication tables, factors, and prime numbers. Ask ten students to stand up. Can they get into a solid rectangle shape? (5 x 2) Can they do it a different way? (A long rectangle 10 by 1). Now ask two more learners to stand up. Now how many different rectangles can they make? Now ask a thirteenth person to join in. What happens now? Why is this?

2. Sum of the angles in a polygon. Three students form a triangle. A fourth student moves around the inside of the triangle, being gently  guided by the three corners to make sure they turn through all the angles. When the student returns to where they started, they will be facing the other way because they will have turned through 180 degrees. Now try with a rectangle. What happens now? What about other polygons?

3. Algebraic Graphs. This requires a big space. A playground would be ideal. Mark out the x and y axes, either with chalk or with cards. To start with, each student stands on the x axis and they are told their x value according to where they are standing (x = -2, x = -1, x = 0, x = 1 etc.) and they all hold onto a long piece of string. You can give the more able students the negative numbers for differentiation. Then you give the students an equation such as y = 2x – 1. Each student has to move to the correct position. They should note what shape they make – a straight line for a linear equation and a curve for a quadratic. You can even solve simultaneous equations in this way – use two groups of students and two pieces of string. The point where the two strings cross over is the solution to the equations.

4. Loci. This is best done outside where there is plenty of room, but can be adapted for the classroom. Ask the students to stand approximately two metres from you. Ask them to note what shape they are making. (They should be roughly standing in a circle.) Now if you have two trees nearby, ask them to stand so that the trees are equidistant from them. You could also use two chairs, two students, or any other objects. What shape are you making now? The students should be in a straight line. This activity can also be used to show the loci of all points a certain distance from a straight line (just draw a line on the floor), the bisector of an angle (stand so that two walls are the same distance from you). Perhaps you can think of others.