The purpose of this activity is to engage students in applying their knowledge of fractions in a geometric context.
This activity assumes the students have experience in the following areas:
The problem is sufficiently open ended to allow the students freedom of choice in their approach. It may be scaffolded with guidance that leads to a solution, and/or the students might be given the opportunity to solve the problem independently.
The example responses at the end of the resource give an indication of the kind of response to expect from students who approach the problem in particular ways.
Here are two equilateral triangles. One has sides that are 3cm long and the other has sides that are 6cm long.
What fraction of the large triangle’s area is the small triangle?
The following prompts illustrate how this activity can be structured around the phases of the Mathematics Investigation Cycle.
Introduce the problem. Allow students time to read it and discuss in pairs or small groups.
Discuss ideas about how to solve the problem. Emphasise that, in the planning phase, you want students to say how they would solve the problem, not to actually solve it.
Allow students time to work through their strategy and find a solution to the problem.
Allow students time to check their answers and then either have them pair share with other groups or ask for volunteers to share their solution with the class.
The student fills the larger equilateral triangle with a tessellation of smaller equilateral triangles and uses this to pattern to express the area relationship as a fraction.
Click on the image to enlarge it. Click again to close.
The student creates a physical model of the large triangle and folds it into equal parts. They use a fraction to express the part-whole relationship.
Printed from https://meaningfulmaths.nt.edu.au/mmws/nz/resource/big-and-small at 8:50pm on the 26th February 2024