Handouts containing problem which have multiple approaches

Research says that problems with multiple approaches towards the solution generate engagement and student confidence. They also help develop a growth mindset towards the subject. Here are some examples of such activities.

The area of the leaf problem.

This problem which only requires the very basic knowledge of the area of a circle or a square is probably the first problem which got me interested in offering problems with multiple approaches in class. Good warm problem that anyone can attempt. The challenge is to find the area of the leaf with four petals. Even more interesting when only a single petal is given.

(The image extracted from http://mathworld.wolfram.com/Circle-CircleIntersection.html

The hex Chair activity (I am not the creator of the original activity). A very interesting activity that can be offered in an intermediate algebra class. Students come up with different ways of answering the questions.

Quadratic Progressions "Volcano" growth (Proposed by Jo Boaler, (http://www.youcubed.org/)

This activity asks students to identify the pattern of growth shown below. There are multiple ways to arrive at the same answer which creates an exciting activity for students.