This chapter turns the theoretical into practical, by providing concrete examples of making rich math tasks. Traditional math classroom teachers show the methods for solving math first and then the students would solve similar problems over and over. To make math engaging and exciting for students, the reverse needs to happen: give students problems and challenges and then see if they can develop methods. In this chapter, various examples and case studies are presented, as well as six guiding questions for teachers to develop these tasks.

The one that made an impact on me, is “Can you add a visual component?” We forget that math is a visual process of seeing patterns and manipulating spaces. Most teachers, when presented with the requirement of teaching type of triangles (right, obtuse, acute, equilateral/angular, scalene, isosceles) will rely on showing examples, labeling each kind, and then having the students follow up with a worksheet or two. Unfortunately students might not learn that a triangle can have multiple characteristics, and might not have the opportunity to think “Can a triangle have two obtuse angles?” An example task that I have created helps make this triangle requirement more engaging.

- Provide construction paper, scissors, rulers to each student.
- Form groups of about 2-4.
- Using the ruler, fill up the whole paper with only triangles. Each triangle should be bigger than their fist.
- Cut out the triangles.
- Have the students sort the triangles. (Most students will sort by color and size.)
- Challenge them to sort another way.
- Challenge them to sort still another way. Every triangle has to be sorted, no triangle can be left out. Keep challenging them.

At the end, each group displays their favorite sorting, and then the rest of the groups get an opportunity to view them, with each group presenting how they sorted them.

We discuss each of the ways and they use words like straight angles, or two long sides, or all sides the same or all sides different. We see that a triangle can be sorted multiple ways and we make two categories of sides and angles. They use their words to describe each of the types and then I tell them “What great mathematicians you all are” and “Here are the terms that previous mathematicians used”. Then I tell them the actual terms and we match them up. They are now hooked and totally listening. At this point they want to “capture” this moment, so I let them make posters, brochures, etc, with the triangles they cut out.

##### My Big Takeaway

Try to reverse the traditional teaching method.

##### Three Tips for me to remember when planning math

**1. Add more visual opportunities for my students to explore math**

**2. Provide opportunities for students to work as a group and present their findings to each other**

**3. Don’t worry! Take the time to create rich tasks, make it a priority!**

Thanks for reading and let’s revolutionize math learning!