Team Building Activity:
Set up: For this team building activity, students will be in small groups of 3 – 4 students.
Materials: Each group will receive a set of 3 sticks, 6 colored rings and the following prompt:
Set up: arrange the sticks from left to right. On the leftmost stick, arrange the rings from largest to smallest with the largest ring on the bottom and smallest ring on the top.
Tower of Hanoi: You must move all of the rings from the stick on the left to the stick on the right in the fewest number of moves. The rings should end up in the same order on the right stick as they appear on the left stick now. There are two rules:

This team building activity promotes communication and collaborative group work. Students must communicate with one another in order to be successful. Students need to work together to figure out how to get the rings to the third stick in the order they are currently in with the smallest number of moves. Students also need to be creative with their solutions to ensure that they have used the minimum number of moves possible to get all of the rings from the first stick to the last stick.
If you haven’t seen the problem before, check it out here: Tower of Hanoi
Discussion: After teams have completed the activity, the class will participate in a discussion and address the following questions as a group:
 What strategies worked?
 What strategies didn’t work?
 How can you ensure you had the least number of moves?
 How did your teammates help you?
 What communication methods worked for your group? Are there ways you could have communicated better?
Group activity 2: After participating in the group discussion, each individual group will address the question, “how does this relate to mathematics?”
Extension Questions:
 What would the function look like if we graphed it?
 How would the game change if we had 4 or more pegs instead of 3?
 What is the least number of pegs needed for this game and why?
This will spark great group discussions that also encourage communication to build strong team relationships.
This TED talk on the power of introverts is a great way to introduce how every member of a team can bring unique views to their group. Definitely a great video to show students at the beginning of the school year to set the tone for cooperative learning.
Lesson Plan: Jigsaw II: Representations of Quadratic Functions
Lesson Objective: After completing this lesson, students will have a strong knowledge of how to use all aspects of quadratic functions, including what situations it is most appropriate to graph, find the min/max and solve. Students will also be able to connect their prior knowledge of quadratic functions to scenarios that exist outside of the classroom.
Lesson Outline:
This lesson focuses on students becoming experts in a small aspect of quadratic functions so that they can teach their peers in their area of expertise. Students already have a strong background knowledge of quadratic functions. This lesson acts as an extension of prior knowledge while continuing to build upon prior knowledge (ie: students know how to solve quadratic functions, but not necessarily scenarios to apply their solutions)
Lesson Timing: This lesson is designed to take two 45 minute class periods. The first class period is allotted for students to work on their tasks with their homogenous groups and break into heterogeneous groups to have their group discussion. The second class period begins with a whole class discussion of what each heterogeneous group discussed and feedback from their peers. The rest of the class period is given to students to complete the assessment activity with their heterogenous group.
Standards:
Set up: Students are divided into groups of three. Each group of three will be given an activity that corresponds to different aspects of quadratic functions: solving, graphic representation, and maximums/minimums. The activities will contain multiple examples of the representation. Students will all be given the same example, but will be asked to represent the activity with respect to their expertise area.
Solving Quadratic Functions (factoring, quad form, etc): This group will receive the following prompt:
You are standing on a deck 10 feet off the ground. From the deck, you use a slingshot to launch a water balloon to your friends below. The water balloon launch can be modeled by the equation f(t)=16t2+38t+10.
Algebraically determine how long it will take for the rocket to reach the ground.
Graphic Representation: This group will receive the following prompt:
You are standing on a deck 10 feet off the ground. From the deck, you use a slingshot to launch a water balloon to your friends below. The water balloon launch can be modeled by the equation f(t)=16t2+38t+10.
Graphically represent the water balloon’s launch path and label each part of the graph.
Maximum/Minimum: This group will receive the following prompt:
You are standing on a deck 10 feet off the ground. From the deck, you use a slingshot to launch a water balloon to your friends below. The water balloon launch can be modeled by the equation f(t)=16t2+38t+10.
What is the maximum height the water balloon will reach? How long will it take to reach that height? Rewrite the equation in vertex form.
Jigsaw: Once students have been given time to become experts on their own aspects of quadratic functions, they will get into heterogeneous groups (one graph expert, one solving expert, and one max/min expert) and will be able to teach their groups what they have discovered as experts in their area. As a group, they will discuss the following questions:
 What are the benefits of each different aspect of quadratic functions?
 When would you need one representation over another? Why would that representation be most helpful?
 Describe a scenario in which knowing the maximum or minimum would be most beneficial, a scenario where having a graphic representation is most beneficial and a scenario where solving the quadratic function would be most beneficial (hint: these should be 3 different scenarios)
Share & Discuss: The group will then share their discussion ideas and individual scenarios with the class so that there is a wide variety of examples for all students.
Assessment: The heterogenous group will then complete this activity to ensure that they have understood all aspects properties of quadratic functions.
Materials:
 Access to Desmos activity (computers, tablets, mobile devices)
 Materials for individual groups
 Discussion questions
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Amy, like Steph said, your use of Tower of Hanoi as a teambuilding activity is really cool! I especially like the questions that your students will answer/reflect on after doing the activity (almost more important than the activity itself!). I think that with any group activity, those questions are so important to answer to help students be continuously thinking about improving their group work skills.
I like the content that you chose to use with the jigsaw – I think it can be difficult in math to find a topic where there are 34 different aspects of it that don’t need to be taught in order. Your questions for comparing/contrasting different aspects of solving quadratics is so helpful. Great job!
Thanks so much Courtney! I agree finding a math topic that doesn’t need to be taught in succession is difficult! But there are a few topics that can be taught this way, so it might be fun to try next year … we’ll see how it goes!
Hi Amy, I appreciated your use of the TedTalk and how this could be incorporated at the beginning of the year. I think that I am probably an introvert too and as a student struggling through school this would have been really beneficial to hear. Not only can students benefit from hearing how their ideas and participation is still valuable but also teachers can benefit from hearing the TedTalk. Cain goes in to talking about the layout of the classroom and how we teach toward a culture of extroversion. How can we think about ways to teach to benefit introverts too?
Thanks for the feedback, Lauren!
I love your question and it is definitely something that is so pertinent in mathematics (and all others) classrooms. Definitely something to think about when designing future lessons. 🙂
Ah, yes I am SUCH an introvert, so that is definitely something I can relate to! I know for me, having a consistent small group of students (23) that I talk with, instead of talking in front of the whole class or rotating groups that I was in, was super helpful when I was in high school.
Amy,
I really like your lessons! I would love to try them in my own classroom as well. I especially like your TED talk selection for setting the stage for cooperative learning. I have successfully used Ted talks in my own classroom to introduce activities. I think you would really enjoy TedEd (links below). Some of the videos are perfect for integration into the classroom.
https://www.ted.com/topics/education
http://ed.ted.com/
Thanks Audrey! I will definitely check out the links and I can’t wait to use them in my classroom!
Amy,
Great job on your lesson! You show a a great understanding of the Jigsaw schema and I look forward to using this lesson in the upcoming year. I love how you have a graphing expert, a solving expert, etc, come into a group to share their expertise.
GB
Thanks Grady! Let me know how it goes in your class if you use it. I’m still skeptical on the expert idea and not having all students learn the same material, but I’m working on being open towards it. 🙂
Amy, I like how you decided to use the Tower of Hanoi as a team building activity. This problem can be so challenging, so it we definitely encourage interdependence among your students. It is also a great way to tie a team building exercise to the mathematical practices, as it causes students to problem solve and look for patterns.
If students are curious after leaving class about how to generalize the minimum number of steps it takes to move the disks, here is a website I found that explains it.
http://mathforum.org/dr.math/faq/faq.tower.hanoi.html
What a great link to sum up the activity for students. Thanks so much, Steph!