25 Math Explorations - Center for Inspired Teaching

Click for more Inspired2Learn activities like this one. If you try this activity with your student(s), we’d love to see what you do; share with the #Inspired2Learn hashtag on your preferred social platform!

Created by: Aleta Margolis
Discipline: math, and also writing, science, and more
Age level: any
Time: a few minutes to as long as you want
Materials: many activities don’t require any materials; some require things like pencil and paper, compass, protractor, drawing materials, dice, or playing cards

What to do:

The intent for these ideas is to have the learners do them. The teacher or parent sets the stage and asks the questions, but it is the students who undertake the explorations, and figure out the mathematical concepts. If things go well, they will generate more questions as they engage in the activities. If learners can find answers – on their own, in (virtual!) conversation with friends, or with an adult’s help – that’s great. If not, that’s great too! Giving the brain something to puzzle through is good mental exercise anytime, especially now when our learners’ brains might be beginning to miss the daily stimulation of a face-to-face classroom.

Some ideas are more appropriate for young children, some for older students. But all can be adapted to fit any age group. So, adapt away!

And now…the list!

Find examples of shapes (squares, circles, triangles, etc.) and concepts (perimeter, circumference, area) inside or outside, or both.
List all the geometric shapes and/or concepts you see on your search. If you want, snap photos or bring your drawing supplies and sketch them.
Bring a protractor, pencil, and paper outside and see what happens.
Estimate the height of a tree.
Then, try and figure out how to measure it exactly.
Figure out what time it is in Japan, Senegal, and La Paz.
Read Dot and Line: A Love Story in Lower Mathematics, by Norton Juster. (And check out this short film adaptation!)
Draw a picture with one point perspective (single vanishing point).
Watch Multiplication Rock, part of the Schoolhouse Rock series.
Play games with dice, or cards, or both.
Have M&Ms at home? Put on some disposable rubber gloves and go through the bag and count the number of candies in each color. Graph your results. See how many days it takes to eat them.
Use your bathroom scale to weigh something different each day. First predict how much it will weigh, then find out! Consider pots and pans, toys, dolls, pets (you might need to hold your pet in your arms and then compare your weight with Penelope to your weight without her), shoes, books, stools, flower pots, etc.
Choose a room in your home and (with an adult’s permission!) arrange the furniture in a symmetrical formation.
Choose a room in your home and (with an adult’s permission!) arrange the furniture in an asymmetrical formation.
Figure out the probability of winning today’s lottery if you buy one ticket. If you buy 5 tickets.
Put a bunch of different colored marbles in a bag—3 or 4 colors, and lots of marbles. Keep track of how many marbles of each color go into the bag. Close your eyes and choose one marble at a time. Predict the likelihood of choosing a red marble, a blue marble, etc., i.e. “I think my chances of choosing a red marble are 1 in 4.”
Graph the results of the marble picking exercise.
Make it more challenging. Predict the likelihood of choosing two red marbles in a row; of choosing no red marbles in five tries; of choosing a red followed by a blue.
Make it simpler. Do the above three activities tossing a coin.
Calculate the amount of soda you consume in a week.
Calculate the number of calories of soda you consume in a week. (Soda cans provide the information you need for this one, and the one above.)
Calculate the number of hours you spend in a day, then in a week, watching TV.
Calculate the number of minutes, hours, etc. you spend in a day, in a week on your phone.
Keep a math journal—focusing on feelings/fears/successes about math; focusing on places you found math that surprised you; focusing on how you solve math problems; or all of the above.
Figure out how old you are in months, days, hours, minutes.

Inspired Teaching connection:

Because these exercises come in the form of ideas, not fully articulated lessons, it’s up to the students to figure out how to execute them. Students get to decide which activities to try, how long to spend on each activity, how and whether to extend their learning, and more. These activities place the learner in the driver’s seat, in line with Inspired Teaching’s Core Element Student As Expert. The activities further engage students in the Wonder-Experiment-Learn Cycle, as they estimate the height of a tree, predict the likelihood of drawing a green marble (or eating a green M&M), or create symmetry with the furniture in their living room.

See our instructional model here.

Micaiah Anderson

Community Outreach Specialist

As a Community Outreach Specialist, Micaiah is responsible for program promotion and outreach support for Inspired Teaching events and workshops. Micaiah has a passion for collaborating with community members to build-power and connect. She is an educator with a heart for youth and has experience supporting students fight injustices within their schools and communities. She has a BA in Political Science from, the real HU, Hampton University & anticipates graduating in May 2024 with a Masters of Arts degree in Educational Policy Transformation from Georgetown University.

AUTONOMY

"I want to have a say in what happens to me."

Autonomy is the need for independence; the ability to make choices, to create, to explore, and to express oneself freely; to have sufficient space, to move around, and to feel unrestricted with opportunities to exercise free will.

Brady Maiden

Outreach Coordinator

As the Outreach Coordinator, Brady helps maintain Inspired Teaching’s social media presence and supports the organization’s mission to connect with DC community leaders, educators, and parents. Brady has her Master’s in Public Policy from George Mason University and her BS in Political Science from Northern Arizona University. She is passionate about community, equity, and coalition building recognizing that learning and growing with the community at large is how we continue to be impactful.

What brings you joy in life?

I find joy in spending time with my friends and family and meeting new people. I like going to concerts and festivals, and finding new books to read.

The Learner’s Cycle, Wonder-Experiment-Learn, and the Teacher’s Cycle, Observe-Plan-Instigate, comprise Inspired Teaching’s approach to engaging students in inquiry-based learning.

When they are engaged in the Wonder-Experiment-Learn Cycle, students are immersed in learning. They take the lead in designing authentic learning experiences around their own interests and their school’s standards of learning. Each discovery leads to a new question which in turn leads to more wondering and more learning. In the Wonder-Experiment-Learn Cycle, Learn is not a destination or an endpoint; it is a deeper understanding, leading to a deeper wondering and new possibilities that create new entry points to further exploration. The cycle continues because what students have learned generates more wonderings that require more experiments that foster more learning – and on and on.

The Observe-Plan-Instigate Cycle is the work of an Inspired Teacher. While a student is expected to follow the Wonder-Experiment-Learn Cycle, the teacher joins them on the learning journey while following their own cycle of Observe-Plan-Instigate. This cycle ultimately serves to ensure an inquiry-based atmosphere is at play in the classroom.

Jaqueta Abbey

Teaching and Learning Specialist

Jaqueta is the Teaching and Learning Specialist for Inspired Teaching. In addition to her current role with Inspired Teaching, Jaqueta is a first-grade teaching assistant. Her background features a variety of traditional and non-traditional experiences in the field of education, including working as an adjunct professor, teaching summer reading programs to children and adults, and tutoring children in the foster care system. Jaqueta earned a B.A. in Communication Studies from the University of North Carolina at Chapel Hill, and an M.A. in Interactive Media from Elon University.

What brings you joy in life?

Creative self-expression! In addition to my passion for storytelling, I love dancing of all kinds. I've studied belly dance, bachata, and Brazilian Zouk among other styles. I also enjoy glass fusing, crocheting, photography, and cross stitching. These art forms allow me to express myself and build connections with other people at the same time. I think life would be a lot less vibrant without artists and storytellers!

Michelle Welk

Communication & Marketing Specialist

As Communications and Marketing Specialist, Michelle is responsible for finding and creating new ways to highlight Inspired Teaching and promote its programs in order to expand and deepen the organization's impact. Michelle has worked in communications in an array of settings, from creative agencies to state politics to national nonprofits. She has a BA in Journalism from Temple University in Philadelphia and is passionate about education, access, and equity.

What brings you joy in life?

My son, the beach, making a persuasive argument and good food!

Max Peterson

Real World History Assistant Teacher

Max received his Bachelor’s degree in History and African American Studies from Boston University in May 2016. He has worked in museum curation at the Museum of the White Mountains in New Hampshire and the Smithsonian National Museum of American History. Max has worked with young people of varying ages from young children to young adults transitioning to college.

Feedback and Accountability

We grow through feedback and an understanding that the quality of our work is a reflection of what we are learning, but the shift to remote learning this spring disrupted a lot of the tools teachers were used to using to evaluate student growth. How might we do things differently this fall? Participants in this workshop will explore ways to bring meaningful assessment into the virtual and/or socially-distanced classroom and approaches to student feedback that strengthen motivation, and build relationships and achievement.