25 Math Explorations 

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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!

  1. Find examples of shapes (squares, circles, triangles, etc.) and concepts (perimeter, circumference, area) inside or outside, or both.
  2. 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.
  3. Bring a protractor, pencil, and paper outside and see what happens.
  4. Estimate the height of a tree.
  5. Then, try and figure out how to measure it exactly.
  6. Figure out what time it is in Japan, Senegal, and La Paz.
  7. Read Dot and Line: A Love Story in Lower Mathematics, by Norton Juster. (And check out this short film adaptation!) 
  8. Draw a picture with one point perspective (single vanishing point).
  9. Watch Multiplication Rock, part of the Schoolhouse Rock series.
  10. Play games with dice, or cards, or both.
  11. 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.
  12. 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.
  13. Choose a room in your home and (with an adult’s permission!) arrange the furniture in a symmetrical formation.
  14. Choose a room in your home and (with an adult’s permission!) arrange the furniture in an asymmetrical formation.
  15. Figure out the probability of winning today’s lottery if you buy one ticket. If you buy 5 tickets.
  16. 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.”  
  17. Graph the results of the marble picking exercise.
  18. 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.
  19. Make it simpler. Do the above three activities tossing a coin.
  20. Calculate the amount of soda you consume in a week. 
  21. 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.)
  22. Calculate the number of hours you spend in a day, then in a week, watching TV.
  23. Calculate the number of minutes, hours, etc. you spend in a day, in a week on your phone.
  24. 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.
  25. 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.

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