Show Me the Math! ~ Activities that Promote Divergent Thinking (K-8)

Recently, I ran across “5 Simple Ways to Add Creativity in Mathematics,” and was prompted to spotlight a few engaging math activities that are open-ended, have high ceilings, and can be adapted for any grade level. Even if you are using these in your classroom, you might like to skim through to read about possible extensions.

WHICH ONE DOESN’T BELONG?

HOW IT WORKS: Do you remember the Sesame Street® activity and song, “One of these things is not like the other…?” Well, this challenge, inspired by the book Which One Doesn’t Belong by Christopher Danielson, is similar in that students are presented with four math-related images (e.g. numbers, shapes) and must figure out which one doesn’t belong. However, there’s a SPIN on this puzzle! EACH one of the four doesn’t belong with the others, for different reasons. Students practice flexible thinking as they consider the attributes, and all answers are accepted as long as they can be justified and explained. If this puzzle is new to you, you can find a more detailed explanation in this blog post.

Matt Coaty, who shares about his students’ “math adventures” on the blog Educational Aspirations, created this WODB board where problems are displayed for two to three weeks and students use sticky notes to post their responses. If you work with different grade levels each day, this is one display that would invite responses from students of all ability levels. You can read more about how Matt has used WODB here, and follow him on Twitter® @Mcoaty.

High-school teacher Mary Bourassa was inspired to create the WODB website, where new problems are posted and submissions of new puzzles are accepted. Students could be encouraged to create their own and challenged to go beyond numbers and shapes to make WODB puzzles with patterns, graphs, equations, etc. You could also post kid-created problems on the board or in an online class and have classmates respond.

Playful adaptations of “Which One Doesn’t Belong” can be found on Twitter® @WODBMath, and many ventures across disciplines. Because this activity focuses on attributes, there are many possibilities. Selected images could spark conversations in science (e.g. four creatures), social studies (four U.S. Presidents), and language arts (four novels or vocabulary words). Update 4/21: Ian Byrd has just written about this idea HERE.

1 + 1 = 5 and OTHER UNLIKELY ADDITIONS

This fun book presents “unlikely” equations that make perfect sense: 1 goat + 1 unicorn = 3 horns, for example. Amy Chandler, a friend and former colleague, challenged her kindergarten GT students to “think like Isabel the Inventor” from the PETS™ curriculum and create their own. You can see examples and read about the activity here.

Here’s a possible extension: What if the quirky equation came first, and students were challenged to come up with ideas that made it true? Even older students could have fun with this.

Post the equation 1 + 1 = 6 and see how many ideas students can generate. A few possibilities:

• 1 ANT + 1 EARTHWORM = 6 LEGS
• 1 DUET + 1 QUARTET = 6 MUSICIANS
• 1 CIRCLE + 1 HEXAGON = 6 SIDES
  • 1 CAR + 1 BICYCLE = 6 WHEELS

Entitle a bulletin board “QUIRKY EQUATIONS” and have students tack on their responses to a different wacky equation each week. Students could also create their own and make a guessing game book or bulletin board with lift-the-flaps.

As with many activities, such as my TRIPLE-A ANALOGIES (for 4th-8th), consider your students and whether or not these playful equations might cause them any confusion!

CREATE A NEW MATHEMATICAL OPERATION

Ian Byrd’s website and video lessons (Byrdseed TV) are my #1 recommended sources of lessons with depth and complexity and this particular lesson inspires the math-imagination. Even if you are not currently a subscriber, you can view a preview of the lesson through September 20th. In his step-by-step written explanation, Ian discusses the importance of slowly scaffolding and suggests how to increase the complexity in order to get the most out of this lesson.

One idea I love is to have students combine their operations! I’m also wondering if students could present their “operation inventions” in a guessing-game format by sharing several true equations that incorporate their original mathematical signs and challenging classmates to figure out what is happening to inputs.

This FUNCTION MACHINE presents only unary operations, but there are three levels of difficulty for using with different age groups, and it may spark some ideas for sharing.

HOW MANY?

Here’s another book by Christopher Danielson that can be used across grade levels to spark math conversations and evoke many different kinds of responses depending on the age and ability of the student. The prompt is a photograph or picture with an invitation to count “how many.” Deciding WHAT to count is up to the viewer! Older students can show their thinking in a variety of ways.

For example, this photo of chocolate candies could generate many different kinds of responses using not just whole numbers but also fractions and decimals. The challenge would be to generate as many creative responses as possible.

HERE is a great example of a more complex picture prompt with sample responses to the task.

At the hashtag #unitchat, many teachers from all grade levels post photographs and strategies they use with students, and there are dozens of shared photographs HERE.

There are so many fantastic sources of open-ended problems! I hope to spotlight more in future posts. In the meantime, here is a wonderful collection of math resources generously shared by the creators. If you have used any of those mentioned above and can share additional thoughts or ideas, please leave a comment below! NOTE: If you’re new to this site, I encourage you to check out the VIDEO TOUR, which will help you find things more quickly.