# Twenty Questions For Math Class

In a conventional game of Twenty Questions, one person thinks of something and everyone else tries to guess what it is by taking turns asking one yes-no question at a time. If questions are chosen thoughtfully to eliminate broad categories of information with each response, a correct answer often is attainable within twenty questions.

The challenge and fun of Twenty Questions increases exponentially if you place a mystery math word or expression on the back of each student in your class and let students wander about with the double goal of trying to figure out "What am I?" by asking useful questions that can be answered by yes or no, and providing helpful yes-no responses as their peers tackle their own mysteries.

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This word-on-the-back version of Twenty Questions is a great way to review and synthesize new math vocabulary and concepts at the end of a unit.

## "WHAT AM I?" A GAME OF TWENTY QUESTIONS FOR MATH CLASS

Write math vocabulary words or expressions connected to the current unit of study on sticky notes or slips of paper. Place easier terms near the top of the stack and more difficult terms near the bottom of the stack so you can give each student an appropriate challenge when play begins.

* numbered record sheets and pencils for recording questions asked and responses * math vocabulary lists with definitions for the terms under study (optional but recommended) * tape for attaching or reattaching papers to students' backs if needed.

Wendy Petti is the creator of the award-winning Math Cats Web site, author of Exploring Math with MicroWorlds EX (LCSI, 2005), and a frequent presenter at regional and national math and technology conferences. She teaches grade 4 math at Washington International School.

Procedure:
* Play one demonstration round as a class to model useful questions that start out broad and gradually narrow the field. Most questions will target math concepts, but a few might address linguistic matters, such as: "Am I just one word?" "Am I a noun?"
* Pass out vocabulary lists and numbered sheets for recording questions and answers.
* Place a mystery word or expression on each student's back, drawing from the top, middle, or bottom of the stack as needed to accommodate different proficiency levels.
* The students circulate, asking questions and recording responses, while also answering questions asked by their classmates.
* As students figure out their mystery words, they may receive a new word or expression from the teacher and begin a new round.
*Students who cannot guess correctly within twenty questions may opt to keep guessing or to "give up" and see their words, then start over with new mystery words or expressions.

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## LEARNING DURING A REVIEW GAME

Twenty Questions is a great review game; however, you also might find students solidifying or acquiring new knowledge during play, when unexpected questions lead them to consider familiar terms from new angles.

As an example, let's peek in at a game of Twenty Questions featuring geometry vocabulary in a grade 5 class. Students step out of the game briefly to ask the teacher such questions as

• "I know a line is one-dimensional, but what about intersecting lines?"
• "Is a face considered two-dimensional, even if it is part of a three-dimensional polyhedron?"
• "Ron's word is degrees. He asked me if he has any angles. I know angles are measured in degrees, but you can't say degrees have angles, can you? Could I say sort of, since degrees are so connected to angles?"

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But what if...

What if there aren't enough math vocabulary terms in the unit for each student to have a unique term?
There should be no problem in placing duplicate terms on some backs.

What if there are fewer than twenty math vocabulary terms in the unit, so a student simply could ask each word in turn and solve the mystery within twenty questions?
There are several solutions:

• Modify the game so the mystery must be solved within a smaller number of questions.
• Require that students ask and record a systematic series of questions that progressively narrow the possibilities.
• Include extra math vocabulary words from earlier units or years of study.
• Include an assortment of relevant numbers along with math terms. (For instance, include some fractional numbers in a unit on fractions.)

What if my stronger students don't need a math vocabulary review?
Strong students can challenge themselves to solve their mystery term in the fewest possible number of questions or they can "debrief" afterward to determine a more efficient path to the solution or to rank-order questions. Some students also might enjoy these extensions of the activity:

• Design a flow chart, logic table, or Venn diagram to illustrate effective questions and categorization of terms.
• Determine which terms would require the most and least number of questions to be solved.
• Write additional math terms for their advanced peers, drawing from all math vocabulary learned to date, and see if any math term still can be deduced within twenty questions.
• For ideas on integrating Twenty Questions and technology in the classroom, see Education World's 20 Questions: Can You Stump the Machine? (Can students begin to develop a plan for teaching a machine to play a math version of Twenty Questions?)

What if certain students cannot solve their mystery words on their own?
In a peer support variation, two students could collaborate to solve the same mystery term; they might carry the word in an envelope for their classmates to peek at, instead of wearing it on their backs. You might pair a helpful stronger student with a weaker student for a few rounds to demonstrate and discuss effective questioning and reasoning.

## BENEFITS OF TWENTY QUESTIONS

What are the benefits of playing the word-on-your-back version of Twenty Questions in math class? Here are twenty answers to one question!

1. The activity engages everyone in the class at the same time.
2. The activity is adaptable for any age, level of preparation, or scope of material.
3. Within one class, the game provides for differentiated instruction and review: Mystery words can be targeted to different levels of math and reasoning skills.
4. Students move freely about the room with a sense of purpose and focus.
5. Students take charge of the activity, determining their own pace and approach.
6. The game builds critical thinking skills as students learn to ask effective questions, categorize and synthesize information.
7. As students alternate between the roles of inquirer and helper, the activity remains fresh.
8. The game integrates math and language arts as students consult study guides and record responses to their questions.
9. The game format promotes cooperative learning as students respond to one anothers questions.
10. The game is a grand equalizer: Even the strongest students need help from their peers to succeed, and even the weakest students can provide helpful information.
11. The game format promotes friendly competition: Students are motivated to solve their mystery terms, but everyone can be a winner. It doesn't matter who finishes first or how many questions are asked.
12. A student who is stumped can start over or put more attention to responding to others' questions without a sense of failure.
13. The game provides a fun context for: * reviewing
* clarifying
* solidifying
* synthesizing
*and extending math vocabulary and concepts at the end of a unit or term.
14. The game is an effective, informal tool for self-assessment.
15. A teacher circulating during the activity can assess and assist informally.
16. It's fun, and your students will beg to play again!