There’s something intriguing about guessing games. The mystery of not knowing the answer and having to use clues to figure it out has always been something that motivates children. All I have to do is to say, “I’m thinking of a secret number, what do you think it is?” and students are immediately excited and ready to play.

There are so many good reasons for playing math guessing games with your students. First and foremost, these games help our students develop their logical reasoning skills and their intuition about numbers and shapes. Guessing games show kids that mistakes are welcome, especially when we learn from them. When students play math guessing games, children begin to use the important problem solving skill of guessing and checking. And finally, math guessing games create a positive learning environment that leaves children hungry for more math.

Following are some favorites we’ve used with students from TK through the middle school grades.

**Guess My Rule**

This is a game that is highly adaptable and encourages children to consider attributes of numbers and then to sort and classify them. Because the game can be challenging, I usually play a non-math version called *Mr. Picky Food* to get the students acquainted with guessing a rule in a friendly and accessible way.

I begin the game by telling students that I have a friend who is very picky about his food. He chooses a secret rule and only eats foods that fit his rule. Following are the steps to the game.

Think of a rule for Mr. Picky Food (for example, Mr. Picky Food might only eat vegetables; or he might only eat things that are orange; or he might only eat fruit). Keep this rule a secret for now.

Draw a t-table and label the two sides “Likes” and “Doesn’t Like.”

Elicit food guesses from students.

Write the students’ guesses on the t-table according to the secret rule.

Stop occasionally to have students hypothesize about what the rule might be, what the items in each column have in common.

Here’s what the t-chart looked like about half-way through a game I played with a group of fifth graders. Can you guess what Mr. Picky Food’s rule is?

The key to playing this game with students is to pause after a few guesses and ask them to talk about what they notice and hypothesize about possible rules. To spice things up, I sometimes add items to the chart that are unfamiliar to students, like quiche or Croque Monsieur (ham and cheese sandwich) to expand their food horizons and pique their interest. But I usually end up learning more about food from the students’ guesses than they do from me.

*Mr. Picky Food* is fun, accessible, and a great way to ease students into playing the math version of *Guess My Rule*.

**Guess My Rule: The Math Version**

Choose a rule (e.g. odd numbers, multiples of three, prime numbers).

Draw a circle on the board and explain the activity to students. Remind them not to shout out the rule when they have figured it out.

Ask a student to tell you a number.

Put the number in the circle if it fits your rule. Put it outside the circle if it doesn’t fit your rule.

Continue eliciting numbers and placing them in the appropriate area.

After recording several numbers, have students discuss the information they have so far.

Ask students for numbers that will either go inside the circle or go outside.

Ask the class to state the rule.

For older students, repeat the activity with two different rules about numbers and a two-circle Venn diagram.

Here’s an example of one game. Can you guess what my rule is? (*see the answer at the end of this post)

As with *Mr. Picky Food*, the key to *Guess My Rule: The Math Version* is to pause periodically and have students discuss what they notice and hypothesize about possible rules. This allows the class to hear one another’s ideas and analyze the data they’ve collected.

**Guess My Number**

This game is adaptable for almost any grade level. Students try to guess a secret number from within a given range of possibilities.

Playing the game with a group of kindergartners, I show them a number line from 0-10:

I tell the students that I’m thinking of a secret number on the number line and elicit guesses. If my secret number is 6 for example, and a student guesses 10, I put a post-it-note on their guess (10) and tell the class my secret number is less than 10. If another student guesses 4, I put a post-it-note on their guess (4) and tell the class my secret number is greater than 4. We continue until a student guesses my number.

*Guess My Number* is a good context for introducing key math vocabulary (*greater than, less than*) and using language to explain reasoning. During the game, I encourage students to explain their guesses in complete sentences, assisting them with the following sentence frame:

I think the number is _____. I think this because ___________.

For first and second graders, check out this version of *Guess My Number* from the Math Transformations website called ** Mystery Number Routine**.

For older students, start the game by telling them that you are thinking of a secret number that is less than 1. Students are sometimes stumped by this, not having thought of fractions as numbers or that there can be numbers that are less than one. Number lines can be helpful scaffolds in this version as well.

Using the number line, an even more challenging fraction variation for older students is to not give them all the numbers on the number line. Using the number line below, I begin by saying, “I’m thinking of a number between one and two. What might my number be?”

Students have to generate rational numbers. For example, if a student guesses one-half, I mark one-half on the number line (or you can have the student place it) and then I say, “My number is greater than one-half.” Below is what it would look like after two student guesses.

It gets tricky as the game goes on. The game board below shows where a class might be after 4 guesses. In this example, students are challenged to come up with numbers between ⅞ and 1 ¼. That pushes on students’ understanding of fractions in an intriguing way.

Whether you are working with basic whole numbers or rational numbers, Guess My Number can be differentiated to be both fun and cognitively challenging for all students in the classroom.

**Numbers and Me**

This guessing game is one of my favorites. I like it because it helps students see the usefulness of numbers in the world. Through playing this guessing game, students learn that numbers can be used in different ways, including to quantify, to label, to order, and to locate things. The game also helps students see that some numbers are appropriate in some cases, and not in others. Here are the teaching directions at a glance.

Where everyone in the class can see it, write between ten and fifteen numbers that have some significance to your (the teacher’s) life.

Give a clue about each number (for example, “One of these numbers stands for the number of years I’ve been teaching” or “One of these numbers stands for the number of miles on my car”) and ask the students to decide which number best suits each clue.

Have the students write down, on a piece of paper, ten or fifteen numbers that have some significance in their life. On a separate piece of paper, ask them to write a sentence that describes each number. For example:

*2011* This is the year in which I was born.

*3 * This is the number of siblings I have.

*33 1/3* This is the percentage of the day I spend sleeping.

*½ * This is the portion of our class that are girls.

4. Have the students, in pairs, exchange their lists of numbers, then take turns reading their clues (at random) and guessing which number fits which clue.

The following list of numbers are my “personal numbers.” Can you guess what they stand for?

*66 5/12*

* 4th*

* 2614*

* 11*

* 41*

For younger students, I send home a worksheet for children to complete with their families:

I am _____ years old.

I measure about ____ feet tall.

My address is _____________.

I have _____ brothers and _____ sisters.

My favorite number is ______.

I am in ____ grade.

I have ____ pets.

Students bring this worksheet back to school and I share one student’s sheet at a time. I post the numbers and the class tries to guess what the numbers stand for.

**Guessing Games Engage Students in Logical Reasoning**

When I play math guessing games with students, they end up using mathematical thinking without even knowing it by puzzling over clues and thinking about numbers in ways they haven’t experienced before. One of the biggest benefits to math guessing games is that they engage students in logical reasoning. And students get better at this reasoning if they get a chance to discuss their ideas and hear one another’s logic. By discussing their hypotheses, students can move from making wild guesses to basing their ideas on the data they’ve collected.

Math guessing games take very little time and hardly any preparation. Try some of these out and have fun!

*Answer: *My rule is **Square Numbers*

I want more math guessing games.