I’m Thinking of a Number
Math Concepts
Comparing, Number line
Materials
Paper and pencil – or – None
Players
2
Set up
Use the paper and pencil to keep track of the questions and answers. If you play verbally, no paper is needed. Choose roles– one player is the Puzzler and the other is the Questioner. The Puzzler starts by saying “I’m thinking of a number between 1 and <#>.”
Play
The Questioner asks questions of the form: “How does your number compare to <#>?” The Puzzler
answers by saying that their number is greater than, equal to, or less than that number.
Goal
The Questioner tries to guess the Puzzler’s number with as few questions as possible.
Example game
The Puzzler thinks of 6 and starts with “I’m thinking of a number between 1 and 10.”
Questioner: “How does your number compare to 5?”– Puzzler: “My number is greater than 5.”
Questioner: “How does your number compare to 7?”– Puzzler: “My number is less than 7.”
Questioner: “How does your number compare to 6?”– Puzzler:“Congratulations, my number is equal to 6!”
Discussion and Tips
Discuss which number is best to ask about at a given moment in the game.
Discuss how much information a certain guess gives you. How many numbers can you cross off after a given guess?
Discuss what is a reasonable number of questions for a given range of numbers.
Variations
Question limit: Set a limit and challenge your children to discover the answer in at most that many questions.
Scoring: Count the number of questions asked over several rounds. The player with the lowest total wins.
Number line: Use a number line to keep track of the information and to practice with a number line. Each time a question is answered, mark off the numbers that are no longer possible. For example, if the range is 0 to 12 and the number is larger than 6, then the numbers 0, 1, 2, 3, 4, 5, and 6 are crossed off.
Grade 2: Use an extended range of numbers, say up to 100.