Squeeze - Guess my Number

A peg is put at each end of a number line, for example, on 0 and 100. A student chooses a number between the pegs and writes it on a piece of paper. The rest of the students ask “less than” or “greater than” questions to find the mystery number. With each question, a peg is moved to eliminate numbers. For example, if “Is it greater than 25?” is answered by “Yes”, then the zero peg is shifted up to 25 to eliminate all the numbers 25 and under.

If “Is it less than 75?” is answered by “Yes”, then the top peg is shifted down to 75 to eliminate all the numbers 75 and over.

This continues until the mystery number is finally found by squeezing in from above and below.

Note that this game can be played on various number lines, including whole-number lines starting at other than zero, and decimal or fraction number lines.

Alternatively, use a flip hundreds board, showing all the numbers in black and flipping the numbers over to red as they are eliminated.

When the students are confident, remove the number line and do the activity by visualising. List the numbers on the whiteboard:

“I’m thinking of a number between 0 and 5.” Write 0 5

“Is it greater than 2.5?” “Yes” Write 2.5 5

“Is it less than 3.6?” “Yes” Write 2.5 3.6

“Is it greater than 3.0?” “No” Write 2.5 3.0

The game continues until the number is found. Note that the question, “Is it greater than 3.0?” did not eliminate 3.0 itself as the answer was “No.” The underlining of 3.0 shows the mystery number could be 3.0.

Where the mystery number is a three-place decimal, like 0.456, draw a very long number line on the board board or modelling book showing 0 to 1 at either end. Progressively subdivide the number line until the decimal is found.