Equations (statements of equality) are familiar to students. Statements of inequality that use the symbols < (less than) and > (greater than) may be less familiar.
This problem explores statements of inequality and the ways these are recorded using symbols. The problem itself may not be numerically challenging for your students, however understanding relationships and expressions of these is an important aspect of algebra. The number line representations of the inequality expressions shown in the solution make the relationships evident.
Ben has a box with a number in it that is greater than 7.
Moana has a box with a number in it that is less than 9.
Tom has a box with a number in it that is greater than 5.
They all have the same number. What is it?
Make up your own 3 clue problems for others to solve.
Students should recognize that for Ben the number can be 8 or any number greater than this. Each student's statement can be represented on a number line:
Comparing two lines, we notice that only 8 is on both Ben's line and Moana's line. Can Tom can have 8 in his box? Draw his line.
This shows clearly that 8 is the number that satisfies all of the inequalities.