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?

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.

### Problem

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?

### Teaching sequence

- Write the symbol = and have your students explain its meaning. (The number or expression on one side of = has the same value as the number or expression on the other side. This makes a statement of equality, or an 'equation'). Record your students' responses.
- Have students suggests some equations. Record these and read them using the words, '........is equal to......'
- Write these symbols: 3, 4, 7, <, >, 1 and have your students write and read some expressions using these.

Eg. 3 < 4, "three is less than 4". - Discuss the ways in which these symbols express inequality.
- Pose the problem.
- As the students work on the problem ask questions that focus on the use of the inequalities.

*Could you write a statement for the first clue?* - Share solutions including the ways in which students have recorded.

#### Extension to the problem

Make up your own 3 clue problems for others to solve.

### Solution

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.