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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.

Teaching sequence

1. Introduce the problem by asking a group of 3 students to stand at the front of the class. Next to them stand a group of 4 students.
2. Ask the students to think of ways to describe what you have done using the symbols you have written on the board (3, 4, 7, = <, >, 1 ).
   Eg 3 + 4 = 7, 7 – 4 = 3, 3 < 4
3. Record the sentences, discussing the use of the symbols.
4. Pose the problem.
5. 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?
6. Share solutions.

Extension to the problem

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

Solution

A nice way to do this problem is to use a drawing. We can represent each of the numbers in the students’s boxes by a line. The line has regular numbers on.  We have drawn arrows where the possible numbers are.

If we compare those two lines I think that we notice that only 8 is on both Ben's line and Moana's line. So is it possible that Tom can have 8 in his box? Draw his line.

Yes 8 is definitely bigger than 5. Hence 8 is the number we want because it satisfies all of the inequalities.