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?

What is this problem about?
To do this problem, children have to understand inequalities. So they have to know that every number from 8 on is a possible number for Ben. The problem can also give practice at using the symbols for inequalities.
< (less than)
> (greater than)

Achievement Objectives
Algebra (Level 2)
- use the mathematical symbols =, <, > for the relationships "is equal to", is less than", and "is greater than".

Mathematical Processes
- devise and use problem solving strategies to explore situations mathematically (be systematic, make a drawing, use equipment).

Resources
number tiles (1-10)
Blackline master of the problem

Specific learning outcomes
The children will be able to:
- write and talk about number sentences using <, >
- work systematically to solve a problem

1. Introduce the problem by asking a group of 3 children to stand at the front of the class. Next to them stand a group of 4 children.
2. Ask the children 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 children 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 children’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.