Why do this problem?
Although inequalities look visually like equations,
inequalities do not add or subtract in the same way that
equations do. This question will lead students to realise that
inequalities must be manipulated in different ways.
Possible approach
You might suggest trial and error to get started, or begin
with one of the key questions.
You can also let the students try 'algebraic' approaches
which might lead to nonsense answers. For example, simply
subtracting the two inequalities naively might lead to
statments such as
Students could be encouraged to work our where their logic
was flawed.
Key questions
How do the inequalities on
affect the possible values of
Possible extension
Suppose that you were only given the four inequalities at the
end of the question. What information would you be able to
deduce about the ranges of a, b, c and d from this?
Possible support
The negative numbers make this question more tricky.
The lesson could be steered to focus on one of more of
these processes
Students may try
| work logically towards results and solutions,
recognising the impact of constraints and
assumptions |
manipulate numbers, algebraic expressions and
equations and apply routine algorithms |
identify the mathematical aspects of the situation or
problem |
| Students must always remember that all inequalities
must be satisfied. There are several if-then cases to
consider |
Students will need to focus on how to combine
inequalities together. |
Students are likely to simply add or subtract each
side of the inequalities at first. They will need to
appreciate that inequalities work in different way to
equations when negative numbers are involved |