Lunch Menu Investigation Solution
 What are the possible meals you could have?
 Give each item a price, and work out the cost of each meal.
Today’s Menu
As there are several courses and different choices for each course
shown on the menu, it becomes difficult to mentally visualise the different
possibilities.
It is likely, therefore, that you resorted to one or more of a number of
representations (e.g. drawing pictures of types of food on plates, using
word labels to represent food items, using initial letters or symbols to
represent food items etc.). Being able to represent a problem is a key
skill in Using and Applying activities. Note that there are different
degrees of abstraction in different types of representation.
Also, you probably organised these representations in some way e.g. in a
table or list or diagram. Working in an organised systematic way is important
in many using and applying activities because it ensures that all possibilities
are exhausted and excludes any repetitions and it makes it much easier to
recognise any patterns or relationships which exist.
One possible representation of the problem is given on the next page:
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Using a list
1. Spaghetti Special + Jacket Potato + Orange
2. Spaghetti Special + Jacket Potato + Yogurt
3. Spaghetti Special + Jacket Potato + Ice cream
4. Spaghetti Special + Salad + Orange
5. Spaghetti Special + Salad + Yogurt
6. Spaghetti Special + Salad + Ice cream
7. Vegetable Pie + Jacket Potato + Orange
8. Vegetable Pie + Jacket Potato + Yogurt
9. Vegetable Pie + Jacket Potato + Ice cream
10.
Vegetable Pie + Salad + Orange
11.
Vegetable Pie + Salad + Yogurt
12.
Vegetable Pie + Salad + Ice cream
(Giving us 12 possible choices)
We could also use a diagrammatic representation. The tree diagram
below is one possibility.
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A further possible approach to this problem is to simplify it so that there
are less courses or less choices available. By systematically altering the
number of options, one could then identify how the number of options
and the number of choices relate to the number of different meals which
are possible. You may have produced a completely different approach of
your own. In the same way, when working with children a number of
different approaches are likely to be adopted by different groups or
individuals.
Whatever approach is taken, there are 12 different meals which could be
selected from the given menu because 2 options × 2 options × 3 options
= 12 combinations.
By trying different meal menus with different numbers of choices and
options we can arrive at a general statement which summarizes the
relationship involved. In general, for any meal with any number of
choices and options
The number of meals = number of 1st choice options × number of
2nd choice options × number of 3rd choice options × ..... etc.
Assigning prices to items and working out possible costings is an
alternative way of asking children to extend this problem.
If this problem had arisen out of real-life circumstances (e.g. the school
wanting to change its school meals menu) and the solutions were going
to be used or implemented (e.g. to affect the way the school offered
lunches to pupils), the problem would have additional relevance for the
children. Solving a problem with a real purpose in mind is a very valuable
experience for children because it enables them to perceive how
mathematics can be used in everyday life.
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