3. Background and Abstract
In this investigation, I am to use non-linear algebra in estimating packaging dimensions that are
cost effective and sustainable.
I will use 3 methods in this parabolic investigation. They are:
1) Arithmetic – Define Arithmetic approach in algebra
2) Procedural – Define Procedural approach in algebra
3) Conceptual – Define
Each of these three methods have its merits and is dependent on the availability of resources.
However, efficiency is maximized when we employ the conceptual method as it minimizes
wastage and keeps the process sustainable. XXXXXXXXXXXX* Provide more insights on the three
methods..
6. Arithmetic Approach (Concrete Models)
If x = 6,
length of box = 2
Width of box = 2
If x = 10,
length of box = 6
Width of box =
If x = 6,
length of box = 2
Width of box = 2
If x = 6,
length of box = 2
Width of box = 2
8. What do I notice about the rectangles?
• XXXXXXX
• Are the dimensions different?
• How have they changed?
• Is there a pattern to this change?
• What is the pattern?
• Can this pattern be recorded using a set of algebraic
equations/expressions? How?
9. Capacity investigation
• Capacity of box 1 =
• Capacity of box 2 =
• Graph of capacity (y) against x: Insert graph here
• How do we determine the maximum capacity?
10. Procedural Algebraic Approach
• INSERT TABLE HERE
• Highlight your class intervals
• X values that are impossible are as follows:
12. Steps in calculating the Apex
• Note the difference between the 2 graphs
• Why is each graph important? And under what conditions do we use
each of these graphs?
13. Conceptual Algebraic Approach
• Translate the dimensions of the box into a series of mathematical
equations:
• Length?
• Width?
• Diagonal?
