Module 3 - Investigation Structure
TL;DR
The structured investigation is an easy entry point to the investigation.
It comprises the same four components every time:
Predict more terms in a table (1 mark);
Describe any patterns you see (2 marks);
Write down the general rule (2 marks);
Verify your general rule (3 marks).
The first part of the investigation question is always a Structured Investigation.
The structured investigation always follows a very similar format, the only thing that changes is the context that leads to the sequence.
However, this context is NOT required to answer any part of the structured investigation, if you know how to approach the problem.
The format for the structured investigation is:
(a) predict more values by completing the table of values (1 mark);
(b) describe the patterns that you see (2 marks);
(c) determine the general rule for the sequence (2 marks);
(d) verify the general rule (3 marks).
Throughout this section we will use the sequence in the table given as an example.
Predict
The first stage is to complete the table of values for the sequence.
Normally you are given the first 4 values of the sequence in the table, and you have to complete the next two or three values.
This should be straight forward, and usually the structured investigation is a simple linear sequence, making it easy to continue the pattern.
You can reveal the values you should have found in the table by clicking on the cells.
| Stage (\(n\)) | Length (\(L\)) |
|---|---|
| 1 | 14 |
| 2 | 20 |
| 3 | 26 |
| 4 | 32 |
| 5 | 38 ? |
| 6 | 44 ? |
| 7 | 50 ? |
Describe the Pattern
The next stage is to describe the patterns you see for the sequence in words.
Usually they as for a specific number of patterns, either one or two.
Good descriptions include things like:
it is a linear sequence;
it increases / decreases by …
the values are always even / odd / a multiple of three / etc
NOTE - this must NOT link back to the stage number at this point. It is all about how you get from one term to the next.
For the example the question would be:
Describe in words two patterns in the table for the length \(L\).
And we might answer with “\(L\) is a linear sequence that increases by 6 each time”.
General Rule
Now we come up with the general rule, using all the skills we learned in the previous sections.
Be aware of any hidden structures that you need to include in the general rule.
The general rule is always for the given variable, in this case \(L\), and in terms of \(n\) (but do check the letters used, and make sure you use the right one).
For the example, the question would be:
Write down a general rule for \(L\) in terms of \(n\).
The answer is \(L=6n+8\).
NOTE - you must include the \(L=\) at the start of the general rule to get both the marks for this question.
Verify
Now we use a single value of \(n\) to check if the rule we have come up with works for the values we predicted in the table.
For the MYP, the word verify means to check the rule for a value of \(n\) that you predicted, not one that you were given.
In the majority of cases, this means you will use one of \(5\), \(6\) or \(7\) for the value of \(n\). There is one mark for choosing a correct value of \(n\) to use for verify.
The second mark is for substituting this value of \(n\) into your general rule and getting the correct answer.
You can get the first two marks even if your general rule is incorrect.
To get the third mark, you have to explicitly state that the value from your general rule matches the value you predicted by continuing the pattern.
For the example, the question would be:
Verify your general rule for \(L\).
The answer would be:
“Using \(n=5\) we get \(L=6\times 5 +8=38\) which matches the value I predicted by continuing the pattern.”
Structured Investigation
a) Write down the missing values in the table up to row 6.
b) Describe in words two patterns in the table for the number of .
c) Write down a general rule for in terms of \(n\).
d) Verify your general rule for .