Investigation

The structured investigation is broken into several parts to help scaffold the approach for students. These parts are:

a) by looking at the table or the simulation, predict 2 (or 3) more terms of the sequence;

b) describe some patterns in words for the sequence (e.g. it goes up by 5 each time);

c) give a general rule for the sequence. This sequence is often linear, so something like A=5n+1. To get both marks you must simplify your general rule, and include the A= (using whichever letter has been given in the question);

d) verify your general rule. This has a very specifical meaning in the MYP, and is always worth 3 marks. The marks are:

1. substitute a value of n greater than those given to you in the table into your general rule (this can be one of your predicted values)

2. correctly work out the value of the sequence using your general rule

3. compare the value you have calculated with the one in the table that you found using the pattern

The unstructured investigation is always linked to the structured investigation, either looking at a slighlty different aspect, or building upon the structured investigation. You essentially have to do a set of steps, which are always the same, but it is not broken down into parts for you. The sequence is also normally more difficult than in the structured investigation. You are given a set of bullet points as a reminder of what to include, which essentially says the stages below, in less detail.

The steps you have to follow (and their rubric criteria and associated marks) are:

a) Predict more terms (P1 or P2) - start by using the patterns you spot to fill in the missing values in a table;

b) Describe any patterns you spot (D) - describe patterns for the sequence in words;

c) Give the general rule (D4 or D5) - state the general rule for the sequence (for these marks you do not need to give any working for how you found the rule, just state the rule);

d) Test the general rule (T2) - in MYP test means to substitute in a value of n that you were given in the table (normally 1, 2, 3 or 4), and to calculate the term of the sequence. Then you must validate that this matches the value in the table;

e) Verify the general rule (V3) - in MYP verify means to substitute in a value of n that you were NOT given in the table (normally 5 or above), and to calculate the term of the sequence. Then you must validate that this matches the value you predicted in the table;

f) Justify the general rule (J3 or J4) - this means to explain why the rule will always work. For J1 you can do two further verifications. For J2 you can use 'formal methods' for determining a general term from the sequence of numbers e.g. using the method to determine a quadratic sequence, or the formula to determine a geometric sequence. For higher marks in J, you must explain mathematically why the rule will continue to work, and deduce this from the context of the problem. This often involves algebra around areas;

g) Good Mathematical Notation and Terminology (N3) - these are communication marks and are awarded for using correct terminology when describing patterns (e.g. increasing rather than goes up), and for simplifying the general rule fully and ensuring it has A= (or whatever is the appropriate letter);

h) Coherence (L3) - these are communication marks and are awarded for a coherent answer that is easy to follow and includes all relevant sections. You normally have to have at least four of parts (b) to (f) to get all the marks, along with clearly indicating what you are doing at each stage. For example, using titles for each part: Description of Patterns; General Rule; Testing; Verifying; Justifying. Often, to get L3 you have to score full marks in J as a pre-requisite.

The hardest part of the investigation is the Justification. It is possible to get most of the marks without doing this thoroughly. For example, if you do two extra verifications then you would only lose 2-4 marks out of 20-23 marks (depending on how the marks are awarded for a particular investigation).

You can practice the open investigation without the justify step here.

In Extended Maths, both quadratic sequences and geometric sequences are on the syllabus, and students are given the formula for the geometric sequence. It is common for the unstructured investigation to include geometric sequences, but again, the focus is on deducing the general rule from the context, not just using the formula to find it.