Four things go up in a two-by-two grid and the question is always the same: which one doesn’t belong? There is no answer key. Every corner can be defended, and the defence is the point. In Grade 11 the grids compared values, and the vocabulary you needed was type. This year they compare choices — four containers, four algorithms — and the vocabulary you need is the one you will use to justify a design decision to a teammate who wanted to do it the other way.
Grid one: four things you can do to a collection
names.append("Cy") | hours["Tuesday"] |
waiting.pop(0) | undo.pop() |
Only one puts something in. Only one takes nothing out, and finds what it wants by name rather than position. Only one removes from the front, and pays for it — every remaining item shuffles down a place, so the cost grows with the size of the collection. Only one removes the item added most recently, which is the entire personality of a stack.
Four corners, four defensible claims, and four ideas from Choosing a Data Structure that are about to decide how your team stores its data.
Grid two: four sorts
| Bubble sort | Insertion sort |
| Selection sort | Merge sort |
Only one is normally written as a function that calls itself, and it is also the only one that needs a second list to work in rather than shuffling the original in place — on a very large list, that is not a detail. Only one keeps a finished region at the front and slides each new item back into place, exactly the way people sort a hand of cards. Only one moves each item at most once, making the same small number of swaps whatever the data looks like. And only one can notice it is already finished and stop after a single pass.
Watch for the corner nobody picks. If the whole room says merge sort because it is the odd one on speed, push back: what makes bubble sort odd? What makes selection sort odd? An argument you can only make one way is not an argument yet.
How to run it
- Show the grid. One quiet minute, and everyone picks a corner.
- Hands up by corner. Every corner should have takers; if one is empty, somebody argues it anyway.
- Defenders speak. The rule: name the property, not the vibe. “It is the only one whose cost grows with the length of the list” beats “it feels slower”.
- Close by collecting on the board the vocabulary the defences used. That list is your justification language for The Structure Study.
One variation
Students build the grids. A good grid needs four properties that overlap three ways each, which is much harder than solving one — and building a single grid teaches more than defending ten. The best student grids this year tend to come from real disagreements inside a team about which container to use.
Argue the corner you did not pick
Once your own corner is safe, take a different one and defend it just as hard. This is rehearsal: in The Code Review you will have to state the case for a design you would not have chosen, and do it well enough that its author agrees you understood it.
Curriculum connection
C1.1
decompose a problem into modules, classes, or abstract data types (e.g., stack, queue, dictionary) using an object-oriented design methodology (e.g., CRC [Class Responsibility Collaborator] or UML [Unified Modeling Language]);
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C1.4
apply the principle of reusability in program design (e.g., in modules, subprograms, classes, methods, and inheritance).
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