Lecture 09 — Aggregation Patterns

Position in the course

This is lecture 9 of 32. It belongs to the course arc described in the course outline and uses the standard interactive case method: display, attempt (5 minutes), discuss, reveal, name the technique.

Learning objectives

Implement running totals, min/max, and counting loops
Combine aggregation with filtering
Initialise accumulators correctly

By the end of this lecture students can do all three under time pressure, which is what the four cases exercise.

Prerequisite knowledge

Before this lecture: Lectures 04–06 — Loops, state, accumulation

Assumed fluencies:

running totals
min/max tracking
counting loops

Preparation task: Write a running-total loop for cs-033 from memory.

Detailed topic outline

Core (mandatory):

running totals, counts, min/max, argmax
comparison against a best-so-far
streaks and state resets
fixed and variable windows

Extension (optional enrichment):

two-pass thinking
choosing the right aggregation for a question

Case sequence

Case	Title	Difficulty
cs-033	The Reading Log	Beginner
cs-142	The Tallied Vote	Beginner
cs-034	Stockroom Spikes	Foundational
cs-035	The Longest Streak	Intermediate
cs-036	Rainfall Windows	Advanced

Display each case full-screen from the student page (cases cs-033–cs-036); instructor pages cs-033–cs-036 under case-studies/instructor/ hold the full solutions, reveal guides, and discussion prompts. Applied additions cs-142 extend the session as optional extra attempts or homework; they share the lecture's theme but teach an applied, real-world angle.

Timing plan (120 minutes)

Minutes	Segment
0–10	Framing: where this fits; recall of the previous lecture
10–30	Case 1 (cs-033): 5-minute attempt, then discussion and reveal
30–50	Case 2 (cs-034): same rhythm
50–70	Case 3 (cs-035): same rhythm, harder case
70–75	Break
75–100	Case 4 (cs-036): same rhythm, hardest case
100–115	Synthesis: name the techniques; misconceptions check
115–120	Exit questions, homework, next-lecture preview

Timing flexes with the room: if a case ignites the class, let the discussion run and compress the synthesis; if the attempts stall, harvest partial attempts rather than extending the clock.

Worked examples

cs-036 rainfall windows: two passes — first totals, then the window answer — and why one pass is possible but harder.

Instructor demonstration to open the lecture: Compute the reading-log totals (cs-033) with running totals, then re-ask the question with min/max to show the pattern family.

Classroom activities

#	Activity	Minutes	Format and prompt
1	Running-total simulation	6	One student reads numbers aloud, one keeps the total, one keeps the max; swap roles mid-stream.
2	Window slide demo	7	A meter-stick slides along a taped number line of rainfall values; the class calls out each window sum.
3	Pattern naming	5	Six aggregation questions are shown; teams name the pattern (total, count, min, argmax, streak, window) before solving.

Board plan

Left third: the case statement, kept visible for the whole cycle.
Middle third: students' contrasting attempts (two maximum).
Right third: the reference trace or table, revealed last.
Bottom strip, written during the cycle: the name of the technique and the one-line invariant or rule this case taught.

Instructor explanation notes

Reading the room. Aggregation patterns are the workhorses of data science; name them precisely (total, count, min, max, argmax, streak, window) so later lectures can invoke them by name.

Running the reveal. The window cases (cs-036) are the hardest; two-pass thinking is the accessible route and is worth celebrating.

Lecture focus. One sentence to repeat verbatim: Name the pattern, then write the loop.

Common misconceptions

Recomputing totals inside the loop instead of maintaining them.
Forgetting to reset streak state after a miss.
Confusing max with argmax — the value versus its position.
Sliding windows by recomputing each sum from scratch.

Each case's instructor page lists the specific wrong turn to expect; the reveal should address it by name.

Student practice exercises

Core:

Implement running total, count, min, and argmax over one provided reading log.
Compute the longest streak of on-target days for cs-035's sample data by hand, then in code.
Solve cs-036 for window size 3 with the two-pass method; then attempt one pass.

Enrichment (optional):

Solve cs-036 with the one-pass method and compare its clarity honestly.
Find an aggregation bug in any app you use (streaks and averages are fertile ground).

Formative assessment

Exit questions (choose one; answer on a card in 60 seconds):

Name the aggregation pattern for 'which day had the most sales'. Expected: argmax: track best-so-far value and its index/key

Why reset streak state? Expected: a streak is consecutive; a miss must zero the counter, not stop it

What is two-pass thinking and when does it pay? Expected: compute intermediate aggregates first, then answer; pays when one pass tangles state

Cards are skimmed before the next lecture; three answers become the framing. Persistent wrong answers route students to the review stations of lecture 16 or to office hours.

Homework and preparation

Before: skim the four student pages; attempt case 1 on paper.
After: write a five-line pseudocode solution for any case you did not finish in class; bring one question to the next lecture.
Enrichment (optional): the stretch question on each case page.

Learning-outcome mapping

Primary outcomes: LO4, LO9 — Aggregation patterns are the data-science workhorses.
Coverage details: learning outcomes; assessed via the scheduled quizzes, labs, assignments, and term project in the assessment plan.

Differentiation

Beginners: aim for a correct plan in pseudocode; Python is optional.
Intermediate: full Python on cases 1–3, plan on case 4.
Advanced students: finish early, then answer "what breaks at 10x scale?" and present the alternative-approach bullet from the instructor page.
Everyone: state one assumption out loud before writing anything.