Week 14 — Laps That Add Up

Assignment 13 of the term — trace a recursive function call by call, count the calls it makes, catch a base case in the wrong place, and explain it all to someone who has never programmed.

This adaptive assignment uses a coaching dialogue to help you turn a first attempt into a clear, evidence-based report. You remain the author. The coach asks questions, checks the reasoning you show, and waits for you to revise before it produces the required report. This builds on Week 7, where every function call got its own frame and return handed a value back, and on Week 9, where a slice such as laps[1:] built a new, shorter list. This week's lecture tutorial, quiz, discussion, and Coding Lab practise the same ideas from other angles; this assignment is where you put them together.

The task

A cousin who helps coach a youth swim team wrote a short program to add up the laps four swimmers swam at practice:

def total_laps(laps):
    if len(laps) == 1:
        return 0
    return laps[0] + total_laps(laps[1:])

print(total_laps([10, 8, 13, 6]))

It printed 31. Your cousin says, "Recursion must skip a swimmer sometimes." Your job is to check what Python really did, the way a programmer would: predict each output before you run it, run it in a free browser Python runner, and explain what happened. All four problems are illustrative; Problem 1 uses this week's reading log, and Problems 3 and 4 use the cousin's laps, repaired so that the base case is the empty list:

def total_laps(laps):
    if laps == []:
        return 0
    return laps[0] + total_laps(laps[1:])

Work these four problems. For each one, write your prediction first, then run the code and write the actual output beside your prediction:

1. The reading log's Week 14 function, total_pages, is called on the first three days, total_pages([12, 40, 25]), and the program prints the value. What does it print?
2. The pinned factorial from this week's chapter is called as print(factorial(4)). What does it print?
3. The repaired total_laps is called on [10, 8, 13, 6]. Add print("call with", laps) as the first line of its body and run it. How many calls does it make in all, counting the base-case call?
4. The program runs print(total_laps([10, 8, 13, 6])) with the repaired function. What does it print?

Beside each answer, add one brief interpretation:

• Problem 1: name the base case of total_pages, and report what print(total_pages([])) prints when you run it.
• Problem 2: list the values the calls hand back as the frames unwind, and explain why each call keeps its own n.
• Problem 3: explain why there is one more call than there are swimmers, and explain why each slice leaves the original list alone.
• Problem 4: run your cousin's original version, report what it prints, name what is wrong with its base case, and explain why a base case on the empty list fixes it.

Explain it to a non-programmer

Write a 3–5 sentence message to your cousin that explains, in everyday words, why one swimmer went missing from the total, and how changing the stopping rule fixes it. Use the idea that each call hands the rest of the list to the next call and that the last call, with nothing left, should answer zero, and name one limit or caveat, such as what happens if a function's input never shrinks toward its stopping rule. Explain any technical term in everyday words. More than one good message is possible.

For a different, ungraded example, imagine a friend whose countdown for a game prints Go! before the numbers. Model message: "Your countdown asks the next, smaller countdown to run before it says its own number, so every number waits until the very last step has shouted Go Python did exactly what the instruction said, which is why there was no error message, only numbers in an odd order. If you move the line that says the number above the line that starts the smaller countdown, the numbers come first. One catch: the smaller countdown has to reach zero at some point, or the program never stops."

Use that pattern for your cousin's question, with your own wording and evidence.

Part 1 — Student instructions

1. Draft all four predictions, the four actual outputs, the four brief interpretations, and your message to your cousin before opening a chatbot. Run every program yourself in a browser Python runner.
2. Open any course-approved chatbot. Copy the entire Coach Prompt box, including its first and last marker lines, and paste it as one message. The coach will ask for your draft and then work one question at a time.
3. Answer in your own words. Show your traces when asked. Use the coach's feedback to revise at least one trace or explanation, even if your first attempt was correct.
4. Continue until the prompt's exit condition is met.
5. Save the chat's share link and copy the final report exactly as the coach gives it.

The chatbot is a coach, not a ghostwriter. It must draw out your reasoning rather than write the work for you, and it does not run your code; your own runs settle every output.

Coach Prompt

COPY EVERYTHING BELOW THIS LINE
ROLE: You are a careful learning coach for an introductory computer science course taught in Python 3. Draw out and challenge MY thinking about base cases, recursive cases, the call stack, and how a recursive function builds its total on the way back. Do not write my assignment for me, do not invent work I did not show, never invent a statistic, a study, or a quotation, and never tell me what a line of code prints: ask me to run it in my own browser Python runner and tell you what appeared.

ASSIGNMENT: Work through these four problems in order, one at a time. Do not invent, replace, or reorder a problem. All four are illustrative. For each one I write a prediction first, then run the code and report the actual output beside it.
PROBLEM P1: The reading-log function that sums a list recursively is called on the first three days, 12, 40, and 25 pages, and its total is printed. What does the program print?
PROBLEM P2: The pinned factorial function is called with 4, and the value it hands back is printed. What does the program print?
PROBLEM P3: The repaired lap-total function, whose base case is the empty list, is called on the four swimmers' laps 10, 8, 13, and 6. How many calls does it make in all, counting the base-case call?
PROBLEM P4: The repaired lap-total function, whose base case is the empty list, is called on the four swimmers' laps 10, 8, 13, and 6, and its total is printed. What does the program print?
After the four answers, I must briefly interpret each one: for P1, name the base case and run the same function on the empty list and say what prints; for P2, list the values the calls hand back as the frames unwind and say why each call keeps its own n; for P3, say why there is one more call than there are swimmers and why each slice leaves the original list alone; for P4, run the cousin's original version, say what it prints, name the misplaced base case, and say why a base case on the empty list fixes it. I must then write a 3-5 sentence message to a cousin whose program left one swimmer out of the total, explaining in everyday words why, how one change fixes it, and naming one limit or caveat. I must explain technical terms in everyday words.

SCORING CRITERIA: Score only evidence I supply: correct traces (40 points), reasoning about how recursion works (32 points), clarity for a non-programmer (16 points), and showing the trace and the run (12 points). For each of P1-P4, give 2, 1, or 0 evidence units per criterion; one unit is worth 5 trace points, 4 reasoning points, 2 clarity points, or 1.5 showing points. Sum all four problems within each criterion. Count my final message only with P4, not again with P1-P3.
TRACE UNITS: A reported value that matches the run, including equivalent notation = 2; the right calls and steps with only an arithmetic or counting slip = 1; a missing value or the wrong calls or steps = 0. Do not penalize an alternative valid way of showing the trace.
REASONING UNITS: For P1-P3 separately, an interpretation that meets both parts named for that problem = 2; exactly one part = 1; neither = 0. For P4, the original run reported AND the misplaced base case named and explained AND a cousin message with the fix and a named limit = 2. If full P4 evidence is absent but at least one accurate substantive part appears, give 1. No accurate reasoning = 0; naming a term alone does not earn a unit. A counting slip alone is not a reasoning error.
CLARITY UNITS: For each problem, labeled evidence understandable to someone who has never programmed, with technical terms explained = 2; intelligible evidence that needs rereading because of ambiguity or jargon = 1; absent or unintelligible evidence = 0. Include the final message with P4 if submitted. Missing reasoning alone does not lower clarity for otherwise clear submitted work.
SHOWING UNITS: For each problem, a step-by-step trace of the calls plus the reported output of an actual run = 2; a relevant but incomplete step or run output = 1; a final value alone or no trace = 0. A visible trace stays checkable despite a counting slip.

Do NOT invent grading rules.

DIALOGUE RULES: Ask exactly one question per message and wait for my answer. Start by asking for my complete first attempt. Build each next question from my exact words. Probe an unsupported claim and ask me to examine its evidence, usually by running the program again or stepping through it in Python Tutor. Keep the conversation focused on questions rather than completed work.

ENGAGEMENT GUARDS: A greeting, copied prompt, yes/no reply, or one-word answer is not a substantive exchange. Do not flatter or accept agreement as evidence. Praise only a concrete move I made. If evidence is missing, say what is missing and ask for it. Require a real revision plus a short reflection on why the revision is better. Do not issue the report early.

EXIT CONDITION: Continue until at least five substantive exchanges have occurred AND I have supplied all four answers with their runs and brief interpretations AND written my message to the cousin AND revised at least one trace or explanation AND reflected on the revision. Stop only after whichever requirement happens last.

REPORT: After the exit condition is satisfied, output exactly these labelled lines in this order. Replace X with the exact earned score; it may end in .5 and must not be rounded to a whole number. Base every line only on evidence in this chat; write "Not supplied" for missing evidence and never raise the score for polished chatbot prose.
STUDENT'S SCORE: X/100
EVIDENCE FOR THE SCORE: [specific evidence from my traces, runs, and reasoning]
REVISION MADE: [what I changed and why]
STRENGTH: [one earned strength]
NEXT STEP: [one concrete improvement]
Then tell me to submit this report, my revised work, and the share link.
COPY EVERYTHING ABOVE THIS LINE

Deliverables

Submit these three items in the assignment entry:

• your revised work with all four predictions and actual outputs, their brief interpretations, the runs of print(total_pages([])), the traced call count, and your cousin's original version, and your message to your cousin — written, or recorded as audio or video with a transcript, or as a labelled screen capture of your runs with a short note for each; every form is graded by the same scoring criteria;
• the coach's five-line report; and
• the conversation share link.

Submit in any accessible file type or as a link; a recorded response may be submitted as audio or video with a transcript, or as text.

Equivalent route (no AI required)

This route assesses the same Week 14 skills — tracing a recursive function call by call, naming its base case, following the values back up the call stack, and spotting a base case that stops the calls too early — for comparable time and effort, about 60 to 90 minutes, the same as the coached route. Complete the same four problems with your predictions and runs, the four brief interpretations, the run of print(total_pages([])), the traced call count, your cousin's original version, and the message to your cousin. Then audit your own first draft against the attached scoring criteria, criterion by criterion, and write a second draft. Add a 150–200 word revision memo that names one trace or explanation you changed, the evidence that prompted the change (for example, a run that disagreed with your prediction), and one question you still have. Submit the revised work, your completed criteria checklist, and the revision memo in the assignment entry; together they replace the share link and the coach's report. This route uses the same scoring criteria and the same points, with no penalty for choosing it.

How you'll be graded

The full analytic rubric is attached to this assignment in Canvas.

Academic integrity and AI use

The predictions, runs, reasoning, revision, and final report must be your own. Do not ask the chatbot to create the assignment, to tell you what a program prints, or to add evidence you did not produce. Submit an honest share link from your own dialogue. The equivalent route keeps the same workload and evidence and requires no AI account.

Built with The Course Maker · samples.thecoursemaker.com