← VCE Software Development U3O1

Recursion: a function calling itself

A function that calls itself with a smaller problem each time, and stops at a base case that returns without calling itself. With no base case, Python raises a RecursionError.

Part of: VCE Software Development - U3O1 - Programming — Module 151

Understanding Recursion: a function calling itself in VCE Software Development U3O1

What it does: The if n == 0 line is the base case that returns without a further call, and countdown(n - 1) is the recursive case with a smaller number. A recursive function calls itself. The first one calls countdown(n - 1) inside its own body, but the second only prints. Each call must make the problem smaller. Starting from a positive n, adding 1 moves away from 0 and never stops.

Common mistakes: A single = assigns a value, so it cannot be used in a condition. The base case check must use == to compare: if n == 0:. A function header must end with a colon. It should be def factorial(n):.

Class: _____________________ · Name: _____________________ · Date: _________

Free printable worksheet with full answer key — or add this module to a class and your students practise it interactively.

🖨 Print worksheet + answer key Add Recursion: a function calling itself to a class →

This module's key terms are also in a printable crossword (Modules 142–155) and word search (Modules 142–166).

Take this worksheet further — free with Cloodit

Each concept is reinforced from every angle — learned, then applied, then tested.

Learning

Duo

Which function is recursive?

def countdown(n): ... print(n)def countdown(n): ... countdown(n - 1)

Matches

def factorial(n): return n * factorial(n - 1)

↓

There is no base case, so the function never stops and raises a RecursionError. Add if n == 0: return 1 first.

Applying

Meanings

Term

recursion

Meaning

A function that calls itself with a smaller problem each time, and stops at a base case that returns without calling itself. With no base case, Python raises a RecursionError.

Practice

def countdown(n):

Testing

Gaps

Check Answer

Spots

1def count_down(n):

2 if n = 0:

Cloodit turns curriculum-aligned coding content into journeys students work through one biome at a time.

Students earn collectable badges

Over 100 of them, across seven natural biomes.

Study Buddy

Students build a real study resource

Turns their work into revision material ready for Flash Cards and Exam study.

Diamond Dash — one of Cloodit's live, competitive Sprint games

Students lock in with Sprints

Live, competitive practice for the start of the lesson or a teacher-led lesson finisher.

A Cloodit certificate of achievement, ready to personalise and print

Custom printable certificates

Honour your top performers, or encourage a student who's trying hard — ready to print in seconds.

Add to class →

Quick Questions

1. Which function is recursive?

A. def countdown(n): ... countdown(n - 1) ✓

B. def countdown(n): ... print(n)

A recursive function calls itself. The first one calls countdown(n - 1) inside its own body, but the second only prints.

2. What is the job of the base case in a recursive function?

A. It stops the recursion by returning without calling the function again ✓

B. It makes the function call itself one more time

The base case is the stopping point. It returns a value without another recursive call, so the chain of calls can end.

3. Which line is the base case of a factorial function?

A. if n == 0: return 1 ✓

B. return n * factorial(n - 1)

The base case returns straight away without calling factorial again. The other line is the recursive case.

4. Which line is the recursive case in a countdown function?

A. if n == 0: return

B. countdown(n - 1) ✓

The recursive case calls the function again with a smaller problem. Here n - 1 is closer to the base case.

5. What does Python raise if a recursive function has no base case?

A. SyntaxError

B. RecursionError ✓

With no base case the function keeps calling itself until Python hits its recursion limit and raises a RecursionError. The code is valid syntax, so it is a runtime error.

Match the Pairs

if n == 0: return 1 → The base case: it returns a value without calling the function again, so the recursion stops

return n * factorial(n - 1) → The recursive case: the function calls itself with a smaller problem (n - 1)

A countdown function stops at its base case and otherwise calls itself with a smaller number → def countdown(n): if n == 0: return countdown(n - 1)

A function with no base case never stops calling itself, so Python raises a RecursionError → def forever(n): return forever(n - 1)

def factorial(n): return n * factorial(n - 1) → There is no base case, so the function never stops and raises a RecursionError. Add if n == 0: return 1 first.

def countdown(n): if n == 0: return countdown(n + 1) → The recursive call makes the problem bigger (n + 1), so n never reaches the base case. It should be countdown(n - 1).

Key Term

recursion

A function that calls itself with a smaller problem each time, and stops at a base case that returns without calling itself. With no base case, Python raises a RecursionError.

Fill in the Blanks

1. def factorial(n): if n == 0: return 1

Hint: Type the keyword that ends the function at the base case without another call.

2. def fact(n): if n <= 1: return 1 return n * fact(n - 1)

Hint: Type the function name that the recursive case calls inside itself.

3. def total(n): if n == 0: return 0 return n + total(n - 1)

Hint: Type the operator that makes the problem smaller on each call.

4. def forever(n): return forever(n + 1) # Raises RecursionError

Hint: Type the error name Python raises when there is no base case.

5. def countdown(n): if n == 0: return countdown(n - 1)

Hint: Type the keyword that starts the base case check.

Spot the Error

Question 1

A def count_down(n):

B if n = 0:

C return

D print(n)

E count_down(n - 1)

Line B — A single = assigns a value, so it cannot be used in a condition. The base case check must use == to compare: if n == 0:

Question 2

A def factorial(n)

B if n <= 1:

C return 1

D return n * factorial(n - 1)

Line A — A function header must end with a colon. It should be def factorial(n):

Question 3

A def blast_off():

B if n == 0:

C print("Blast off!")

D return

E print(n)

F blast_off(n - 1)

Line A — The function needs the parameter n. The body uses n and the recursive call passes n - 1, so the header should be def blast_off(n):

Question 4

A def total(n):

B if n == 1:

C return 0

D return n + total(n - 1)

Line B — The base case should be n == 0 so that total(0) returns 0. Stopping at 1 returns 0 for 1, so total(3) gives 5 instead of 6.

Question 5

A def say_hi(n):

B if n == 10:

C return

D print("Hi")

E say_hi(n - 1)

Line B — n counts down from a small number such as 3, so it never equals 10. The base case is never reached and Python raises a RecursionError. It should be if n == 0:

Student with a class code? Join your class →