Star patterns with nested loops
Run two loops, one inside the other, to print a triangle of stars. Change the number of rows, count how many times the inner loop runs, and work out how to turn the triangle into a square.
Core concept
In nested loops the inner loop runs completely for every turn of the outer loop; when the inner loop goes from 1 to row, row r prints r stars and n rows print n(n + 1)/2 stars
Topic: Loops and patterns
A loop: Steps that repeat, either a set number of times or until something becomes true. All key words repeats some lines. A nested loop is a loop inside another loop: for each turn of the outer loop, the inner loop runs all the way through. Think of a clock: for every hour the minute hand goes round 60 times. To print a triangle, the outer loop counts the rows (row = 1 to n) and the inner loop prints the stars in that row (col = 1 to row). Row 1 gets 1 star, row 2 gets 2, and so on, so n rows hold 1 + 2 + … + n = n(n + 1)/2 stars. Change what the inner loop counts to and the shape changes: counting to n every time makes a square of n × n stars.
What you will learn
- Trace a nested loop and say how many times the inner loop runs in each row.
- Count the total runs of the inner loop: n(n + 1)/2 for a triangle, n × n for a square.
- Change a loop's bounds to change the pattern.
- Write the lines of a nested loop in order.
Before you start
- Know for loops and how a counter changes.
Materials
- A notebook to draw the patterns
Equipment
- None
Procedure
- Run the program with 4 rows and look at the pattern.
- Step through it and watch row and col change.
- Try 6 rows and count the stars.
- Answer the practice challenges.