The Lumenary · Grades 3–5

Repetition and decisions

Name: ______________________

Date: ______________________

You will learn to

Use a loop to shorten a sequence of repeated instructions, such as "repeat 4 times — forward, turn right 90°" for a square
Write if–then–otherwise rules for sorting objects or playing a game, and explain why the order of the conditions can matter
Follow a "repeat until" loop, predict when it stops, and spot a stopping condition that can never become true
Explain the written method for column addition as a loop over the place values with a carry, and why the carry is never more than 1

1.
The loop repeat 5 times: forward, turn right, clap is written out in full, one instruction after another. How many instructions is that?
2.
Which program makes the turtle draw an equilateral triangle (three equal sides, ending where it started)?
- A.repeat 3 times: forward, turn right 120°
- B.repeat 3 times: forward, turn right 60°
- C.repeat 3 times: forward, turn right 90°
- D.repeat 4 times: forward, turn right 120°
3.
The program repeat 6 times: forward, turn right ☐ degrees draws a regular hexagon. What number goes in the box?
4.
Start at 5. Repeat: add 4, until the number is bigger than 30. How many times is "add 4" done?
5.
Which of these loops never stops?
- A.Start at 20. Repeat: take away 4, until the number is exactly 0.
- B.Start at 15. Repeat: take away 2, until the number is exactly 0.
- C.Start at 15. Repeat: take away 2, until the number is less than 1.
- D.Start at 0. Repeat: add 7, until the number is bigger than 50.
6.
In FizzBuzz (FizzBuzz for multiples of 3 and 5; otherwise Fizz for multiples of 3; otherwise Buzz for multiples of 5; otherwise the number), which numbers from 1 to 20 are said as "Fizz"? Write them separated by commas, like {1, 2}.
7.
Add 476 + 358 with the column method. How many times do you carry 1?
8.
When you add two numbers with the column method, why is the carry never 2?
- A.A column total is at most 9 + 9 + 1 = 19, which has only one ten.
- B.Because the rule says you may only carry 1.
- C.Because the numbers we add are always small.
9.
In Lean, run home p is where the robot ends up after following program p from home, and repeatBlock 4 [.forward, .turnRight] is the loop "repeat 4 times: forward, turn right". Which statement says that the square loop brings the robot home?
- A.run home (repeatBlock 4 [.forward, .turnRight]) = home
- B.(repeatBlock 4 [.forward, .turnRight]).length = 8
- C.run home (repeatBlock 3 [.forward, .turnRight]) = home
10.
Write a function fizzbuzz(n) that returns what a player says for the number n: "FizzBuzz" for multiples of 3 and 5, otherwise "Fizz" for multiples of 3, otherwise "Buzz" for multiples of 5, otherwise the number as text (for example "7"). In Python, n % 3 == 0 is the condition "n is a multiple of 3".
Computational — Practice

Answer key — Repetition and decisions

1.
Each pass of the loop does 3 instructions (forward, turn right, clap), and the loop runs 5 times: $5 \times 3 =$ 15 instructions. The loop says it all in one line.
2.
The turtle's turns must add up to a whole turn: $360° \div 3 = 120°$ . So the program is repeat 3 times: forward, turn right 120°. Each corner of the triangle measures 60° inside, and the turtle turns through the outside angle, $180° - 60° = 120°$ .
3.
The 6 turns add up to one whole turn: $360° \div 6 =$ 60°. (Each corner of a regular hexagon measures 120° inside, and $180° - 120° = 60°$ .)
4.
$5 \to 9 \to 13 \to 17 \to 21 \to 25 \to 29 \to 33$ . After 7 steps the number is 33, which is bigger than 30, so the loop stops.
5.
Start at 15, take away 2 until exactly 0 never stops: the number is always odd (15, 13, …, 1, −1, −3, …), and 0 is even, so the condition never becomes true. The other loops stop: 20 reaches 0, the "less than 1" loop reaches −1, and the counting-up loop passes 50.
6.
The multiples of 3 up to 20 are 3, 6, 9, 12, 15, 18. But 15 is also a multiple of 5, and the FizzBuzz rule is checked first, so 15 is said as "FizzBuzz". The "Fizz" numbers are 3, 6, 9, 12, 18.
7.
Ones: $6 + 8 = 14$ → write 4, carry 1. Tens: $7 + 5 + 1 = 13$ → write 3, carry 1. Hundreds: $4 + 3 + 1 = 8$ → write 8, no carry. So there are 2 carries, and $476 + 358 = 834$ .
8.
Each digit is at most 9, and (starting with no carry, and by the same reasoning for each column) the carry into a column is at most 1. So a column total is at most $9 + 9 + 1 = 19$ , which contains only one ten. The carry out is again 0 or 1. (Adding three numbers is different: $9 + 9 + 9 = 27$ can carry 2.)
9.
run home (repeatBlock 4 [.forward, .turnRight]) = home says that after the square loop the robot is back at home: the same square and the same direction. In the lesson's Lean file this is square_returns. The length statement is true but about something else, and the 3-repeat statement is false (that is three_repeats_not_home).
10.
```
def fizzbuzz(n):
    if n % 15 == 0:
        return "FizzBuzz"
    elif n % 3 == 0:
        return "Fizz"
    elif n % 5 == 0:
        return "Buzz"
    else:
        return str(n)
```
The FizzBuzz case must come first. If n % 3 == 0 were checked first, 15 would return "Fizz", and "FizzBuzz" would never be returned. A loop such as for n in range(1, 101): print(fizzbuzz(n)) then plays the whole game.