Project: a change maker and a clock

What you will be able to do

After this lesson you can

• plan a program from a real problem in steps,
• use // and % as a pair to split an amount into groups,
• check a program with a number that you can work out by hand, and
• test the edge cases, such as zero.

Project 1: a change maker

A shop must pay back 387 rupees in change. It has notes of 100, 50, 20, 10 and 5 rupees and coins of 1 rupee. We want the fewest pieces. How many of each?

Step 1: do it by hand

Start with the biggest note and take as many as you can.

• 387 has three hundreds (300). 87 is left.
• 87 has one fifty. 37 is left.
• 37 has one twenty. 17 is left.
• 17 has one ten. 7 is left.
• 7 has one five. 2 is left.
• 2 is paid in 1 rupee coins: two coins.

The answer is: 3 of 100, 1 of 50, 1 of 20, 1 of 10, 1 of 5 and 2 of 1.

Step 2: see the pattern

Each step has the same two actions. How many of this note fit? That is //. What is left? That is %. So every step is a pair: // and %.

Step 3: write the program

Step 4: test it

A program that works for one number may fail for another. Test with these.

• amount = 100. The answer must be one note of 100, and nothing else.
• amount = 0. Everything must be 0.
• amount = 4. Only coins: four of 1 rupee.
• amount = 995. Nine hundreds, one fifty, two twenties, zero tens, one five. Check it by hand.

Project 2: a clock

A video lasts 10000 seconds. How long is it in hours, minutes and seconds?

The idea is the same as for the change: the biggest unit first. An hour has 3600 seconds, and a minute has 60 seconds.

Check by hand: 2 * 3600 + 46 * 60 + 40 = 7200 + 2760 + 40 = 10000. It works. This kind of check, putting the parts back together, is a good test for any program that splits a number.

The slider stops just before 12 hours, so the hour hand goes round once. A whole day would need a 24 hour clock.

Make it your own

1. Change total_seconds = 10000 to 90, to 3600 and to 0. Is each answer right?
2. Add a day to the clock: days = hours // 24 and hours = hours % 24. Try 100000 seconds.
3. Make the change maker work with a 2 rupee coin as well.
4. Write a program that tells the time 100 hours from now, if now is 4 o'clock, with the clock arithmetic of the last lesson.

Common mistakes

• Forgetting to store the remainder back in amount. Then every note works on the whole amount.
• Using / instead of //. You get 3.87 hundreds, and not 3.
• Changing the order of the notes. The biggest note must come first, so that the pieces are the fewest.
• Not testing zero. Edge cases are where programs break.

Practice

Start with two quick questions. Each New numbers gives you a fresh one, so you can practise as long as you like.

Then the labs and the problems:

1. Warm-up. Open the lab Take a number apart.
2. Build. Open the lab Project: the change maker. Write the program. The checker tests it with four amounts.
3. Stretch. Open the lab Project: seconds to a clock, and make it work for any number of seconds.

Remember these

• // tells how many, % tells what is left. Use them as a pair, from the biggest unit to the smallest.
• Store the remainder back, so that the next step works on what is left.
• Check a program with an answer that you worked out by hand, and put the parts back together.
• Test the edge cases: zero, an exact amount, and a small amount.

Check yourself

Try each one on your own first. If you are stuck, open a hint. Then check with Show the answer.

1. How many 100 rupee notes and how much is left from 250?

2. Why is / wrong in a change maker?

3. 200 seconds is how many minutes and seconds?