Project: tables and patterns

What you will be able to do

After this lesson you can

• plan the output of a program on paper before you write the loops,
• build a program in small steps, from one table to a whole book,
• test it against the plan, and
• extend it with a pattern of your own.

The goal

We want a times table book. For the numbers 2, 3 and 4 it should print

and so on, with a blank line between the tables. We also want to draw a pyramid at the end.

Step 1: one table

Start with the smallest part: the table of one number. If this works, we can repeat it.

Step 2: many tables

Now wrap that loop in another one, which goes through the numbers.

This way of building, one small part first, and then a loop around it, is a good habit. It works for most programs with loops.

Step 3: patterns

Patterns use the same ideas.

Check one row by hand before you trust the loop: for height 4, row 3 has 1 space and 5 stars.

Step 4: test against the plan

Write down, on paper, the first and the last line that you expect. For the book of the tables of 2, 3, 4: the first line is Table of 2, the last line with a number is 4 x 5 = 20. Run the program and compare. A mistake of one in the range() stop shows at the last line.

Step 5: extend it

Pick one of these, and do it without looking at a solution.

1. A neat grid. Print the whole book as one grid, with the numbers 1 to 10 across the top and down the side.
2. Only the even products. Print a table where the odd products are shown as a dot.
3. Another pattern. A hollow rectangle, or a pyramid upside down.
4. A sum for each table. After each table, print the total of the ten products.

Common mistakes

• Building everything at once. Start with one table.
• A stop value that is off by one, so the table has 9 lines or 11.
• The wrong place for the blank line. It belongs after the inner loop, but inside the outer one.
• Not planning the pattern. Count the spaces and stars of the first rows on paper.

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 Project: the table book. The checker runs your program and tests the shape of its output.
2. Build. Do Step 5 for one extension.
3. Stretch. Open the problem A times table again and make it print only the products that are even.

Remember these

• Plan the output first. Then build one small part, and wrap a loop around it.
• A loop inside a loop gives tables and grids.
• Test against the plan, especially the first and last lines.
• Count the numbers of a pattern on paper before you write the code.

Check yourself

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

1. Why do we build one table before the whole book?

2. How many lines does the table of one number have, if we use range(1, 11)?

3. In a pyramid of height 4, how many stars are in row 3?