Computer Science in Algebra

The Design Recipe

Writing intelligent functions, intelligently

Vocab

• Design Recipe - a sequence of steps to document, test, and write functions
• Purpose Statement - a brief description of what a function does
• Independent Variable - The value that the experimenter controls. The input.
• Dependent Variable - The value that changes based on the independent variable. The output.
• Constant - A fixed number in a relationship.

Roadmap to Function-land

1. Write a Contract that describes the problem
2. Write Examples based on the Contract
3. Define a Function that matches the examples

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Design Recipe Step 1

• Takes an argument for size (what type should it be?)
• Returns an outlined purple star (what type is that?)

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purple-star: Number -> Image

Define a function ’purple-star’ that takes in the size of the star and returns an outlined, purple star of the given size.

Design Recipe Step 1

• Takes a single argument (what type should it be?)
• Returns a value 50 less than the argument (what type is that?)

50less: Number -> Number

Write a function called “50less” that takes in a number, and returns a number that is 50 less.

Design Recipe Step 2a

50less(45) = 45 - 50

Write an example of what your function should produce, given some input (in this case 45)

Design Recipe Step 2b

50less(70) = 70 - 50

Write another example of what your function should produce, given some input (in this case 70)

Design Recipe Step 2c

50less(45) = 45 - 50

50less(70) = 70 - 50

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Compare the two examples to see what changes

Design Recipe Step 3

Write a function called “50less” that takes in a number, and returns a number that is 50 less.

50less(x) = x - 50

Design Recipe Step 1

• Takes a single argument (what type should it be?)
• Returns a solid purple star of that size

purple-star: Number -> Image

Define a function ’purple-star’ that takes in the size of the star and returns an solid, purple star of the given size.

Design Recipe Step 2a

purple-star(45) = star(45, “solid”, “purple”)

Write an example of what your function should produce, given some input (in this case 45)

Design Recipe Step 2b

purple-star(120) = star(120, “solid”, “purple”)

Write another example of what your function should produce, given some input (in this case 120)

Design Recipe Step 2c

Compare the two examples

size

Design Recipe Step 3

Define a function ’purple-star’ that takes in the size of the star and returns an solid, purple star of the given size.

Collaborative Design

Each member of your group will take on one role:

• Contract
• Examples
• Function

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Use the Collaborative Design Recipe Worksheets to complete the following problems

Collaborative Design

1. Define a function ’spot’, that takes in a color and produces a solid circle of radius 50, filled in with that color
2. To find the average of two numbers, they should be added together and divided by two. Define a function ’average’, which takes in two numbers and produces their average
3. A company logo is a word drawn in big, red letters, rotated some number of degrees. Define a function ’logo’, that takes in a company name and a rotation, and produces a logo for that company