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Lessons

    Aligns to:

    (Also available in Pyret)

    Students learn to connect function descriptions across three representations: Contracts (a mapping between Domain and Range), Examples (a list of discrete inputs and outputs), and Definitions (symbolic).

    Lesson Goals

    Students will be able to:

    • identify patterns where a function would be useful

    • define their own function

    • match examples, contracts, and definitions for the same function

    Student-Facing Lesson Goals

    • Let’s define our own functions, by writing contracts and examples to help us identify patterns.

    Materials

    Supplemental Materials
    Glossary
    contract

    a statement of the name, domain, and range of a function

    example

    shows the use of a function on specific inputs and the computation the function should perform on those inputs

    function

    a relation from a set of inputs to a set of possible outputs, where each input is related to exactly one output

    function definition

    code that names a function, lists its variables, and states the expression to compute when the function is used

    variable

    a name or symbol that stands for some value or expression, often a value or expression that changes

    🔗Three Representations of a Function 55 minutes

    Overview

    Students will practice describing functions using all 3 representations (in programming syntax), and test their code against the examples in the editor.

    Launch

    • Open the bc Starter File. Look at the Contract, some Examples, and the Function Definition for gt.

    • What do you Notice? What do you wonder?

    We know that…​

    1 Every function has a Contract.

    ; gt :: Number -> Image

    2 We can write examples illustrating how a function should work to help us identify the pattern.

    3 Function definitions replace whatever changes in the examples with a variable describing what changes.

    In the gt Function Definition, we see that the changing numbers in the examples have been replaced by the word "size", the variable that describes them, such that when gt applies size, triangle applies size, "green" and "solid

    If we use the correct syntax, we can include all three of these function representations in our WeScheme files. Let’s take a look!

    • Click "Run". * Change (EXAMPLE (gt 10) (triangle 10 "solid" "green")) to (EXAMPLE (gt 10) (triangle 15 "solid" "green"))

    • Click "Run". What happens?

      • The editor lets us know that the function doesn’t match the examples so that we can fix our mistake!

    Examples not only help us to identify the pattern to define a function, they also let us double check that the functions we define do what we intend for them to do!

    Investigate

    Think about these three representations of functions by completing:

    For more practice, complete these Desmos card sort activities:

    There are many more materials for students to work with in the Additional Practice section at the end of the lesson!

    Synthesize

    • What strategies did you use to match the examples with the contracts?

    • What strategies did you use to match the examples with the function definitions?

    🔗Defining bc and Other Functions

    Overview

    Using gt as an example, students will write the Contract, examples, and definition for several other functions.

    Launch

    • Turn to Contracts, Examples & Definitions - bc

    • On the top half of the page, you will see the Contract, examples, and function definition for gt.

    • Circle what is changing and label it with the word size.

    • Using gt as a model, complete the Contract, examples and function definition for bc.

    When students have completed the above steps, direct them to type the Contract, Examples and Definition into the Definitions Area. They will then click “Run”, and make sure all of the examples pass!

    Check-in with students to gauge their confidence level. (Thumbs up? Thumbs to the side? Thumbs down?) How confident do students feel in writing the Contract, examples and function definition on their own if they were given a word problem about another shape function?

    Investigate

    As students work, walk around the room and make sure that they are circling what changes in the examples and labeling it with a variable name that reflects what it represents.

    Optional Project: Create Your Own Function

    In this lesson, students defined functions given a specific set of parameters. In Project: Create Your Own Function, students get additional practice thinking about functions before developing and defining a function of their own.

    Synthesize

    • How were each of the representations helpful?

    • Why is it important to write examples in our code?

    🔗Additional Exercises

    These materials were developed partly through support of the National Science Foundation, (awards 1042210, 1535276, 1648684, 1738598, 2031479, and 1501927). CCbadge Bootstrap by the Bootstrap Community is licensed under a Creative Commons 4.0 Unported License. This license does not grant permission to run training or professional development. Offering training or professional development with materials substantially derived from Bootstrap must be approved in writing by a Bootstrap Director. Permissions beyond the scope of this license, such as to run training, may be available by contacting contact@BootstrapWorld.org.