(Also available in WeScheme)
Students identify solutions and non-solutions of inequalities using an interactive starter file. This lesson also reviews the Boolean data type.
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🔗Booleans 20 minutes
Overview
While students have been cursorily introduced to the Boolean data type in our Simple Data Types lesson, Booleans are so different from other data types and so foundational to inequalities that this section reintroduces students to Booleans (by way of Circles of Evaluation and a starter file) in preparation for working with inequalities in the second section of the lesson.
Launch
To get ourselves warmed up, evaluate these Circles of Evaluation, convert them into code, and then log into code.pyret.org (CPO) and test them out.
(+ 1 2)
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(- 4 5)
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(* 8 0)
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Take a minute to think about the Circles of Evaluation below: What do you think the expressions mean? What do you expect them to evaluate to?
Then convert these Circles of Evaluation to code and test them out.
(> 1 2)
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(< 4 5)
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(== 8 0)
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Values like true and false obviously aren’t Numbers or Images. But they also aren’t Strings, or else they would have quotes around them. We’ve found a new data type, called a Boolean.
Boolean is just another data type, like Number or Image. There are only two Boolean values: true and false.
Investigate
Turn to Boolean Functions and use the Boolean Starter File to complete the questions.
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Students will see functions in this activity that they’ve never encountered before (
is-odd,is-even,is-less-than-one,is-continent, andis-primary-color)! All five functions produce Booleans. -
Instead of answering their questions, encourage them to make a guess about what they do, and then type it in to discover for themselves.
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Explicitly point out that everything they know still works! They can use their reasoning about Circles of Evaluation and Contracts to figure things out.
Common Misconceptions
Many students - especially traditionally high-achieving ones - will be very concerned about writing examples that are "wrong." The misconception here is that an expression that produces false is somehow incorrect. You can preempt this by explaining that our Boolean-producing functions should sometimes return false.
Synthesize
How would you describe what a Boolean is?
🔗Introducing Inequalities 20 minutes
Overview
Students discover (or expand their understanding of) inequalities by identifying solutions and non-solutions and connecting expressions to graphic representations.
Launch
How are equations different from inequalities?
Equations typically have finite solution sets: there’s only one answer for an unknown, or perhaps several answers.
Inequalities, on the other hand, can have infinite solutions. Inequality expressions divide all of the numbers in the universe into two categories: solutions and non-solutions.
It is important that students learn to recognize that there are many possible solutions and non-solutions to an inequality and are able to identify whether or not a given number is or isn’t part of the solution set.
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We are going to practice identifying whether or not a given number is part of the solution set.
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Open the Simple Inequalities Starter File and click "Run".
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This starter file includes a special
inequalityfunction that takes in a function (which tests numbers in an inequality) and a list of 8 numbers (to test in the function). -
Look at the graph that appears (image below), as well as the provided code.
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What do you Notice? What do you Wonder?
Be sure to surface the following:
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When we click "Run", we see a graph of the inequality on a number line.
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The solution set is shaded in blue.
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The 8 numbers provided in the list are shown as dots on the number-line. They will appear:
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green when they’re part of the solution set
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red when they are non-solutions
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Find line 17 in the Simple Inequalities Starter File. Edit the list of values by changing one of the negative values to positive.
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Hit "Run". Examine the graph that appears (sample image below).
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How is this graph different from the one you first produced?
A successful input in this starter file will include 4 solutions and 4 non-solutions; in other words, the image returned will show 4 green dots and 4 red dots.
When students modify the list of numbers, they will see there are now 3 green dots and 5 red dots - along with a message that says, "Challenge yourself: Find 4 true examples and 4 false".
Investigate
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Complete Simple Inequalities with a partner, identifying solutions and non-solutions to each inequality and testing them in the Simple Inequalities Starter File.
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For each inequality, you must find four solutions and four non-solutions.
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Try using negatives, positives, fractions and decimals as you generate your lists.
Synthesize
What patterns did you observe in how the inequalities worked?
🔗Additional Exercises
These materials were developed partly through support of the National Science Foundation, (awards 1042210, 1535276, 1648684, 1738598, 2031479, and 1501927). 
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