Students will be able to...
- Define and identify Boolean expressions and operators.
- Evaluate Boolean expressions.
- Utilize Boolean operators,
and,or,not, to create compound conditions.
- Do now 2.5
- 2.5 slide deck
- The box variable activity
- Lab 2.5 - Triangles of all kinds (docx) (pdf)
- Exterior angles review
- Heron's formula
- Unit 2 tips
- https://youtu.be/XXS9aDlN14s
- Video Quiz: See Additional Curriculum Materials accessed from the TEALS dashboard.
| Duration | Description |
|---|---|
| 5 minutes | Welcome, attendance, bell work, announcements |
| 20 minutes | Review and lecture |
| 20 minutes | Triangles activity |
| 10 minutes | Debrief and wrap-up |
Remind students about conditional statements, and ask what the blocks that can go in the holes in if blocks have in common.
Blocks are "pointy" and all are "yes/no" or "true/false" questions.
Define Boolean expressions as expressions that evaluate to true or false.
- If desired, explain that the term "Boolean" is derived from George Boole.
Present the three Boolean operators: and, or and not.
- Define the operators and describe when each will return true.
- Show the truth tables for each operator and explain how to read them (see below for truth table example).
- Truth tables are simply one way of expressing how the Boolean operators work; if students are struggling, other depictions (such as an exhaustive list of all possible results) can be substituted.
- Emphasize that since Boolean operators are themselves Boolean expressions, they can be nested.
Practice evaluating Boolean expressions, starting simple and moving to more complex nested operations.
- Start with simple expressions: e.g.
5 < 7 AND 4 > 2.
Introduce variables: e.g. x = 7; x < 5 OR x > 10.
- Nest operations: e.g.
(x = 4; y = -3; x == y OR (x > 0 AND y < 0)). - Discuss short-circuiting in evaluation of Boolean expressions.
- Discuss situations in which the Boolean operators might be needed.
Students should complete the Triangles of all kinds activity individually or in diverse pairs (students who have not interacted previously, by ability, etc.).
A number of geometric concepts (Triangle Inequality Theorem, Pythagorean Theorem, etc.) are used in this lab, but students need not have a deep understanding of them. The necessary points are explained in the lab.
Encourage students to think about whether an "and" or an "or" is appropriate in each case. Draw out truth tables if necessary.
As done previously in the unit, you can make the Exterior angles review available to students.
Walk through a student's response.
- Point out uses of Boolean operators.
Discuss how nested or chained if blocks could potentially be used to obtain the same behavior, but would result in longer, less-readable programs.
| p | q | p and q |
|---|---|---|
| true | true | true |
| true | false | false |
| false | true | false |
| false | false | false |
| p | q | p or q |
|---|---|---|
| true | true | true |
| true | false | true |
| false | true | true |
| false | false | false |
| p | not p |
|---|---|
| true | false |
| false | true |
Students that have not taken Geometry made be intimidated by some of the concepts in the lab. Deep understanding of the theorems is not necessary; encourage the students to simply focus on the equations and inequalities presented.
If the students continue to struggle, help them build the necessary expressions, but encourage them to assemble them into the full condition on their own.
Advanced students, especially those who have taken higher levels of math, can be encouraged to add additional functionality, such as using Heron's formula to calculate the triangles area or using trigonometry to attempt to draw the triangle.