(c) George Gadanidis 2021

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# ABOUT INEQUALITIES

What is an “inequality” in mathematics?

Below is an example of a mathematical inequality (** x > 0**) and some of the ways it may be represented.

#### ALGEBRAICALLY

**x > 0**, where x is an integer

#### AS A set

{1, 2, 3, 4, 5 …}

#### AS A graph on a number line

*Imagine placing masking tape**on your classroom floor**to create a number line.**How would the graph change if x is a real number?*

HINT: Real Numbers are all the numbers on a number line

#### AS A graph on a 2-D grid

*Imagine adding a second number line on your classroom floor, perpendicular to the first.**How would the graph change if x & y are real numbers?*

#### AS A graph on a 3-D grid

*Imagine taping a string where the 2 number lines meet on the floor and stretching the string vertically to the ceiling.**How would the graph change if x, y & z are real numbers?*

#### IN 1-D, 2-D or 3-d?

All of the graphs below are valid representations of the inequality x > 0.

Which graph is most appropriate depends on the mathematical context.

#### ABOUT THE PUZZLES

These are **math + coding** puzzles.

*You are given Scratch code that plots an inequality**You then have to alter the code to solve the puzzle*

The puzzles below all “live” on a 2-D coordinate grid.

The coordinates (x,y) have integer values.

# PUZZLE #1

Go to https://scratch.mit.edu/projects/540216861/editor/

*Run the code.**The output is shown below.*

#### TO DO #1

**A. **Alter the code to get the following output.

**B.** Alter the code to get the following output.

#### TO DO #2

**Alter the code in other ways and notice the effect.**

*What part of the code do you understand?**What part of the code do you have questions about?*

#### TO DO #3

*Let’s discuss*.

# PUZZLE #2

*Run the code.**The output is shown below.*

#### TO DO #1

**A. **Alter the code as shown below.

*Predict how the output will change.**Run the code to test your prediction.**Explain the result.*

**B.** Alter the code as shown below.

*Predict how the output will change.**Run the code to test your prediction.**Explain the result.*

**C.** Alter the code to get the output shown below.

**D.** Alter the code as shown below. [Notice that “and” changed to “or”]

*Predict how the output will change.**Run the code to test your prediction.**Explain the result.*

#### TO DO #2

**Alter the code in other ways to get similar results.**

*What have you learned about about inequalities and their graphs?**What else do you want to know?*

#### TO DO #3

*Let’s discuss*.

# PUZZLE #3

Go to https://scratch.mit.edu/projects/507100358/editor

*The code and the output as shown below.**Run the code.*

#### TO DO #1

**A. **Alter the code to get the following output.

**B.** Alter the code to get the following output.

#### TO DO #2

**Alter the code in other ways and notice the effect.**

*What more have you learned about about inequalities and their graphs?**What else do you want to know?*

#### TO DO #3

*Let’s discuss*.

# PUZZLE #4

Go to https://scratch.mit.edu/projects/540225499/editor/

*Run the code.**The output is shown below.*

#### TO DO #1

**A. **Alter the code as shown below.

*Predict how the output will change.**Run the code to test your prediction.**Explain the result.*

**B.** Alter the code as shown below.

*Predict how the output will change.**Run the code to test your prediction.**Explain the result.*

**C.** Alter the code as shown below.

*Predict how the output will change.**Run the code to test your prediction.**Explain the result.*

#### TO DO #2

**Alter the code in other ways to get similar results.**

*What more have you learned about inequalities and their graphs?**What else do you want to know?*

#### TO DO #3

*Let’s discuss*.

# SHARE

#### TO DO #1

Think back to the 4 puzzles above.

*What surprised most you mathematically? Why?**What new ideas, concepts or relationships did you better understand? Explain.*

#### TO DO #2

Share your favourite inequality experience with family and friends.

*How will you share your experience so others may also:**Experience mathematical surprise?**Better understand a math idea, concept or relationship?*

- Ask them:
*What surprised you?**What did you learn?**What else do you want to know?*

#### TO DO #3

Back in class:

*Share and discuss your sharing experience.**Share and discuss comments of your family and friends.*