# 4 Inequality Puzzles

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.

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

• 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 else do you want to know?

#### TO DO #3

• Let’s discuss.

# PUZZLE #3

• 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

• 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?