4 Inequality Puzzles

Prepared by George Gadanidis for:

MENU

ABOUT INEQUALITIES

What are some inequalities in our society?

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

x > 0, where x is a real number

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.

x > 0 in 1-D, 2-D & 3-D

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.