Prepared by George Gadanidis for:
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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.