mathematics + coding puzzles 3

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3. INEQUALITIES

“Good math = math you want to talk about.”
― George Gadanidis

INEQUALITIES MENUMATH + CODING MENU
3. Inequalities
— In the classroom
3A. Inequalities in 1D, 2D & 3D
3B. Puzzle 1
3C. Puzzle 2
3D. Puzzle 3
3E. Puzzle 4		Home page
1. Squares and spirals — introducing variables [gr. 3-9]
2. Making 10 — random coordinates line up [gr. 1-10]
3. Inequalities — in 1D, 2D & 3D [gr. 1-10]
4. Infinity — it’s big but fits in your hand [gr. 3-12]
5. Binary choice — probability, Pascal’s triangle & algebra [gr. 1-12]

Inequalities + Coding

IN THE CLASSROOM

Ontario Curriculum
  • Gr. 1/2
    • B2.2 – addition facts up to 10/20
  • Gr. 3-8
    • C3.1 – solve problems and create computational representations of mathematical situations by writing and executing code 
  • Gr. 4-8
    • C2.3/C2.4 – solve inequalities and verify and graph solutions 
  • Gr.5-8
    • C3.2 – read and alter existing code, (including code that involves conditional statements and other control structures) 
  • Gr. 6-8
    • C1.2 – linear growing patterns, constant rates & initial values
  • Gr. 9
    • C1.1 – research an algebraic concept to tell a story
    • C4.2 graph relations represented as algebraic equations and their associated inequalities, and identify various characteristics and the points and/or regions defined by these equations and inequalities
    • C2 – apply coding skills to represent mathematical concepts and relationships dynamically, and to solve problems, in algebra and across the other strands
  • Gr. 10
    • inequalities
Implementation
  • Gr. 1-2
    • Students find pairs of numbers whose sum is less than 10 (_+_<10).
  • Gr. 3-9
    • Students use masking tape and a string taped from the floor to the ceiling to represent 3D coordinates in the classroom.
    • Students discuss the meaning of x > 3 in 1D, 2D and 3D.
  • Gr. 3-10
    • Students use Scratch code that plots an inequality in 2D, they solve puzzles where they edit the code to match other inequality plots.
    • The complexity of the plots varies with grade level.

3A. INEQUALITIES in 1D, 2D & 3D

Using masking tape, divide the classroom floor using x and y axes, and add a scale to each axis, from -5 to 5. Then, tape a string vertically, from where the x/y axes meet to the ceiling.

Q1. If you live on the x-axis (in 1D), where is x > 3?

Q2. If you live on the x-y plane (in 2D), where is x > 3?

Q3. If you live on the x-axis (in 3D), where is x > 3?

3B. PUZZLE 1

Q4. Run the code below at https://scratch.mit.edu/projects/540216861/editor

  • What does the code do?
  • How does it do it?

Q5. Edit the code to get the following inequality graphs.

3C. PUZZLE 2

Q6. Run the code below at https://scratch.mit.edu/projects/540229313/editor

  • What does the code do?
  • How does it do it?

Q7. Alter the code as shown below.

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

A.

B.

Q8. Alter the code to get the output shown below.

Q9. 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.

3D. PUZZLE 3

Q10. Run the code below at https://scratch.mit.edu/projects/1059421111/editor

  • What does the code do?
  • How does it do it?

Q11. Edit the code to get each of the following.

3E. PUZZLE 4

Q12. Run the code below at https://scratch.mit.edu/projects/540225499/editor

  • What does the code do?
  • How does it do it?

Q13. Alter the code as shown below.

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

Q14. Alter the code as shown below.

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

Q15. Alter the code as shown below.

  • Explain the result.
  • Predict how the output will change.
  • Run the code to test your prediction.
INEQUALITIES MENUMATH + CODING MENU
3. Inequalities
— In the classroom
3A. Inequalities in 1D, 2D & 3D
3B. Puzzle 1
3C. Puzzle 2
3D. Puzzle 3
3E. Puzzle 4		Home page
1. Squares and spirals — introducing variables [gr. 3-9]
2. Making 10 — random coordinates line up [gr. 1-10]
3. Inequalities — in 1D, 2D & 3D [gr. 1-10]
4. Infinity — it’s big but fits in your hand [gr. 3-12]
5. Binary choice — probability, Pascal’s triangle & algebra [gr. 1-12]

by George Gadanidis, PhD