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# 3. INEQUALITIES

“Good math = math you want to talk about.”

― George Gadanidis

INEQUALITIES MENU | MATH + 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
- 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 MENU | MATH + 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