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# 1. SQUARES & SPIRALS

“One person’s constant is another person’s variable.”

― Susan Gerhart (computer scientist)

SQUARES & SPIRALS MENU | MATH + CODING MENU |

1. Squares & spirals — Constants, variables & coding — In the classroom 1A. Puzzle 1 – squares 1B. Puzzle 2 – code a spiral 1C. Puzzle 3 – match spirals 1D. Puzzle 4 – create math art | 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] |

#### Constants, variables & computer programing

by George Gadanidis, PhD

#### IN THE CLASSROOM

###### Ontario Curriculum

**Gr. 3**- E1.4 – give and follow multistep instructions involving movement from one location to another, including distances and half- and quarter-turns

**Gr. 3/4**- C2.1 – use variables in various contexts
- C.3.2 – read and alter existing code; sequential, concurrent, and repeating & nested events

**Gr. 4-6**- E2.4 – identify and classify angles

**Gr. 9**- C2.1 – use coding to demonstrate an understanding of algebraic concepts (including variables)
- C1.1 research an algebraic concept to tell a story
- E1.1

###### Implementation

**Gr. 3-6**- To walk a
**square**, we may repeat 4 times: walk 5 steps and turn right (90 degrees or 1/4 turn). Notice that the number of steps is**constant**. - To walk a
**spiral**, the number of steps keeps changing. The number of steps is**variable**. - The process of drawing a square and then drawing a spiral
**anchors student understanding**of constants and variables. - The need for a variable is especially important when we use
**Scratch****code**to draw the spiral, as the turn angle is constant and the number of steps varies.

- To walk a
**Gr. 7-9**- The above may be used as a
**review**of the meaning of constant & variable.

- The above may be used as a

#### 1A. PUZZLE 1 – SQUARES

Below are 2 different ways to draw a square with code. You can click and run the code at https://scratch.mit.edu/projects/1055180217/editor/

**Q1.** Edit SQUARE 1 code to draw a smaller square.

**Q2.** Edit SQUARE 2 code to draw a smaller square.

**Q3.** How is the code for SQUARE 1 and the code for SQUARE 2 similar or different?

**Q4.** Which code do you like better? Why?

#### 1B. PUZZLE 2 – CODE A Spiral

**Q5.** Edit SQUARE 1 code to draw a spiral like the ones shown below.

**Q6.** Editing SQUARE 2 code to draw a spiral like the ones shown below is not as simple. Why?

**Q7.** Below is one way to edit SQUARE 2 code to draw a spiral. How is SPIRAL 2 code different from SQUARE 2 code?

#### 1C. PUZZLE 3 – Match Spirals

You can click and run the SPIRAL 2 code at https://scratch.mit.edu/projects/1055189920/editor

**Q8.** Edit the code to create each of the following spirals.

#### 1D. PUZZLE 4 – CreatE Math Art

**Q9.** Edit the SPIRAL 2 code to create your own math art.

SQUARES & SPIRALS MENU | MATH + CODING MENU |

1. Squares & spirals — Constants, variables & coding — In the classroom 1A. Puzzle 1 – squares 1B. Puzzle 2 – code a spiral 1C. Puzzle 3 – match spirals 1D. Puzzle 4 – create math art | 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