# 1. SQUARES & SPIRALS

“One person’s constant is another person’s variable.”
― Susan Gerhart (computer scientist)

#### 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 research a geometric concept to tell a story
###### 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.
• Gr. 7-9
• The above may be used as a review of the meaning of constant & variable.

#### 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.

by George Gadanidis, PhD