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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]

by George Gadanidis, PhD

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

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.

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?

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?

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

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