Spin City Worksheet SPIN CITY WORKSHEET
Rotational Symmetry Exploration
Name: ____________________________________
Date: ________________
Warm-Up: The Full Turn
As we rotate the pen on the desk, answer these quick questions:
1. How many degrees are in one full circle/rotation?
2. If you rotate a shape halfway, how many degrees is that?
Video Lab: Order & Magnitude
Order
The number of times a figure matches itself in one full 360° turn.
Magnitude
Magnitude = 360° ÷ Order
Object from Video Order Magnitude (Show Work) Equilateral Triangle Jamaican Flag Snowflake Liberian Flag
Symmetry Hunters
Partner up! Find objects in the classroom with rotational symmetry. Estimate their properties below.
Object Found
Est. Order
Magnitude Calc
Point of Rotation?
LOGO LAB
Design Challenge
Create a corporate logo that has an Order of 5. What is its magnitude?
Magnitude Calculation:
Spin Cycle Slides SPIN CITY
Mastering Rotational Symmetry
Order Magnitude
Warm-Up: Pen Spin
"Shout STOP when the pen returns to its exact starting position!"
Think-Pair-Share
How many degrees are in that full turn?
VIDEO STUDY
Exploring Symmetry with Justin
PAUSE: 7:21 & 9:08
Embedded media
Current Goal
Find the Order of the Snowflake
Key Formula
360° ÷ Order
Watch For
Figures with "No Symmetry"
The "Spin" Lexicon
Order
The number of times a shape "matches" itself in one full circle (360°).
Magnitude
The angle you have to rotate each time to find a match.
MAG = 360° ÷ ORDER
Always use this "Recipe" to find the degrees of rotation!
Symmetry Hunters
1
Grab a partner and your worksheet.
2
Hunt for rotational objects (Clock, Floor Tiles, Posters).
3
Identify the Center, estimate the Order, and calculate Magnitude.
Wait! If a shape only matches at 360°...
IS IT SYMMETRIC?
THE LOGO
CHALLENGE
Your mission is to design a logo for a new brand.
Requirement
ORDER 5
Requirement
360 ÷ 5 = ?
Requirement
MAGNITUDE
Rotation Station Anchor Chart THE ROTATION STATION
A Guide to Rotational Symmetry
Order
The number of times a figure "matches" its original position during one full 360° turn.
1
2
3...
Magnitude
"The angle of the turn"
\( \frac{360^\circ}{\text{Order}} \)
Case Studies
Triangle
Order 3
Magnitude: 120°
Square
Order 4
Magnitude: 90°
Hexagon
Order 6
Magnitude: 60°
The "Order 1" Rule
If a shape only looks like itself after a full 360° turn, its Order is 1. We say it has NO rotational symmetry!
Symmetry Scout Teacher Guide Symmetry Scout Guide
Instructional Facilitation Notes
7th Grade Math
Objective
Calculate the Order and Magnitude of rotational symmetry for regular polygons and real-world objects.
Key Materials
Spin Cycle Slides
Spin City Worksheet
Rotation Station Anchor Chart
Pens for Warm-up
Prep Time
5 Minutes (print worksheets, set up anchor chart, cue video start at 4:48).
1
Warm-Up: The Desk Spin (5 min)
Have students place a pen on their desk. Rotate it slowly. They shout "STOP" when it returns to its start. Use this to establish that a full circle is 360°.
Discussion Prompt: "If it looks the same halfway through, what would that angle be? Why?"
2
Video Deep Dive (15 min)
URL: https://www.youtube.com/watch?v=Tnt04\_YJmb0
Primary Focus: 4:48 - 9:35
Pause at 7:21: Challenge students to calculate the Jamaican Flag magnitude (Order 2, Magnitude 180°).Pause at 9:08: Discuss why the Liberian flag has no rotational symmetry. Define this as "Order 1."
3
Symmetry Hunters (15 min)
Send student pairs on a hunt. Encourage them to look for clocks (Order 12), ceiling tiles (Order 4), or posters. They must identify the Center of Rotation before estimating.
Teaching Tip: If a student finds an object with Order 1, affirm that it has NO rotational symmetry. This is a crucial distinction.
Answer Key: Spin City Worksheet
Object Order Magnitude Equilateral Triangle 3 360 ÷ 3 = 120° Jamaican Flag 2 360 ÷ 2 = 180° Snowflake 8 360 ÷ 8 = 45° Liberian Flag 1 360° (None)
Logo Challenge Example
Requirement: Order 5
Calculation: 360 ÷ 5 = 72°
(Common examples: Starfish, Pentagram, certain flowers)
Common Misconceptions
Confusing Rotational Symmetry with Reflectional (Line) Symmetry.
