Learning-Focused Strategies Extending/ Refining Lesson Plan: EATS
6th Grade: Lindsey Kane
Unit 2: Proportions
Title:
Golden Ration MYSTERY
Type:
Lesson Plan
Subject:
Math
Grade Range:
6
Description:
Golden Ratio
Duration:
55+ Minutes
Author(s):
Lindsey Kane
Instructional
Unit Content
E
Date: TBA
At the end of this lesson the student will understand that:
- gain a deeper understanding of proportional reasoning through instruction and practice
- develop and use multiplicative thinking
- develop a sense of proportional reasoning
- develop the understanding that ratio is a comparison of two numbers or quantities
- develop the understanding of the golden ratio and how it is related
Standard (s) MCC6.RP.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship
between two quantities.
MCC6.RP.2 Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0 (b not equal to
zero), and use rate language in the context of a ratio relationship.
MCC6.RP.3 Use ratio and rate reasoning to solve real-world and mathematical problems, e.g. by reasoning
about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
STANDARDS FOR MATHEMATICAL PRACTICE:
2. Reason abstractly and quantitatively.
TAG Standard Advanced Communication Skills
10. The student supports and defends his/her own opinions while respecting the opinions of others.
Advanced Research Skills
5. The student gathers, organizes, analyzes, and synthesizes data from multiple sources to support or
disprove a hypothesis.
Higher Order Critical Thinking Skills
11. The student draws conclusions based upon relevant information while discarding irrelevant
information.
Creative Thinking & Creative Problem Solving Skills
1. The student questions accepted practices, rules, and existing principles to discover new knowledge.
4. The student demonstrates skills in fluency and flexibility to solve problems or create new products.
Summary/ The focus of this less is to give students the opportunity to assess their own understanding of how to
Overview
- Make decisions about what they need to do to improve their understanding/skill.
- Solve a mystery to develop an understanding of the golden ratio and how it is related to objects
around them.
- Gain a deeper understanding of proportional reasoning.
Enduring At the end of this lesson the student will understand:
Understanding
- gain a deeper understanding of proportional reasoning through instruction and practice
- develop and use multiplicative thinking
- develop a sense of proportional reasoning
- develop the understanding that ratio is a comparison of two numbers or quantities
- develop the understanding of the golden ratio and how it is related
Essential
Question What do our skeletons have in common mathematically with nature, Greek statues, and artwork?
Concepts to 
Maintain 


Measuring
Proportions
Ratios
Converting ratios (fractions) to decimals
Evidence of What students should know:
Learning
a. Set up and compare ratios.
b. Work mathematically with proportions
What students should be able to do
a. Develop a sense of proportional reasoning
b. Understand that mathematics is connected to them and the world.
Suggested
Vocabulary Ratio, proportion, Golden ratio, equivalent
PROCEDURES
A
T
PHASE 1:
Hook/
Activating
Strategy
Teaching
STRATEGIES:
☐ KWL
☐ Wordsplash
☒ Draw Pic/Diagram
☐ Brainstorm
☐ Draw Pic/Diagram
☐ Anticipation Guide
☐ Activating Acrostic
☐ Dear Teacher
☐ Sponge
☐ Other:
Details of Activator:
Teacher will post a picture of Leonardo da Vinci Vitruvian man. The students will not have a lot of
background information on the picture. Can anyone identify the artist of the drawing? Does anyone know
the name of the famous drawing? Has anyone seen it before? If, so where? Discuss with class. What do
you notice mathematically about the Vitruvian man? How is this picture related to our essential questions,
What do our skeletons have in common mathematically with nature, Greek statues, and artwork?
☐ Peer Tutoring
☐ Simulations
☐ Hands On
☐ Lecture
☐Independent Activities
☐ Cooperative Learning
☐ Visuals
☐ Graphic Organizers
☐ Pairings
☐ Centers
☐ Whole group
instruction
☐ Projects
☐ Technology
Integration
☐ Guided Reading
☐ Response Cards
☐ Gallery Walk
☐ Quick Write
☒ Other:
Details of Strategies:
Mystery – solve a mystery to explore students’ ideas of the golden ratio and how it is related to the world.
Differentiation
STRATEGIES:
☐ Anchor Activities
☐ Choices of Review
☒ Flexible grouping/ seating
☐ Simulations
☐ Games
☐ Centers
☐ Centers
☐ Lit Circles
☐ Cubing
☐ Menus/ Choice Boards
☒ Multiple levels of
questions
☐ Think-Pair- Share
☐ Interest Groups
☐ Multiple
Intelligence
☐ Jigsaw
☐ Varied Modes of
Products
☒ OTHER: Mystery
Students will be grouped according to their Unit 2 pre-test. Students will be arranged in groups of 3 to 4
students. There will be a range of ability levels in each group. Multiple levels of questions will be asked
throughout the lesson.
Rigor & Relevance
☐A
☐B
☒C
☐D
Level of DOK
☐1
☐ 2
☒3
☐4
PHASE 2/3:
Examine the
Content/
Synthesis
Activity
S
Summarizing
STRATIGIES
(Students are doing
the summarizing)
2: Examine the Content
Share the Mystery
Distribute the “The Mystery of the Gold Ratio,” written by : Nikhat Parveen. Students read the mystery
independently. “You are now going to be broken up into groups to solve the mystery of the golden ratio.
Do you think this is something real? Do you think mathematicians and artists both use the same thing?”
Share the Clues
Students are broken up into range of ability levels groups. Students will cut the clues out. Students then
will take turns reading the clues. Students sort into groups. Teacher does not give the students titles for
specific categories. “You need to work together as a team to sort the cards in which you believe they
should be sorted. You will use a piece of butcher paper to create a poster to explain you thinking. You will
write a title for the different groups that you create. You will paste the cards in the groups you created.
You will also write a few sentences explaining why you put the clues in the groups you did and why you
gave the groups the specific titles. You will also write a hypothesis. Based upon patterns/data found
within the clues, each team will write a hypothesis and propose a solution to the mystery of the golden
ratio.” Students will work in their groups to complete their solution poster.
Share Solutions and Hypotheses/Discussion
Once the posters are completed, students will complete a gallery walk to review the groups’ solutions and
hypothesis for the mystery. Class will then have a discussion about the hypothesis and solution of the
mystery. “Is there really something that has a perfect ratio? If so, what, where, and why? Where can you
find the perfect ratio? How can you use it as a mathematician, artist, doctor, advertisement company?”
3: Synthesis Activity.
“Now that you have worked a little with the golden ratio, you are going to investigate whether or not you
are “golden.” Class discussion on whether or not we are golden. Students are required to work with a
partner. Students will be given an activity sheet that directs the students to what measurements they
should find. Students will be give yarn, adding-machine tape, yardsticks, rulers, and measuring tapes. All
students do not have the same measuring device; since they are to negotiate how to measure their body
parts within their partnership. Students are not directed how to best attain any given measurement.
Students work with their partner to obtain the measurements, record the information and add it to their
data chart. After all data is collected and reordered, students are asked to represent the ratios as
decimals. Students may use calculators to complete the computations. Each group will then prepare a
poster or technology presentation of their data, ratios, and final decimal representations of the ratios as a
mathematician. “Remember you are presenting as if you were a mathematician. Make sure you have
strong vocabulary in your presentation.” Each group will present its data to the class and share some
aspects of how the measurements were attained. “What are some things that might have gone wrong
throughout the measuring process? What are some things that worked really well?” After presentations
students will have a class discussion. “What do you find interesting or surprising about the data? Reflect
on the activity as a whole. Are we golden? Explain.”
☐ Answer EQ
☐ Hand Signals
☐ Journal Entry
☒ TOTD
☐ ABC Summary
☐ Oral Questioning
☐ One Minute Essay ☐ Index Card Summary
☒ Other: Sum – It – Up!
☐ Debriefing
Details of the Summarizer (What are students doing?):
Students will complete a Tick Out the Door answering the following questions.
- After investigating ourselves, are we golden? Explain your thinking.
- What do our skeletons have in common mathematically with nature, Greek statues, and artwork?
Describe other aspects of life that are represented by the golden ratio.
Resources Resource(s):
https://www.nctm.org/uploadedfiles/articles_and_journals/mtms/are_we_golden.pdf
http://mathematics.knoji.com/interesting-facts-about-the-golden-ratio-in-nature-art-math-andarchitecture/
Anchor Text(s):
“The Mystery of the Gold Ratio,” written by : Nikhat Parveen
Technology:
Projector for Opener
PowerPoint or Prezi for students’ synthesis activity presentation
Handouts:
Handout 1: “The Mystery of the Gold Ratio,” written by : Nikhat Parveen
Handout 2: Clues Handout
Handout 3: Investigate Golden Ratio
Handout 4: Investigate Golden Ratio Presentation checksheet.
Handout 5: Ticket Out the Door