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Backwards Design Unit Planning
Teacher/School: Michael M. Leung / ASPIRES JHS185 Magnet School
New York City Department of Education
Magnet Program District 25 & 28
School Name
ASPIRES JHS185 Magnet School
Ratios and
Proportions
Essential Question: How do proportions allow us to
design buildings?
Suggested Time Frame: 5 weeks
Theme: Architecture – Blueprints, Scale Models
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Backwards Design Unit Planning
Teacher/School: Michael M. Leung / ASPIRES JHS185 Magnet School
Stage 1- Desired Results
Standards-Based Learning Goals:
6N1 Read and write whole numbers to trillions
6N2 Define and identify the commutative and
associative properties of addition and multiplication
6N3 Define and identify the distributive property of
multiplication over addition
6N4 Define and identify the identity and inverse
properties of addition and multiplication
Big Ideas for this Unit
Relationships
 Actual Measurements and Models/Drawings
 Enlargements and Reductions
 Interdependent Quantities
 Cost
6N5 Define and identify the zero property of
multiplication
6N6 Understand the concept of rate.
6N7 Express equivalent ratios as proportions.
6N8 Distinguish between rate and ratio.
6N9 Solve proportions using equivalent fractions.
6N10 Verify proportionality using cross
multiplication.
Concepts
Magnet School Theme:
Architecture
Relevant/Connected Big Idea:
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Maps
Scale Drawings and Models
Floor plans and Blueprints
Quantities of Building Materials
Enduring Understandings
Overarching Essential Question(s):
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Planning is essential for successful execution.
Plans can be modified, preserving intended
relationships.
Balance drives building design.
Quantities are interdependent-changes in one
cause changes in others.
Content
Students will know…
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Rates
Unit rate
Ratios
Equivalent ratios
Proportion
Means/Extremes
Cross Product
Scale
Golden Ratio
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How do rates allow us to follow a budget?
Are proportions used in the design process?
How do we make reasonable predictions?
How can we make organized plans that will guide
construction?
How do we enlarge or reduce quantities while
following a plan?
Content and Skills
Skills
Students will be able to…
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Represent ratios as fractions.
Determine whether two fractions are equivalent.
Determine unit rates.
Identify proportions within context.
Solve proportion problems.
Create/Interpret scale drawings and models.
Determine cost given unit rate.
Adapt designs to meet specifications.
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Backwards Design Unit Planning
Teacher/School: Michael M. Leung / ASPIRES JHS185 Magnet School
Stage 2- Summative Assessment Evidence
If students understand, know and are able to do the items in Stage 1, they should be able to show their
understanding by completing an authentic task found in the world beyond the classroom.
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Design the Culminating/Summative Task:
G- (goal)
The students will create an ambitious design for apartments in a new building. The design is to be submitted to the
building developer, who has provided multiple specifications the design must meet.
R- (role)
The students are taking the role of architect and interior designer, who is trying to win a contract to design the interior
of a new apartment building.
A- (audience)
The interior design plan will be reviewed by the developer of the apartment building. In addition, a panel of real estate
specialists will critique the design, considering: (1)Accessibility; (2)Furniture; (3)Reasonableness of Dimensions;
(4)Environmentally-Friendly Elements; (5) Vision Statement.
S- (situation)
A new apartment building is under construction in New York City. Only the structural frame and exterior of the
building have been completed. The building requires a plan for the interior walls, doors, windows, and placement of
furniture. The developer and investors want to market the building as an environmentally-friendly building.
P- (purpose and product)
The students will produce a proposal for the interior of the apartment building consisting of the following items:
 Floor plan for a one-bedroom apartment (1000 sq. ft.).
 Floor plan for a two-bedroom apartment (1600 sq. ft.).
 Floor plan for a three-bedroom apartment (2000 sq. ft.).
 Itemized list of furniture, including cost, quantity, dimensions, and description for each type of apartment.
 Explanation of environmentally-friendly features of the apartments.
S- (standards for performance)
Stay within budget.
Create dimensionally accurate floor plans.
Accurately calculate costs.
Creative use of space.
Application of Golden Ratio.
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Backwards Design Unit Planning
Teacher/School: Michael M. Leung / ASPIRES JHS185 Magnet School
Student Task
In the space below, write the task exactly as students will see it.
455 Madison Avenue
Live Like You Mean It
A new apartment building is under construction in New York City. Only the structural frame and exterior of the building have
been completed. The building requires a plan for the interior walls, doors, windows, and placement of furniture. The
developer and investors want to market the building as an environmentally-friendly building. Many prominent interior
designers have been invited to submit proposals for design of the apartments.
The developer requests the following documents in the proposal.
 Floor plan for a one-bedroom apartment (1000 sq. ft.). Select a scale to fit on letter paper.
 Floor plan for a two-bedroom apartment (1600 sq. ft.). Select a scale to fit on letter paper.
 Floor plan for a three-bedroom apartment (2000 sq. ft.). Select a scale to fit on letter paper.
 Itemized list of furniture, including cost, quantity, dimensions, and description.
 Explanation of environmentally-friendly features of the apartments.
Each apartment must consist of the following rooms:
 Bedroom(s)
 Bathroom(two bathrooms in three-bedroom apartment)
 Kitchen
 Dining Room (not in one-bedroom apartment)
 Living Room
Each room must contain at least:
 One table (any type, such as dining table, side table, coffee table, night stand, etc.)
 Two seats (any type, such as sofa, chair, stool, etc.)
 One window
 Two other pieces of furniture (such as bed, cabinet, dresser, etc.)
The furniture must also be listed with cost, quantity, dimensions, and description. Select furniture so that the total cost does
not fall below $2500 and does not exceed $4500.
Create the exterior of the building with a creative and appealing design. Apply the Golden Ratio in at least 5 design elements,
such as:
 Windows
 Entrance/Exit Doors
 Building Height
 Building Footprint
 Decorations (artwork, window mullions, ornamentation, signage, etc.)
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Backwards Design Unit Planning
Teacher/School: Michael M. Leung / ASPIRES JHS185 Magnet School
Rubric for Culminating Project
Level 4
Level 3
Level 2
Level 1
Floor Plans
Floor plan is attractive,
colorful. Dimensions and
furniture labeled. Scale
correctly applied.
Floor plan mostly is attractive,
colorful. Dimensions and
furniture mostly labeled. Scale
correctly applied.
Floor plan is somewhat
colorful, attractive. Few
dimensions and furniture
labeled. Scale not correctly
applied.
Floor plan is not attractive.
Dimensions are not labeled.
Scale is not correctly applied.
Furniture List
Furniture pieces are clearly
listed. All calculations are
correct.
Furniture pieces are generally
clearly listed. Most
calculations are correct.
Furniture pieces are not clearly
listed. Major errors in
calculations.
List is not provided or is
completely incorrect.
Architectural
Elements
Applied Golden Ratio
correctly 5 or more times.
Uses at least 5 architectural
terms in proposal.
Applied Golden Ratio
correctly 3 or more times.
Uses at least 3 architectural
terms in proposal.
Applied Golden Ratio
correctly 1 or more times.
Uses at least 1 architectural
term in proposal.
Does not apply Golden Ratio
correctly. Does not use
architectural terms in
proposal.
Presentation
Student consistently makes
connections between different
disciplines, past and present,
cause-effect relationships.
Student mostly makes
connections between different
disciplines, past and present,
cause-effect relationships.
Student sometimes makes
connections between different
disciplines, past and present,
cause-effect relationships.
Student does not make
connections between different
disciplines, past and present,
cause-effect relationships.
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Backwards Design Unit Planning
Teacher/School: Michael M. Leung / ASPIRES JHS185 Magnet School
GRID TEMPLATE
Essential Question: How do proportions allow us to design buildings?
Mini-Unit
Title
Big ideas of
the mini-unit
/ concept
statement
(macro)
Knowledge
(Important Content
to Know about
Mini-Unit)
(Micro)
Ratios
Relationships
A comparison of
numbers by division.
Equivalent ratios.
Write ratios in simplest form
Write a ratio by converting
units
Compare ratios
Determine whether ratios are
equivalent
Compare the height and width
of design elements by writing
a ratio.
Analyze Classical architecture
to find the Golden Ratio.
Are proportions used in the
design process?
How do we enlarge or reduce
quantities while following a
plan?
Rates
Relationships
Unit rates
Rates
Fractions
Find unit rates
Choose the best buy
Cost per item of building
materials.
Speed of construction.
How do rates allow us to
follow a budget?
How do we make reasonable
predictions?
Proportions
Relationships
Equivalent ratios.
Cross multiplication /
products.
Identify a proportion.
Solve proportion problems.
Write proportions within a
context.
Cost of quantity of materials
given cost of one unit.
Predict time to complete a
construction project given the
rate work has been completed.
Scale
Relationships
Scale drawings and
models
Scale
Create and interpret scale
drawings
Determine the scale
Scale drawings
How do rates allow us to
follow a budget?
Are proportions used in the
design process?
How do we make reasonable
predictions?
How can we make organized
plans that will guide
construction?
How do we enlarge or reduce
quantities while following a
plan?
How do rates allow us to
follow a budget?
Are proportions used in the
design process?
How do we make reasonable
predictions?
How can we make organized
plans that will guide
construction?
How do we enlarge or reduce
quantities while following a
plan?
GRASPS
Skills
What should the
students be able to do?
How does this
connect to the theme
of your school
(rule of thumb - skills are
verbs – knowledge is a noun)
Possible List of
Topical Essential
Questions / Focusing
Questions
Mini-Unit
Assessment
Given a ratio, write it
in simplest form.
Given two ratios,
determine if they are
equivalent.
Given geometric
figures, determine the
ratio of two of its
dimensions.
Given a rate, convert
it to a unit rate.
Given various prices,
determine the best
buy.
Given two ratios,
determine if they are
equivalent.
Determine the
missing number in a
proportion.
Given a scale and a
drawing, determine
actual measurements
and vice versa.
Benchmar
ks /
Scaffoldin
g towards
culminatin
g project
Culminating
Project
Understand
the Golden
Ratio. Apply
the Golden
Ratio in
design.
SEE STAGE
2
Understand
unit rates to
compare the
cost of
building
materials.
Determine
total cost given
unit price.
SEE STAGE
2
Understand
how to
convert
between actual
measurements
and scaled
measurements.
SEE STAGE
2
SEE STAGE
2
SEE STAGE 2
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Backwards Design Unit Planning
A Week at a Glance – Copy as Necessary
WHERE is the student going and what is expected
HOOK with needed skills to experience and explore
Opportunity to REVISE and RETHINK their understanding
Allow students to EVALUATE work and implications
TAILOR work to student needs
Be ORGANIZED to maximize engagement
Session 1
Session 2
Session 3
Session 4
Session 5
Content Focus:
What is a ratio?
Content Focus:
What are equivalent ratios?
Content Focus:
What is a unit rate?
Content Focus:
Are rates used in architecture?
Hook:
How many times bigger are the
heads on Mount Rushmore
than the actual heads? Can we
express this relationship as a
fraction?
Hook:
The ratio of fish to gallons of
water should be 2 to 9. There
are 6 fish in 45 gallons of water.
Is this the correct number of
fish?
Content Focus:
What is the difference between
a rate and a ratio?
Hook:
A hundred bricks cost a
construction company $5000.
Was this a reasonable cost for
the bricks?
Hook:
An office building has 15
elevators for 300 employees.
How many people does each
elevator serve?
Daily Assessment:
Given a verbal statement, write
a ratio representing the
relationship expressed.
Daily Assessment:
Determine if two ratios are
equivalent by simplifying the
ratios.
Daily Assessment:
Given a variety of rates,
determine the unit rates and
compare them.
Daily Assessment:
Create a unit rate for one aspect
of the design process. For
example, 4 gallons of water
must mix with 1 pounds of
cement.
Hook:
How can you determine what is
the best buy when you are
shopping?
Daily Assessment:
Supermarkets A and B have the
same product, but in different
sizes and costs. Determine the
best buy using unit rates.
Weekly Assessment:
Students must demonstrate an understanding of unit rate. In a quiz, students must translate verbal expressions, such as 20 tons of concrete cost $4000, into a rate and then
convert it into a unit rate.
What have the students produced that scaffolds towards the units culminating assessment?
The students have learned the concept of unit rate and have applied it in a variety of settings. They have understood its applications in architecture and construction.
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Backwards Design Unit Planning
A Week at a Glance – Copy as Necessary
WHERE is the student going and what is expected
HOOK with needed skills to experience and explore
Opportunity to REVISE and RETHINK their understanding
Allow students to EVALUATE work and implications
TAILOR work to student needs
Be ORGANIZED to maximize engagement
Session 6
Session 7
Session 8
Session 9
Session 10
Content Focus:
What is the Golden Ratio?
Content Focus:
What are proportions?
Content Focus:
What is cross multiplication?
Hook:
Show pictures of two classical
structures. Identify the Golden
Ratio in both structures.
Hook:
Buildings must have 3 exits for
every 75 people in the building.
A building with a capacity of
600 people has 24 exits—is this
correct?
Content Focus:
How do we write proportions
within context?
Content Focus:
How is the Golden Ratio used
in the design process?
Daily Assessment:
Given geometric figures,
determine if the figure contains
the Golden Ratio.
Daily Assessment:
Write two rates and determine
proportionality using equivalent
fractions.
Hook:
Concrete costs $15 for 3 cubic
feet. Nine cubic feet of
concrete costs $45. Can you
write this statement as a
proportion?
Daily Assessment:
Given a verbal statement, write
a proportion representing the
relationships expressed.
Hook:
Construction workers build two
floors of a building every nine
days. How long would it take
to complete a thirty-story
building?
Daily Assessment:
Solve a set of proportions, each
with a missing number.
Emphasis is on correctly crossmultiplying and solving the
resulting equation.
Hook:
Show examples of modern
buildings that use the Golden
Ratio.
Daily Assessment:
Construct geometric shapes
that contain the Golden Ratio.
A guess and check method may
be used, but students must
prove the dimensions are
proportional to the Golden
Ratio.
Weekly Assessment:
Students will demonstrate the ability to solve proportion problems in various real-life contexts. This will be in the form of a quiz consisting of word problems. Students
will have to correctly and accurately write and solve proportions.
What have the students produced that scaffolds towards the units culminating assessment?
The students have constructed shapes that contain the Golden Ratio. In addition, the students have used proportional reasoning to determine the cost for a specified
quantity of building material. These concepts will be applied in their culminating task.
8
5
Backwards Design Unit Planning
A Week at a Glance – Copy as Necessary
WHERE is the student going and what is expected
HOOK with needed skills to experience and explore
Opportunity to REVISE and RETHINK their understanding
Allow students to EVALUATE work and implications
TAILOR work to student needs
Be ORGANIZED to maximize engagement
Session 11
Session 12
Session 13
Session 14
Session 15
Content Focus:
How do we determine cost
when we know unit price?
Content Focus:
How do we determine the
better buy?
Content Focus:
What is a budget?
Content Focus:
Is it important to create
organized plans before
construction begins?
Content Focus:
How can proportional
reasoning help you enlarge or
reduce quantities?
Hook:
You want 40 cupcakes for a
birthday party. Cupcakes cost
$6 for 5. How much will the 40
cupcakes cost?
Hook:
Companies A and B sell steel
cables. Company A charges
$50 for 10 feet. Company B
charges $70 for 15 feet. Which
company has the better buy?
Hook:
Imagine you are building a
suspension bridge. What are
some problems you may
encounter if you do not create a
list of materials required, and
the time that they will be used?
Hook:
Concrete consists of cement
and gravel, in a ratio of 1L to
6L. This produces 40 pounds
of concrete. How much
cement and gravel is required to
produce 200 pounds of
concrete? 10 pounds of
concrete?
Daily Assessment:
A table provides unit costs for a
variety of building materials. It
also provides the quantity
needed for each material.
Students will use proportional
reasoning to determine the cost
of the required quantity of each
material.
Daily Assessment:
Companies A, B, and C sell
different construction materials.
Company A is cheaper than B,
which is cheaper than C. Prices
for A and C are given, and
students must create unit prices
for Company B, so that it is in
between A and C.
Hook:
What is the trade-off between
cost and quality? Explain the
cost-related quality problems of
Citicorp Center in NYC.
Daily Assessment:
A list of available materials for
floors, walls, doors, and
windows are provided.
Quantity required for each
category and a budget are
provided. Students must select
a combination of building
materials that will satisfy the
budget and quantity
specifications.
Daily Assessment:
Students must be able to
articulate the different types of
plans that can guide
construction, and explain why
each plan is important.
Daily Assessment:
Enlarge and reduce a given set
of proportional quantities.
Weekly Assessment:
Students must demonstrate a deeper understanding of unit rates and proportions. In the assessment, students must apply the concepts in an architectural or constructionrelated context. The skills assessed are: comparing unit rates; increasing and decreasing quantities in rates; using proportional reasoning to determine cost.
What have the students produced that scaffolds towards the units culminating assessment?
The students have created materials lists that conform to budget specifications.
9
5
Backwards Design Unit Planning
A Week at a Glance – Copy as Necessary
WHERE is the student going and what is expected
HOOK with needed skills to experience and explore
Opportunity to REVISE and RETHINK their understanding
Allow students to EVALUATE work and implications
TAILOR work to student needs
Be ORGANIZED to maximize engagement
Session 16
Session 17
Session 18
Session 19
Session 20
Content Focus:
What is a scale drawing?
Content Focus:
How do we read scale
drawings?
Content Focus:
How do we create scale
drawings?
Content Focus:
What is an architectural
blueprint?
Content Focus:
How do we select a scale for
architectural blueprint?
Hook:
A map shows that New York
and Los Angeles are 8 inches
apart. The scale is 1 inch = 300
miles. How far apart are the
two cities?
Hook:
Before a kitchen is renovated, it
is a good idea to make a plan of
what the kitchen would look
like. How do we create such a
drawing, so that we know what
size cabinets, tiles, etc. to
purchase?
Hook:
Maps have symbols that
represent various features. If
you look at a blueprint, you will
see a great variety of symbols.
Hook:
The Empire State Building is
1250 feet tall. A student selects
a scale of 1 inch = 10 feet, and
plans to draw the building on
regular paper. Why might the
student encounter a problem?
Hook:
How do model makers create
models that closely resemble
the actual object?
Daily Assessment:
List and describe 5 types of
scale drawings or models.
Daily Assessment:
Given a map, students will use
proportional reasoning to
determine the distance between
various locations on the map.
Daily Assessment:
Create a scale drawing of a
classroom using a specified
scale. Dimensions will be given
for desks, chairs, windows,
doors, and chalkboard.
Daily Assessment:
After learning the meaning of
the symbols used in
architectural blueprints, revise
the scale drawing of the
classroom so that it includes
these symbols.
Daily Assessment:
Select a scale so that the GE
Building at Rockefeller Center
can fit on a piece of letter
paper. Create this scale
drawing.
Weekly Assessment:
Students must demonstrate an understanding of scale and its relationship to proportional reasoning. In an assessment, an architectural blueprint will be provided with only
scale provided. Students must measure specific elements of the blueprint and determine actual dimensions. In addition, students must create a scale drawing of a given
object.
What have the students produced that scaffolds towards the units culminating assessment?
Students have created and interpreted blueprints, and will apply this skill when creating floor plans and other drawings in the culminating task.
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Backwards Design Unit Planning
Unit Resources
Books:
Websites:
Teacher Materials:
Other:
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