Understanding By Design Unit Template
(Revised & adapted)
Title of Unit
Subject
Developed By
Area and Perimeter
Grade Level
Third
Math
Time Frame
February 4 – March 1
Diana, Laura, Mona
Stage 1 - Identify Desired Results
Narrative about this Unit of Study: (including the Big Idea)
This instructional bundle contains a task aligned to the Content Core standards and additional supports for diverse learners. The task is
embedded in a 4-5 week unit on understanding concepts of area and perimeter using multiplication and addition to measure. Perimeter and
area are two different measurements of the same shape and that each has its own kind of unit of measurement. Area is measured with
square units and perimeter is measured in units of length.
Learning Outcomes – Identified Primary Standards
What relevant goals will this unit address?
3.MD.5 Recognize area as an attribute of plane figures and understand concepts of area measurement.
a. A square with side length 1 unit, called “a unit square,” is said to have “one square unit” of area, and can be used to measure area.
b. A plane figure, which can be covered without gaps or overlaps by n unit squares, is said to have an area of n square units.
3.MD.6 Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).
3.MD.7 Relate area to the operations of multiplication and addition.
a. Find the area of a rectangle with whole‐number side lengths by tiling it, and show that the area is the same as would be found by multiplying the
side lengths.
b. Multiply side lengths to find areas of rectangles with whole‐number side lengths in the context of solving real world and mathematical problems,
and represent whole‐number products as rectangular areas in mathematical reasoning.
c. Use tiling to show in a concrete case that the area of a rectangle with whole‐number side lengths a and b + c is the sum of a × b and a × c. Use
area models to represent the distributive property in mathematical reasoning.
d. Recognize area as additive. Find areas of rectilinear figures by decomposing them into non‐overlapping rectangles and adding the areas of the
non‐overlapping parts, applying this technique to solve real world problems.
3.MD.8 Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths,
finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different
perimeters.
Standards for Mathematical Practice:
MP.1 Make sense of problems and persevere in solving them.
MP.3 Construct viable arguments and critique the reasoning of others.
MP.4 Model with mathematics.
Understandings
What understandings about the big ideas implied in the PLOs are desired?
Essential Questions
What provocative questions will foster inquiry into the content?
Students will understand that (includes key vocabulary)...
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lationship between finding rectilinear area and
multiplication/addition
How to deconstruct a rectilinear space into non-overlapping
rectangles to find the area of the entire space
How to connect mathematical expression to word problems
There are similarities and differences between the measurement
of area and perimeter
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What is area?
How is finding the area of a quadrilateral related to
multiplication and addition?
How can we express the area of a quadrilateral in a
numerical expression?
Why is calculating area important to us in our everyday life?
How can we find the area of a rectilinear space that
incorporates multiple rectangles?
No essential questions that relate to perimeter
Knowledge:
What knowledge will student acquire as a result of this unit?
Skills
What skills will students acquire as a result of this unit?
Students will know...
Students will be able to…
Using mathematics in real world contexts is the focus, specifically the
measurement of area as it relates to multiplication and how perimeter
relates to addition. They will know that being able to accurately
measure the surface area is an essential skill for many professions.
Key concepts that will be covered:
• Measurement: measuring area using tiles and multiplication.
• Number Operations: relating area to multiplication (length x width).
 understand that area is the amount of surface inside a twodimensional figure. (3.MD.5)
 understand that there are two ways to find the area of a square or
rectangle:
1. Count the number of squares/tiles of a certain size that cover
the inside of a shape. (3.MD.6)
2.Multiply side lengths a x b to find the area. (3.MD.7a)
 Students use tiles to create rectangular arrays that show a specific
area. (3.MD.7a)
 Students use tiles to show that the area of a rectangular array is the
same as would be found by multiplying the side lengths. (3.MD.7a)
 Students use tiles to find the area of a rectangle when provided
with the side lengths, within the context of a word problem.
(3.MD.7b)
 Students solve real-life problems related to area using
multiplication and division (without tiles). (3.MD.7b)
Stage 2 – Assessment Evidence
Performance Task
Through what authentic performance task will students demonstrate the desired understandings, knowledge, and skills?
Brief Written Description of the Performance Task
The NYC DoE has an area unit that has 3 examples of performance tasks with rubrics:
1. Ms. Smith’s Planting Predicament
2. Winter Vegetables
3. Fencing the Garden
http://schools.nyc.gov/NR/rdonlyres/CD824F33-84DA-4D5F-8D4A-B450EA8C8000/0/NYCDOE_G3_Math_CityFarmers_Final.pdf
Rubric for Assessment:
Rubrics are included in the unit plan for the above tasks.
Other Evidence
Through what other evidence – student work samples, observations, quizzes, tests, self-assessment or other means – will students demonstrate
achievement of the desired results?
The pre-assessment (included below in the document) has been developed using the sequence of learning that is advocated in the CCLS, that is:
1. Student’s build and understanding about what area and perimeter are.
2. Students begin to establish how many square units fit into rectangles and squares by tiling or counting squares (building counting from skip
counting and repeated addition to multiplication is a key focus of the unit).
3. Decomposing irregular shapes that have the square units identified.
4. Decomposing irregular shapes and calculating the area by using the dimensions of the shape
5. Decomposing irregular shapes, establishing some unknown dimensions from known dimensions and then calculating the area.
From: Wiggins, Grant and J. McTighe. (1998). Understanding by Design, Association for Supervision and Curriculum Development, ISBN # 0-87120-313-8 (pbk)
Objective(s)
Related to knowledge, skills or both?
Using U.S and Metric Units to
measure length.
What is perimeter?
What is perimeter?
What is perimeter?
What is perimeter?
What is perimeter? What is area?
What is area?
Listed Aim or Learning Intention
of Each Lesson.
- Review the length of units of
measure (inch, foot, yard, centimeter
and meter).
- Establishing Measurement
Benchmarks.
- Understand perimeter as the
measure around the outside edges of
a 2-dimensional shape.
- Use U.S standard units and metric
units to accurately measure length.
- Find the perimeter of a polygon
given the side lengths.
- Creating different shapes with the
same perimeter.
- Finding perimeter using standard
units.
- Understanding perimeter as the
measure around the outside edges of
a 2-dimensional figure.
- Understanding perimeter as the
measure around the outside edges of
a 2-dimensional figure.
- Finding perimeter using standard
units.
- Creating different shapes with the
same perimeter.
- Determine how the perimeter and
area of the shape are related.
- Determining the geometric moves
needed (slides, flips, turns) to prove
or disprove congruence between two
shapes.
- Understanding that area is
measured in square units.
- Understanding that when
measuring area, the space being
Assessment
Are students using the
measurement tools accurately?
Are they making reasonable
estimates for each unit of
measure?
Did students choose an
appropriate tool to measure
perimeter?
Resources
Unit 4 Investigations Lesson 1.1 (pg.
22)
Unit 4 Investigations Lesson 1.2 (pg.
29)
Do students add all of the sides
to find perimeter?
Do students accurately measure
the perimeter of each shape?
Are they able to explain why
their predictions may differ from
the actual order?
As above.
Robotic Racing. Lesson Plan in pdf
saved on the server.
Unit 4 Investigations Lesson 1.4 (pg.
45).
This activity has 4 centers you can use
with students. This could be
undertaken over two days or just with
students that need extra perimeter
work.
Unit 4 Investigations Lesson 1.5 (pg.
50)
Ordering shapes based on perimeter
How can I demonstrate my
understanding of area and
perimeter?
Fence the Yard. Lesson Plan in pdf
saved on the server (this lesson can go
for 3-5 days).
Are students able to make all
five tetrominoes?
Unit 4 Investigations Lesson 2.1 (pg.
62).
How do they decide if the
shapes are the same or not?
Students explore all the possible
arrangements of four squares.
measured must be completely
covered with no gaps or overlaps.
What is area? What is perimeter?
What is area?
- determine if rectangles can have
the same perimeter, but different
area.
- Understanding that when
measuring area, the space being
measured must be completely
covered with no gaps or overlaps
- Understanding that area is
measured in square units
What is the relationship
between perimeter and area?
Rectangle Rules. Lesson Plan in pdf
saved on the server.
How do students arrange the
tetrominoes to cover squares?
Unit 4 Investigations Lesson 2.2 (pg.
68).
Do students find larger units
they can use to cover the
space?
Students discuss the meaning of area
and find the area of an 8 by 10
rectangle.
Exploring Area
- Understanding that when
measuring area, the space being
measured must be completely
covered with no gaps or overlaps
- Understanding that area is
measured in square units
The following link has an activity for
students still building their
understanding of area:
http://www.k5mathteachingresources.com/supportfiles/exploringarea.pdf
Exploring Area
- Understanding that area is
measured in square units
Geoboard Areas. Lesson Plan in pdf
saved on the server.
Exploring Area
- Understanding that area is
measured in square units.
Making different shapes that have an
area of four square units on a Geobord:
http://www.k5mathteachingresources.com/supportfiles/areaonthegeobaord.pdf
Exploring Area
- Understanding that area is
measured in square units.
- Students identify, create, and use
square units to measure area.
Tiling a Tabletop. Lesson Plan in pdf
saved on the server.
Exploring perimeter and area
- determine how measures of length
change when the unit of measure
changes.
- what methods can we use to
determine the area of an object.
- Developing strategies for measuring
the area of rectangles.
- Skip counting, repeated addition
and multiplication.
How big is a desk? Lesson Plan in pdf
saved on the server.
Calculating area
Comparing rectangles:
http://www.k5mathteachingresources.com/supportfiles/comparing-rectangles.pdf
Calculating area
Calculating area
Calculating area
Calculating area.
Decomposing irregular shapes with
the units identified
Decomposing irregular shapes with
the units identified
Decomposing irregular shapes with
just the dimensions
Decomposing irregular shapes with
just the dimensions
Decomposing irregular shapes with
just the dimensions
- Developing strategies for measuring
the area of rectangles.
- Skip counting, repeated addition
and multiplication.
- Developing strategies for measuring
the area of rectangles.
- Skip counting, repeated addition
and multiplication.
- Determine the area of a rectangle
by counting square units
- Communicate the process of finding
the area of a rectangle
- students will use the dimensions of
rectangles to determine their areas.
- Students decompose shape and
then apply compute the area of the
shape.
Rectangle Comparison 2. Lesson Plan
in pdf saved on the server.
- Find the area of a rectangle by
breaking it into smaller rectangles
- Discuss how they broke a rectangle
into two smaller rectangles
- Find the area of a large, rectilinear
figure by decomposing it into smaller
rectangles
- Communicate their process of
finding the area of a rectilinear figure
Breaking Apart Arrays. Lesson Plan in
pdf saved on the server.
- Find the area of a large, rectilinear
figure by decomposing it into smaller
rectangles
- Communicate their process of
finding the area of a rectilinear figure
Finding the Area of Complex Figures 2.
Lesson Plan in pdf saved on the server.
- Find the area of a large, rectilinear
figure by decomposing it into smaller
rectangles
- Communicate their process of
Finding the Area of Complex Figures 3.
Lesson Plan in pdf saved on the server.
Incomplete Rectangles. Lesson Plan in
pdf saved on the server.
Mowing for Money. Lesson Plan in pdf
saved on the server.
Sticker Stumper. Lesson Plan in pdf
saved on the server.
This activity from Illustrative
mathematics is a good example of
decomposing shapes with the units
identified:
http://www.illustrativemathematics.org/
illustrations/516
Finding the Area of Complex Figures 1.
Lesson Plan in pdf saved on the server.
Possible Performance Task
finding the area of a rectilinear figure
Decomposing irregular shapes with
some unknown dimensions
These activities still need to be
developed.
- Use clues to determine whether to
find the area or the perimeter to
solve a problem
- Communicate how they solved
problems involving area or perimeter
Area or Perimeter. Lesson Plan in pdf
saved on the server.