MATH | LEVEL 4
Student Edition Sample Page
Name __________________________________________
Unit 25 Introduction
Standards 4.5(C), 4.5(D) – Readiness
1 Makesha’s rectangular tabletop is
5 feet long and 3 feet wide as shown
by the model.
3 Nachele measures her rectangular
bedroom ceiling and buys exactly 48 feet
of wallpaper border to put around the
ceiling. If the length of Nachele’s ceiling is
14 feet, what is the width?
Answer: ______________
Explain how you found your answer.
_______________________________
_______________________________
What is the perimeter of Makesha’s
tabletop?
Answer: ______________
What is the area of Makesha’s tabletop?
Answer: ______________
2 Mr. Carlson wants to carpet the family
room of his house as shown in the
diagram. He multiplied 10  14 to
determine how much carpet to purchase.
4 Trevor folds a square sheet of paper in
half vertically. He then folds the paper
in half horizontally to form 4 congruent
squares. The model below represents the
paper.
The perimeter of each small square is
48 centimeters. What is the perimeter of
Trevor’s original sheet of paper?
10 ft
Answer: ______________
Explain how you found your answer.
14 ft
_______________________________
Why did Mr. Carlson multiply 10  14?
Answer: _______________________
_______________________________
_______________________________
_______________________________
_______________________________
Write and solve an equation to find the
area of Trevor’s original sheet of paper.
Answer: ________________________
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Unit 25 Guided Practice
Standards 4.5(C), 4.5(D) – Readiness
1 Mr. Edison asks his students to design a
rectangular garden with a perimeter of
12 units. Which design does NOT show a
garden with a perimeter of 12 units?
3 City Park has a children’s wading pool
that is surrounded by a rectangular fence.
The diagram shows the pool and the
fence.
10 meters
A
wading pool
8 meters
B
Which of the following is a true statement
about the area of the wading pool?
C
A The area of the wading pool is equal
to 80 square meters.
B The area of the wading pool is less
than 80 square meters.
D
C The area of the wading pool is equal
to 36 meters.
2 Every evening, Candy jogs around her
neighborhood. The block she jogs around
is in the shape of a square.
D The area of the wading pool is greater
than 80 square meters.
4 Mr. Schilling owns a construction
company. He pours a concrete patio that
is 54 feet long and 18 feet wide.
Lemon Lane
Pear Avenue
Peach Street
18 feet
Apple Drive
200
54 feet
What formula can Candy use to
determine how far she jogs each
evening?
Mr. Schilling pays for concrete by the
number of square feet. What is the area
of the patio he pours?
F P=4s
H P=2s
F 144 sq ft
H 942 sq ft
G A=ss
J A=lw
G 972 sq ft
J 486 sq ft
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Unit 25 Independent Practice
Standards 4.5(C), 4.5(D) – Readiness
1 Butch has a square closet in his bedroom.
He wants to find the area of the floor
of the closet. He measures the length
of one side of the floor. What other
measurement does Butch need to find the
area of the closet floor?
4 Melinda has a rectangular flower garden.
The width of her garden is 5 feet. Melinda
uses 60 feet of edging to go around the
garden. What is the length, in feet, of
Melinda’s garden?
Record your answer and fill in the bubbles
on the grid below. Be sure to use the
correct place value.
0
0
0
0
0
1
1
1
1
1
2
2
2
2
2
3
3
3
3
3
A The width of the closet
4
4
4
4
4
5
5
5
5
5
B The height of the closet
6
6
6
6
6
7
7
7
7
7
C The depth of the closet
8
8
8
8
8
9
9
9
9
9
D He does not need any other
measurement.
2 Mrs. Able bought a rectangular rug.
The rug has an area of 48 square feet.
Which of the following could NOT be the
dimensions of Mrs. Able’s new rug?
F Length  16 feet, Width  3 feet
5 Brad’s family is building a new house.
The carpenter allowed Brad to help him
calculate the length of baseboard needed
to go around the bases of the walls in
the dining room. This figure shows Brad’s
dining room.
G Length  12 feet, Width  4 feet
10 ft
H Length  8 feet, Width  6 feet
10 ft
J Length  9 feet, Width  5 feet
3 Mrs. Gardner is paving the sidewalk in
front of her home with square tiles. The
perimeter of each tile is 40 inches. Which
pair of equations can be used to find the
area of each tile in square inches?
baseboard
16 ft
Which of the following expressions could
be used to find the total length, in feet, of
baseboard needed?
A 10  16
A 40  4  10, and 10  10  20
B (2  10)  (2  16)
B 40  4  160, and 160  10  1,600
C 16  10  10
C 40  4  10, and 10  10  100
D 10  (16  10)
D 40  4  44, and 44  4  11
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Unit 25 Assessment
Standards 4.5(C), 4.5(D) – Readiness
1 Travis built a stage for the Summer
Theater Company. The area of the stage
is 720 square feet.
720 square feet
C
B Length 36
Width 20
D Length 35
Width 21
A 64 feet
C 255 feet
B 32 feet
D 510 feet
4 Which equation CANNOT be used to
determine the perimeter of the square
below?
Which could be the dimensions of
the stage?
A Length 40
Width 19
3 Shelby’s parents want to place a fence
around a new dog pen in the backyard.
The length of the pen is 17 feet, and
the width is 15 feet. How many feet of
fencing do they need to buy?
Length 35
Width 15
5 in.
5 in.
2 Ali bought 2 picture frames. The rectangles
represent the sizes of the frames.
F 45P
16 cm
6 cm
19 cm
H (2  5)  (2  5)  P
8 cm
What is the difference, in square
centimeters, between the areas of the
two picture frames?
Record your answer and fill in the bubbles
on the grid below. Be sure to use the
correct place value.
202
0
0
0
0
0
1
1
1
1
1
2
2
2
2
2
3
3
3
3
3
4
4
4
4
4
5
5
5
5
5
6
6
6
6
6
7
7
7
7
7
8
8
8
8
8
9
9
9
9
9
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G 5555P
J 55P
5 The framed painting in Ping’s room has
dimensions of 16 inches wide and 20
inches long. Ping took the painting down
and replaced it with a framed painting
that is 1 inch longer and 1 inch wider
than the old one. What is the area of the
new painting?
A 896 square inches
B 357 square inches
C 120 square inches
D 74 square inches
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Unit 25 Critical Thinking
Standards 4.5(C), 4.5(D) – Readiness
Analysis
Analyze
1 Dell, Anna, Mason, and Jenna each have their own bedroom. The floor of
each bedroom has a different area. The areas are 120 square feet, 121
square feet, 128 square feet, and 132 square feet. Use the clues below
to determine which bedroom belongs to each child.
• Mason’s bedroom floor is a perfect square.
• Anna’s bedroom floor has the same width as Mason’s, but its length is longer.
• Jenna’s floor has a length that is twice its width and a perimeter of 48 feet.
• The width of Dell’s bedroom floor is 1 foot less than the width of Mason’s floor,
and the length is the same as the length of Anna’s floor.
Complete the table to show which bedroom belongs to each child, and record the
dimensions of the rooms.
Bedroom Dimensions
Child
Area
Length
Width
Dell
Anna
Mason
Jenna
nthesis
Sy
C re a t e
2 Mrs. Davis plans for 2 fourth-grade classes to watch a movie. She
arranges 39 carpet squares so that every student has one carpet square
to sit on while watching the movie. After Mrs. Davis arranges the carpet
squares, Maria counts to find that the perimeter of the sitting area is
32 units. In the space below, draw a diagram to show how the carpet
square arrangement might look.
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MATH | LEVEL 4
Student Edition Sample Page
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Unit 25 Journal/Vocabulary Activity
Standards 4.5(C), 4.5(D) – Readiness
Analysis
Journal
Think about what you know about the perimeter and area of a rectangle.
Draw all possible rectangles with an area of 36 square units. Label the lengths
and widths of the rectangles, then find the perimeter of each rectangle.
Analyze
What generalization can you make about the perimeters of rectangles in relation to the
shapes of the rectangles (long and thin versus square)?
____________________________________________________________________
____________________________________________________________________
____________________________________________________________________
____________________________________________________________________
Vocabulary Activity
Work in groups of 3-5. Write the vocabulary words from the word bank on index
cards. Shuffle the cards and place them face down in the middle of the group.
Word Bank
area
length
side
dimension
perimeter
square
formula
rectangle
square unit
width
Use
motions
or
gestures.
Draw a
picture.
Use
words
to
describe.
In turn, each player selects the top card and, using
a pencil and paper clip, spins the spinner. The
player must use the method shown on the spinner
to try to get the other players in the group to say the word. The first player to state
the correct word scores 1 point, and the person giving the clues scores 1 point.
When all words have been used, the cards may be reshuffled, and the game may
be replayed.
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Unit 25 Motivation Station
Standards 4.5(C), 4.5(D) – Readiness
Motivation Mike says, “You’ve outdone yourself!”
Capture the Block
Play Capture the Block with a partner. Each player uses a different color to create
rectangular blocks on the game board. In turn, players roll two dice. The product of
the numbers rolled indicates the number of line segments a player may draw to try to
create a rectangular block. For example, if a player rolls 4 and 6, the player marks 24
line segments on the game board. The player may choose to draw a closed figure with a
perimeter of 24 units, or the player may choose to simply mark 24 units of a larger block,
hoping to complete the block on another turn. The player who closes any rectangular
block is the one who captures the block. Blocks created must include whole squares only
(no diagonals). When a player closes a block, he/she colors the area and records both the
area and perimeter in the space. The winner is the player with the greater total area.
Player 1
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Unit 25 Homework
Standards 4.5(C), 4.5(D) – Readiness
1 Carmen plans to put plastic edging
around a rectangular flower bed. The
width of the flower bed is 12 feet, and
the length is twice the width. What is the
perimeter of Carmen’s flower bed?
2 Several Olympic sports are played on
indoor courts. The table shows three
Olympic sports and the dimensions, in
feet, of the rectangular courts on which
they are played. Find the areas and
perimeters of the courts.
Sport
l
w
Answer: ______________
Basketball
28
15
Carmen decides to spread fertilizer over
the top of the flower bed. She purchases
a bag of fertilizer.
Volleyball
18
9
Badminton
13
6
FERTILIZER
P
A
3 Liam’s dad built a deck in the backyard.
The rest of the yard is planted with grass.
A diagram of the backyard is shown.
Will Carmen have enough fertilizer for the
flower bed?
10 meters
Wooden
Wooden
Deck
Deck
Answer: ______________
15 meters
Explain your answer.
= 1 square meter
_______________________________
_______________________________
_______________________________
✁
What is the area planted with grass?
Answer: _______________________
Parent Activities
1. Use small square crackers (saltines, graham crackers) to create a rectangle.
Work with your child to identify the perimeter of the cracker rectangle. Have
your child draw the rectangle on paper and record the perimeter and area. Then
challenge your child to make and record as many rectangles as possible with
the same perimeter but different areas. Repeat the activity and find rectangles with the same
area but different perimeters.
2. Have your child use a measuring tape to find the lengths and widths of rectangular rooms in
the house to the nearest whole foot. Use the dimensions to find the perimeter of each floor by
adding the lengths. Use the dimensions to find the area of each floor by multiplying the length
and width.
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Teacher Edition Sample Page
Unit 25
Use Formulas and Models to Solve Problems
with Perimeter and Area
TEKS 4.5(C), 4.5(D) – Readiness
Unit 25 Standards
(Student pages 199–206)
Reporting
Category
3
Geometry and Measurement
The student will demonstrate an understanding of how to represent and apply geometry
and measurement concepts.
Domain
TEKS
Student
Expectation
Algebraic Reasoning
4.5
The student applies mathematical process standards to develop concepts of
expressions and equations.
4.5(C)
This student expectation is not identified as readiness or supporting.
Use models to determine the formulas for the perimeter of a rectangle
(l + w + l + w or 2l + 2w), including the special form for perimeter of a square (4s) and
the area of a rectangle (l x w).
4.5(D) – Readiness Standard
Solve problems related to perimeter and area of rectangles where dimensions are whole
numbers.
Mathematical Process TEKS Addressed in This Unit
The student uses mathematical processes to acquire and demonstrate mathematical understanding.
4.1(A)
4.1(B)
4.1(C)
4.1(F)
4.1(G)
Apply mathematics to problems arising in everyday life, society, and the workplace.
Use a problem-solving model that incorporates analyzing given information, formulating
a plan or strategy, determining a solution, justifying the solution, and evaluating the
problem-solving process and the reasonableness of the solution.
Select tools, including real objects, manipulatives, paper and pencil, and technology as
appropriate, and techniques, including mental math, estimation, and number sense as
appropriate, to solve problems.
Analyze mathematical relationships to connect and communicate mathematical ideas.
Display, explain, and justify mathematical ideas and arguments using precise
mathematical language in written or oral communication.
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Unit 25
Use Formulas and Models to Solve Problems
with Perimeter and Area
TEKS 4.5(C), 4.5(D) – Readiness
Unpacking the Standards
In grade 3, students found the perimeters of polygons or found a missing side length when given
the perimeter and the remaining side lengths. While students did not formally work with formulas to
calculate perimeter or area, they used multiplication of whole numbers related to the number of rows
times the number of square units in each row to find the areas of rectangles and reported areas in
square units. They also used an additive model for area as they decomposed figures formed by up to
three non-overlapping rectangles and understood that the total area of the composite figure could be
calculated by finding the sum of the areas of the smaller rectangles. In grade 4, students investigate
formulas for perimeter and area using models and tools (e.g., geoboards, tiles, grid paper) and record
the findings in whole number measures. Students reason about the relationship between side lengths
of rectangles and their perimeters and areas. They will use P = l + w + l + w or P = 2l + 2w for perimeter.
Students will also use the formula P = 4s for the perimeter of a square and A = l x w to find the area
of a rectangle. Students show their understandings of finding perimeter and area by applying derived
formulas to real-world problems. Problems may require students to find a missing side length before
computing area, or use a given area and the measure of length or width to determine the missing
measure of a side in order to compute perimeter. All calculations to find area and perimeter in
grade 4 are limited to whole numbers.
Getting Started
Introduction Activity
The teacher reads the book Spaghetti and Meatballs for All by Marilyn Burns. Students or student pairs
use Color Tiles® to represent tables and paper clips to represent chairs. As the story is read, students
use the tiles and clips to model the described seating arrangements, recording the arrangements as
sketches in math journals or on centimeter grid paper. Next, the teacher leads students to informally
define area as the number of tables and perimeter as the number of chairs placed around the tables. The
teacher may opt to introduce these ideas as questions, as students may remember the concepts from
third grade. As an extension, students brainstorm methods of finding the areas and perimeters of tables
without counting all the tiles or paper clips. As a class, students work together to develop the formulas for
area and perimeter: A = l x w, P = 2 x (l + w), P = (2 x l) + (2 x w), or P = 2l = 2w.
(DOK: 3, Bloom’s/RBT: Application/Apply, ELPS: (c)1.C, (c)1.E, (c)1.H, (c)2.E, (c)2.I, (c)3.D, (c)3.E, (c)5.B)
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Teacher Edition Sample Page
Unit 25
Use Formulas and Models to Solve Problems
with Perimeter and Area
TEKS 4.5(C), 4.5(D) – Readiness
Suggested Formative Assessment
The teacher asks probing questions to determine students’ understanding of area and perimeter.
• When Mrs. Comfort’s relatives push the tables together, what happens to the total number of people
who can eat at the tables? Why?
• Is it possible for two rectangles to have the same area but different perimeters? Justify your answer.
• In the story, what table arrangement seated the greatest number of people? Why?
• How can you prove that the formula A = l x w will help calculate the area of a table?
• What is a general rule you can use for finding the perimeter of a rectangle? How can you express this
rule using numbers and symbols, in which l represents length and w represents width?
• Suppose you know that the width of a table is 7 units and the area is 42 square units. How can you
find the length?
• Suppose a table is square and its area is 25 square units. How can you find its length and width?
(DOK: 2, Bloom’s/RBT: Analysis/Analyze, ELPS: (c)1.C, (c)1.E, (c)1.H, (c)2.C, (c)2.E, (c)2.I, (c)3.D, (c)3.E, (c)3.F, (c)3.H)
Children’s Literature Connections
Chickens on the Move – Pam Pollack and Meg Belviso
Perimeter and Area at the Amusement Park – Dianne Irving
Perimeter, Area, and Volume: A Monster Book of Dimensions – David A. Adler
Racing Around: Perimeter – Stuart J. Murphy
Sam’s Sneaker Squares – Nat Gabriel
Sir Cumference and the Isle of Immeter – Cindy Neuschwander
Spaghetti and Meatballs for All!: A Mathematical Story – Marilyn Burns
Vocabulary Focus
The following are essential vocabulary terms for this unit.
area (A)
length (l)
rectangle
square unit
dimension
model
side
width (w)
formula
perimeter (P)
square
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Unit 25
Use Formulas and Models to Solve Problems
with Perimeter and Area
TEKS 4.5(C), 4.5(D) – Readiness
Vocabulary Activity
Word Web
The teacher provides a topic for the middle space of a word web. Students complete the webs
connecting vocabulary words to everyday activities. An example follows.
installing
baseboards
in a room
placing a
border around
a bulletin board
completing a
home run in
baseball
Activities that
Involve Perimeter
installing a
fence around
a garden
using a
weedeater
around the
edges of a yard
decorating the
edges of a cake
with frosting
Other topics for word webs might include:
• Activities that Involve Area
• Activities in Which Dimensions Must be Measured
• Objects Measured in Square Units
(DOK: 3, Bloom’s/RBT: Analysis/Analyze, ELPS: (c)1.C, (c)1.E, (c)1.H, (c)2.E, (c)2.I, (c)5.B, (c)5.G)
Suggested Formative Vocabulary Assessment
Students write short stories about situations in which they would need to determine the area or
perimeter of an object or space. Students use a minimum of four vocabulary words in the stories. The
teacher gathers and evaluates evidence of understanding demonstrated by student stories and plans
additional vocabulary activities as needed.
(DOK: 2, Bloom’s/RBT: Application/Apply, ELPS: (c)1.E, (c)1.H, (c)5.B, (c)5.G)
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Teacher Edition Sample Page
Unit 25
Use Formulas and Models to Solve Problems
with Perimeter and Area
TEKS 4.5(C), 4.5(D) – Readiness
Suggested Instructional Activities
1. Students use painter’s tape or other colored tape to outline rectangles and squares found on tile
floors or walls of the classroom or hallway. The teacher guides students as they identify the lengths
and widths of the rectangles in units. Then, the teacher identifies the perimeter of an outlined
rectangle and students work together to discover the formula for finding the perimeter of a rectangle.
Next, the teacher identifies the area of the same outlined rectangle. The teacher and students work
together, as a class, to discover the formula used to calculate the area of a rectangle. The teacher
records the formulas on the board and students use them to find the areas and perimeters of the
other outlined rectangles and squares.
(DOK: 2, Bloom’s/RBT: Analysis/Analyze, ELPS: (c)1.C, (c)1.E, (c)1.H, (c)2.E, (c)2.I, (c)3.D, (c)3.E, (c)4.C)
2. The teacher provides students with geoboards and rubber bands. Students enclose
the smallest square possible. The teacher defines the distance from one peg to the
next (vertically or horizontally) as 1 unit and counts the rim of the rectangle to find a
perimeter of 4 units. The teacher further defines the amount of space enclosed by the
rubber band as one square unit, identifying this as area. Then, the teacher repeats the
process with a larger rectangle such as the one shown in the example. The teacher
asks probing questions, leading students to understand the formulas for finding
perimeter. Questions might include the following.
Example
• What is the number of units on one long side of the rectangle?
• What is the number of units on one short side of the rectangle?
• How many long sides are on the rectangle? The longer sides are called length. Do both lengths
have the same measure?
• How many short sides are on the rectangle?
• The shorter sides are called width. Do both widths have the same measure?
• Using what you know about perimeter, what is one way to find the perimeter of this rectangle using
an addition equation?
• Since we added two 4s and two 3s, what is another way to write this equation?
• If 2 represents length, w represents width, and P represents the perimeter, what formula could be
used to find the perimeter of a rectangle?
• From our knowledge of the Distributive Property of Multiplication, how else can we write this
formula?
Next, students count squares to determine the area of the rectangle. Students count the number
of squares in each row and the number of squares in one column. In the example above, students
count four square units horizontally and three square units vertically. The teacher again uses probing
questions to help students generalize the formula for finding the area of a rectangle. Questions might
include the following.
• Look at the rectangle enclosed by the rubber band. What is another mathematical term for a
rectangular figure made of rows and columns?
• How many square units are in the top row of the array? How many square units are in the second
row? How many square units are in the bottom row?
• Do all rows contain the same number of square units?
• What addition and multiplication equations could be used to find the total number of square units?
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Unit 25
Use Formulas and Models to Solve Problems
with Perimeter and Area
TEKS 4.5(C), 4.5(D) – Readiness
• If l represents the length, w represents the width, and A represents the total area, what formula
could be used to find the area of a rectangle?
Students apply the generalizations to other rectangles on the geoboard.
(DOK: 2, Bloom’s/RBT: Analysis/Analyze, ELPS: (c)1.C, (c)1.E, (c)1.H, (c)2.E, (c)2.I, (c)3.D, (c)3.E, (c)3.F, (c)3.H, (c)4.C)
3. Given a perimeter, area, and one dimension (e.g., perimeter = 30 units, area = 50 square units,
and length = 10 units), small groups work to find and record a rectangle that meets all given
specifications. Students use the information to show how the formulas for area and perimeter can
be used in reverse to determine the missing dimensions (e.g., A = l x w, so A ÷ l = w). Students then
write real-world scenarios that could be applied to the given parameters. Groups exchange and solve
problems, using the appropriate formulas.
(DOK: 2, Bloom’s/RBT: Application/Apply, ELPS: (c)1.C, (c)1.E, (c)1.H, (c)2.E, (c)2.I, (c)3.D, (c)3.E, (c)3.G, (c)3.H, (c)4.F, (c)4.J,
(c)5.B, (c)5.G)
Suggested Formative Assessment
The teacher uses agreement circles to assess student understanding of applying the area and perimeter
formulas for rectangles. The teacher develops three or four statements about this concept. Students
form a circle in the classroom. The teacher reads the statements, allows think time, and students
then move toward the center of the circle to show agreement with the statement or remain on the
circumference of the circle to show disagreement. The teacher then groups students into small groups
and provides time for students to discuss and solidify understandings. The teacher uses the results from
this assessment to plan additional instruction and/or provide interventions.
(DOK: 2, Bloom’s/RBT: Analysis/Analyze, ELPS: (c)1.C, (c)1.E, (c)1.H, (c)2.C, (c)2.E, (c)2.I, (c)3.D, (c)3.E, (c)3.G)
Suggested Reflection/Closure Activity
Students draw rectangles and squares on centimeter grid paper. The teacher displays a four-column
table on the board with the headings Length, Width, Perimeter, and Area. Student volunteers describe
the rectangles by length, width, perimeter, and area. The teacher records students’ measurements on
the table. As a class, discuss patterns between the columns.
(DOK: 2, Bloom’s/RBT: Application/Apply, ELPS: (c)1.C, (c)1.E, (c)1.H, (c)2.E, (c)2.I, (c)3.D)
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MATH | LEVEL 4
Teacher Edition Sample Page
Unit 25
Use Formulas and Models to Solve Problems
with Perimeter and Area
TEKS 4.5(C), 4.5(D) – Readiness
Suggested Formative Assessment
Students fold sheets of centimeter grid paper in half and then in half again to create four columns.
Students draw and shade a rectangle on the top half of the paper. On the bottom half of the paper,
students title the columns Length, Width, Perimeter, and Area and fill in the table with the measurements
for the shaded rectangle. Students write the formulas they used to determine the perimeter and
area in the corresponding columns and show their work. The teacher reviews student tables, noting
misconceptions about perimeter and area and makes instructional adjustments to meet identified
student needs.
(DOK: 2, Bloom’s/RBT: Application/Apply, ELPS: (c)1.C, (c)1.E, (c)1.H, (c)2.E, (c)2.I, (c)3.D, (c)5.B)
Interventions
1. The teacher provides pairs or small groups of students with an assortment of Color Tiles® and
assigns each group an area, for example, 36 square units. Each group uses the tiles to make as
many squares and rectangles as possible with the given area. Repeat the activity with perimeter. The
teacher asks students follow-up questions.
•
•
•
•
How many different squares and rectangles were you able to make?
Why does the perimeter of each shape change?
Why doesn’t the area of each shape change?
How would this activity change if you were given a perimeter instead of area?
Explain your answer.
(DOK: 2, Bloom’s/RBT: Analysis/Analyze, ELPS: (c)1.C, (c)1.E, (c)1.H, (c)2.E, (c)2.I, (c)3.D, (c)3.E)
2. The teacher provides students with Color Tiles® and grid paper to build the rectangles described
below.
• Rectangle 1 has a perimeter between 10 and 15 units and an area between 10 and 15 square units.
• Rectangle 2 has a perimeter between 20 and 24 units and an area between 30 and 36 square units.
Next, students draw the two rectangles on the grid paper. Students color, cut out, and display the
rectangles on black construction paper. Students record the perimeters and areas for the rectangles
on the black paper. The teacher displays students’ rectangles around the room. Students discuss the
similarities and differences among the rectangles.
(DOK: 2, Bloom’s/RBT: Application/Apply, ELPS: (c)1.C, (c)1.E, (c)1.H, (c)2.E, (c)2.I, (c)3.D, (c)3.E, (c)3.F)
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Unit 25
Use Formulas and Models to Solve Problems
with Perimeter and Area
TEKS 4.5(C), 4.5(D) – Readiness
3. The teacher wraps a length of string around the rim of a rectangle to measure the perimeter. The
teacher cuts the length of the string to match the perimeter. Then, the teacher straightens the string
and measures its length with a ruler. The teacher emphasizes that perimeter is a linear measure.
Students use strings to find the perimeters of rectangles on an activity sheet. The teacher emphasizes
the connection between the string activity and the formulas for the perimeters of rectangles and
squares.
Next, the teacher uses Color Tiles® to cover as much of the surface of a book in rows and columns as
possible, and then counts the number of tiles needed to cover the surface. The teacher emphasizes
that area is a measure of the number of square units contained in a space. Students use Color Tiles®
to find the areas of rectangles on an activity sheet. The teacher emphasizes the connection between
the tiles and formulas for the areas of rectangles and squares.
(DOK: 1, Bloom’s/RBT: Application/Apply, ELPS: (c)1.C, (c)1.E, (c)1.H, (c)2.E, (c)2.I)
Suggested Formative Assessment
The teacher gives each student three note cards. On the first note card, students draw a rectangle or
square and label its length and width or show the length and width using centimeter squares. On the
second note card, students write an equation to show how to determine the perimeter of the drawn
shape. On the third card, students write an equation to show how to determine the area of the drawn
shape. The teacher collects, shuffles, and distributes three cards to each student. Students trade cards
with classmates until they have a set of three matched cards. The teacher observes students as they
match cards and plans additional instruction and/or interventions as needed.
5
P=5+5+3+3
3
A=5×3
(DOK: 2, Bloom’s/RBT: Analysis/Analyze, ELPS: (c)1.C, (c)1.E, (c)1.H, (c)2.E, (c)2.I, (c)3.D, (c)3.E, (c)3.F, (c)4.C, (c)4.F, (c)5.B)
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MATH | LEVEL 4
Teacher Edition Sample Page
Unit 25
Use Formulas and Models to Solve Problems
with Perimeter and Area
TEKS 4.5(C), 4.5(D) – Readiness
Extending Student Thinking
Students investigate the relationship of the formula for finding the area of a rectangle to the formula for
finding the area of a triangle. Students use tangrams to form rectangles. Using their knowledge of area,
students generalize and justify a formula for finding the area of a triangle. Students create models using
grid paper and/or geoboards to support their generalizations and share their results with the class.
(DOK: 3, Bloom’s/RBT: Synthesis/Create, ELPS: (c)1.C, (c)1.E, (c)1.H, (c)2.E, (c)2.I, (c)3.D, (c)3.E, (c)3.G, (c)3.H)
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Unit 25
Use Formulas and Models to Solve Problems
with Perimeter and Area
TEKS 4.5(C), 4.5(D) – Readiness
Answer Codings
(Student pages 199–201)
Page Question
Process
TEKS
Answer
Bloom’s Original/
Revised
DOK
Level
4.1(A)
Application/Apply
1
(c)1.C, (c)1.E, (c)1.H,
(c)4.G
4.1(A)
Comprehension/Understand
2
(c)1.C, (c)1.E, (c)1.H,
(c)4.G, (c)5.B
4.1(A)
4.1(G)
Application/Apply
2
(c)1.C, (c)1.E, (c)1.H,
(c)4.G, (c)5.G
4
96 centimeters
Answers may vary. Students may explain
that they first divided the perimeter of
the small square, 48, by 4 to find the
length of each side. They then multiplied
12 x 2 = 24 to find the length of 1 side
of the original sheet of paper. They could
then use the formula for finding the
perimeter of a square,
P = 4s to multiply P = 4 x 24.
The perimeter is 96 cm.
A = 24 x 24 = 576 square centimeters
4.1(B)
4.1(G)
Application/Apply
2
(c)1.C, (c)1.E, (c)1.H,
(c)4.G, (c)5.G
1
C
4.1(A)
Application/Apply
2
(c)1.C, (c)1.E, (c)1.H,
(c)4.G
2
F
4.1(A)
Comprehension/Understand
2
(c)1.C, (c)1.E, (c)1.H,
(c)4.G
3
B
4.1(A)
Analysis/Analyze
2
(c)1.C, (c)1.E, (c)1.H,
(c)4.G
4
G
4.1(A)
Application/Apply
1
(c)1.C, (c)1.E, (c)1.H,
(c)4.G
1
D
4.1(F)
Analysis/Analyze
2
(c)1.C, (c)1.E, (c)1.H,
(c)4.G
2
J
4.1(B)
Application/Apply
2
(c)1.C, (c)1.E, (c)1.H,
(c)4.G
3
C
4.1(B)
Application/Apply
2
(c)1.C, (c)1.E, (c)1.H,
(c)4.G
4
25
4.1(B)
Application/Apply
2
(c)1.C, (c)1.E, (c)1.H,
(c)4.G
5
B
4.1(A)
Application/Apply
1
(c)1.C, (c)1.E, (c)1.H,
(c)4.G
1
2
3
199
16 feet; 15 square feet
Answers may vary. Students should
explain that carpet covers the area of
a space. To find the area of a rectangle
multiply l x w, therefore 14 x 10 is used
to find the area of the room.
10 feet
Answers may vary.
Students should explain that if the
perimeter of a rectangle is 48 feet,
then the measure of one length and one
width is half the perimeter, or 24 feet.
Since the length is 14 feet, the width
must be 24 – 14 = 10 feet.
200
201
298
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MATH | LEVEL 4
Teacher Edition Sample Page
Unit 25
Use Formulas and Models to Solve Problems
with Perimeter and Area
TEKS 4.5(C), 4.5(D) – Readiness
Answer Codings
(Student pages 202–205)
Page Question
202
Process
TEKS
Answer
Bloom’s Original/
Revised
DOK
Level
ELPS
1
B
4.1(A)
Application/Apply
2
(c)1.C, (c)1.E, (c)1.H, (c)4.G
2
256
4.1(B)
Application/Apply
2
(c)1.C, (c)1.E, (c)1.H, (c)4.G
3
A
4.1(A)
Application/Apply
1
(c)1.C, (c)1.E, (c)1.H, (c)4.G
4
J
4.1(C)
Application/Apply
1
(c)1.C, (c)1.E, (c)1.H, (c)4.G
5
B
4.1(B)
Application/Apply
2
(c)1.C, (c)1.E, (c)1.H, (c)4.G
4.1(B)
Analysis/Analyze
3
(c)1.C, (c)1.E, (c)1.H, (c)4.G
4.1(B)
Analysis/Analyze
2
(c)1.C, (c)1.E, (c)1.H, (c)4.G
4.1(F)
4.1(G)
Analysis/Analyze
3
(c)1.C, (c)1.E, (c)1.H,
(c)4.G, (c)5.B, (c)5.G
4.1(D)
Comprehension/Understand
2
(c)1.C, (c)1.E, (c)1.H, (c)3.E,
(c)4.G
Comprehension/Understand
2
(c)1.C, (c)1.E, (c)1.H, (c)3.E,
(c)4.G
Bedroom Dimensions
Area
(square feet)
Length
(feet)
Width
(feet)
Dell
120
12
10
Anna
Mason
132
12
11
121
128
11
16
11
8
Child
1
Jenna
Answers may vary. One possible
arrangement is shown. Accept all
responses with a perimeter of 32
units.
203
2
36
1
P = 74
18
2
P = 40
9
12
3
P = 30
4
P = 26
6
Journal
204
205
6
P = 24
Answers will vary. Students should
explain that the more spread out a
rectangle is, the greater its perimeter;
the more compact (closer to square) a
rectangle is, the smaller its perimeter.
Vocabulary
Activity
Answers may vary.
Motivation
Station
Results may vary.
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MATH | LEVEL 4
Teacher Edition Sample Page
Unit 25
Use Formulas and Models to Solve Problems
with Perimeter and Area
TEKS 4.5(C), 4.5(D) – Readiness
Answer Codings
(Student page 206)
Answer
Process
TEKS
72 feet; no
Based on the dimensions of Carmen’s
garden, the area is 288 square feet.
The bag only covers 250 square feet.
Carmen will not have enough fertilizer.
4.1(B)
4.1(G)
Application/Apply
2
(c)1.C, (c)1.E, (c)1.H,
(c)4.G, (c)5.B
4.1(A)
Application/Apply
2
(c)1.C, (c)1.E, (c)1.H, (c)4.G
4.1(B)
Application/Apply
2
(c)1.C, (c)1.E, (c)1.H, (c)4.G
Page Question
1
Bloom’s Original/
Revised
DOK
Level
ELPS
206
2
3
300
Sport
I
W
P
A
Basketball
28
15
86
420
Volleyball
18
9
54
162
Badminton
13
6
38
78
90 square meters
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