a.keresztes - unit plan area

Running head: Curriculum Planning: Area 1

Curriculum Planning: Area

Concept/Skill:

Grade 3 Mathematics: Area

This unit will build on the foundations of area that the students in the third grade have already

learned in class. Students will have been using shape blocks to manipulate what and how many

of a shape can fill an outline. Before starting this unit, students will learn that some shapes will

not accurately fill a space. When we begin this, students will use the ones squares from the base-

10 blocks to find area using unit squares instead of triangles, parallelograms and other shapes.

After developing concrete understanding of the foundations, the unit will move on to discuss the

important concepts of area measurement necessary to understanding area and connecting the

concept to the students’ prior experiences with arrays and multiplication. At the end of the

concepts portion, students will be associating the side lengths and area to parts of a

multiplication equation and multiplying (or at the very least, skip counting) to determine the total

area of a given rectangle.

What is conceptually difficult about the concept/skill?

According to Van de Walle, Karp, and Bay-Williams in Elementary and Middle School

Mathematics Teaching Developmentally, one of the most difficult points when learning about

area is elementary school student’s trouble in understanding of formulas (388) in mathematics.

Additionally, if area and perimeter are taught in close relation, students are likely to confuse the

two (388). The emphasis on “length times width” as the area formula can be difficult when

students move beyond squares and rectangles because the bottoms of some shapes are referred to

as the base of the figure (389). The terminology involved with area can be one of the most

difficult parts of coming to a true understanding of the concept (389).

If students do not have a strong foundational base, it is highly likely that students will struggle

throughout their math careers. Students must build on the foundations and learn the concepts

before they begin to learn the formulas and terminology that could otherwise confuse them.

Strategies identified by our text:

According to Van de Walle, Karp, and Bay-Williams in Elementary and Middle School

Mathematics Teaching Developmentally, students will best learn the concept of area by gradually

building their foundational skills and becoming comfortable with them before addressing

formulas and terminology related to area. In the beginning, comparison activities can be helpful

to students to show them that an area can be the same regardless of the shape it is shown in and

regardless of how a rectangle is drawn (384). Models should also be used when students are

building up their early skills; models should be both as outlines and as manipulatives to find the

space that is taken up within that outline (385-386).

Curriculum Planning: Area 2

Before moving on to side lengths and units like centimeters and inches, students need to

understand that area is tiling. Once this is understood students can begin to transfer their

knowledge to paper, using just squares and then moving towards units. Students must slowly

progress through these ideas and begin to build their knowledge with guidance and on their on to

associate pictures to side lengths and area and eventually connecting each piece to parts of a

multiplication equation.


Learning Objectives:

After Lesson 1, students will be able to:

o Manipulate unit squares to form different rectangles that will create a given area.

o Model tiling with centimeter and inch unit squares as a strategy to measure area.

o Count the number of squares in a rectangle to determine the area of a rectangle.

o Recreate given rectangles on inch and centimeter grid paper that have the same side

lengths.

o Identify that two rectangles have the same area regardless of the size of the unit

squares.


o Relate side lengths with the number of tiles on a side.

o Measure the length of the side of a rectangle by using both centimeter and inch rulers.

o Associate that the opposite sides of a rectangle have equal side lengths.

o Determine whether it is best to use inches or centimeters to measure the sides of a

figure.


o Use a ruler to fill in the missing squares in a rectangle.

o Form rectangles by tiling with unit squares to make arrays (either both side lengths or

a single side length and the area of the figure).

o Use skip counting to find the area of a rectangle more quickly.

o Relate side lengths to the factors of a multiplication sentence and the area to the

product of a multiplication equation.


o Draw rows and columns to determine the area of a rectangle, given an incomplete

array.

o Determine the area of a rectangle even if some of the space is covered over.


o Interpret area models to form rectangular arrays.

o Determine the area of a figure by subtracting the area of the rectangle that surrounds

it.

o Identify that units are important to the actual area of a figure.


o Find the area of a rectangle through multiplication of side lengths.

o Relate the side lengths to the factors and the area to the product of a multiplication

sentence (with at least 85% accuracy).


Lesson One

Grade/Content

Area

Mathematics: Foundations of Area

Grade 3

Lesson Title From Shapes to Squares!

Standards

Common Core

or GLE/GSE

(state level)

AND

National

Standards

Math (Common Core)

CCSS.Math.Content.3.MD.C.5a

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.

CCSS.Math.Content.3.MD.C.6

Measure area by counting unit squares.


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.

Context of the

Lesson

Students have already been using manipulatives to determine the areas of

different shapes. They have analyzed how shapes with different appearances

can have the same amount of a manipulative fill them and created different

shapes with a set type and number of manipulatives.

Now that the students have had the opportunity to use manipulatives to

discover area, they will begin transferring that knowledge over to paper and

using grids to further develop their understanding of area.

This lesson should take approximately 45 minutes, however it could take

more or less time depending on how students seem to understand the lesson.

This lesson is based off of the Engage NY curriculum (which is used by

the school that I am working in).

Opportunities

to Learn

The students will begin by using their individual whiteboards to solve a

problem related to what they did in the previous lesson. The students in this

class seem to always enjoy using their whiteboards so if I can begin with this

step, students will show interest in succeeding; when they have used their

whiteboards in the past, the students have shown greater interest in the lesson

and they also seem to be more motivated to get through the problems.*

The students will be building on the knowledge that they have gained

through the earlier lessons on area. Since we will be building on and

furthering their knowledge by asking the students to work with the early

knowledge that they’ve been building on, but still gradual enough that they

are able to do a lot of the work themselves with some guidance. For the

students who are a little bit more ahead, this lesson will allow them to begin

to recognize that the number of units on each side is directly linked to the

length of the side.*

Students will be doing work as a whole group, individually, and in small

http://www.corestandards.org/Math/Content/3/OA/D/8




groups. This allows the students to work through problems alone and with

one another to help each other when a group member is struggling. In

addition, while walking around, I will be able to point out and assist students

further.*

For this lesson, I will be creating a sheet where the problems build on one

another. The students will use their whiteboards to start off the lesson, and

then we will move onto a worksheet, and finish with an exit ticket. I will

need copies of the worksheet, exit ticket and a half sheet of each centimeter

and inch grid paper (photocopied onto the same page for comparison

purposes). For my own use, I will use the SmartBoard and/or the Elmo

projector in the room to work through the problems in sequence with the

students.*

Objectives Students will be able to:

Manipulate unit squares to form different rectangles that will create a

given area.

Model tiling with centimeter and inch unit squares as a strategy to

measure area.

Count the number of squares in a rectangle to determine the area of a

rectangle.

Recreate given rectangles on inch and centimeter grid paper that have

the same side lengths.

Identify that two rectangles have the same area regardless of the size of

the unit squares.

Instructional

Procedures

Opening (10-15% of lesson):

To activate student’s prior knowledge, I will put up a problem similar to

what they did in the day before for them to do on their whiteboards.

“Each □ is 1 square unit. Find the area of the rectangle

below (2 tall by 12 long equals 24 square units). Then draw

another rectangle with the same number of square units.”

As the students solve the problem they will hold their boards up to show

that they have an accurate solution. When we regroup, the students will

share some of the solutions that they came up with. (1x24, 3x8, 4x6).

“Today we will work on similar problems, but on grid paper of different

sizes. We are going to learn about the size of the squares and how to

connect them to areas.”

Engagement (60-70% of lesson):

After working through each problem individually, I will have the class

discuss their answers in their math groups and talk through the

problems. This will help them verbalize why they believe their opinion

and will also allow other students to help correct one another’s


misconceptions.

As students are discussing, I will be walking around asking students

further questions about the size of the squares and whether or not

changing the size of the squares will change the area as well.

If I see during the discussion that there are multiple students having

difficulties with a problem, I will address the specific problem as a

class and facilitate student discussion to have students solve the

problem out loud before they begin writing it down on their sheet.

After they see that they are able to answer the problem out loud, they

will be less likely to be intimidated by doing the same problem on

paper.

Throughout the lesson, I will ask students individually if the area of the

rectangles is the same, more, or less than another rectangle’s area. The

students will also compose rectangles of the same area on both

centimeter and inch grid paper, so I will question the students as to

whether or not they have the same area and what makes them different.

Closure (20-25% of lesson):

At the end of the lesson we will regroup and talk about whether or not

the size of the squares changes the area of a rectangle. We will also

discuss if there is only one way to make a rectangle with a specific

area. These two points will assure that the students have understood

the major points of the lesson.

To conclude, the students will complete an exit ticket to determine

their complete understanding of the lesson. The exit ticket will be

submitted at the end of the lesson and returned to them by the start of

the next lesson.

Assessment

Throughout the lesson, I will be asking the students questions and

walking around the room to assure that they understand the lesson.

At the end of the lesson, students will be presented with an exit ticket

that will be graded to determine their understanding of the major points

of the lesson. The grids provided on the exit ticket will have

centimeter squares. The exit ticket will have two questions:

“Each □ is 1 square unit. Write the area of Rectangle A (3

tall by 4 long equals 12 square units). Then draw another

rectangle with the same area in the space provided.”

Underneath the question, a grid will be provided that

shows Rectangle A and empty space for students to draw

another rectangle. A blank will also be provided that says

“Area = _________”

“Each □ is 1 square unit. Does this rectangle have the same area as


Rectangle A? Explain.”

Underneath the question, a grid will show another rectangle.

The rectangle will be 3 long and 5 tall equaling 15 square units,

so no the rectangle does not have the same area because this

rectangle has a larger area.

This will be graded on a check system and given back to the students

by the beginning of the next day’s lesson.

A - will indicate that a student has no knowledge of what he/she is

being asked to do. The student will either have nothing written or

will have something written that shows no understanding of the

lesson.

A will indicate that a student appears to understand what they

have learned. The student will have two of the three pieces of the

questions on the exit ticket correct.

A + will indicate that a student has complete knowledge of what

he/she is being asked to do. The student will have all questions

answered fully and prove that they understand the lesson.


Lesson Two

Grade/Content

Area

Mathematics: Foundations of Area

Grade 3

Lesson Title How long are my sides?

Standards

Common Core

or GLE/GSE

(state level)

AND

National

Standards (in

all areas

except Math

and ELA-use

Common Core

for those)

Math (Common Core)









side lengths.

CCSS.Math.Content.3.MD.C.7b

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.

CCSS.Math.Content.3.MD.C.7d

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.

Context of the

Lesson




shapes with a set type and number of manipulatives. In the last lesson, they

also began transferring their knowledge of area from manipulatives to grids.




This lesson should take approximately 45-60, however it could take more

or less time depending on how students seem to understand the lesson.



Opportunities

to Learn

The students will begin by using their individual whiteboards to solve a

problem related to what they did in the previous lesson. The students in this

class seem to always enjoy using their whiteboards so if I can begin with this

step, students will show interest in succeeding; when they have used their







whiteboards in the past, the students have shown greater interest in the lesson

and they also seem to be more motivated to get through the problems.*









Students will be doing work as a whole group and individually. This

allows the students to work through problems alone and learn from one

another as students explain their thought processes. In addition, while

walking around, I will be able to point out and assist students further.*



then we will move onto a worksheet, and finish with an exit ticket. I will need

copies of the worksheet, exit ticket and a half sheet of each centimeter and

inch grid paper (photocopied onto the same page for comparison purposes).

For my own use, I will use the SmartBoard and/or the Elmo projector in the

room to work through the problems in sequence with the students.*


Relate side lengths with the number of tiles on a side.

Measure the length of the side of a rectangle by using both centimeter

and inch rulers.

Associate that the opposite sides of a rectangle have equal side lengths.

Determine whether it is best to use inches or centimeters to measure the

sides of a figure.

Instructional

Procedures


To activate student’s prior knowledge, I will put up a problem similar to

what they did in the day before for them to do on their whiteboards.

“Cam uses 16 square-centimeter tiles to make a rectangle.

Annie uses 15 square-centimeter tiles to make a rectangle.

a) Draw what Cam’s and Annie’s rectangles might look

like. Write each student’s name over their rectangle.

b) Whose rectangle has a bigger area? How do you

know?”

As the students solve the problem they will hold their boards up to show

that they have an accurate solution. If their solutions are accurate, I will

have them keep their solution on their board. If not, I will have them try


again or offer them help if they are really struggling.

“Today we will take what you learned the past few days a step further.

We are going to determine how to determine how long the sides are on a

rectangle.”


“Let’s look back at the drawings we made on our whiteboards. Can

anyone tell me how we might figure out the length of each side?”

(Students will give some answers, one or two will likely point out that

side length is found by counting the number of squares.) “Right, so we

can count the squares to find the length of the sides, but what tool can

we use if the rectangle doesn’t have squares already?” (Students will

hopefully get at using a ruler.)

The students will be presented with a 6 question worksheet and we are

going to do the first one as a class. They will finish off the front side

individually and then we will go through each on the front together. If

there are no issues with the front, we will move on to the back side of

the sheet and do each problem individually.

Throughout the lesson, I will ask students individually why some

rectangles would be better to mention in centimeters or inches and what

makes them think that way. I will also ask some of the students who

appear to be grasping the lesson well if they see a similarity between the

rectangles and anything else that we have been working with (arrays)

and if they can think of a faster way to find area (length times width).


At the end of the lesson we will regroup and talk about when it is

appropriate to use centimeters and when it is appropriate to use inches,

as well as if we need to measure all four sides of the shape or if there is

a trick.

To conclude, the students will complete an exit ticket to determine their

complete understanding of the lesson. The exit ticket will be submitted

at the end of the lesson and returned to them by the start of the next

lesson.

Assessment





of the lesson. The exit ticket will have three rectangles, two of which

will have inch squares and one will have centimeter squares, on the left

side of the paper and three total areas written on the right-hand side of

the paper.


Label the side lengths of each rectangle. Then match the

rectangle to its total area.

This will be graded on a check system and given back to the students by

the beginning of the next day’s lesson.




lesson.








Lesson Three

Grade/Content

Area

Mathematics: Concepts of Area Measurement

Grade 3

Lesson Title Label the sides and fill in the blanks!

Standards

Common Core

or GLE/GSE

(state level)

AND

National

Standards (in

all areas

except Math

and ELA-use

Common Core

for those)

Math (Common Core)









side lengths.




and represent whole-number products as rectangular areas in mathematical

reasoning.





problems.

Context of the

Lesson




shapes with a set type and number of manipulatives and began transferring

their knowledge of area from manipulatives to grids. In the past lesson, they

related the grids on a square to the length of a side.




This lesson should take approximately 60 minutes.


the Orlo Avenue Elementary School).

Opportunities The students will begin by using their math notebooks to solve a problem


to Learn related to what they did in the previous lesson. A sheet with a problem

building on what they learned in yesterday’s lesson will be glued into their

notebook prior to the lesson. On the bottom half of the sheet, there will be a

problem related to the lesson we will be doing during the day.*


through the earlier lessons on area. For the students who are a little bit more

ahead, this lesson will allow them to begin to recognize that the number of

units on each side is directly linked to the length of the side and each side is a

factor of a multiplication sentence whereas the total area is directly related to

the product of the equation.*




addition, there will be two opportunities to work with one of the instructors in

the room so, if a group is struggling we can pinpoint where and when this is

happening.*


another. The students will use their math notebooks to start off the lesson, and

then we will move into math groups for the centers, and finish with an exit

ticket. I will need copies of the opening worksheet, center worksheet, and exit

ticket as well as SmartBoard problems for the center using the SmartBoard. I

will use the SmartBoard and/or the Elmo projector in the room to work

through the problems in sequence with the students.*


Use a ruler to fill in the missing squares in a rectangle.

Form rectangles by tiling with unit squares to make arrays (either both

side lengths or a single side length and the area of the figure).

Use skip counting to find the area of a rectangle more quickly.

Relate side lengths to the factors of a multiplication sentence and the

area to the product of a multiplication equation.

Instructional

Procedures


To activate student’s prior knowledge, I will have a problem similar to

what was done in the previous day’s lesson glued into their notebook.

Below the related problem, the same rectangle will be present, but

flipped on its side, with only a few squares visible – students will be

instructed to not yet do anything with this rectangle.

“Phillip uses square-centimeter tiles to find the side lengths of the

rectangle below. Label each side length, and then find the total


area.” (The rectangle will be 8 long by 4 tall)

“Today we will work on similar problems, but the rectangles might not

be completely filled in. You can see an example of this rectangle under

the problem you already solved. How can we fill in the missing inside

of the rectangle below?” (Students should suggest using their rulers)

“Good now let’s fill in the missing squares using our rulers. Make sure

that you follow the lines that are already there.”


For this lesson we will be working in math groups. There will be four

centers:

Center 1: Students will fill in the missing piece of the grid in a

rectangle and label the sides. They will then skip count to find the

total area. (Group work on the SmartBoard; the rectangles will be

missing part of the grid and students will go through a set of slides)

Center 2: Students will be given a problem to solve. “Trevor makes

a rectangle with 45 square-inch tiles. He arranges the tiles in 5

equal rows. What are the side lengths of the rectangle? Use words,

pictures, and numbers to support your answer.” (Individual;

students will complete the problem in their math notebook)

Center 3: Two-step problem with multiple rectangles from one area.

“Frankie has a total of 36 square-inch tiles. He uses 28 square-inch

tiles to build one rectangular array. He uses the remaining square-

inch tiles to build a second rectangular array. Draw two arrays that

Frankie might have made. Then write multiplication sentences for

each.” (Group work with teacher; this is a two-step problem and

students may need some guidance)

Center 4: Leftover area problem, students must rework the square

created in part one to determine if it works with another particular

length side. “Kim makes a rectangle with 42 square-centimeter

tiles. There are 6 equal rows of tiles. a) How many tiles are in each

row? Use words, pictures, and numbers to support your answer. b)

Can Kim arrange all of her 42 square-centimeter tiles into 8 equal

rows? Explain your answer.” (Group work with teacher; because of

the second part of this problem, students may need some extra help)


At the end of the lesson we will regroup and talk about how to fill in

missing parts of a square and how to use skip counting as a strategy to

find area quickly. We will also discuss how to find a missing side

length if an area is provided.


To conclude, the students will complete an exit ticket to determine

their complete understanding of the lesson. The exit ticket will be

submitted at the end of the lesson and returned to them by the start of

the next lesson.

Assessment

Throughout the lesson, both instructors in the room will be meeting with

groups of students. While we are



of the lesson. The exit ticket will have one question with a couple extra

parts:

“Darren has a total of 28 square-centimeter tiles. He arranges them

into 7 equal rows. Draw Darren’s rectangle. Label the side lengths,

and write a multiplication equation to find the total area.”



A - (approaching proficiency or lower) will indicate that a student

has no knowledge of what he/she is being asked to do. The student

will either have nothing written or will have something written that

shows no understanding of the lesson.

A (proficient) will indicate that a student appears to understand

what they have learned. The student will have two of the three

pieces of the questions on the exit ticket correct.

A + (exceeds proficiency) will indicate that a student has complete

knowledge of what he/she is being asked to do. The student will

have all questions answered fully and prove that they understand the

lesson.


Lesson Four

Grade/Content

Area


Grade 3

Lesson Title What if part of the rectangle is covered up?

Standards

Common Core

or GLE/GSE

(state level)

AND

National

Standards (in

all areas

except Math

and ELA-use

Common Core

for those)

Math (Common Core)









side lengths.










problems.

Context of the

Lesson





their knowledge of area from manipulatives to grids. The students have been

connecting the number of units in an object to the length of the side of a

figure. In the previous lesson, the students formed their own rectangles and

connecting it to the use of arrays that they used in earlier lessons on

multiplication.














Opportunities

to Learn

The students will begin by using their math notebooks to solve a problem

related to what they did in the previous lesson. A sheet with a problem


notebook prior to the lesson.*













further.*









Draw rows and columns to determine the area of a rectangle, given an

incomplete array.

Determine the area of a rectangle, even if some of the space is covered

over.

Instructional

Procedures


To activate student’s prior knowledge, I will have a problem

similar to what was done in the previous day’s lesson glued into

their notebook.

“Gabi makes a rectangle with 16 square-centimeter tiles.

There are 4 equal rows of tiles.

How many tiles are in each row? Use words, pictures,

and numbers to support your answer.

Can Gabi arrange all of her 16 square-centimeter tiles

into 6 equal rows? Explain your answer.”

As the students solve the problem and I will be walking around to make


sure that they are on the right track, especially with the second part.

“Today we will work on similar problems, but some of the tiles will be

completely covered.”



centers:

Center 1: Matching incomplete arrays to their complete arrays and

writing a multiplication sentences. (Partner Work; students will be

provided with a folder with 6 incomplete arrays and their complete

matches, they will draw the complete array in their math notebooks

and write the multiplication sentence to explain the area)

Center 2: Explain whether or not an incomplete array has a certain

area. Students will need to state if the area is correct or not and if

wrong, state the correct answer. (Individual; students will be

provided with a worksheet with three problems, this will be the first

problem that has two incomplete arrays for the students to determine

if the area is correct or incorrect)

Center 3: Students will need to state the area of the entire grid with a

‘rug’ covering a portion of the grid. (Individual; students will be

provided with a worksheet with three problems, this will be the

second problem that has one array with a rug covering over a portion

of the grid)

Center 4: Determine the area of a portion of a rectangle. (Group

work with teacher; this can a two-step problem so students may need

extra guidance to determine the area of the blank rectangle,

otherwise it is a one-step problem but students will need to

determine the side lengths)


At the end of the lesson we will regroup and talk about whether or not

the size of the squares changes the area of a rectangle. We will also

discuss how to determine the area of a rectangle if a piece of it is

covered over.




lesson.

Assessment






of the lesson. The exit ticket will have one question:

“The tiled floor in Mickey’s diner has a rug on it as shown.

How many square tiles are on the floor, including the tiles

under the rug?”


shows a ‘rug’ covering over a part of the grid.






lesson.








Lesson Five

Grade/Content

Area


Grade 3

Lesson Title What about the size of the squares?

Standards

Common Core

or GLE/GSE

(state level)

AND

National

Standards (in

all areas

except Math

and ELA-use

Common Core

for those)

Math (Common Core)









side lengths.










problems.

Context of the

Lesson







figure. Students have formed their own rectangles and connected them to the

use of arrays that they used in earlier lessons on multiplication. The students

have recently been connecting rows and columns to the length and width of a

figure, even if the rectangle is not completely filled with a grid; they have

been able to fill in the missing boxes when necessary to display the area of a

rectangle.














Opportunities

to Learn

















further.*









Interpret area models to form rectangular arrays.

Determine the area of a figure by subtracting the area of the rectangle

that surrounds it.

Identify that units are important to the actual area of a figure.

Instructional

Procedures




their notebook.

“The tub in Mackenzie’s bathroom covers the tile floor as

shown below. How many square tiles are on the floor,

including the tiles under the tub?”

We will then go over the problem on the SmartBoard as a class; students


will contribute by raising their hand and coming up to the board to show

how they solved the problem.

“Today we will work on similar problems to what we did in class

yesterday, but we will talk about what the measurement of each square

means related to the area of the shape.”


After working through each problem on the day’s worksheet

individually. When students finish each problem, they will put their

pencil down on their desk and after all students have finished each

problem, the class will discuss their answers as a whole. We will be

working as an entire class and doing the problem out loud after working

through it on paper by themselves.

As students are discussing, I will be walking around asking students

further questions about the size of the squares and whether or not

changing the size of the squares will change the area as well.


At the end of the lesson we will regroup and talk about what the size of

the squares means and whether bigger squares or smaller squares have

more area.




lesson.

Assessment





of the lesson. The exit ticket will have two questions:

“Label the side lengths of Rectangle A on the grid below.

Use a straight edge to draw a grid of equal size squares

within Rectangle A. Find the total area of Rectangle A.”


shows Rectangle A. Students will be expected to fill in

the grid within the rectangle and label the side lengths. A

blank will also be provided that says “Area =

_________”

“Olivia makes a rectangle with 16 square-inch tiles. Elliott makes a

rectangle with 16 square-centimeter tiles. Whose rectangle has a

bigger area? Explain your answer.

Under this question, a large blank space will be available and


students may use pictures and/or words to explain their

reasoning.






lesson.








Lesson Six

Grade/Content

Area


Grade 3

Lesson Title But wait, you can make it easier! Multiply!

Standards

Common Core

or GLE/GSE

(state level)

AND

National

Standards (in

all areas

except Math

and ELA-use

Common Core

for those)

Math (Common Core)









side lengths.










problems.

Context of the

Lesson







figure. Students have formed their own rectangles and connected them to the

use of arrays that they used in earlier lessons on multiplication. The students

have recently been connecting rows and columns to the length and width of a

figure, even if the rectangle is not completely filled with a grid; they have

been able to fill in the missing boxes when necessary to display the area of a

rectangle.














Opportunities

to Learn

















further.*









Find the area of a rectangle through multiplication of side lengths.

Relate the side lengths to the factors and the area to the product of a

multiplication sentence.

Instructional

Procedures




their notebook.

“The tub in Mackenzie’s bathroom covers the tile floor as

shown below. How many square tiles are on the floor,

including the tiles under the tub?”

We will then go over the problem on the SmartBoard as a class; students

will contribute by raising their hand and coming up to the board to show


how they solved the problem.

“Today we will work on similar problems to what we did in class

yesterday, but we will talk about what the measurement of each square

means related to the area of the shape.”



centers:

Center 1: Writing multiplication sentences for rectangles given.

(Group work on the SmartBoard; some of the rectangles will be

missing the area and others will be missing one of the sides)

Center 2: Students will be given a centimeter grid and be asked to

create at least one rectangle for each of these three areas: 32, 48, and

27. They must also label the side lengths of each rectangle. While

working with partners, students should also be aware of the

commutative property and check each other if they make the same

rectangle two different ways. (Partner work; students will be

provided with a centimeter grid and colored pencils/crayons, each

area should be done in a different color)

Center 3: Students will solve two problems. One problem will list

side lengths; students must find the area and explain their answer.

The second problem will give a side length and the area; students

must find the missing side length and explain their answer.

(Individual; will be done in math notebooks)

Center 4: Compare the areas of two bedrooms. “Matt’s bedroom

measures 6 feet by 8 feet. His brother’s bedroom measures 7 feet by

9 feet. Matt says their rooms have the same exact floor area. Is he

right? Why or why not?” (Group work with teacher; this problem

involves comparing the areas of two rectangles but only provides

side lengths so the group work will allow for conversation and

teacher assistance)


At the end of the lesson we will regroup and discuss how multiplying

the sides of rectangle to find the area directly relates to something we

have done in the past. (Multiplying the rows and columns in to find the

total contents in an array.)




lesson.

Assessment Throughout the lesson, I will be asking the students questions and





of the lesson. The exit ticket will have two questions:

“Write a multiplication sentence to find the area of the

rectangle below.”

Underneath the question, a rectangle will be provided

with the two side lengths labeled. A blank multiplication

sentence will be provided for the students to fill in their

answer.






lesson.








Assessment 1:

At the end of the Foundations of Area portion of the unit, students will be asked to complete an

area project. The Foundations of Area portion of the unit is composed of interacting with shapes

prior to actually beginning to work with the concept of area and the first two lessons in this unit.

This project will be to create a robot on centimeter grid paper and to correctly give the area of

each part of the robot. The instructions will be:

Create and color in a robot on the grid paper provided. You may decide how big each

shape is, but the neck must have an area of 1 square centimeter. You must color full

squares. It must have the following body parts:

o Head

o Neck (1 square centimeter)

o Body

o Two arms

o Two legs

You must make a key that tells me the area of each body part.

o In this key, you should also have the rectangles drawn and label each side of the

rectangle.

You must also tell me the total area of your robot (add all of the body parts together).

If you decide to add any extra pieces to your robot or create a robot pet, you must also

give those areas and add it to the total area of your robot.

The project will allow the students to be creative and enjoy the early concepts of area. Students

will demonstrate their understanding of the first couple lessons in the unit before we move on to

working more with the more difficult aspects of area.

Students will be creating this robot almost entirely on their own. Except for the neck, they will

be responsible for creating rectangles for each body part on the robot and then they will be

required to give the area and the side lengths of each body part they created. They must also add

up all of the areas of the different parts of the robot to determine the total area of the robot. They

will also be responsible for using the proper units when they give the area.

This assessment will be graded on a 1-4 scale. A 1 will indicate that the student does not meet

the standard/has no understanding of the concept. A 2 will indicate that the student is in progress

to meet the standard/ cannot completely apply the skill or concept on his own, but has some

understanding. A 3 will indicate that the student is meeting the standard/ understands the skill or

concept and shows a clear thought process. And a 4 will indicate that the student has mastered

the standard/can apply a certain skill or concept independently and correctly, showing a higher

level of thinking.


Assessment 2:

The second assessment will be given after the students have completed this unit: both the

Foundations of Area and the Concepts of Area Measurement. They will take a test that covers

the most important points of the unit. The test will have problems that are set up similarly to the

exit tickets and cover the same aspects. The exit tickets that students completed at the end of

each lesson tie back to the objectives, so by setting up the test with questions similarly to the

questions on the exit tickets, I will ensure that the unit objectives have been met.

Some of the questions on the test will be:

Each □ is 1 square-centimeter. What is the area of Rectangle A (6 centimeters tall by 4

centimeters long for an area of 24 square-centimeters)?

o Does Rectangle A have the same area as Rectangle B (3 centimeters tall by 7

centimeters long for an area of 21 square-centimeters) below?

o On the grid provided, draw another rectangle with the same area as Rectangle A.

Stan has 18 square-centimeter tiles. He arranges the tiles into 6 equal rows. Draw Stan’s

rectangle and label the side lengths.

o Can Stan arrange his 18 square-centimeter tiles into 4 equal rows? Explain your

answer.

The tiled floor in Mrs. Simms’s bathroom has a rug on it as shown below. How many

square-inch tiles are on the floor, including the tiles under the rug? (On the 5 inches tall

by 8 inches long for an area of 40 square-inch grid).

Amanda makes a square with 9 square-inch tiles. John makes a square with 9 square-

centimeter tiles. Whose rectangle has a bigger area? Explain your answer.

Measure the sides of the rectangle (4 centimeters tall by 9 centimeters long for an area of

36 square-centimeters) below with the centimeter side of your ruler and label the sides.

o Next, fill in the multiplication sentence below to find the area of the rectangle.

o Be sure to write the area with proper units.

This assessment will be graded on a 1-4 scale. A 1 will indicate that the student does not meet

the standard/has no understanding of the concept. A 2 will indicate that the student is in progress

to meet the standard/ cannot completely apply the skill or concept on his own, but has some

understanding. A 3 will indicate that the student is meeting the standard/ understands the skill or

concept and shows a clear thought process. And a 4 will indicate that the student has mastered

the standard/can apply a certain skill or concept independently and correctly, showing a higher

level of thinking.


References

Connell, G. (2012). 10 hands-on strategies for teaching area and perimeter. Retrieved from

https://www.scholastic.com/teachers/top-teaching/2012/12/10-hands-strategies-teaching-

area-and-perimeter

Engage NY. Engage NY, (2013). Grade 3 mathematics module 4. Retrieved from website:

http://www.engageny.org/resource/grade-3-mathematics-module-4

National Governors Association Center for Best Practices, Council of Chief State School

Officers. (2010). Common core state standards for mathematics. Retrieved from

National Governors Association Center for Best Practices, Council of Chief State School

Officers, Washington D.C. website: http://www.corestandards.org/Math

Van De Walle, J., Karp, K., & Bay-Williams, J. (2013). Elementary and middle school

mathematics teaching developmentally. (8th ed., pp. 384-391). Boston: Pearson

Education.

https://www.scholastic.com/teachers/top-teaching/2012/12/10-hands-strategies-teaching-area-and-perimeter

https://www.scholastic.com/teachers/top-teaching/2012/12/10-hands-strategies-teaching-area-and-perimeter

http://www.engageny.org/resource/grade-3-mathematics-module-4

http://www.corestandards.org/Math

a.keresztes - unit plan area

Documents

concept of area

foundations of area

area conceptskill

area formula

total area

students prior experiences

unit squares

understanding of formulas