Grade 3: 3.MD.C.5-7, Geometric measurement: understand concepts of area and relate area to
multiplication and addition
Lesson Plan: 3.MD.C.7-7a, Using Tiling to Find Area (This lesson should be adapted, including instructional time, to meet the needs of your
students.)
Content/Grade Level
Background Information
Mathematics/Grade 3
Unit/Cluster:
Geometric Measurement: 3.MD.C: Understand concepts of area and relate area to multiplication and
addition
Essential Questions/Enduring
Understandings Addressed in the
Lesson
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Why do area formulas work?
How do we find the area of shapes for which we do not know or cannot recall a formula?
How can we count the squares more efficiently?
How could we get a more precise approximation of the area?
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Area is a measure of the space inside a region or how much it takes to cover a region.
3.MD.C.7: Relate area to the operations of multiplication and addition.
3.MD.C.7a: 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.
Standards Addressed in This
Lesson
Lesson Topic
Relevance/Connections
It is critical that the Standards for Mathematical Practice are incorporated in ALL lesson activities
throughout the unit as appropriate. It is not the expectation that all eight Mathematical Practices will be
evident in every lesson. The Standards for Mathematical Practice make an excellent framework on which
to plan your instruction. Look for the infusion of the Mathematical Practices throughout this unit.
Finding the area of a rectangle by tiling it and providing an opportunity for students to develop their own
formula (rule) for finding the area of a rectangle.
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Perimeter, multiplication, fluency maintenance of addition and subtraction facts
Thinking about a real problem in the classroom
3.OA.A: Represent and solve problems involving multiplication and division.
3.OA.C: Multiply and divide within 100.
July 17, 2013
Page 1 of 11
Grade 3: 3.MD.C.5-7, Geometric measurement: understand concepts of area and relate area to
multiplication and addition
Student Outcomes
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Students will use tiling to determine the area of a specific rectangle.
Students will generate a rule (formula) for finding the area of a rectangle.
Students will discuss the importance of a standard unit of measure.
Prior Knowledge Needed to
Support This Learning
Students already have a solid background that area is the interior measurement of a plane figure and by
counting the inside “unit squares” they will be able to know the area of a given figure (3.MD.C.5a and
3.MD.C.5b).
Method for determining student
readiness for the lesson
Use Warm Up as a pre-assessment (see below).
Learning Experience
Materials Needed:
 12 square tiles for each student
Which Standards for Mathematical
Practice(s) does this address? How is the
Practice used to help students develop
proficiency?
SMP 4: Model with mathematics. – Students use
the 12 to make various arrays.
Using 12 square tiles, students will create an array using
their 12 tiles. Discuss the different configurations that they
could make.
SMP 2: Reason abstractly and quantitatively –
Students discuss the different configurations that
they made using the 12 tiles.
Component
Warm Up
Motivation
Details
Pose a real-world mathematical problem for students to
solve.
I would like to create a reading corner in our
classroom with 1’ x 1’ carpet squares. I don’t want to
spend more money than I have to and I don’t want to
come up short or have too many extra. How can I
accurately find out how many carpet tiles I need?
Discuss how we can begin to solve this problem. What
July 17, 2013
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Grade 3: 3.MD.C.5-7, Geometric measurement: understand concepts of area and relate area to
multiplication and addition
Learning Experience
information do we still need?
Activity 1
UDL Components
 Multiple Means of
Representation
 Multiple Means for
Action and
Expression
 Multiple Means for
Engagement
Key Questions
Formative Assessment
Summary
Materials Needed:
 5 x 7 inch index card (one per student)
 Post it notes of different sizes
 Base ten unit cubes
 Hundreds chart
 Cheese-it crackers
Note: avoid using one-inch color tiles at this time.
 Resource Sheet 1: Exit Slip: Similarities &
Differences
Rather than having us all work in the same corner, I
will give you a piece of paper that will represent our
reading corner.
SMP 1: make sense of problems and persevere
in solving them – Students use tiling to explore
the need for a standard unit of measure.
SMP 4: Model with mathematics – Students use
square units to determine the area of the index
card.
SMP 3: Construct viable arguments and critique
the reasoning of others – Students compare the
area measurements of each other and discuss
why they are different.
Distribute a 5 x 7 index card to each student. This will
represent the reading corner on a smaller scale. Each
student will be given different “unit squares” [sticky notes,
cheddar cheese crackers, base-10 unit cubes (ones), 100s
chart (students can place the index card on top of the chart
and trace around its perimeter), or any other square
manipulative]. Avoid using tiles at this time. Your goal is
that students will see the need for a standard unit of
measurement. Student should cover the index card with
their manipulatives.
Discuss findings. Encourage discussion and debate.
 Why did some students end up with a different
answer?
 What do we notice about the size of the unit square
and the area found? (The larger the unit, the smaller
the area and the smaller the unit, the larger the area.)
July 17, 2013
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Grade 3: 3.MD.C.5-7, Geometric measurement: understand concepts of area and relate area to
multiplication and addition

Learning Experience
Are there situations where you would want to use a
smaller square unit? (Finding the area of a small
object – the area of a footprint) When would it be
appropriate to use a large square unit? (Finding the
area of a large object – the area of a football field.)
Students should realize the importance of using a common
unit of measure. Since the teacher will be purchasing carpet
tiles that are 1’ x 1’, we should agree on one unit of measure
for our index cards.
Formative Assessment: Distribute Resource Sheet 1: Exit
Slip: Similarities & Differences and allow time for students to
record their thinking.
What are some of the similarities and differences that
we saw when we covered our index cards using
different manipulatives? Why do you think these
differences occurred?
Activity 2
UDL Components
 Multiple Means of
Representation
 Multiple Means for
Action and
Expression
 Multiple Means for
Engagement
Key Questions
Formative Assessment
Summary
Materials Needed:
 12 one-inch tiles per student
 5 x 7 inch index card (one per student)
 Resource Sheet 2: Exit Ticket: Rules for Finding Area
SMP 1: Make sense of problems and persevere
in solving them – Students explore ways to find
the area when they don’t have enough tiles to
cover the index card.
Based on the discussion from Activity 1, students will know
the importance of using a standard unit of measure.
SMP 3: Construct viable arguments and critique
the reasoning of others – Students explain
strategies they used to determine the area of the
index card.
Yesterday we discussed how we were going to tile
one section of our classroom with carpet tiles. I was
able to purchase 12 carpet tiles since they come in a
pack of 12. I didn’t buy any more packages, because
I don’t want too many extra or not enough.
July 17, 2013
SMP 8: Look for and express regularity in
repeated reasoning – Students used their
knowledge of repeated addition or the
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Grade 3: 3.MD.C.5-7, Geometric measurement: understand concepts of area and relate area to
multiplication and addition
Learning Experience
Distribute 12 one-inch square tiles to each student and the
index card from the previous lesson (this represents the 12
carpet squares already purchased). Have students explore
ways of finding the area using the tiles. Students will quickly
realize they don’t have enough tiles to cover the whole area.
Pose questions to elicit discussion.
 What are some solutions to not having enough tiles?
It wouldn’t make sense to buy more tiles right now, so
what can we do?
distributive property to make sense of the
problem and find the solution.
The discussion should lead the students to figuring out that
the area of a rectangle can be found in a variety of ways.
Have the students come together to discuss their solutions
and to find commonalities and differences between different
strategies.
Here are a few potential strategies you might see in your
classroom. Remember, do not explicitly tell the students a
formula for finding area of rectangles!
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Students can use the additive property to figure out
the remainder of space not covered.
“I knew one row has 7 tiles and there can be 5 rows so
7 + 7 + 7 +7 + 7= 35.”
 Students can use the distributive property to figure
out the remainder of the space not covered.
July 17, 2013
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Grade 3: 3.MD.C.5-7, Geometric measurement: understand concepts of area and relate area to
multiplication and addition
Learning Experience
“I know 10 makes 2 columns so 6 columns gave me 30.
There was one more column left over, so that would be 5
more for a total of 35.”
 Students can find the lengths of the sides to
determine the area.
“I knew one side measures 5 and the other measures 7,
so 5 x 7 = 35.”
Closure
Go back to the classroom problem regarding the classroom
reading corner.
If our reading corner is 5’ x 7’ and each tile is 1’ x 1’,
how many carpet tiles do I need to purchase? If the
tiles come in packs of 12, how many packages do I
need to get?
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Construct viable arguments and critique the
reasoning of others.
Attend to precision.
Formative Assessment: Distribute Resource Sheet 2: Exit
Slip: Rules for Finding Area
What would be a good rule for finding the area of a rectangle
if you do not have enough square units to cover the entire
July 17, 2013
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Grade 3: 3.MD.C.5-7, Geometric measurement: understand concepts of area and relate area to
multiplication and addition
Learning Experience
area? Explain and provide an example.
Interventions/Enrichments
 Special Education/Struggling
Learners
 ELL
 Gifted and Talented
Materials
Supporting Information
-Use previous exit slip to sort students into groups. Possible activities for the following groups:
o Struggling students- Give more tiles, then slowly remove them so they can answer the question.
o
Enrichments- Using Resource Sheets 3A&B “Uh-Oh” Cards, give students a problem with the wrong
solution. Ask them to explain what went wrong and how to fix it. For example, instead of the
response of 35, they say 12. What did they do wrong? Example 2: Instead of the response of 35,
they said 20. What could they have done wrong? Example 3: Student said they got an area of 24.
Provide advice to a student that said 24. What did they do wrong?
If you did not have square tiles and only had rectangular tiles that were 1 x 2, how could you use
them instead?
-
Square tiles
5 x 7 index cards per student (one per student)
Post it notes of different sizes
Base ten unit cubes
Hundreds chart
Cheese-it crackers
12 one-inch tiles per student
5 x 7 inch index card (one per student)
Resource Sheet 1: Exit Slip: Similarities & Differences
Resource Sheet 2: Exit Ticket: Rules for Finding Area
Resource Sheets 3A&B: “Uh-Oh” Cards - Extension questions
Technology
Elmo or other projector, if available for student use when sharing solutions and modeling arrays
Resources
(must be available to all
stakeholders)
See Resource List in Unit Plan
July 17, 2013
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Grade 3: 3.MD.C.5-7, Geometric measurement: understand concepts of area and relate area to
multiplication and addition
Resource Sheet 1
Exit Slip: Similarities & Differences
Name _____________________________
Date _____________________
What are some of the similarities and differences that we saw wen we covered our index cards using
different manipulatives?
Why do you think these differences occurred?
July 17, 2013
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Grade 3: 3.MD.C.5-7, Geometric measurement: understand concepts of area and relate area to
multiplication and addition
Resource Sheet 2
Exit Ticket: Rules for Finding Area
Name_________________________________
Date__________________________
What would be a good rule for finding the area of a rectangle if you do not have enough square units
to cover the entire area? Explain and provide an example.
July 17, 2013
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Grade 3: 3.MD.C.5-7, Geometric measurement: understand concepts of area and relate area to
multiplication and addition
Resource Sheet 3A
“Uh-Oh” Cards
Juacinto and Molly used their tiles
to cover a 5 x 7 card. They decided
on a final answer of “12 square
inches” What did they do wrong?
What advice would you give to
them?
July 17, 2013
Janice and Deshawn placed
1”square tiles on their 5 x 7 card and then
concluded that the card had an area of 30
square inches. Oops! What did they do
wrong, and how can they fix it? Give them a
clue of what they might do…
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Grade 3: 3.MD.C.5-7, Geometric measurement: understand concepts of area and relate area to
multiplication and addition
“Uh-Oh” Cards
Resource Sheet 3B
Sue, Danny, and Kim
covered their 5 x 7 index card with
1”square tiles and determined that the
area was 24 square inches. Something
went wrong, but they can’t figure it out.
What might you suggest to them?
July 17, 2013
There are no more 1”square
tiles left to determine the area of the 5 x 7
index card. All you can find are 1 x 2 inch
rectangles or little right angle triangles that
fit together on the square tiles. Can you
cover the 5 x 7 index card and determine
the area? Why so? Or why not?
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