Download Elementary - Madison County Schools

MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 3
Unit Description
Big Idea(s)
What enduring
understandings are essential
for application to new
situations within or beyond
this content?
Unit 5
Area
Suggested Length 2 to 3 weeks
Enduring Understandings
Develop an Understanding of the structure of rectangular arrays and
area.
Enduring Skills Rubric measures competency of the following skills:
Understands area measurement by:
*counting unit squares
*tiling
*multiplying side lengths
*distributive property
*decomposition of rectangular figures and addition of area.
Can use knowledge of area to solve real world problems.
Essential Question(s)
What questions will provoke
and sustain student
engagement while focusing
learning?
Choose the essential question(s) that best fits the needs of your
student(s).
● Can the same area measurement produce different size rectangles?
(Ex. 24 sq. units can produce a rectangle that is a 3 X 8, 4 X 6, 1 X24, 2
X 12)
● Do different factors with the same area cover the same amount of
space? (Ex. Is a 3 X8 the same area as a 1 X 24?)
● How are patterns related to multiplication?
● How can area be determined without counting each square?
● How can multiple math operations be used to solve real world
problems?
● How can multiplication and addition be used to determine a
rectangle’s area?
● How can multiplication used when reading a pictograph?
Curriculum and Instruction
2015-2016
Page 1 of 9
MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 3
● How can the knowledge of area be used to solve real world
problems?
● How can the same area measure produce rectangles with different
dimensions? (Ex. 24 square units can produce a rectangle that is a 3 x
8, 4 x 6, 1 x 24, 2 x 12)
● How do estimation, multiplication, and division help us solve
problems in everyday life?
● How do rectangle dimensions impact the area of the rectangle?
● How do two-step word problems differ from one-step word
problems?
● How does knowing the area of a square or rectangle relate to
knowing different multiplication facts?
● How does knowing the dimensions of a rectangle relate to
multiplication?
● How does understanding the distributive property help us multiply
large numbers?
● How is the commutative property of multiplication evident in an area
model?
● How is the decomposition of a factor in an equation related to the
distributive property of multiplication?
● What does it mean to decompose a number?
● What is the connection between area models and skip counting?
● What is tiling?
● Why are square units commonly associated with finding area?
● Why is an area model a representation for multiplication?
Standards
Curriculum and Instruction
Standards for Mathematical Practice
1. Make sense of problems and persevere in solving them.
Students make sense of problems involving area.
2015-2016
Page 2 of 9
MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 3
2. Reason abstractly and quantitatively. Students demonstrate
abstract reasoning by connecting area with multiplication and arrays.
3. Construct viable arguments and critique the reasoning of others.
Students construct and critique arguments regarding area by creating
or drawing arrays or area models to prove answers.
4. Model with mathematics. Students use arrays or area models to find
area.
5. Use appropriate tools strategically. Students use tiles and drawings
to solve area problems.
6. Attend to precision. Students use vocabulary such as area, array,
area model, and dimensions with increasing precision to discuss their
reasoning when solving area problems.
7. Look for and make use of structure. Students compare rectangles
with the same area but different dimensions and look for patterns in
the shapes of the rectangles.
8. Look for and express regularity in repeated reasoning. Students will
notice that arrays and multiplication can be used to solve area
problems.
Standards for Mathematical Content
3.MD.5
Recognize area as an attribute of plane figures and
understand concepts of area measurement.
a.
A square with side length 1 unit, called “a unit square,” is said to
have “one square unit” of area, and can be used to measure area.
b.
A plane figure which can be covered without gaps or overlaps
by n unit squares is said to have an area of n square units
3.MD.6
Measure areas by counting unit squares (square cm,
square m, square in, square ft, and improvised units)
3.MD.7
addition.
Relate area to the operations of multiplication and
a.
Find the area of a rectangle with whole-number side lengths by
tiling it, and show that the area is the same as would be found by
multiplying the side lengths.
Curriculum and Instruction
2015-2016
Page 3 of 9
MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 3
b.
Multiply side lengths to find areas of rectangles with whole
number side lengths in the context of solving real world and
mathematical problems, and represent whole-number products as
rectangular areas in mathematical reasoning.
c.
Use tiling to show in a concrete case that the area of a
rectangle with whole-number side lengths a and b + c is the sum of a
× b and a × c. Use area models to represent the distributive property in
mathematical reasoning.
d.
Recognize area as additive. Find areas of rectilinear figures by
decomposing them into non-overlapping rectangles and adding the
areas of the non-overlapping parts, applying this technique to solve
real world problems.
3.MD.8
Solve real world and mathematical problems involving
perimeters of polygons, including finding the perimeter given the side
lengths, finding an unknown side length, and exhibiting rectangles with
the same perimeter and different areas or with the same area and
different perimeters
Supporting Standard(s)
Which related standards will
be incorporated to support
and enhance the enduring
standards?
3.OA.1 Interpret products of whole numbers, e.g., interpret 5 × 7 as the
total number of objects in 5 groups of 7 objects each. For example,
describe a context in which a total number of objects can be
expressed as 5 × 7.
3.OA.2 Interpret whole-number quotients of whole numbers, e.g.,
interpret 56 ÷ 8 as the number of objects in each share when 56
objects are partitioned equally into 8 shares, or as a number of shares
when 56 objects are partitioned into equal shares of 8 objects each.
For example, describe a context in which a number of shares or a
number of groups can be expressed as 56 ÷ 8.
3.OA.3 Use multiplication and division within 100 to solve word
problems in situations involving equal groups, arrays, and
measurement quantities, e.g., by using drawings and equations with a
symbol for the unknown number to represent the problem. (See
Glossary)
3.OA.4 Determine the unknown whole number in a multiplication or
division equation relating three whole numbers. For example,
determine the unknown number that makes the equation true in each
of the equations 8 × ? = 48, 5 = � ÷ 3, 6 × 6 = ?.
Curriculum and Instruction
2015-2016
Page 4 of 9
MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 3
3.OA.5 Apply properties of operations as strategies to multiply and
divide. (Students need not use formal terms for these properties.)
Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known.
(Commutative property of multiplication.) 3 × 5 × 2 can be found by 3
× 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative
property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one
can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive
property.)
3.OA.6 Understand division as an unknown-factor problem. For
example, find 32 ÷ 8 by finding the number that makes 32 when
multiplied by 8.
3.OA.7 Fluently multiply and divide within 100, using strategies such as
the relationship between multiplication and division (e.g., knowing
that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the
end of Grade 3, know from memory all products of two one-digit
numbers
3.OA.8 Solve two-step word problems using the four operations.
Represent these problems using equations with a letter standing for the
unknown quantity. Assess the reasonableness of answers using mental
computation and estimation strategies including rounding. (This
standard is limited to problems posed with whole numbers and having
whole number answers; students should know how to perform
operations in the conventional order when there are no parentheses
to specify a particular order (Order of Operations).)
3.OA.9 Identify arithmetic patterns (including patterns in the addition
table or multiplication table), and explain them using properties of
operations. For example, observe that 4 times a number is always
even, and explain why 4 times a number can be decomposed into
two equal addends.
Instructional Outcomes
What must students learn
and be able to do by the
end of the unit to
demonstrate mastery?
I am learning to….
3.MD.5
 Explain using a “unit square” to measure an area of rectangular
space.

Cover the area of a plane figure with n unit squares without any
gaps or overlaps and identify the area as n square units.
3.MD.6
 Measure area by counting square units (cm, m, in, ft, and
Curriculum and Instruction
2015-2016
Page 5 of 9
MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 3
others).
3.MD.7
 Use tiling to show the relationship between multiplication and
area.

Solve word problems by multiplying to find the area.

Break apart a figure into non-overlapping rectangles.

Add areas of rectangles together to find the total area of a
figure when solving real world problems.
3.MD.8
 Solve problems that involve finding the perimeter of a polygon
given an unknown side or given the side lengths
.
 Create or draw rectangles with the same perimeter but
different areas.
Create or draw rectangles with the same area but different
perimeters.
Essential Vocabulary (Assessed)
Array, tiling, unit square

Essential Vocabulary
What vocabulary must
students know to
understand and
communicate effectively
about this content?
Resources/Activities
What resources could we
use to best teach this unit?
Supporting Vocabulary
Arithmetic patterns, array, associative property of Multiplication,
Commutative Property of Multiplication, decompose, Distributive
Property, divide, dividend, divisor, equal, equal groups, equation,
expression, fact family, factor, inverse operations, multiple,
Multiplicative Identity Property of 1, multiply, number line, odd number,
pattern, product, quotient, reasonableness, related facts, repeated
addition, repeated subtraction, skip count, tiling, unit square, variable,
Zero Property of Multiplication
Resources/Activities
Making Math Magic Resources:
http://www.makingmathmagic.net/kcm.html
Perimeter & Area
o Arnie the Area Aardvark
o Fields
Stepping Stones www.origoeducation.com
3.MD.5
o Module 10: Lesson 1, 2
3.MD.6
Curriculum and Instruction
2015-2016
Page 6 of 9
MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 3
o
Module 10: Lesson 1, 2
3.MD.7
o Module 10: Lesson 3, 4, 6, 7, 8
3.MD.8
o Module 10: Lesson 5
K-5 Math Teaching Resources www.k-5mathteachingresources.com
Games are easy to find. Go the website listed above and click on 3rd
grade. Click on 3 – 5 Measurement/Data on the left hand side.
3.MD.5
o Exploring Area
o Area on the Geoboard
3.MD.6
o Find the Area
o Area Compare
o Rectangles with Color Tiles
o Comparing Rectangles
o Rectangular Area Cards
3.MD.7
o Finding the Area of a Rectangle
o Area Word Problems
o Jack’s Rectangles
o Designing a Flower Bed
o What’s the Area?
o Rectangular Robot
3.MD.8
o Measuring Perimeter
o Perimeter on the Geoboard
o Perimeter with Color Tiles
o Designing a Rabbit Enclosure
o The Perimeter Stays the Same
o The Area Stays the Same
o Perimeter Word Problems
Remember there are other sources in your school that may not be
listed on this common resources list due to variation in each individual
school. Examples of other great resources your school may have
access to include: Everyday Math Games, Investigations, Everyday
Partner Games, AVMR file folders, Ongoing Assessment Project, etc.
The Kentucky Numeracy Project is also a great resource that can be
searched by AVMR strand, CCSS, and grade level. Find this resource at
http://knp.kentuckymathematics.org/#!/page_knphome. Kentucky
teachers can use it for free. Just put in your school email address and
Curriculum and Instruction
2015-2016
Page 7 of 9
MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 3
the username “mathfun”, and password is “859”.
Curriculum and Instruction
2015-2016
Page 8 of 9
Curriculum and Instruction
2015-2016
Page 9 of 9