denville township school district...shark swimathon brainpopjr (lv)- adding and subtracting tens;...
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ROCHELLE PARK TOWNSHIP SCHOOL DISTRICT
Math 3-5 Curriculum Guide
BOE Approval: 02/12/2015
2
ROCHELLE PARK TOWNSHIP SCHOOL DISTRICT
Math 3-5 Curriculum Guide
Table of Contents
DTSD Mission Statement 3
Department Vision 3
Affirmative Action Compliance Statement 3
Curriculum and Planning Guides
Grade 3 Units 4 – 35
Grade 4 Units 35 – 64
Grade 5 Units 65 - 96
STANDARDS FOR MATHEMATICAL PRACTICE
The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all
levels should seek to develop in their students. These practices are integrated throughout our curriculum
at all grade levels.
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Use appropriate Tools strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.
INTERDISCIPLINARY THEMES
Planned interdisciplinary activities can help students to make sensible connections among subjects,
while limiting the specialist's tendency to fragment the curriculum into isolated pieces. Such activities
provide students with broader personal meaning and the integrated knowledge necessary to solve real-
world problems. Teachers are encouraged to independently and cooperatively develop lessons which
cover multiple areas simultaneously
3
MISSION STATEMENT
The Rochelle Park School District’s envisions an educational community which inspires and empowers
all students to become self-sufficient and thrive in a complex, global society
DEPARTMENT VISION
It is the firm belief of the Rochelle Park Township School District that mathematics provides students
with a common language that allows them to actively participate in collaborative problem solving
scenarios. This common language will provide our students with a foundation of a deeper understanding
of their future fiscal responsibilities within the global economy they participate in. We encourage our
students to advocate for their communities by acting as a driving force, so that we may build a more
sustainable economy in the future.
This guide is to provide focus for the learning that will take place in this course, but is completely
modifiable based upon the needs and abilities of the students and their Individual Education Plans.
Curriculum implementation follows best practice and adheres to the New Jersey Core Content
Standards. At the same time, for students with disabilities, the Individual Education Plan, specifically
the Goals and Objectives of the plan, supersede any curricular adherence or suggestion.
21ST
CENTURY THEMES & SKILLS
Embedded in much of our units of study and problem based learning projects are the 21st Century
Themes as prescribed by the New Jersey Department of Education. These themes are as follows:
Global Awareness
Financial, Economic, Business, and Entrepreneurial Literacy
Civic Literacy
Health Literacy
AFFIRMATIVE ACTION COMPLIANCE STATEMENT
The Rochelle Park Township School District are committed to the achievement of increased cultural
awareness, respect and equity among students, teachers and community. We are pleased to present all
pupils with information pertaining to possible career, professional or vocational opportunities which in
no way restricts or limits option on the basis of race, color, creed, religion, sex, ancestry, national origin
or socioeconomic status.
4
ROCHELLE PARK TOWNSHIP SCHOOL DISTRICT
Math 3-5 Curriculum Guide
Grade: 3 Unit: Topic 1- Numeration Time Frame: 8 lessons
ENDURING UNDERSTANDINGS ESSENTIAL QUESTIONS
The base-ten numeration system is a scheme
for recording numbers using digits 0-9, groups
of ten, and place value.
Numbers can be used for different purposes,
and numbers can be classified and represented
in different ways.
The set of real numbers is infinite and ordered.
Whole numbers, integers and fractions are real
numbers. Each real number can be associated
with a unique point on the number line.
Numbers, expressions, measures, and object
can be compared and related to other numbers,
expressions, measures, and object in different
ways.
Mathematics content and practices can be
applied to solve problems.
How are greater numbers read and written?
How can whole numbers be compared and
ordered?
KNOWLEDGE SKILLS STANDARDS
Students will know:
our number system in based on
groups of ten. Whenever we get
10 in one place value, we move
to the next greater place value.
the place-value periods ones,
thousands, millions and so
forth, are used to read and write
large numbers.
place value can be used to name
numbers in different ways.
Uses of numbers include telling
how many and showing a date
or an address.
each whole number can be
associated with a unique point
on the number line. Zero is the
least whole number on the
number line and there is no
greatest number. The distance
between any two consecutive
whole numbers on a given
number line is the same.
Students will be able to:
read and write 3-digit and 4-
digit numbers.
name numbers in different
ways.
read and write numbers in the
ten and hundred thousand.
locate and compare whole
numbers on a number line.
identify the pattern on a
number line or graph scale,
and calculate missing labels.
compare 3-digit and 4-digit
whole numbers.
order 3-digit and 4-digits
whole numbers.
make an organized list to
represent information given a
problem.
3.NBT.1
3.NBT.2
5
equal distances on the number
line must correspond to equal
differences in the numbers. The
scale of some graphs is a
number line.
place value can be used to
compare whole numbers.
place value can be used to order
whole numbers.
some problems can be solved by
generating a list of outcomes
and organizing that list in a
systematic way so all outcomes
are accounted for.
VOCABULARY RESOURCES/MATERIALS ASSESSMENT/PROJECT
digits
place value
standard form
expanded form
word form
period
compare
order
place value blocks (or Teaching
Tools 18 and 19)
number lines (Teaching Tool 10)
Teaching Tool 31
Calendar Math:
Daily depositor (ongoing)
Calendar (ongoing)
Counting Tape (ongoing)
Computations and Connections
(ongoing)
Optional Additional Resources:
Math Start Series (LV)- Earth Day
Hooray!
BrainPopJr (LV)- comparing
numbers; making ten; place value
Smartboard activities
Study Island
Formative:
homework
teacher observation
differentiated activities
quizzes
timed fact drills
end of lesson quick checks
Summative:
End of Topic test
6
ROCHELLE PARK TOWNSHIP SCHOOL DISTRICT
Math 3-5 Curriculum Guide
Grade: 3 Unit: Topic 2- Number Sense: Addition & Subtraction Time Frame: 9 lessons
ENDURING UNDERSTANDINGS ESSENTIAL QUESTIONS
● There are multiple interpretations of addition,
subtraction, multiplication, and division of rational
numbers and each operation is related to other
operations.
● For a given set of numbers there are relationships
that are always true called properties, and these are
the rules that govern arithmetic and algebra.
● There is more than one algorithm for each of the
operations with rational numbers. Most algorithm
for operations with rational numbers both mental
math and paper and pencil, use equivalence to
transform calculations into simpler ones.
● Numbers can be approximated by numbers that are
close. Numerical calculations can be approximated
by replacing numbers with other numbers that are
close and easy to compute with mentally.
● Any number, measure, numerical expression.,
algebraic expression, or equation can be represented
in an infinite number of ways that have the same
value.
● Mathematics content and practices can be applied to
solve problems.
● How can sums and differences be found
mentally?
● How can sums and differences be estimated?
KNOWLEDGE SKILLS STANDARDS
Students will know:
● some real-world problems
involving joining, separating, part-
part-whole, or comparison can be
solved using addition or subtraction
● fact families show addition and
subtraction relationships
● two numbers can be added in any
order; the sum of any number and 0
is that number; and three or more
numbers can be grouped and added
in any order
● there is more than one way to do a
mental calculation. Techniques for
doing addition or subtraction
calculations mentally involve
changing the numbers or the
expressions so the calculation is
easy to do mentally.
Students will be able to:
concrete materials and
concepts of addition to
model the Commutative,
Associative, and Identity
Properties of Addition. • recognize situations when
subtraction is used to solve a
problem and write number
sentences. • solve problems by adding with
mental math. • will solve problems by
subtracting with mental math. • round two-digit and three-digit
whole numbers to the nearest
ten or hundred , by comparing
to the number halfway
between or by using place
value.
3.NBT.1
3.NBT.2
7
● rounding is a process for finding the
multiple of 10, 100, etc. closest to a
given number.
● there is more than one way to
estimate a sum or difference.
● rounding and substituting
compatible numbers are two ways
to estimate sums and differences.
● different numerical expressions can
have the same value. Or the value
of one expression can be less than
(or greater than) the value of
another expression
● an equation shows a balance
between what is on the right side
and what is one the left side of the
equal sign
● answers to problems should always
be checked for reasonableness, and
this can be done in different ways.
Two ways are to use estimation and
when appropriate and to check the
answer against the question and
conditions in the problem.
• solve problems by estimating
sums. • solve problems by estimating
differences. • decide whether both sides of
an equation are equal and they
will determine the value of an
unknown number in an
equation. • solve word problems and
check their answers for
reasonableness.
VOCABULARY RESOURCES/MATERIALS ASSESSMENT/PROJECT
addends sum Commutative Property of Addition Associative Property of Addition Identity Property of Addition difference fact family round estimate compatible numbers equation
two color counters
Teaching Tool 17
Teaching Tool 33
Calendar Math:
Daily depositor (ongoing)
Calendar (ongoing)
Counting Tape (ongoing)
Computations and Connections
(ongoing)
Exemplars- Ant in the Well;
Bulletin Board Border; Kwanza
Celebration
Optional Additional Resources:
Math Start Series (LV)- Betcha!;
Shark Swimathon
BrainPopJr (LV)- adding and
subtracting tens; adding with
regrouping; basic adding; basic
subtraction; rounding
Smartboard activities
Study Island
Formative:
homework
teacher observation
differentiated activities
quizzes
timed fact drills
end of lesson quick checks
Summative:
End of Topic test
8
ROCHELLE PARK TOWNSHIP SCHOOL DISTRICT
Math 3-5 Curriculum Guide
Grade: 3 Unit: Topic 3- Using Place Value to Add and Subtract Time Frame: 10 lessons
ENDURING UNDERSTANDINGS ESSENTIAL QUESTIONS
There is more than one algorithm for each of
the operations with rational numbers. Some
strategies for basic facts and most algorithms
for operations with rational numbers, both
mental math and paper and pencil, use
equivalence to transform calculations into
simpler ones.
For a given set of numbers there are
relationships that are always true called
properties, and these are the rules that govern
arithmetic and algebra.
Mathematics content and practices can be
applied to solve problems.
What are standard procedures for adding and
subtracting whole numbers?
KNOWLEDGE SKILLS STANDARDS
Students will know:
the expanded algorithm for
adding 3-digit numbers
breaks the addition problem
into a series of easier
problems based on place
value. Answers to the
simpler problems are added
together to determine the
final sum.
models and the standard
algorithm for adding 3-digit
numbers are just and
extension to the hundreds
place of the models and
standard algorithm for adding
2-digit numbers.
the expanded algorithm for
subtracting 3-digit numbers
breaks the subtraction
problem into a series of
easier problems based on
place value. Answers to the
simpler problems are used to
find the final difference.
models and the standard
algorithm for subtracting 3-
digit numbers are just an
extension to the hundreds
Students will be able to:
solve 3-digit addition problems
using an expanded algorithm.
add 3-digit numbers using place
value blocks or pictures and
record the results using the
standard addition algorithm
add 3-digit numbers using
paper-and-pencil methods and
use addition to solve problems.
add 3 or more 2- and/or 3-digit
numbers using paper- and-
pencil methods and use addition
to solve problems.
draw a picture to solve a
problem.
solve 3-digit subtraction
problems by breaking them into
smaller, easier subtraction
problems.
subtract 3-digit numbers using
place value blocks or pictures
and record the results using
standard subtraction algorithm.
subtract 3-digit numbers using
paper-and-pencil methods and
use subtraction to solve
problems.
3.NBT.1
3.NBT.2
3.OA.8
9
place of the models and
standard algorithm for
subtracting 2-digit numbers.
place value relationships can
help simplify subtracting
across zero.
three or more whole numbers
can be grouped and added in
any order.
information in a problem can
often be shown using a
picture or diagram and used
to understand and solve the
problem. Some problems can
be solved by writing and
completing a number
sentence or equation.
subtract 3-digit numbers using
paper-and-pencil methods and
use subtraction to solve
problems.
solve problems by writing a
number sentence based on a
picture they have drawn
describing the problem.
VOCABULARY RESOURCES/MATERIALS ASSESSMENT/PROJECT
no new vocabulary introduced
Place-value blocks or Teaching
Tool 18
Teaching Tool 34
Teaching Tool 35
Problem-solving recording sheet
(Teaching Tool 1)
Calendar Math:
Daily depositor (ongoing)
Calendar (ongoing)
Counting Tape (ongoing)
Computations and Connections
(ongoing)
Optional Additional Resources:
Math Start Series (LV)- Earth Day
Hooray!; Betcha!; Shark
Swimathon
BrainPopJr (LV)- comparing
numbers; making ten; place value
adding and subtracting tens; adding
with regrouping; basic adding;
basic subtraction; rounding
Smartboard activities
Study Island
Formative:
homework
teacher observation
differentiated activities
quizzes
timed fact drills
end of lesson quick checks
Summative:
End of Topic test
10
ROCHELLE PARK TOWNSHIP SCHOOL DISTRICT
Math 3-5 Curriculum Guide
Grade: 3 Unit: Topic 4 – Meanings of Multiplication Time Frame: 5 lessons
ENDURING UNDERSTANDINGS ESSENTIAL QUESTIONS
There are multiple interpretations of addition,
subtraction, multiplication, and division of
rational numbers and each operation is related
to other operations.
For a given set of numbers there are
relationships that are always true, called
properties, and these are the rules that govern
arithmetic and algebra.
Mathematics content and practices can be
applied to solve problems.
What are different meanings of multiplication?
How are addition and multiplication related?
KNOWLEDGE SKILLS STANDARDS
Students will know:
repeated addition involves
joining equal groups and is
one way to think about
multiplication.
an array involves joining
equal groups and is one
way to think about
multiplication.
some real-world problems
involving joining or
separating equal groups or
comparison can be solved
using multiplication.
two numbers can be
multiplied in any order and
the product remains the
same.
mathematical explanations
can be given using words,
pictures, numbers, or
symbols. A good
explanation should be
correct, simple, complete,
and easy to understand.
Students will be able to:
write multiplication number
sentences for given equal
group situations, using the x
symbol.
write multiplication sentences
for arrays and use arrays to
find products.
write multiplication sentences
for arrays, use arrays to find
products, and use the
Commutative Property of
Multiplication.
write math stories for given
multiplication facts.
use objects, words, pictures,
numbers, and technology to
provide a written explanation
reflecting their understanding.
3.0A.1
3.0A.3
3.0A.5
11
VOCABULARY RESOURCES/MATERIALS ASSESSMENT/PROJECT
multiplication
factors
product
array
Commutative (Order) Property
of Multiplication
two-color counters (Teaching
Tool 17)
Calendar Math:
Daily depositor (ongoing)
Calendar (ongoing)
Counting Tape (ongoing)
Computations and Connections
(December and April activities)
Exemplars- A Very Fishy Story;
Carpet Caper; Checkerboard
Investigation; Harvest Dinner; Job
Hunting
Optional Additional Resources:
Math Start Series (LV)- Too
Many Kangaroo Things to Do!
BrainPopJr (LV)- Arrays
Smartboard activities
Study Island
Formative:
homework
teacher observation
differentiated activities
quizzes
timed fact drills
end of lesson quick checks
Summative:
End of Topic test
Benchmark- Topic 1-4
12
ROCHELLE PARK TOWNSHIP SCHOOL DISTRICT
Math 3-5 Curriculum Guide
Grade: 3 Unit: Topic 5- Multiplication Facts: Use Patterns Time Frame: 7 lessons
ENDURING UNDERSTANDINGS ESSENTIAL QUESTIONS
Relationships can be described and
generalizations made for mathematical
situations that have numbers or objects that
repeat in predictable ways. For some
relationships, mathematical expressions and
equations can be used to describe how
members of one set are related to members of a
second set.
Mathematics content and practices can be
applied to solve problems.
What patterns can be used to find certain
multiplication facts?
KNOWLEDGE SKILLS STANDARDS
Students will know:
there are patterns in the
products for multiplication
facts with factors of 2 and
5.
there are patterns in the
products for multiplication
facts with a factor of 9.
there are patterns in the
products for multiplication
facts with factors 0 and 1.
there are patterns in the
products for multiplication
facts with factors of 2, 5
and 9.
patterns can be used to find
products involving factors
of 10.
basic facts and place-value
patterns can be used to find
products when one factor is
a multiple of 10.
sometimes the answer to
one problem/question is
needed to find the answer
to another
problem/question.
Students will be able to:
use patterns to multiply with 2
and 5 as factors.
use patterns to multiply with 9
as a factor.
use patterns and properties to
multiply with 0 and 1 as
factors.
use patterns to find products
with factors of 2, 5 and 9.
use patterns to multiply with
10 as a factor.
use basic multiplication facts
and number patterns to
multiply by multiples of 10.
solve for one problem and use
the solution to complete a
second problem.
3.OA.3
3.OA. 9
3. NBT.3
13
VOCABULARY RESOURCES/MATERIALS ASSESSMENT/PROJECT
multiples
identify (one) property of
multiplication
zero property of multiplication
Teaching Tool 36
Two-color counters (Teaching
Tool 17)
Teaching Tool 37
Teaching Tool 38
Hundred chart (Teaching Tool 7)
Teaching Tool 39
Calendar Math:
Daily depositor (ongoing)
Calendar (ongoing)
Counting Tape (ongoing)
Computations and Connections
(April activities)
Exemplars- A Very Fishy Story;
Carpet Caper; Checkerboard
Investigation; Harvest Dinner; Job
Hunting
Optional Additional Resources:
Math Start Series (LV)- Too
Many Kangaroo Things to Do!
BrainPopJr (LV)- Mutiplying by
zero and one
Smartboard activities
Study Island
Formative:
homework
teacher observation
differentiated activities
quizzes
timed fact drills
end of lesson quick checks
Summative:
End of Topic test
14
ROCHELLE PARK TOWNSHIP SCHOOL DISTRICT
Math 3-5 Curriculum Guide
Grade: 3 Unit: Topic 6 -Multiplication Facts: Use Known Facts Time Frame: 9 lessons
ENDURING UNDERSTANDINGS ESSENTIAL QUESTIONS
For a given set of numbers there are
relationships that are always true, called
properties, and these are the rules that govern
arithmetic and algebra.
There is more than one algorithm for each of
the operations with rational numbers. Some
strategies for basic facts and most algorithms
for operations with rational numbers, both
mental math and paper and pencil, use
equivalence to transform calculations into
simpler ones.
There are multiple interpretations of addition,
subtraction, multiplication, and division of
rational numbers, and each operation is related
to other operations.
Mathematics content and practices can be
applied to solve problems.
How can unknown multiplication facts be
found using known facts?
KNOWLEDGE SKILLS STANDARDS
Students will know:
the disruptive property can be
used to break a large array into
two smaller arrays.
three or more numbers can be
grouped and multiplied in any
order.
basic multiplication facts with
3 as a factor can be found by
breaking apart the unknown
fact into known facts. The
answers to the known facts are
added to get the final product.
basic multiplication facts with
4 as a factor can be found by
breaking apart the unknown
fact into known facts. The
answers to the known facts are
added to get the final product.
basic multiplication facts with
6 or 7 as a factor can be found
by breaking apart the unknown
facts into known facts. The
answers to the known facts are
added to get the final product.
Students will be able to:
use the distributive property to
simplify multiplication
problems by breaking apart
large arrays that represent
multiplication facts into
smaller arrays that represent
other multiplication facts.
use known facts to find
products with 3 as a factor.
use known facts and doubles to
find products with 4 as a factor.
use known facts to find
products with 6 and 7 as
factors.
use known facts and doubles to
find products with 8 as a factor.
multiply three numbers and use
the associative property of
multiplication.
use known facts and patterns to
find products.
3.OA.3 3.OA5 3.OA.8 3.MD.7.c 3.MD.8
15
basic multiplication facts with
8 as a factor can be found by
breaking apart the unknown
facts into known facts. The
answers to the known facts are
added to get the final product.
patterns and known facts can
be used to find unknown
multiplication facts.
finding the number of
combinations that are possible
between the members of one
group and the members of
another group is one meaning
of multiplication.
some problems can be solved
by the first finding and solving
a sub-problem(s) and then
using that answer(s) to solve
the original problem.
use objects, pictures, and
multiplication to find the
number of possible
combinations of data or objects
in a problem.
solve multiple-step problems.
VOCABULARY RESOURCES/MATERIALS ASSESSMENT/PROJECT
Distributive Property
Associative (Grouping) Property
of Multiplication
Teaching Tool 40
Two Color Tiles
Teaching Tool 16
Teaching Tool 17
Two color counters
Calendar Math:
Daily depositor (ongoing)
Calendar (ongoing)
Counting Tape (ongoing)
Computations and Connections
(January, February, and April
activities)
Exemplars- A Very Fishy Story;
Carpet Caper; Checkerboard
Investigation; Harvest Dinner; Job
Hunting
Optional Additional Resources:
Math Start Series (LV)- Too Many
Kangaroo Things to Do!
Smartboard activities
Study Island
Formative:
homework
teacher observation
differentiated activities
quizzes
timed fact drills
end of lesson quick checks
Summative:
End of Topic test
16
ROCHELLE PARK TOWNSHIP SCHOOL DISTRICT
Math 3-5 Curriculum Guide
Grade: 3 Unit: Topic 7 - Meanings of Division Time Frame: 6
lessons
ENDURING UNDERSTANDINGS ESSENTIAL QUESTIONS
There are multiple interpretations of addition,
subtraction, multiplication, and division of
rational numbers, and each operation is related
to other operations.
Mathematics content and practices can be
applied to solve problems.
What are different meanings of division?
How is division related to other operations?
KNOWLEDGE SKILLS STANDARDS
Students will know:
some real-world problems
involving joining or
separating equal groups or
comparison can be solved
using division.
sharing involves separating
equal groups and is one way
to think about division.
repeated subtraction
involves separating equal
groups and is one way to
think about division.
any division problem can be
thought of as a
multiplication fact with a
missing factor. Then, an
answer can be found using a
multiplication table.
sharing and repeated
subtraction both involve
separating equal groups and
are two ways to think about
division.
frequently word problems
can be solved by writing
equations that represent the
quantitative relationships
involved.
information in a problem
can often be shown by using
objects to act it out or by
using a picture or diagram in
order to understand and
solve the problem.
Students will be able to:
use models to solve division
problems involving sharing
and record solutions using
division number sentences.
use models to solve division
problems involving repeated
subtraction and record
solutions using division
number sentences.
use multiplication tables to
find answers to division
problems.
solve word problems by
writing equations that
represent the problem
situations.
write and solve number
stories involving division.
solve problems by using
objects and drawing a
picture.
3.0A.2
3.0A.3
3.0A.4
3.0A.6
3.0A.9
17
VOCABULARY RESOURCES/MATERIALS ASSESSMENT/PROJECT
division
two-color counters (Teaching
Tool 17); Teaching Tool 41
multiplication table (Teaching
Tool 9)
division sentence cards (one per
group)
Calendar Math:
Daily depositor (ongoing)
Calendar (ongoing)
Counting Tape (ongoing)
Computations and Connections
(March)
Exemplars- Camping; Cookie
Cutters; Is Dan Losing His
Marbles?; M&M Cookie
Combos;
Optional Additional Resources:
Math Start Series (LV)- Divide
and Ride
BrainPopJr (LV)- Repeated
Subtraction; Making Equal
Groups
Smartboard activities
Study Island
Formative:
homework
teacher observation
differentiated activities
quizzes
timed fact drills
end of lesson quick checks
Summative:
End of Topic test
18
ROCHELLE PARK TOWNSHIP SCHOOL DISTRICT
Math 3-5 Curriculum Guide
Grade: 3 Unit: Topic 8- Division facts Time Frame: 9 lessons
ENDURING UNDERSTANDINGS ESSENTIAL QUESTIONS
There are multiple interpretations of addition,
subtraction, multiplication, and division of
rational numbers, and each operation is related
to the other operations.
For a given set of numbers, there are
relationships that are always true, called
properties, and these are the rules that govern
arithmetic and algebra.
Any number, measure, numerical expression,
algebraic expression, or equation can be
represented in an infinite number of ways that
have the same value.
Mathematical situations and structures can be
translated and represented abstractly using
variables, expressions, and equations.
Mathematics content and practices can be
applied to solve problems.
How can an unknown division fact be found
by thinking of a related multiplication fact?
KNOWLEDGE SKILLS STANDARDS
Students will know:
multiplication and division
have an inverse
relationship.
the inverse relationship
between multiplication and
division can be used to find
division facts; every
division fact has a related
multiplication fact.
pattern and known facts
can be used to find
unknown multiplication
facts. Division facts can be
found by thinking of a
related multiplication fact.
any number (except 0)
divided by itself is equal to
1. Any number divided by
1 is that number. Zero
divided by any number
(except 0) is zero. Zero
cannot be a divisor.
Students will be able to:
give a multiplication fact, state
a related division fact and vice
versa.
give quotients for division
facts with divisors 2, 3, 4 and
5.
give quotients for division
facts with divisors of 6 and 7.
give quotients for division
facts with divisors of 8 and 9.
use previously learned skills to
solve multiple-step problems.
learn how to use
multiplication and division
facts to decide whether both
sides of an equation are equal.
They will also learn to
determine the value of an
unknown in an equation.
use patterns and fact families
to find answers to division
facts with 0 and 1.
3.OA.3
3.OA.7
19
different numerical
expressions can have the
same value. Or, the value
of one expression can be
less than (or greater than)
the value of the other
expression.
an equation shows a
balance between what is on
the right side and what is
on the left side of the equal
sign.
some problems can be
solved by first finding and
solving one or more sub-
problems and then using
the answer(s) to solve the
original problem.
information in a problem
can be often be shown by
using a picture or diagram
and used to understand and
solve the problem. Some
problems can be solved by
writing and completing a
number sentence or
equation.
use multiplication and division
facts to solve problems.
solve division problems
involving sharing and repeated
subtraction by drawing a
picture and writing a number
sentence.
VOCABULARY RESOURCES/MATERIALS ASSESSMENT/PROJECT
dividend
divisor
quotient
two-color counters (Teaching
Tool 17)
Calendar Math:
Daily depositor (ongoing)
Calendar (ongoing)
Counting Tape (ongoing)
Computations and Connections
(April and May activities)
Exemplars- Camping; Cookie
Cutters; Is Dan Losing His
Marbles?; M&M Cookie Combos;
Optional Additional Resources:
Math Start Series (LV)- Divide
and Ride
BrainPopJr (LV)- Repeated
Subtraction; Making Equal
Groups
Smartboard activities
Study Island
Formative:
homework
teacher observation
differentiated activities
quizzes
timed fact drills
end of lesson quick checks
Summative:
End of Topic test
Benchmark- Topic 5-8
20
ROCHELLE PARK TOWNSHIP SCHOOL DISTRICT
Math 3-5 Curriculum Guide
Grade: 3 Unit: Topic 9- Understanding Fractions Time Frame: 8 lessons
ENDURING UNDERSTANDINGS ESSENTIAL QUESTIONS
● The set of a real numbers is infinite and ordered.
Whole numbers, integers, and fractions are real
numbers. Each real number can be associated
with a unique point on the number line.
● Numbers can be approximated by numbers that
are close. Numerical calculations can be
approximated by replacing numbers with other
numbers that are close and easy to compute with
mentally. Some measurements can be
approximated using known referents as the unit
in the measurement process.
● Mathematics content and practices can be applied
to solve problems
● What are different interpretations of a
fraction?
KNOWLEDGE SKILLS STANDARDS
Students will know:
● a region can be divided into
equal-sized parts in different
ways. Equal-sized parts of a
region have the same area but
not necessarily the same shape.
● a fraction describes the division
of a whole number (region, set
segment) into equal parts. The
bottom number in a fraction
tells how many equal parts the
whole is divided into. The top
number tells how many equal
parts are indicated. A fraction
is relative to the size of the
whole.
● finding a unit-fractional part of
a whole is the same as dividing
the whole denominator of the
fraction.
● some points between whole
numbers on a number line can
be labeled with fractions or
mixed numbers. The
denominator of the fraction can
be determined by counting the
number of equal parts between
two consecutive whole
numbers.
Students will be able to:
● identify regions that have
been divided into equal-sized
parts and divide regions into
equal-sized parts.
● associate the model, symbol,
and words used to describe a
fractional part of a whole
region.
● associate the model, symbol,
and words used to describe a
fractional part of a set.
● find a fractional part of a set.
● identify fractional parts and
mixed numbers on a number
line.
● use benchmark fractions to
estimate fractional parts.
● associate the model, symbol,
and words used to describe a
fractional part of the length
of an object.
● make a table and look for a
pattern to solve a problem.
3.NF.1 3.NF.2 3.NF.2a 3.NF.2b 3.OA.3
21
● fractions can be approximated
by other fractions that are close.
● some problems can be solved by
reordering and organizing data
in a table and by finding and
using numerical patterns in the
table. VOCABULARY RESOURCES/MATERIALS ASSESSMENT/PROJECT
halves thirds fourths fifths sixths eighths tenths twelfths fraction unit fraction numerator denominator mixed numbers benchmark fractions
centimeter grid paper
(Teaching Tool 11) Teaching Tool 45 crayons two Color counters Teaching Tool 17 8 1/2 inch X 1 inch paper strips number lines fraction Strips (Teaching Tool
22)
Calendar Math:
Daily depositor (ongoing)
Calendar (ongoing)
Counting Tape (ongoing)
Computations and Connections
(ongoing)
*use February calendar pieces
Exemplars- Disappearing
Cookies; Post Office Display
Optional Additional Resources:
Math Start Series (LV)- Jump
Kangaroo Jump!
BrainPopJr (LV)- Basic Parts
of a Whole; More Fractions
Smartboard activities
Study Island
Formative:
homework
teacher observation
differentiated activities
quizzes
timed fact drills
end of lesson quick checks
Summative:
End of Topic test
22
ROCHELLE PARK TOWNSHIP SCHOOL DISTRICT
Math 3-5 Curriculum Guide
Grade: 3 Unit: Topic 10- Fraction Comparison and Equivalence Time Frame: 9
lessons
ENDURING UNDERSTANDINGS ESSENTIAL QUESTIONS
Numbers, expressions, measures, and objects
can be compared and related to other numbers,
expressions, measures, and objects in different
ways.
The set of real numbers in infinite and ordered.
Whole numbers, integers, and fractions are real
numbers. Each real number can be associated
with a unique point on the number line.
Any number, measure, numerical expression,
algebraic expression, or equation can be
represented in an infinite number of ways that
have the same value.
Mathematics content and practices can be
applied to solve problems.
What are different ways to compare fractions?
KNOWLEDGE SKILLS STANDARDS
Students will know:
if two fractions have the same
denominator, the fraction with
the greater numerator is the
greater fraction.
if two fractions have the same
numerator, the fraction with
the lesser denominator is the
greater fraction.
fractions can be compared to
each other by comparing them
to benchmark numbers such
as 0, ½, and 1.
number lines can be used to
compare fractions with like
denominators or like
numerators.
a fraction is relative to the size
of the whole. Models can be
used to compare fractional
amounts.
number lines can be used to
compare fractions with like
denominators or like
numerators.
Students will be able to:
use models and quantitative
reason to compare fractions
with the same denominator.
use models and reasoning
to compare fractions with
the same numerator.
use benchmark numbers to
compare fractions with the
same numerator or the
same denominator.
use number lines to
compare fractions with like
denominators or like
numerators.
use models to find
equivalent fractions.
use number lines to identify
equivalent fractions.
use fraction strips and
number lines to find
fraction names for whole
numbers.
compare and order
fractions to solve problems.
3.NF.2
3.NF.3
3.NF.3.a
3.NF.3.c
3.NF.3.d
23
equivalent fractions name the
same point on a number line.
if a fraction aligns with a
whole number on a number
line or to a whole number
fraction strip, the whole
number is equivalent to that
fraction.
the same fractional amount
can be represented by an
infinite set of different but
equivalent fractions.
equivalent fractions name the
same point on a number line.
if a fraction aligns with a
whole number on a number
line or to a whole number
fraction strip, the whole
number is equivalent to that
fraction.
information in a problem can
often be shown using a picture
or diagram and used to
understand and solve the
problem.
draw a picture to solve
problems.
VOCABULARY RESOURCES/MATERIALS ASSESSMENT/PROJECT
equivalent fractions
simplest form
Fraction models: strips
(Teaching Tool 22- 2 sets per
pair)
Number lines (Teaching Tool
10)
Calendar Math:
Daily depositor (ongoing)
Calendar (ongoing)
Counting Tape (ongoing)
Computations and Connections
(ongoing)
*use February calendar pieces
Exemplars- Disappearing
Cookies; Post Office Display
Optional Additional Resources:
Math Start Series (LV)- Jump
Kangaroo Jump!
BrainPopJr (LV)- Equivalent
Fractions; Mixed Numbers
Smartboard activities
Study Island
Formative:
homework
teacher observation
differentiated activities
quizzes
timed fact drills
end of lesson quick checks
Summative:
End of Topic test
24
ROCHELLE PARK TOWNSHIP SCHOOL DISTRICT
Math 3-5 Curriculum Guide
Grade: 3 Unit: Topic 11- Two Dimensional Shapes and Their Attributes Time Frame: 9
lessons
ENDURING UNDERSTANDINGS ESSENTIAL QUESTIONS
Two and three dimensional objects with or
without curved surfaces can be described,
classified, and analyzed by their attributes. An
object’s location in space can be described
quantitatively.
Mathematics content and practices can be
applied to solve problems.
How can two-dimensional shapes be
described, analyzed, and classified?
KNOWLEDGE SKILLS STANDARDS
Students will know:
lines and line segments are
sets of points in space that
can be used to describe
parts of other geometric
lines, shapes, and solids.
an angle is formed by two
rays with a common
endpoint. Angles can be
classified by their size.
plane shapes have many
properties that make them
different from one another.
polygons can be described
and classified by their sides
and angles.
polygons can be put
together or taken apart to
make other polygons.
some problems can be
solved by breaking apart or
changing the problem into
simpler ones, solving the
simpler ones, and using
those solutions to solve the
original problem.
commonalities in attributes
of objects or situations can
be found and used to make
and test generalizations
about relationships.
Students will be able to:
identify lines and line
segments and explore their
different relationships
identify and classify angles in
relation to right angles
identify and classify polygons
identify and classify triangles
identify and classify
quadrilaterals
create new shapes by
combining shapes or by
separating shapes
make a new shape by cutting
apart a shape and rearranging
the pieces
solve a problem by first
solving a simpler problem
identify commonalities among
objects or situations to make
and test generalizations
3.G.1 3.G.2
25
VOCABULARY RESOURCES/MATERIALS ASSESSMENT/PROJECT
point line line segment intersecting lines parallel lines ray angle vertex right angle perpendicular acute angle obtuse angle polygon side vertex diagonal triangle quadrilateral pentagon hexagon octagon decagon equilateral triangle isosceles triangle scalene triangle right triangle acute triangle obtuse triangle trapezoid parallelogram rectangle rhombus square
ruler or straight edge 2 pipe cleaners or 2 strips of paper
and 1 paper fastener Dot Paper (Teaching Tool 14) Teaching Tool 43 scissors glue Teaching Tool 44 Polygons B, H, K, M, N, O from
polygons (Teaching Tool 29) 1 inch grid paper ( Teaching Tool
12) tape polygons (Teaching Tool 29) two color tiles (Teaching Tool 16)
Calendar Math:
Daily depositor (ongoing)
Calendar (ongoing)
Counting Tape (ongoing)
Computations and Connections
(ongoing)
*use April calendar pieces
Optional Additional Resources:
Math Start Series (LV)- Hamster
Champs
BrainPopJr (LV)- Plane Shapes
Smartboard activities
Study Island
Formative:
homework
teacher observation
differentiated activities
quizzes
timed fact drills
end of lesson quick checks
Summative:
End of Topic test
26
ROCHELLE PARK TOWNSHIP SCHOOL DISTRICT
Math 3-5 Curriculum Guide
Grade: 3 Unit: Topic 12 - Time Time Frame: 5 lessons
ENDURING UNDERSTANDINGS ESSENTIAL QUESTIONS
Some attributes of objects are measurable and
can be quantified using unit amounts.
Mathematics content and practices can be
applied to solve problems.
How can lengths of time be measured and
found?
KNOWLEDGE SKILLS STANDARDS
Students will know:
time can be expressed
using different units that
are related to each other.
the minute hand takes 5
minutes to move from one
number to the next on a
typical clock face. The
minute hand takes 1 minute
to move from one mark to
the next on a typical clock
face.
there are different units for
measuring time. Many
clock times can be
expressed in more than one
way.
the duration of an event
can be measured if one
knows the start and end
times for the event.
some problems with the
initial data point unknown
can be solved by starting
with the end result,
reversing the steps and
processes, and working
backward to the initial data
point.
Students will be able to:
tell time to the nearest half
hour and quarter hour using
analog and digital clocks, and
identify times as A.M. and
P.M.
tell to the nearest minute using
analog and digital clocks.
perform simple conversations
for units of time.
find elapsed time in intervals
of minutes.
use the strategy work
backward to solve problems.
3.MD.1
27
VOCABULARY RESOURCES/MATERIALS ASSESSMENT/PROJECT
hour
half hour
quarter hour
minute
seconds
A.M.
P.M.
elapsed time
clock face (Teaching Tool 25)
calendar (Teaching Tool 26)
Calendar Math:
Daily depositor (ongoing)
Calendar (ongoing)
Counting Tape (ongoing)
Computations and Connections
(ongoing)
Clock Activities (October;
November; December; March)
Exemplars: Busy Day; To the
Detail
Optional Additional Resources:
Math Start Series (LV)- Game
Time!; Rodeo Time
BrainPopJr (LV)- Calendar and
Dates; Parts of a Clock; Time to
the Minute; Time to the Quarter
and Half Hour
Smartboard activities
Study Island
Formative:
homework
teacher observation
differentiated activities
quizzes
timed fact drills
end of lesson quick checks
Summative:
End of Topic test
Benchmark- Topic 9-12
28
ROCHELLE PARK TOWNSHIP SCHOOL DISTRICT
Math 3-5 Curriculum Guide
Grade: 3 Unit: Topic 13- Perimeter Time Frame: 5 days
ENDURING UNDERSTANDINGS ESSENTIAL QUESTIONS
Some attributes of objects are measurable and
can be quantified using unit amounts.
Mathematics content and practices can be
applied to solve problems.
How can perimeter be measured and found?
KNOWLEDGE SKILLS STANDARDS
Students will know:
the distance around a
figure is its perimeter. To
find the perimeter of a
polygon, add the lengths of
the sides.
in a given measurement
situation, the type of
measuring Tool and the
measurement units it
contains determine the
appropriateness of the
Tool.
to find the perimeter of a
polygon, add the lengths of
the sides.
shapes can be made with a
given perimeter. Different
shapes can have the same
perimeter.
some problems can be
solved by making a
reasoned first try for what
the answer might be and
then, through additional
reasoning, arrive at the
correct answer.
Students will be able to:
use standard units to find the
perimeter of a shape.
select appropriate Tools and
units to find perimeter.
use standard units to find the
perimeter of a common shape.
match shapes to a given
perimeter and learn that
different shapes can have the
same perimeter.
solve a problem through the
process of try, check, and
revise.
3.MD.8
29
VOCABULARY RESOURCES/MATERIALS ASSESSMENT/PROJECT
perimeter
mile
centimeter grid paper (Teaching
Tool 11)
inch ruler (or Teaching Tool 24)
yardstick
measuring tape
string
Teaching Tool 46
straws
craft sticks
tooth picks
colored chalk
Calendar Math:
Daily depositor (ongoing)
Calendar (ongoing)
Counting Tape (ongoing)
Computations and Connections
(ongoing)
Measurement (January pgs 78-80)
Optional Additional Resources:
Math Start Series (LV)- Racing
Around
BrainPopJr (LV)- Perimeter
Smartboard activities
Study Island
Formative:
homework
teacher observation
differentiated activities
quizzes
timed fact drills
end of lesson quick checks
Summative: End of Topic test
30
ROCHELLE PARK TOWNSHIP SCHOOL DISTRICT
Math 3-5 Curriculum Guide
Grade: 3 Unit: Topic 14 - Area Time Frame: 10 lessons
ENDURING UNDERSTANDINGS ESSENTIAL QUESTIONS
Some attributes of objects are measureable and
can be quantified using unit amounts.
Mathematics content and practices can be
applied to solve problems.
What does area mean?
What are different ways to find the area of a
shape?
KNOWLEDGE SKILLS STANDARDS
Students will know:
the amount of space inside a
shape is its area, and area can
be estimated or found using
square units.
square units can be used to
create shapes with given
areas.
standard measurements units
are used for consistency in
finding and communicating
measurements.
the amount of space inside a
shape is its area and area can
be estimated or found using
square units. Formulas exist
for finding the area of some
polygons.
the area of rectangles can be
used to model the Distributive
Property.
the area of some irregular
shapes can be found by
breaking apart the original
shape into other shapes for
which the areas can be found.
there are relationships
between the perimeter and
area of a polygon.
equal-area parts of a figure
can be used to model unit
fractions.
some problems can be solved
by breaking apart or changing
the problem into simpler ones,
solving the simpler ones, and
using those solutions to solve
the original problem.
Students will be able to:
measure the area of a shape
by counting the number of
square units that cover a
region.
use square units to make
figures with given areas.
use standard units of area
and counting to measure
the area of a shape.
find the area of rectangles
by counting square units or
by using a formula.
use the areas of rectangles
to model the Distributive
Property.
solve complex problems
asking for the area of
irregular shapes.
find the area of irregular
shapes.
compare different
rectangles with same area
to discover the change in
perimeter.
select appropriate units
and Tools for measuring
the area of given items.
3.MD.5
3.MD.5.a
3.MD.5.b
3.MD.6
3.MD.7
3.MD.7.a
3.MD.7.b
3.MD.7.c
3.MD.7.d
3.MD.8
3.G.2
31
in a given measurement
situation, the type of
measuring Tool and the
measurement units it contains
determine the appropriateness
of the Tool.
VOCABULARY RESOURCES/MATERIALS ASSESSMENT/PROJECT
area
square units
centimeter grid paper
(Teaching Tool 11); tracing
shapes (circle) (per pair)
1 –inch grid paper (Teaching
Tool 12)
index cards (per pair)
scissors (per pair)
Calendar Math:
Daily depositor (ongoing)
Calendar (ongoing)
Counting Tape (ongoing)
Computations and Connections
(ongoing)
Measurement Activities
(January 78-80)
Optional Additional Resources:
Math Start Series (LV)-
Bigger, Better, Best!
BrainPopJr (LV)- Area
Smartboard activities
Study Island
Formative:
homework
teacher observation
differentiated activities
quizzes
timed fact drills
end of lesson quick checks
Summative:
End of Topic test
32
ROCHELLE PARK TOWNSHIP SCHOOL DISTRICT
Math 3-5 Curriculum Guide
Grade: 3 Unit: Topic 15- Liquid, Volume, Mass Time Frame: 5 lessons
ENDURING UNDERSTANDINGS ESSENTIAL QUESTIONS
● Some attributes of objects are measurable and
can be quantified using unit amounts.
● Mathematics content and practices can be applied
to solve problems.
● What are the customary units for measuring
capacity and weight?
● What are the metric units for measuring capacity
and mass?
KNOWLEDGE SKILLS STANDARDS
Students will know:
● capacity is a measure of the
amount of liquid a container
can hold.
● mass is a measure of the
quantity of matter in an
object. Weight and mass are
different.
● the weight of an object is a
measure of how heavy an
object is.
● information in a problem can
often be shown using picture
or diagram and used to
understand and solve the
problem. Some problems
can be solved by writing and
completing a number
sentence or equation.
Students will be able to:
● choose an appropriate unit and
Tool, estimate, and measure in
cups, pints, quarts, and gallons.
● identify objects which hold
about a cup, a pint, a quart, or a
gallon.
● choose an appropriate unit and
Tool, estimate, and measure in
milliliters and liters.
● identify objects that hold about a
liter or a milliliter.
● choose an appropriate unit and
Tool, estimate, and measure in
grams and kilograms.
● identify objects with a mass of
about one gram or one kilogram.
● choose an appropriate unit and
Tool, estimate, and measure in
ounces, pounds, and tons.
● identify objects that weigh about
an ounce, a pound, or a ton. draw a picture to solve a problem
involving units of capacity and
mass.
3.MD.2
33
VOCABULARY RESOURCES/MATERIALS ASSESSMENT/PROJECT
capacity cup pint quart gallon milliliter liter mass gram kilogram weight ounce pound ton
Teaching Tool 47 liter containers water sand rice pan balance dollar bill stapler
Calendar Math:
Daily depositor (ongoing)
Calendar (ongoing)
Counting Tape (ongoing)
Computations and Connections
(ongoing)
Measurement Activities (February
pgs 91-93; March pgs 105-106;
April pgs 120-121)
Optional Additional Resources:
Math Start Series (LV)- Room for
Ripley
BrainPopJr (LV)- Cups, Pints,
Quarts, Gallons; Grams and
Kilograms; Ounces, Pounds, and
Tons
Smartboard activities
Study Island
Formative:
homework
teacher observation
differentiated activities
quizzes
timed fact drills
end of lesson quick checks
Summative: End of Topic test
34
ROCHELLE PARK TOWNSHIP SCHOOL DISTRICT
Math 3-5 Curriculum Guide
Grade: 3 Unit: Topic 16- Data Time Frame: 6 lessons
ENDURING UNDERSTANDINGS ESSENTIAL QUESTIONS
Some questions can be answered by collecting
and analyzing data, and the question to be
answered determines the data that needs to be
collected and how best to collect it. Data can
be represented visually using tables, charts and
graphs. The type of data determines the best
choice of visual representation.
Mathematics content and practices can be
applied to solve problems.
How can data be represented, interpreted and
analyzed?
KNOWLEDGE SKILLS STANDARDS
Students will know:
line plots allow data to be
compared more easily than
in a list or a table.
line plots can be used to
organize and represent data
generated by measuring
lengths.
each type of graph is most
appropriate for certain
kinds of data. Pictographs
and bar graphs help to
compare data.
the key for a pictograph
determines the number of
pictures needed to
represent each number in a
set of data.
in a bar graph, the scale
determines how long the
bar needs to be to represent
each number in a set of
data.
some problems can be
solved by making, reading
and analyzing a graph.
Students will be able to:
use a line plot to organize the
results of an experiment
generate data by measuring
lengths to the nearest fourth of
an inch and make line plots to
organize their data and draw
conclusions.
read and interpret data from a
pictograph and a bar graph.
make a pictograph from a
table or tally chart.
make a bar graph to represent
the data in a table or tally
chart.
solve problems by using tables
and graphs to draw
conclusions.
3.MD.3
3.MD.4
35
VOCABULARY RESOURCES/MATERIALS ASSESSMENT/PROJECT
line plot
pictograph
key
bar graph
scale
line Plots (Teaching Tool 48)
rulers (Teaching Tool 24)
reading pictographs and bar
graphs (Teaching Tool 49)
making Pictographs (Teaching Tool
50) centimeter Grid paper (Teaching
Tool 11) sandwich Survey (Teaching Tool 30)
Calendar Math:
Daily depositor (ongoing)
Calendar (ongoing)
Counting Tape (ongoing)
Computations and Connections
(ongoing)
Graph Activities- (September pgs
28-29; October pgs 44-45;
January pgs 84-85; March pgs
112-113; May pgs 134-135)
Optional Additional Resources:
Math Start Series (LV)-
Lemonade For Sale
BrainPopJr (LV)- Pictographs;
Tally Charts and Bar Graphs
Smartboard activities
Study Island
Formative:
homework
teacher observation
differentiated activities
quizzes
timed fact drills
end of lesson quick checks
Summative:
End of Topic test
Benchmark- Topic 13-26
End of the year test
36
ROCHELLE PARK TOWNSHIP SCHOOL DISTRICT
Math 3-5 Curriculum Guide
Grade: 4 Unit: Topic 1- Multiplication and Division Time Frame: 10 Lessons
ENDURING UNDERSTANDINGS ESSENTIAL QUESTIONS
There are multiple interpretations of addition,
subtraction, multiplication, and division of
rational numbers, and each operation is related
to the other operations.
Relationship can be described and
generalizations made for mathematical
situations that have numbers or objects that
repeat in predicable ways.
For a given set of numbers there are
relationships that are always true called
properties, and these are the rules that govern
arithmetic and equations
Some strategies for basic facts use equivalence
to transform calculations into simpler ones.
Mathematical situations and structures can be
translated and represented abstractly using
variables, expressions, and equations.
Mathematics content and practices can be
applied to solve problems.
How can patterns and properties be used to
find some multiplication facts?
How can unknown multiplication facts be
found by breaking them into known facts?
How can unknown division facts be found by
thinking about a related multiplication fact?
KNOWLEDGE SKILLS STANDARDS
Students will know:
some real-world problems
involving joining or separating
equal groups or comparison can be
solved using multiplication.
Repeated addition and arrays
involve joining equal groups and
are two ways to think about
multiplication.
there are patterns in the products
for multiplication facts with factors
of 2, 5, and 9.
two numbers can be multiplied in
any order. The product of any
number and 0 is zero. The product
of any number and 1 is that
number.
basic multiplication facts with 3,
4, 6, 7, or 8 as a factor can be
found by breaking apart the
unknown fact into known facts.
some problems can be solved by
Students will be able to:
recognize multiplication as
repeated addition of equal
groups used in equal
groups used in arrays.
use products with factors
of 2, 5, and 9.
use multiplication
properties to simplify
computations.
use the Distributive
Property to find products
of the factors of 3,4, 6, 7,
and 8 by breaking apart
problems into simpler
problems.
recognize patterns and be
able to continue the
pattern.
use and draw models to
solve division problems.
use arrays to write and
4.OA.1
4.OA.2
4.OA.3
4.OA.4
4.OA.5
37
identifying elements that repeat in
a predictable way.
some real-world problems involve
joining or separating equal groups
or comparison can be solved using
division.
Sharing and repeated subtraction
involve separating equal groups
and are two ways to think about
multiplication.
multiplication and division have an
inverse relationship. The inverse
relationship between multiplication
and division can be used to find
division facts: every division fact
has a related multiplication fact.
any number (except 0) divided by
itself is equal to 1. Any number
divided by 1 is that number. Zero
divided by any number (except 0)
is zero. Zero cannot be a divisor.
information in a problem can often
be shown using a picture or
diagram and used to understand
and solve the problem. Some
problems can be solved by writing
and completing a number sentence
or equation.
complete multiplication
and division fact families.
use multiplication facts
with 0 and 1 to learn about
special division rules with
0 and 1.
identify multiplication
facts related to division
facts in order to solve
division problems.
draw pictures to problem
solve multiplication
situations and use their
pictures to write number
sentences.
VOCABULARY RESOURCES/MATERIALS ASSESSMENT/PROJECT
array
product
factors
multiple
Commutative Property of
Multiplication
Zero Property of Multiplication
Identity Proper
Identity Property of Multiplication
Distributive Property
inverse operations
fact family
centimeter grid paper
place-value blocks
crayons
colored pencils
colored chalk
markers
hundred chart
index cards
counters
Calendar Math Aug/Sept
Calendar pieces, Counting
Tape, Daily Depositor
Formative
Homework
Teacher observation
Differentiated activities
Quizzes
Summative
Topic test
38
ROCHELLE PARK TOWNSHIP SCHOOL DISTRICT
Math 3-5 Curriculum Guide
Grade: 4 Unit: Topic 2- Generate and Analyze Patterns Time Frame: 6 Lesson
ENDURING UNDERSTANDINGS ESSENTIAL QUESTIONS
Patterns, Relationships, and Functions.
Relationships can be described and
generalizations made for mathematical
situations that have numbers or objects that
repeat in predictable ways.
For some relationships, mathematical
expressions and equations can be used to
describe how members of one set are related to
members of a second set. Practices, Processes,
and Proficiencies.
Mathematics content and practices can be
applied to solve problems.
How can patterns be used to describe how two
quantities are related?
How can a relationship between two quantities
be shown using a table?
KNOWLEDGE SKILLS STANDARDS
Students will know:
patterns, relationships, and
functions
some patterns consist of
shapes or numbers arranged in
a unit that repeats.
some sequences of geometric
objects change in predicable
ways that can be described
using mathematical rules.
some real world quantities
have a mathematical
relationship; the value of one
quantity can be found if you
know the value of the other
quantity.
some real world quantities
have a mathematical
relationship; the value of one
quantity can be found if the
value of the other quantity is
known.
patterns can be used to
identify some relationships
some sequences of geometric
objects change in predicable
ways that can be described
using mathematical rules.
Students will be able to:
identify and extend repeating
geometric or repeating number
patterns
identify and extend whole
number patterns involving
addition and subtraction.
extend tables of ordered pairs for
situations involving
multiplication, addition, or
subtraction.
find a rule and extend the table,
given a table of number pairs.
extend patterns of cubes or tiles.
use the strategies Act It Out and
Use Reasoning to solve problem.
4.OA.5
39
some problems can be solved
by using objects to act out the
information in the problem.
some problems can be solved
by reasoning about the
conditions in the problem.
VOCABULARY RESOURCES/MATERIALS ASSESSMENT/PROJECT
compare
divide
multiply
regroup
repeating pattern
pattern blocks or tangram pieces,
recording sheets: Number
Sequences, two-color counters,
Recording Sheet: Writing Rules for
Situations, Cubes, centimeter grid
paper, two –color counters
Calendar Math Aug/Sept Calendar
pieces, Counting tape, Daily
Depositor
Formative
Homework
Teacher observation
Differentiated activities
Quizzes
Summative
Topic test
40
ROCHELLE PARK TOWNSHIP SCHOOL DISTRICT
Math 3-5 Curriculum Guide
Grade: 4 Unit: Topic 3- Place Value Time Frame: 6 Lessons
ENDURING UNDERSTANDINGS ESSENTIAL QUESTIONS
The Base Ten Numeration System The Base Ten
Numeration System is a scheme for recording numbers
using digits 0-9, groups of ten, and place value.
Comparison and Relationships. Numbers, expressions,
measures, and objects can be compared and related to
other numbers, expressions, measures and objects in
different ways.
Numbers can be approximated by numbers that are
close.
Mathematics content and practices can be applied to
solve problems.
How are greater numbers read and
written?
How can whole numbers be compared
and ordered?
KNOWLEDGE SKILLS STANDARDS
Students will know:
our number system is based on
groups of ten. Whenever we get 10
in one place value, we move to the
next greater place value.
in a multi-digit whole number, a
digit in one place represents tem
times what it would represent in
the place immediately to its right.
place value can be used to compare
and order number.
rounding whole numbers is a
process for for finding the multiple
of 10, 100, and so on the the
closest number.
some problems can be solved by
generating a list of outcomes and
organizing that list in a systematic
way so all outcomes are accounted
for.
Students will be able to:
students will read and write
3 digit and 4 digit numbers.
students will learn how
digits within a multi-digit
whole number relate to each
other by their place value.
students will compare
whole number through
hundred thousands.
students will apply their
knowledge of place value to
compare and order numbers.
students will show place
value to round whole
numbers.
students will systematically
find and record all possible
outcomes for a situation.
4.NBT.1
4.NBT.2
4.NBT.3
VOCABULARY RESOURCES/MATERIALS ASSESSMENT/PROJECT
odd
even
period
number line
digits
place value
standard form, expanded form,
word form
compare
place-value blocks
recording sheet: Comparing and
Ordering Whole Numbers
number lines,
Calendar Math: Oct. Calendar
pieces, coin counter, Daily
Depositor , measurement lesson
Teacher Manual pg.36-38
Formative
Homework
Teacher observation
Differentiated activities
Quizzes
Summative
Topic test
41
ROCHELLE PARK TOWNSHIP SCHOOL DISTRICT
Math 3-5 Curriculum Guide
Grade: 4 Unit: Topic 4- Addition and Subtraction of Whole Number Time Frame: 6 Lessons
ENDURING UNDERSTANDINGS ESSENTIAL QUESTIONS
Any number, measure, numerical expression, algebraic
expression, or equation can be represented in an
infinite number of ways that have the same value.
There is more than one algorithm for each of the
operations with rational numbers. Some strategies for
basic facts and most algorithms for operations with
rational numbers, both mental math and paper and
pencil, use equivalence to transform calculations into
simpler ones.
Numbers can be approximated by numbers that are
close. Numerical calculations can be approximated by
replacing numbers with other numbers with other
numbers that are close and easy to compute mentally.
Some measurements can be approximated using
known referents as the unit in the measurement
process.
Mathematics content and practices can be applied to
solve problems.
How can sums and differences of
whole numbers be estimated?
What are standard procedures for
adding and subtracting whole numbers?
KNOWLEDGE SKILLS STANDARDS
Students will know:
representing numbers and
numerical expressions in
equivalent forms can make
some calculations easy to do
mentally.
there is more than one way to
do a mental calculation.
the standard addition and
subtraction algorithms for
multi-digit numbers break the
calculation into simpler
calculations using place value
starting with the ones, then the
tens, and so on.
there is more than one way to
estimate a sum or difference.
Each estimation technique
gives a way to replace numbers
with other numbers that are
close and easy to compute with
mentally.
Students will be able to:
apply a variety of methods to
add and subtract whole
numbers mentally.
round whole numbers to
estimate sums and
differences.
add numbers to hundreds and
thousands with and without
regrouping.
subtract numbers to
thousands with and without
regrouping.
subtract numbers with zeros
to thousands.
use a picture or diagram to
translate an everyday
situation into a number
sentence or equation.
4.NBT. 3
4.NBT.4
4.OA.3
42
information in a problem can
often be shown using a picture
or diagram and used to
understand and solve the
problem. Some problems can
be solved by writing and
completing a number sentence
or equation.
VOCABULARY RESOURCES/MATERIALS ASSESSMENT/PROJECT
breaking apart
compensation
counting on
Commutative Property of Addition
Associative Property of Addition
Identity Property of Addition
Inverse Operations
place-value blocks
place-value chart
Calendar Math: October
calendar pieces, coin counter,
clock, Daily Depositor, Counting
Tape measurement lesson
Teacher Manual pg.36-38
Formative
Homework
Teacher observation
Differentiated activities
Quizzes
Summative
Topic test
43
ROCHELLE PARK TOWNSHIP SCHOOL DISTRICT
Math 3-5 Curriculum Guide
Grade: 4 Unit: Topic 5- Number Sense: Multiplying by 1-Digit Numbers Time Frame:6 Lessons
ENDURING UNDERSTANDINGS ESSENTIAL QUESTIONS
There is more than one algorithm for each of the
operations with rational numbers. Some
strategies for basic facts and most algorithms for
operations with rational numbers, both mental
and paper and pencil, use equivalence to
transform calculations into simpler ones.
Relationship can be described and
generalizations made for mathematical situations
that have numbers or objects that repeat in
predictable ways. For some relationships,
mathematical expressions and equations can be
used to describe how members of one set are
related to members of a second set.
Numbers can be approximated by numbers that
are close. Numerical calculations can be
approximated by replacing numbers that are
close and easy to compute mentally. Some
measurements can be approximated using known
referents as the unit in the measurement process.
Mathematics content and practices can be
applied to solve problems.
How can some products be found mentally?
How can products be estimated?
KNOWLEDGE SKILLS STANDARDS
Students will know:
making an array with place-value
blocks provides a way to
visualize and find products.
provides a way to visualize and
find products. A 2-digit by 1-
digit multiplication calculation
can be broken into simpler
problems: a basic fact and a 1-
digit number times a multiple of
10. Answers to the simpler
problems can be added to give
the product.
there is more than one way to do
a mental calculation. Techniques
for doing multiplication
calculations mentally involve
changing the numbers or the
expression so the calculation is
easy to do mentally.
Students will be able to:
use arrays to multiply by 10
and 100.
multiply by multiples of 10
and 100.
break apart factors to
multiply.
use compensation to multiply
mentally.
use rounding to estimate
products.
decide if the answer to a
problem is reasonable.
4. NBT.3
4.NBT.5
4.OA.3
44
basic facts and place value
patterns can be used to find
products when one factor is 10 or
100.
rounding is one way to
estimating products.
answers to problems should
always be checked for
reasonableness and this can be
done in different ways. Two
ways are to use estimation and to
check the answer against the
question and conditions in the
problem.
VOCABULARY RESOURCES/MATERIALS ASSESSMENT/PROJECT
partial products
compensation
place-value blocks
1/4-inch grid paper
multiplication recording sheet
rounding recording sheet.
Calendar Math :
October/November calendar
pieces, Counting Tape, Daily
Depositor, measurement lesson
Teacher Manual pg.52-54
Formative
Homework
Teacher observation
Differentiated activities
Quizzes
Summative
Topic test
45
ROCHELLE PARK TOWNSHIP SCHOOL DISTRICT
Math 3-5 Curriculum Guide
Grade: 4 Unit: Topic 6- Multiplying by 1 Digit Numbers Time Frame: 6 Lessons
ENDURING UNDERSTANDINGS ESSENTIAL QUESTIONS
Algorithms: There is more than one algorithm
for each of the operations with rational
numbers. Most algorithm for operations with
rational numbers, both mental math and paper
and pencil, use equivalence to transform
calculations into simpler ones
Equivalence: Any number, measure, numerical
expression, algebraic expression, or equation
can be represented in an infinite number of
ways that have the same value.
Practices, Processes, and Proficiencies:
Mathematics content and practices can be
applied to solve problems.
How can arrays be used to find products?
What is a standard procedure for multiplying
multi digit numbers?
KNOWLEDGE SKILLS STANDARDS
Students will know:
there is an expanded algorithm
for multiplying where numbers
are broken apart using place
value and the parts are use to
find partial products. The partial
products are then added together
to find the product.
the standard multiplication
algorithm is just a shortened way
of recording the information in
the expanded multiplication
algorithm
the standard multiplication
algorithm is a shortcut for the
expanded algorithm. Regrouping
is used rather than showing all
partial products.
the standard algorithm for
multiplying three digit by one
digit numbers is just an extension
to the hundreds place of the
algorithm for multiplying two
digits by one digit numbers.
Students will be able to:
multiply using arrays and an
expanded algorithms.
connect the expanded and
standard algorithms for
multiplication.
multiply 2 digit by 1 digit
numbers.
multiply 3 and 4 digit by 1
digit number
multiply by 1 digit numbers.
evaluate problems for missing
or extra information
4.NBT.5,
4.NBT.3,
4.OA.3
46
the standard algorithm for
multiplication involves breaking
apart numbers using place value,
finding partial products, and then
adding partial products to get the
final product. The process is the
same regardless of the size of the
factors.
different numerical expressions
can have the same value. Or, the
value of one expression can be
less than (or greater than) the
value of the other expression.
Information in a problem can
often be shown using a picture or
diagram and be used to
understand and solve the
problem. Some problems can be
solved by writing and
completing a number sentence or
equation.
VOCABULARY RESOURCES/MATERIALS ASSESSMENT/PROJECT
product
array
factor
rounding
Place-value blocks.
Calendar Math October or Nov.
calendar pieces, counting tape,
Daily Depositor, measurement
lesson Teacher Manual pg.52-54
Exemplar; “A Very Fishy Story”
Formative
Homework
Teacher observation
Differentiated activities
Quizzes
Summative
Topic test
47
ROCHELLE PARK TOWNSHIP SCHOOL DISTRICT
Math 3-5 Curriculum Guide
Grade: 4 Unit: Topic 7- Number Sense: Multiplying by 2-Digit Numbers Time Frame:5 Lessons
ENDURING UNDERSTANDINGS ESSENTIAL QUESTIONS
There is more than one algorithm for each of the
operations with rational numbers. Most
algorithms for operations with rational numbers,
both mental math and paper and pencil, use
equivalence to transform calculations into simpler
ones.
Relationships can be described and
generalizations made for mathematical situations
that have numbers or objects that repeat or are
arranged in predictable ways. For some
relationships, mathematical expressions and
equations can be used to describe how members
of one set are related to members of a second set.
Numbers can be approximated by numbers that
are close. Numerical calculations can be
approximated by replacing numbers with other
numbers that are close and easy to compute
mentally. Some measurements can be
approximated using known referents as the unit in
the measurement process.
Mathematics content and practices can be applied
to solve problems.
How can greater products be found
mentally?
How can greater products be estimated?
KNOWLEDGE SKILLS STANDARDS
Students will know:
making an array with place-
value blocks provides a way
to visualize and find
products.
basic facts and place-value
patterns can be used to
mentally multiply a two-digit
number by a multiple of 10
or 100.
products can be estimated by
replacing numbers with other
numbers that are close and
easy to multiply mentally.
some problems can be
solved by first finding and
solving a sub-problem(s) and
then using that answer(s) to
solve the original problem.
Students will be able to:
multiply 2-digit numbers by
multiples of 10, using arrays.
use mental math to multiply
2-digit numbers.
use rounding to estimate.
use compatible numbers to
estimate.
solve multi-step problems.
4.NBT.3
4.NBT.5
4.OA.3
48
VOCABULARY RESOURCES/MATERIALS ASSESSMENT/PROJECT
compatible numbers
¼-inch grid paper
place-value blocks
colored pencils
colored markers
crayons
¼-inch grid paper transparency
calculators
colored chalk,
Calendar Math: Dec Calendar
pieces, counting tape, clock,
measurement lesson Teacher
Manual pg.66-68
Formative
Homework
Teacher observation
Differentiated activities
Quizzes
Summative
Topic test
49
ROCHELLE PARK TOWNSHIP SCHOOL DISTRICT
Math 3-5 Curriculum Guide
Grade: 4 Unit: Topic 8- Developing Fluency: Multiplying by 2-Digit Numbers
Time Frame: 5 Lessons
ENDURING UNDERSTANDINGS ESSENTIAL QUESTIONS
There is more than one algorithm for each of
the operations with rational numbers, both
mental math and paper and pencil, use
equivalence to transform calculations into
simpler ones.
Mathematics content and practices can be
applied to solve problems.
How can arrays be used to find greater
products?
What is a standard procedure for multiplying
multi-digit numbers?
KNOWLEDGE SKILLS STANDARDS
Students will know:
the expanded algorithm for
multiplying by two-digit numbers is
just an extension of the expanded
algorithm for multiplying with one-
digit numbers.
making an array with place-value
blocks provides a way to visualize and
find products using an expanded
algorithm.
the standard algorithm for multiplying
a two-digit number by a multiple of 10
is just an extension of the algorithm
for multiplying multi-digit numbers by
a one-digit number.
the standards multiplication algorithm
is a shortcut for the expanded
algorithm. Regrouping is used rather
than showing all partial products.
sometimes the answer to one
problem/question is needed to find the
answer to another problem/question.
Students will be able to:
multiply 2-digit factors
with arrays.
multiply using arrays and
an expanded algorithm
with partial products.
multiply 2-digit factors by
multiples of 10.
multiply two 2-digit
numbers.
solve problems that involve
two questions.
4.NBT.5
VOCABULARY RESOURCES/MATERIALS ASSESSMENT/
PROJECT
No New Vocabulary Introduced
¼-inch grid paper
centimeter grid paper
colored pencils
crayons
colored chalk
tape
Calendar Math: Dec Calendar
pieces, counting tape, clock,
measurement lesson Teacher
Manual pg.66-68
Formative
Homework
Teacher observation
Differentiated activities
Quizzes
Summative
Topic test
50
ROCHELLE PARK TOWNSHIP SCHOOL DISTRICT
Math 3-5 Curriculum Guide
Grade:4 Unit: Topic 9- Number Sense Dividing by One Digit Divisors Time Frame:6 Lessons
ENDURING UNDERSTANDINGS ESSENTIAL QUESTIONS
Patterns, Relations, and Functions. Relationships
can be described and generalizations made for
mathematical situations that have numbers or
objects that repeat in predicable ways. For some
relationships, mathematical expressions and
equations can be used to describe how members of
one set are related to members of a second set
Estimation. Numbers can be approximated by
numbers that are close. Numerical calculations can
be approximated by replacing numbers with other
numbers that are close and easy to compute
mentally. Some measurements can be
approximated using known referents as the unit in
the measurement process.
Operation Meanings and Relationships. There are
multiple interpretations of addition, subtraction,
multiplication and division of rational numbers,
and each operation is related to other operations.
Practices, Processes and Proficiencies.
Mathematics content and practices can be applied
to solve problems.
What are different meanings of division?
How can mental math and estimation be
used to divide?
KNOWLEDGE SKILLS STANDARDS
Students will know:
basic math facts and place-
value patterns can be used to
dive multiples of 10 and 100
by one digit numbers.
substituting compatible
numbers is an efficient
technique for estimating
quotients
mentally multiplying by
different powers of 10 will
help you arrive at an estimate
for a quotient of a multi-digit
division problem.
the remainder when dividing
must be less than the divisor.
The nature of the question
asked determines how to
interpret and use the
remainder.
Students will be able to:
use basic facts and patterns
of zero to solve division
problems with 3 digit
dividends and 1 digit
divisors.
use compatible numbers and
rounding to estimate
quotients.
estimate quotients of multi-
digit division problems
using multiplication facts
and place value concepts.
divide whole numbers by 1
digit divisors resulting in
quotients with remainders
use words and models to
represent multiplication and
division problems accurately
4.NBT.6
4.NBT.5
4.OA.2
4.OA.3
51
some real – world problems
involving joining equal
groups, separating equal
groups, or comparison can be
solved using multiplication;
others can be solved using
division.
information in a problem can
often be shown using a
picture or diagram and used
to understand and solve the
problem. Some problems can
be solved by writing and
completing a number
sentence or equation.
draw pictures and write
related number sentences to
solve problems
VOCABULARY RESOURCES/MATERIALS ASSESSMENT/PROJECT
divisor
multiple
factor
quotient
product
division
remainder
two color counters
Calendar Math: January
calendar pieces, counting tape,
Daily Depositor , measurement
lesson Teacher Manual 81-82
Formative
Homework
Teacher observation
Differentiated activities
Quizzes
Summative
Topic test
52
ROCHELLE PARK TOWNSHIP SCHOOL DISTRICT
Math 3-5 Curriculum Guide
Grade: 4 Unit: Topic 10- Developing Fluency: Dividing by 1-Digit Divisors Time Frame: 7 Lessons
ENDURING UNDERSTANDINGS ESSENTIAL QUESTIONS
There are multiple interpretations of addition,
subtraction, multiplication, and division of rational
numbers, and each operation is related to the other
operations.
There is more than one algorithm for each of the
operations with rational numbers. Most algorithms
for operations with rational numbers, both mental
math and paper and pencil, use equivalence to
transform calculations into simpler ones.
Numbers can be approximated by numbers that are
close. Numerical calculations can be approximated
by replacing numbers with other numbers that are
close and easy to compute mentally.
Mathematics content and practices can be applied to
solve problems.
How can repeated subtraction be used to
model division?
What is the standard procedure for
dividing multi-digit numbers?
KNOWLEDGE SKILLS STANDARDS
Students will know:
repeated subtraction can be
modeled and solved using
division.
repeated subtraction
situations can be solved
using a division algorithm
different form the standard
algorithm.
the sharing interpretation
of division can be used to
model the standard division
algorithm.
the standard division
algorithm breaks the
calculation into simpler
calculations using basic
facts, place value, the
relationship between
multiplication and division,
and estimation.
the relationship between
multiplication, division,
and estimation can help
determine the place value
of the largest digit in a
quotient.
Students will be able to:
use repeated subtraction to
model division.
record division as repeated
subtraction.
use place value to understand
the algorithm of long division.
use the standard algorithm to
divide 2-digit by 1-digit
numbers.
use the standard algorithm to
divide 3-digit numbers by 1-
digit numbers.
use the standard algorithm to
divide 3-digit numbers by 1-
digit numbers and properly
decide where to begin
dividing.
estimate and find quotients for
4-digit dividends and 1-digit
divisors.
identify the hidden question in
a multi-step problem. Then
use the answer to that hidden
question to solve the original
problem.
4.NBT.6
4.OA.3
53
some problems can be
solved by first finding and
solving a sub-problem(s)
and then using that
answer(s) to solve the
original problems.
VOCABULARY RESOURCES/MATERIALS ASSESSMENT/PROJECT
No New Vocabulary
Introduced
two-color counters
place-value blocks
blank recording sheet
Calendar Math: January calendar
pieces, counting tape, Daily
Depositor, measurement lesson
Teacher Manual pg.81-82,
Exemplar “Camping”
Formative
Homework
Teacher observation
Differentiated activities
Quizzes
Summative
Topic test
54
ROCHELLE PARK TOWNSHIP SCHOOL DISTRICT
Math 3-5 Curriculum Guide
Grade: 4 Unit: Topic 11- Fraction Equivalence and Ordering Time Frame: 7 Lessons
ENDURING UNDERSTANDINGS ESSENTIAL QUESTIONS
Numbers can be used for different purposes,
and numbers can be classified and represented
in different ways.
Any number, measure, numerical expression,
algebraic expression, or equation can be
represented in an infinite number of ways that
have the same value.
Numbers, expressions, measures, and objects
can be compared and related to other numbers,
expressions, measures, and objects in different
ways.
Mathematics content and practices can be
applied to solve problems.
How can the same fractional amount be named
using symbols in different ways?
How can fractions be compared and ordered?
KNOWLEDGE SKILLS STANDARDS
Students will know:
every counting number is
divisible by 1 and itself, and some
counting numbers are also
divisible by other numbers.
some counting numbers have
exactly two factors; others have
more than two.
the product of any nonzero
number and any other nonzero
number is divisible by each
number and is called a multiple of
each number.
the same fractional amount can be
represented by an infinite set of
different by equivalent fractions.
Equivalent fractions are found by
multiplying or dividing the
numerator and denominator by
the same nonzero number.
if two fractions have the same
denominator, the fraction with the
greater numerator is the greater
fraction. If two fractions have the
same numerator, the fraction with
the lesser denominator is the
greater fraction.
Students will be able to:
learn how to find factors of
a number.
learn to identify prime and
composite numbers.
find multiples of a number.
use models and computation
to find equivalent fractions
using a number line.
use benchmark fractions to
compare fractions with
unlike denominators.
use common denominators
and equivalent fractions to
order fractions with unlike
denominators.
write to explain whether an
answer is correct or not.
4.OA.4
4.NF.1
4NF.2
55
ordering 3 or more numbers is
similar to comparing 2 numbers
because each number must be
compared to the other numbers.
mathematical explanations can be
given using words, pictures,
numbers, or symbols. A good
explanation should be correct,
simple, and easy to understand.
VOCABULARY RESOURCES/MATERIALS ASSESSMENT/PROJECT
fraction
denominator
numerator
benchmark fraction
equivalent fractions
prime number composite number
centimeter grid paper
color tiles
fraction models: strips
strips of paper
number lines
Calendar Math: February
calendar pieces, counting tape,
coin counter, graph,
Formative
Homework
Teacher observation
Differentiated activities
Quizzes
Summative
Topic test
56
ROCHELLE PARK TOWNSHIP SCHOOL DISTRICT
Math 3-5 Curriculum Guide
Grade: 4 Unit: Topic 12- Adding and Subtracting Fractions and Mixed Numbers
with Like Denominators Time Frame: 11 Lessons
ENDURING UNDERSTANDINGS ESSENTIAL QUESTIONS
There is more than algorithm for each of the
operations with rational numbers. Some
strategies for basic facts and most algorithms
for operations with rational numbers, both
mental math and paper and pencil, use
equivalence to transform calculations into
simpler ones.
There are multiple interpretations of addition,
subtraction, multiplication, and division of
rational numbers, and each operation is related
to other operations.
The set of real numbers is infinite and ordered.
Whole numbers, integers, and fractions are real
numbers. Each real number can be associated
with a unique point on the number line.
Any number, measure, numerical expression,
algebraic expression, or equation can be
represented in an infinite number of ways that
have the same value.
Mathematics content and practices can be
applied to solve problems.
What does it mean to add and subtract
fractions and mixed numbers with like
denominators?
What is a standard procedure for adding and
subtracting fractions and mixed numbers with
like denominators?
How can fractions and mixed numbers be
added and subtracted on a number line?
KNOWLEDGE SKILLS STANDARDS
Students will know:
a model can be used to add
two or more fractions
when adding fractions with
like denominators, you are
adding portions of the
same size. So you can add
the numerators without
changing the denominator.
one way to add mixed
numbers is to add the
fractional parts and then
add the whole number
parts. Sometimes whole
numbers or fractions need
to be renamed.
Students will be able to:
use models to add fractions
with like denominators.
use computational procedures
to add fractions with like
denominators and solve
problems.
use models to subtract
fractions with like
denominators.
use computational procedures
to subtract fractions with like
denominators and solve
problems.
use the number line to add and
subtract fractions with like
denominators.
4.NF.3
4.NF.3a
4.NF.3c
4.NF.3d
57
one way to subtract mixed
numbers is to subtract the
whole number parts.
Sometimes whole numbers
or fractions need to be
renamed.
models can be used to
show different ways of
adding and subtracting
mixed numbers.
positive fractions can be
added or subtracted by
locating a fraction on the
number line and then
moving to the right to add
or to the left to subtract.
fractional amounts greater
than 1 can be represented
using a whole number and
a fraction. Whole number
amounts can be represented
as fractions. When the
numerator and
denominator are equal, the
fraction equals 1.
a fractional amount can be
decomposed into a sum of
fractions in more than one
way.
information in a problem
can often be shown using a
diagram and used to solve
the problem. Some
problems can be solved by
writing and completing a
number sentence or
equation.
identify and write mixed
numbers as improper fractions
as mixed numbers.
use models to add and subtract
mixed numbers.
use models and computational
procedures to add mixed
numbers.
use models and computational
procedures to subtract mixed
numbers.
decompose fractions and
represent them as
compositions of fractions in a
variety of ways.
will draw a picture and write
an equation to solve a
problem.
VOCABULARY RESOURCES/MATERIALS ASSESSMENT/PROJECT
mixed number
improper fraction
fraction models: strips and circles
colored pencils
Calendar Math: February calendar
pieces, counting tape, coin
counter, graph,
Formative
Homework
Teacher observation
Differentiated activities
Quizzes
Summative
Topic test
58
ROCHELLE PARK TOWNSHIP SCHOOL DISTRICT
Math 3-5 Curriculum Guide
Grade: 4 Unit: Topic 13- Extending Fraction Concepts Time Frame: 10 Lessons
ENDURING UNDERSTANDINGS ESSENTIAL QUESTIONS
Numbers, expressions, measures, and objects can
be compared and related to other numbers,
expressions, measures, and objects in different
ways.
The set of real numbers is infinite and ordered.
Whole numbers, integers and fractions are real
numbers. Each real number can be associated
with a unique point on a number line.
Any number, measure, numerical expression,
algebraic expression, or equation can be
represented in an infinite number of ways that
have the same value.
The base 10 numeration system is a scheme for
recording numbers using digits 0-9, groups of 10
and place value.
Mathematics content and practices can be applied
to solve problems.
How is decimal numeration related to whole
numbers numeration?
How can decimals be compared and
ordered?
How are fractions and decimals related?
KNOWLEDGE SKILLS STANDARDS
Students will know:
physical representations and
symbols can be used to
develop the understanding that
a/b = a x 1/b.
models can be used to find the
product of a whole number and
a fraction.
to multiply a fraction by a
whole number, one must
multiply the whole number by
the numerator of the fraction
and then divide the product by
the denominator of the
fraction.
the decimal is another name for
a fraction.
each fraction, mixed number,
and decimal can be associated
with a unique point on the
number line.
Students will be able to:
use unit fractions and
multiplication to describe
fractions that are multiples of
unit fractions.
multiply a fraction by a whole
number using models.
multiply a whole number and
a fraction to solve problems.
understand how to write
fractions as decimals and
decimals as fraction.
learn to locate and name
fractions and decimals on a
number line.
understand how to use
equivalent fractions to write
fractions as decimals.
use models and place-value
charts to represent decimals to
the hundredths. They will
read and write decimals in
expanded, standard, and word
form.
4.NF.4a,b,c
4.NF.5
4.NF.6
4.NF.7
4.MD.2
59
every fraction can be
represented by an infinite
number of equivalent fractions,
but each fraction is represented
by the same decimal or an
equivalent form.
decimal numeration is just an
extension of whole number
numeration.
place value can be used to
compare and order numbers.
information in a problem can
be shown with a picture or
diagram and used to
understand and used to
understanding and solve the
problem.
use models and place-value
charts to compare decimals to
hundredths. They will use
greater than and less than
symbols to order decimal
numbers.
Use place-value charts to
read, write, and compare
decimal, tenths and
hundredths using money.
solve problems using the
strategy Draw a Picture.
VOCABULARY RESOURCES/MATERIALS ASSESSMENT/PROJECT
unit fraction
decimal point
hundredth, tenth
fraction strips, decimal models
(Teaching Tool 17), number lines
(Teaching Tool 14), Decimal
Place Value (Teaching Tool 31),
Decimal Place- Value Table
(Teaching Tool 32). Bills and
coins (Teaching Tool 19) place-
value charts (Teaching Tool 10)
rulers (Teaching Tool 20 or 21)
Calendar Math: March calendar
pieces, counting tape, coin
counter, measurement, graph,
Exemplar: ‘Disappearing
Cookies”
Formative
Homework
Teacher observation
Differentiated activities
Quizzes
Summative
Topic test
60
ROCHELLE PARK TOWNSHIP SCHOOL DISTRICT
Math 3-5 Curriculum Guide
Grade: 4 Unit: Topic 14- Measurement Units and Conversions Time Frame: 11 Lessons
ENDURING UNDERSTANDINGS ESSENTIAL QUESTIONS
Some attributes of objects are measureable and
can be quantified using unit amounts.
Some measurements can be approximated
using know referents as the unit in the
measurement process.
Relationships can be described and generalized
made for mathematical situations that have
numbers or objects that repeat in predictable
ways. For some relationships, mathematical
expressions and equations can be used to
describe how members of one set are related to
members of a second set.
Mathematics content and practices can be
applied to solve problems.
What are customary and metric units for
measuring length, capacity, and weight/mass,
and how are they related?
KNOWLEDGE SKILLS STANDARDS
Students will know:
length can be estimated and
measured in different systems
(customary, metric) and using
different units in each system
that are related to each other.
capacity is a measure of the
amount of a liquid a container
can be measured in different
systems (customary, metric) and
using different units in each
system that are related to each
other.
the weight of an object is a
measure of how heavy an object
is.
mass is a measure of the
quantity of matter in an object.
Weight and mass are different
measures.
time can be expressed using
different units that are related to
each other.
length can be estimated in
different measurement systems.
Students will be able to:
estimate and measure length
by choosing the most
appropriate unit of length.
estimate fluently with
customary capacity units
(cups, pints, quarts, and
gallons). They will compare
the relative sized of capacity
measurements.
estimate fluently and
measure with units of
weight.
convert between customary
units.
solve and explain the
answers to each problem in
writing.
estimate and measure length
to the nearest centimeter, and
choose the most appropriate
metric unit for measuring
length.
estimate fluently with
milliliters and liters. They
will measure capacity using
these metric units.
4.MD.1
4.MD.2
61
relationships between
customary measurement units
can be expressed as a function
(e.g., 12 inches to 1 ft or 12 in =
1ft.) Relationships exist that
enable you to convert between
customary units of the same
attribute by multiplying or
dividing.
relationships between metric
units can be expressed as a
function (e.g. 10mm to 1 cm or
10mm =1cm). Relationships
exist that enable you to convert
between metric units of the
same attribute by multiplying or
dividing.
mathematical explanations can
be given using words, pictures,
numbers, or symbols. A good
explanation should be correct,
simple, complete, and easy to
understand.
some problems with the initial
data point unknown can be
solved by starting with the end
result by reversing the steps and
processes to work backward to
find the initial data point.
estimate and measure with
units of mass – grams and
kilograms.
convert between metric
units.
compare several different
units of time and freely
convert from one unit of
time to another.
solve problems that require
finding the original times,
measurements, or quantities
that led to a result that is
given.
VOCABULARY RESOURCES/MATERIALS ASSESSMENT/PROJECT
inch
foot
yard
mile
capacity
weight
ounce
pound
ton
millimeter
centimeter
decimeter
meter
kilometer
milliliter
liter
mass
gram
kilogram
rulers
yardstick
masking tape
examples of a cup, pint, quart,
gallon containers
place-value blocks
tag board
eyedropper
1-liter bottle
Calendar Math: March calendar
pieces, counting tape, coin
counter, graph, measurement
Formative
Homework
Teacher observation
Differentiated activities
Quizzes
Summative
Topic test
62
ROCHELLE PARK TOWNSHIP SCHOOL DISTRICT
Math 3-5 Curriculum Guide
Grade: 4 Unit: Topic 15- Solving Measurement Problems Time Frame: 5 lessons
ENDURING UNDERSTANDINGS ESSENTIAL QUESTIONS
Some attributes of objects are measurable and can
be quantified using unit amounts.
Some questions can be answered by collecting
and analyzing data, and the question to be
answered determines the data that needs to be
collected and how best to collect it. Data can be
represented visually using tables, charts, and
graphs. The type of data determines the best
choice of visual representation.
Mathematics content and practices can be applied
to solve problems.
What do area and perimeter mean and how
can each be found?
How can line plots and other tools help to
solve measurement problems?
KNOWLEDGE SKILLS STANDARDS
Students will know:
some problems can be solved by
applying the formula for the
perimeter of a rectangle or the
formula for the area of a
rectangle.
some measurement problems can
be represented and solved using
models.
making change is often easiest
by counting from the smaller
amount to the larger amount.
some data can be represented
using a line plot and the line plot
can be used to answer certain
questions about the data.
some problems can be solved by
breaking apart or changing the
problem into simpler ones.
Recording information in a table
can help one understand and
solve some problems.
Students will be able to:
use the formulas for the
perimeter and area of
rectangles to solve real-
world problems.
use diagrams to show data
and analyze how the
quantities are related to solve
real-words measurement
problems.
solve real-world problems
that involve money and
giving change by counting.
construct line plots using
given data and use the line
plot to answer questions
about the data set.
break a problem into smaller,
more manageable pieces and
find a pattern to fit.
4MD.2
4MD.3
4MD.4
VOCABULARY RESOURCES/MATERIALS ASSESSMENT/PROJECT
perimeter
area
line plot
bills and coins
recording sheet: Line Plot Data
Calendar Math: April/May
calendar pieces, counting tape,
measurement, Daily Depositor,
measurement,
Exemplar: “Carpet Caper”
“Harvest Dinner”
Formative
Homework
Teacher observation
Differentiated activities
Quizzes
Summative
Topic test
63
ROCHELLE PARK TOWNSHIP SCHOOL DISTRICT
Math 3-5 Curriculum Guide
Grade: 4 Unit: Topic 16- Lines, Angles and Shapes Time Frame: 11 Lessons
ENDURING UNDERSTANDINGS ESSENTIAL QUESTIONS
Geometric Figures: Two- and three-
dimensional objects with or without curved
surfaces can be described, classified and
analyzed by their attributes.
Measurement: Some attributes of objects are
measurable and can be quantified using unit
amounts.
Mathematics content and practices can be
applied to solve problems.
How can lines, angles, and shapes be
described, analyzed and classified?
How are angles measured, added and
subtracted?
KNOWLEDGE SKILLS STANDARDS
Students will know:
point, line and plane are the
core attributes of space
objects, and the real world
situations can be used to think
about these attributes
line segments and rays are sets
of points that describe parts of
lines, shapes, and solids.
Angles are formed by two
intersecting lines or by rays
with a common endpoint and
are classified by size.
two-dimensional or plane
shapes have many properties
that make them different from
one another. Polygons can be
described and classified by
their sides and angles
some shapes can be reflected
across one or more lines
passing through the shape so
the shape folds into itself
exactly.
the measure of an angle
depends upon the fraction of
the circle cut off by its rays
the unit for measuring the size
of an opening of an angle is 1
degree
Students will be able to:
identify and describe points,
lines, and planes
learn geometric terms to
describe parts of lines and
types of angles
use unit angles and fractions
of a circle to find angle
measurement
use a smaller angle to
measure a larger angle by
repeating the unit
measure and draw angles
find unknown angle
measures by adding and
subtracting
learn to identify polygons
learn to identify and classify
triangles
identify quadrilaterals
determine if a plane figure
has line symmetry and if so,
how many lines of
symmetry it has
solve problems by making
and testing generalizations
4.G.1
4.G.2
4.G.3
4.MD.5
4.MD.5a
4.MD.5b
4.MD.6
4.MD.7
64
angle measures can be added
or subtracted
commonalities in attributes of
objects or situations can be
found and used to make
generalizations about
relationships
VOCABULARY RESOURCES/MATERIALS ASSESSMENT/PROJECT
point, line, plane, parallel lines,
intersecting lines, perpendicular
lines, line segment, ray, angle,
right angle, acute angle, obtuse
angle, straight angle, degree, unit
angle, angle measure, protractor,
polygon, side, vertex, triangle,
quadrilateral, pentagon, hexagon,
octagon, equilateral triangle,
isosceles triangle, scalene
triangle, right triangle, acute
triangle, obtuse triangle, rhombus,
trapezoid, parallelogram,
rectangle, square, symmetric, line
of symmetry
centimeter ruler(Teaching Tool
4), dot paper (Teaching Tool 7),
clock face (Teacher Tool 23),
pattern blocks (Teacher Tool
25), recording sheet, blank
protractors (Teaching Tool 34),
rulers (Teaching Tool 21),
polygons (Teaching Tool 25),
Calendar Math: January
calendar pieces, counting tape,
coin counter,
Formative
Homework
Teacher observation
Differentiated activities
Quizzes
Summative
Topic test
65
ROCHELLE PARK TOWNSHIP SCHOOL DISTRICT
Math 3-5 Curriculum Guide
Grade: 5 Unit: Topic 1- Place Value Time Frame: 6 lessons
ENDURING UNDERSTANDINGS ESSENTIAL QUESTIONS
The base ten numeration system is a scheme for
recording numbers using digits 0-9, groups of
ten, and place value.
Numbers can be used for different purposes,
numbers can be classified and represented in
different ways.
Numbers, expressions, measures, and objects
can be compared and related to other numbers,
expressions, measures and objects in different
ways.
Mathematics content and practices can be
applied to solve problems.
How are whole numbers and decimals written,
compared, and ordered?
KNOWLEDGE SKILLS STANDARDS
Students will know:
numbers can be used to tell
how many.( 1-1,1-4)
our number system is
based on groups of ten.
Whenever we get 10 in one
place, we move to the next
greater place value. (1-1,1-
2,1-3,1-4)
place value can be used to
compare and order whole
numbers and decimals.(1-
5)
problems can be solved by
identifying elements that
repeat in a predictable way.
(1-6)
Students will be able to:
write the standard expanded,
and word forms of whole
numbers in the billions and
identify the value of digits in
whole numbers. (1-1)
represent decimals (tenths and
hundredths) as fractions.
Students also represent
fractions with denominators of
10 and 100 as decimals. (1-2)
represent decimals
(thousandths) as fractions and
fractions with denominators of
1,000 as decimals. (1-3)
write decimals in standard
form, word form, and
expanded from though
thousandths. (1-4)
Students compare and order
decimals through thousandths.
(1-5)
look for patterns with decimal-
number sets in order to solve
problems. (1.6)
5.NBT.1
5.NBT.3a
5.NBT.3.b
66
VOCABULARY RESOURCES/MATERIALS ASSESSMENT/PROJECT
digits
value
standard form
expanded form
word form
equivalent decimals
Calendar Math:
Daily Depositor
Counting Tape and Daily Decimal
A Fraction a Day
Exemplar:
Chocolate Chip Cookie Rubric
Interactive Learning Recording
Sheet ( Teaching Tool 4)
Fraction Model Strips ( Teaching
Tool 5)
10x10x10 cube
place value chart (Teaching Tool
6)
Comparing and ordering decimals
( Teaching Tool 7)
Problem Solving: Look for a
Pattern ( Teaching Tool 8)
Optional:
Hand-On Standards : Algebra:
Lessons 1-4
Formative
Daily Common core review
Informal observation
Differentiated activities
Leveled Homework
Center activities
Summative
Topic test
Quarterly benchmark
67
ROCHELLE PARK TOWNSHIP SCHOOL DISTRICT
Math 3-5 Curriculum Guide
Grade: 5 Unit: Topic 2- Adding and Subtracting Decimals Time Frame: 8 lessons
ENDURING UNDERSTANDINGS ESSENTIAL QUESTIONS
There is more than one algorithm for each of
the operations with rational numbers, both
mental math and paper and pencil, use
equivalence to transfer calculations into simpler
ones.
The set of numbers is infinite and ordered.
Whole numbers and decimals are real numbers.
Each real number can be associated with a
unique point on a number line.
Numbers can be approximated by numbers that
are close. Numerical calculations can be
approximated by replacing numbers with other
numbers that are close and easy to compute
mentally.
Relationships can be described and
generalizations made for mathematical
situations that have numbers or objects that
repeat in predictable ways.
Mathematics content and practices can be
applied to solve problems
How can sums and differences of decimals be
estimated?
What are the standard procedures for adding
and subtracting whole numbers and decimals?
KNOWLEDGE SKILLS STANDARDS
Students will know:
there is more than one way to
do a mental calculation.
Techniques for doing
addition or subtraction
calculations mentally involve
changing the numbers so the
calculation is easy to do
mentally. (2-1)
a number line can be used to
round whole numbers and
decimals by making it easy to
see which multiple of 10,
100, etc. a number is closest
to. (2-2)
there is more than one way to
estimate a sum or difference.
Each estimation technique
gives one way to estimate by
replacing numbers with other
numbers that are close and
Students will be able to:
compute sums and
differences mentally using
the Commutative and
Associative Properties of
Addition, compatible
numbers, and compensation.
(2-1)
round whole numbers
though millions and
decimals through
thousandths. (2-2)
use rounding and compatible
numbers to estimate sums
and differences of whole
numbers and decimals (2-3)
will add and subtract
decimals in tenths and
hundredths using models.
(2-4)
5.NBT.4
5.NBT.7
68
easy to compute with
mentally. (2-3)
models and algorithms for
adding and subtracting multi-
digit decimals are just an
extension of models and
algorithms for adding or
subtracting multi-digit whole
numbers. (2-4)
information in a problem can
often be shown using a
diagram and used to solve a
problem. Some problems can
be solved by writing and
completing a number
sentence or equation. (2-5)
adding or subtracting multi-
digit decimals is similar to
adding or subtracting multi-
digit whole numbers. (2-6,2-
7)
some problems can be solved
by first finding and solving a
sub-problem(s) and then
using that answer(s) to solve
the original problem. (2-8)
use pictures and write
equations to help them solve
problems. (2-5)
compute sums of decimals
involving tenths,
hundredths, and
thousandths. (2-6, 2-7)
use multiple steps to solve a
variety of problems. (2-8)
VOCABULARY RESOURCES/MATERIALS ASSESSMENT/PROJECT
Commutative Property
Associative Property
compensation
compatible numbers
rounding
Calendar Math:
Daily Depositor
Counting Tape and Daily
Decimal
A Fraction a Day
Exemplar:
Holiday Fair
Place value materials
Teaching Tool (1, 9, 10, 11, 12)
Problem Solving Recording
Sheet
Optional:
Hands-On Standards: Number
and Operations: Lesson 5,6,13
Formative
Daily Common core review
Informal observation
Differentiated activities
Leveled Homework
Center activities
Summative
Topic test
Quarterly benchmark
69
ROCHELLE PARK TOWNSHIP SCHOOL DISTRICT
Math 3-5 Curriculum Guide
Grade: 5 Unit: Topic 3- Multiplying Whole Numbers Time Frame: 9 lessons
ENDURING UNDERSTANDINGS ESSENTIAL QUESTIONS
For a given set of numbers there are relationships,
that are always true called properties, and these are
the rules that govern arithmetic and algebra.
: Relationships can be described and
generalizations made for mathematical situations
that have numbers or objects that repeat in
predictable ways.
Numbers can be approximated by numbers that are
close. Numerical calculations can be
approximated by replacing numbers with other
numbers that are close and easy to compute with
mentally.
Numbers can be used for different purposes,
numbers can be classified and represented in
different ways.
Each operation with rational numbers has more
than one algorithm. Most algorithms for operations
with rational numbers. Both mental math and
paper and pencil, use equivalence to transform
calculations into simpler ones.
Mathematics content and practices can be applied
to solve problems.
What are the standard procedures, for
estimating and multiplying whole
numbers?
KNOWLEDGE SKILLS STANDARDS
Students will know:
the properties of multiplication
can be used to simplify
computation and to verify
mental math and paper and
pencil algorithms. ( 3-1)
basic facts and place-value
patterns can be used to find
products when one factor is a
multiple of 10 or a multiple of
100. ( 3-2)
there is more than one way to
estimate a product.
each estimation technique
gives one way to estimate by
replacing numbers with other
numbers that are close and
easy to compute with mentally.
(3-3)
Students will be able to:
identify and apply the
commutative Associative,
Associative, Identify, and
Zero Properties of
Multiplication.(3-1)
mentally compute products of
whole numbers using place-
value patterns, and the
properties of multiplication.
(3-2)
use rounding or compatible
numbers to estimate products
of whole numbers. (3-3)
use exponential notation.(3-4)
use the Distributive Property
to simplify expressions and
solve equations.(3-5)
5.NBT.2
5.NBT.5
5.NBT.6
70
some numbers can be
represented using a base
number and an exponent.(3-4)
the properties of multiplication
can be used to simplify
computation and to verify
mental math and paper and
pencil algorithms. ( 3-5 & 3-8)
the standard multiplication
algorithm breaks the
calculation into simpler
calculations using place value
starting with the ones, then the
tens, and so on. (3-6 & 3-7)
information in a problem can
often be shown using a
diagram and used to solve the
problem.(3-9)
some problems can be solved
by writing and completing a
number sentence or equation.
(3-9)
use partial products or the
traditional algorithm to
multiply multi-digit numbers
by a one-digit number. (3-6)
multiply two-digit numbers.
(3-7)
multiply two-digit numbers by
factors with more than two
digits. (3.8)
use diagrams and write
equations to solve problems.
(3.9)
VOCABULARY RESOURCES/MATERIALS ASSESSMENT/PROJECT
Commutative Property of
Multiplication
Associative Property of
Multiplication
Identity Property of Multiplication
Zero Property of Multiplication
Distributive Property
factors
product
multiple
overestimate
underestimate
partial product
base
exponent
power
exponential notation
expanded form
standard form
squared
cubed
Calendar Math:
Daily Depositor
Counting Tape and Daily Decimal
A Fraction a Day
Arrays & Factor Figures
Exemplar:
The Great Pizza Dilemma
Two-color counters ( Teaching
Tool 13)
Exponents (Teaching Tool 14)
Distributive Property ( Teaching
Tool 15 and 18)
Straightedges,
colored pencils,
small grid paper ( Teaching Tool
16)
Problem-solving Recording sheet
( Teaching Tool 1)
Optional:
Hands-On Standards: Algebra:
Lesson 5,6,7
Formative
Daily Common core review
Informal observation
Differentiated activities
Leveled Homework
Center activities
Summative
Topic test
Quarterly benchmark
71
ROCHELLE PARK TOWNSHIP SCHOOL DISTRICT
Math 3-5 Curriculum Guide
Grade: 5 Unit: Topic 4- Dividing by 1-Digit Divisors Time Frame: 7 lessons
ENDURING UNDERSTANDINGS ESSENTIAL QUESTIONS
Relationships can be described and generalizations
made for mathematical situations that have numbers
or objects that repeat in predictable ways. For some
relationships, mathematical expressions and
equations can be used to describe how members of
one set are related to members of a second set.
There is more than one algorithm for each of the
operations with rational numbers. Some strategies
for basic facts and most algorithms for operations
with rational numbers, both mental math and paper
and pencil, use equivalence to transfer calculations
into simpler ones.
Numbers can be approximated by numbers that are
close. Numerical calculations can be approximated
by replacing numbers with other numbers that are
close and easy to compute mentally. Some
measurements can be approximated using known
referents as the unit in the measurement process.
Any number, measure, numerical expression,
algebraic expression, or equation can be represented
in an infinite number of ways that have the same
value.
Mathematics content and practices can be applied to
solve problems
What is the standard procedure for
division and why does it work?
KNOWLEDGE SKILLS STANDARDS
Students will know:
basic facts and place-value
patterns can be used to
divide multiples of 10, 100
and so forth by one-digit
numbers. (4-1)
there is more than one way
to estimate a quotient.
Substitute compatible
numbers is an efficient
technique for estimate
quotients. (4-2)
answers to problems
should always be checked
for reasonableness and this
can be done in different
ways. Two ways are to use
Students will be able to:
find the quotient of a division
problem whose dividend is a
multiple of 10, where division
involves a basic fact. (4-1)
use rounding and compatible
numbers to estimate quotients
of whole numbers. (4-2)
check problems for
reasonableness by using
various methods, including
estimation and checking their
final answer. (4-3)
find quotients using the model
of sharing money. (4-4)
5.NBT.6
72
estimation and to check the
answer against the question
in the problem. (4-3)
the sharing interpretation
of division and money can
be used to model the
standard division
algorithm. (4-4, 4-5, 4-6)
information in a problem
can often be shown using a
diagram and used to solve
the problem. Some
problems can be solved by
writing and completing a
number sentence or
equation. (4-7)
divide three-digit whole
numbers by one-digit divisors.
(4-5)
divide with zeros in the
quotient. (4-6)
use pictures and equations to
help them represent
remainders in a problem. (4-7)
VOCABULARY RESOURCES/MATERIALS ASSESSMENT/PROJECT
dividend
divisor
quotient
Calendar Math:
Daily Depositor
Counting Tape and Daily Decimal
A Fraction a Day
Arrays and Factor Figures
April Graphing
Exemplar:
Making a Fair Decision
Multiplication Table
Bills and Coins
Number cubes
Teaching Tool (1,17, 18)
Problem Solving Recording Sheet
Optional:
Hands-On Standards: Numbers &
Operations: Lesson 7,8,15
Algebra: Lesson 8
Formative
Daily Common core review
Informal observation
Differentiated activities
Leveled Homework
Center activities
Summative
Topic test
Quarterly benchmark
73
ROCHELLE PARK TOWNSHIP SCHOOL DISTRICT
Math 3-5 Curriculum Guide
Grade: 5 Unit: Topic 5- Dividing by 2-digit divisors Time Frame: 8 lessons
ENDURING UNDERSTANDINGS ESSENTIAL QUESTIONS
Relationships can be described and
generalizations made for mathematical
situations that have numbers or objects that
repeat in predictable ways. For some
relationships, mathematical expressions and
equations can be used to describe how
members in one set are related to members of a
second set.
Numbers can be approximated by numbers that
are close. Numerical calculations can be
approximated by replacing numbers with other
numbers that are close and easy to compute
with mentally. Some measurements can be
approximated using known referents as the unit
in the measurement process.
There is more than one algorithm for each of
the operations with rational numbers. Most
algorithms for operations with rational
numbers, both mental math and paper and
pencil, use equivalence to transform
calculations into simpler ones.
Doing mathematics involves a variety of
processes including problem solving,
reasoning, communicating, connecting, and
representing.
What is the standard procedure for dividing
with two-digit divisors?
KNOWLEDGE SKILLS STANDARDS
Students will know:
using basic facts and
patterns can be helpful in
dividing by multiples of 10
( 5-1)
there was more than one
way to estimate a quotient.
Substituting compatible
numbers is an efficient
technique for estimating
quotients. (5.2, 5.7)
using area models and
arrays can help understand
the algorithm for dividing
by 2-digit divisors. ( 5-3)
Students will be able to:
find the quotients of division
problems whose dividends and
divisors are multiples of 10,
where the division involves a
basic fact.(5-1)
use estimation to find
approximation solutions to
division problems with two-
digit divisors using compatible
numbers. (5-2)
use arrays and area models to
model division. (5-3)
find quotients with a two-digit
divisor that is a multiple of ten.
(5-4)
5.NBT.6
74
dividing by 2 digit divisors
is just an extension of the
steps for dividing with 1-
digit divisors. Estimation
and place value can help
determine the placement of
digits in the quotient. (5-
4;5-5;5-6)
some real-world quantities
have a mathematical
relationship; the value of
one quantity cab be found
if you know the value of
the other quantity. Patterns
can sometimes be used to
identify the relationship
between quantities. (5.5)
dividing with multi-digit is
just an extension of the
steps for dividing with 1
and 2-digit divisors,
Estimation and place value
can help determine the
placement of digits in the
quotient.(5-7)
some problems can be
solved by writing and
completing a number
sentence or equation. (5-8)
find one-digit quotients where
the divisor is a two-digit
number. (5-5)
divide a three-digit number by a
two-digit number to find a two-
digit quotient (5-6)
solve problems involving
division of numbers with 4 or 5
digits by 2-digit divisors with an
estimate, or by using a
calculator when the exact
answer is needed. . (5-7)
determine which information is
missing identify extraneous
information in problems. (5-8)
VOCABULARY RESOURCES/MATERIALS ASSESSMENT/PROJECT
no new vocabulary introduced
Calendar Math:
Daily Depositor
Counting Tape and Daily Decimal
A Fraction a Day
Exemplar:
Fish Dilemma
grid paper
calculator
Problem Solving Recording Sheet
( Teaching Tool 1)
Optional:
Hands-On Standards: Number and
Operations: Lesson 18,19
Formative
Daily Common core review
Informal observation
Differentiated activities
Leveled Homework
Center activities
Summative
Topic test
Quarterly benchmark
75
ROCHELLE PARK TOWNSHIP SCHOOL DISTRICT
Math 3-5 Curriculum Guide
Grade: 5 Unit: Topic 6- Multiplying Decimals Time Frame: 7 lessons
ENDURING UNDERSTANDINGS ESSENTIAL QUESTIONS
Relationships can be described and generalizations
made for mathematical situations that have
numbers or objects that repeat in predictable ways.
For some relationships, mathematical expressions
and equations can be used to describe how
members in one set are related to members of a
second set.
Numbers can be approximated by numbers that are
close. Numerical calculations can be
approximated by replacing numbers with other
numbers that are close and easy to compute with
mentally. Some measurements can be
approximated using known referents as the unit in
the measurement process.
There is more than one algorithm for each of the
operations with rational numbers. Most algorithms
for operations with rational numbers, both mental
math and paper and pencil, use equivalence to
transform calculations into simpler ones.
Mathematics content and practices can be applied
to solve problems.
What are the standard procedures for
estimating and finding products involving
decimals?
KNOWLEDGE SKILLS STANDARDS
Students will know:
patterns can be used to mentally
multiply decimals by 10, 100,
and 1,000. ( 6-1)
rounding and compatible
numbers can be used to estimate
the product of a whole number
and a decimal. (6-2)
compare each factor to 1 as a
way of determining if you have
placed the decimal point
reasonably.
( 6-3)
the standard multiplication
algorithm involving decimals is
an extension of the standard
algorithm for multiplying whole
numbers. (6-4)
Students will be able to:
mentally multiply decimals by
10,100, and 1,000.(6-1)
use rounding and compatible
numbers to estimate products
of whole numbers and
decimals. Students also
identify estimates as
overestimates or
underestimates. (6-2)
will use number sense and
place value to multiply
decimals. (6-3)
find products of whole
numbers and decimals to ten
thousandths. (6-4)
use a standard algorithm to
multiply a whole number and
a decimal. (6-5)
5.NBT.2
5.NBT.7
76
the steps for multiplying whole
numbers by decimals are similar
to the steps for multiplying two
whole numbers. Place value
determines the placement of the
decimal point in a product.. (6.5)
steps for multiplying decimals
are similar to steps for
multiplying whole numbers.
Place value determines the
placement of the decimal point in
a product. The product of two
decimals less that one is less than
either factor..(6.6)
some problems can be solved by
first finding and solving a sub-
problem(s) and then using that
answer to solve the original
problem .(6.7)
will use the standard
algorithm to multiply
decimals by decimals (6-6)
find the hidden question or
questions to solve multiple-
step problems. (6-7)
VOCABULARY RESOURCES/MATERIALS ASSESSMENT/PROJECT
no new vocabulary introduced
Calendar Math:
Daily Depositor
Counting Tape and Daily
Decimal
A Fraction a Day
Graph and Measurement Nov.
Whole Day Celebration Feb.
Exemplar:
M&M Cookie Combos
Multiplying decimals by
10,100,and 1,000 (Teaching Tool
19)
Estimating the product of a
decimal and a whole number
(Teaching Tool 20)
Decimal Grids (Teaching Tool
21)
Colored pencils
Multiplying a whole number and
a decimal ( Teaching Tool 41)
Multiplying Two Decimals
(Teaching Tool 22)
Optional:
Hands-On Standards: Number
and Operations: Lesson 7
Formative
Daily Common core review
Informal observation
Differentiated activities
Leveled Homework
Center activities
Summative
Topic test
Quarterly benchmark
77
ROCHELLE PARK TOWNSHIP SCHOOL DISTRICT
Math 3-5 Curriculum Guide
Grade: 5 Unit: Topic 7- Dividing Decimals Time Frame: 7 lessons
ENDURING UNDERSTANDINGS ESSENTIAL QUESTIONS
The base-ten numeration system is a scheme
for recording numbers using digits 0-9, groups
of 10, and place value.
Numbers can be approximated by numbers that
are close. Numerical calculations can be
approximated by replacing numbers with other
numbers that are close and easy to compute
mentally. Some measurements can be
approximated using known referents as the unit
in the measurement process.
Numbers, expressions, measures, and objects
can be compared and related to other numbers,
expressions, measures and objects in different
ways.
There is more than one algorithm for each of
the operations with rational numbers. Some
strategies for basic facts and most algorithms
for operations with rational mumbers, both
mental math and paper and pencil, use
equivalence to transfer calculations into simpler
ones.
Any number, measure, numerical expression,
algebraic expression, or equation can be
represented in an infinite number of ways that
have the same value.
Mathematics content and practices can be
applied to solve problems.
What are the standard procedures for
estimating and finding quotients involving
decimals?
KNOWLEDGE SKILLS STANDARDS
Students will know:
place-value patterns can be
used to mentally divide
decimals by 10,100, or 1000
(7-1)
estimating quotients for whole
number divisors and dividends
can be applied to calculations
with decimal dividends and
divisors. Substitute compatible
numbers can be used in most
cases. (7-2)
Students will be able to:
mentally divide decimals by
10, 100, or 1000. (7-1)
will learn to estimate
quotients involving decimals,
and to use reasoning to
understand how the size of
the quotient relates to the
dividend and divisor. (7-2)
will learn how to use
reasoning to correctly place
the decimal point in a
quotient. (7-3)
5.NBT.6
78
the location of decimal points
in decimal division
calculations can sometimes be
decided by reasoning about the
relative size of the given
numbers. (7-3)
the standard division algorithm
involving decimals is an
extension of the standard
algorithm for dividing whole
numbers. (7-4)
a number divided by a decimal
can be represented as an
equivalent calculation using
place value to change the
divisor to a whole number. (7-
5, 7-6)
some problems can be solved
by first finding and solving a
sub-problem(s) and then using
that answer(s) to solve the
original problem. (7-7)
find quotients where the
dividend and/or the quotient
is a decimal. (7-4)
divide whole numbers by
decimals. (7-5)
find quotients of two
decimals. (7-6)
use multiple steps to solve a
variety of problems. (7-7)
VOCABULARY RESOURCES/MATERIALS ASSESSMENT/PROJECT
no new vocabulary introduced
Calendar Math:
Daily Depositor
Counting Tape and Daily
Decimal
A Fraction a Day
Graph and Measurement Nov.
Whole Day Celebration Feb.
Exemplar:
Busy Day
Calculator
Decimal Models
Decimal Grids
Problem Solving Recording
Sheet
Optional:
Hands-On Standards: Number
and Operations: Lesson 17
Formative
Daily Common core review
Informal observation
Differentiated activities
Leveled Homework
Center activities
Summative
Topic test
Quarterly benchmark
79
ROCHELLE PARK TOWNSHIP SCHOOL DISTRICT
Math 3-5 Curriculum Guide
Grade: 5 Unit: Topic 8- Numerical Expressions, Patterns
and Relationships Time Frame: 9 lessons
ENDURING UNDERSTANDINGS ESSENTIAL QUESTIONS
Relationships can be described and generalizations
made for mathematical situations that have
numbers or objects that repeat in predictable ways.
For some relationships, mathematical expressions
and equations can be used to describe how
members in one set are related to members of a
second set.
For a given set of numbers, there are relationships
that are always true, called properties, and these
are the rules that govern arithmetic and algebra.
Any number, measure, numerical expression.
Algebraic expression, or equation can be
represented in an infinite number of ways that have
the same value.
Mathematical situations and structures can be
translated and represented abstractly using
variables, expressions, and equations.
Rules of arithmetic and algebra can be used
together with notions of equivalence to transform
equations so solutions can be found.
Mathematics content and practices can be applied
to solve problems.
How are the values of an algebraic
expression and a numerical expression
found?
KNOWLEDGE SKILLS STANDARDS
Students will know:
some mathematical phrases can
be represented using a variable in
an algebraic expression.(8-1)
there is an agreed upon order for
which operations in a numerical
expression are performed. (8-2)
to simplify a numerical
expression, first compute within
parenthesis. Second, evaluate all
terms with exponents.Then do
any multiplication and division
calculations from left to right
followed by any addition and
subtraction calculations from left
to right
( 8-3; 8-4)
Students will be able to:
write numerical expressions
with variables to represent
relations expressed
verbally.(8-1)
use given values for
variables to evaluate
numerical or algebraic
expressions with three or
more numbers and two or
more operations. (8-2)
use the order of operations
to simplify and solve basic
algebraic expressions. (8-3)
use the order of operations to
evaluate expressions with
whole numbers decimals.
5.OA.1
5.OA.2
5.OA.3
80
patterns can sometimes be used to
identify a relationship between
two quantities. Some real-world
quantities have a mathematical
relationship; the value of one
quantity can be found if you know
the value of the other quantity.
(8-5;8-6)
patterns that repeat in predictable
ways may be used to identify
relationships. (8-7)
some mathematical phrases can
be represented using a variable in
an algebraic expression.(8-8)
some problems can be solved by
using objects to act out the actions
in the problem. Some problems
can be solved by reasoning about
the conditions in the
problem.(8.9)
(8-4)
study completed tables to
determine a rule and write an
expression. (8-5)
study completed tables to
determine a rule and write an
expression. (8-6)
extend patterns in a table
using given rules and will
then look for the relationship
between corresponding terms
in the sequences. (8-7)
translate words into algebraic
expressions. (8.8)
solve problems by showing
how to act our the problem.
Students also use
information given in the
problem to draw conclusions.
(8.9
VOCABULARY RESOURCES/MATERIALS ASSESSMENT/PROJECT
variable
algebraic expression
corresponding
sequence
term
order of operations
Calendar Math:
Daily Depositor
Counting Tape and Daily
Decimal
A Fraction a Day
Sept. calendar
Jan. graphing
Exemplar:
Party Seating
counters
Place-value blocks (Teaching
Tool 24)
Optional:
Hands-On Standards: Algebra:
Lessons 9
Formative
Daily Common core review
Informal observation
Differentiated activities
Leveled Homework
Center activities
Summative
Topic test
Quarterly benchmark
81
ROCHELLE PARK TOWNSHIP SCHOOL DISTRICT
Math 3-5 Curriculum Guide
Grade: 5 Unit: Topic 9- Adding and Subtracting Fractions Time Frame: 10 lessons
ENDURING UNDERSTANDINGS ESSENTIAL QUESTIONS
Any number, measure, numerical expression,
algebraic expression, or equation can be represented
in an infinite number of ways that have the same
value.
The set of numbers is infinite and ordered. Whole
numbers and decimals are real numbers. Each real
number can be associated with a unique point on a
number line.
Numbers can be used for different purposes, and
numbers can be classified and represented in
different ways.
There is more than one algorithm for each of the
operations with rational numbers. Some strategies
for basic facts and most algorithms for operations
with rational numbers, both mental math and paper
and pencil, use equivalence to transfer calculations
into simpler ones.
Numbers can be approximated by numbers that are
close. Numerical calculations can be approximated
by replacing numbers with other numbers that are
close and easy to compute mentally. Some
measurements can be approximated using known
referents as the unit in the measurement process.
Mathematics content and practices can be applied to
solve problems.
What does it mean to add and subtract
fractions with unlike denominators?
What is a standard procedure for
adding and subtracting fractions with
unlike denominators?
KNOWLEDGE SKILLS STANDARDS
Students will know:
the same fractional amount can be
represented by an infinite set of
different but equivalent fractions.
Equivalent fractions are found by
multiplying or dividing the
numerator and the denominator by
the same nonzero number. (9-1)
a fraction is in simplest form when
1 is the only common factor of the
numerator and denominator (9-2)
mathematical explanations can be
given using words, pictures,
numbers, or symbols. A good
explanation should be correct,
simple, complete and easy to
understand. (9-3)
Students will be able to:
write equivalent fractions.
(9-1)
identify fractions that are
in simplest form and find
the simplest form of a
fraction. (9-2)
explain how they estimated
fractional amounts of
objects. (9-3)
will use a number line to
estimate sums and
differences of fractions. (9-
4)
5.NF.1
5.NF.2
82
a number line can be used to
determine the nearest half or whole
a fraction is closest to. (9-4)
all non-zero whole numbers have
common multiples, including at
least one. Sometimes the least
common multiple of two numbers is
one of the numbers (9-5)
fractions with unlike denominators
can be added or subtracted by
replacing fractions with equivalent
fractions with like denominators.
The product of the denominators of
two fractions is a common
denominator of both (9-6, 9-7, 9-8,
9-9)
information in a problem can often
be shown using a diagram and used
to solve a problem. Some problems
can be solved by writing and
completing a number sequence or
equation.(9-10)
will determine the least
common multiples and
least common multiples of
numbers. (9-5)
will find common
denominators for fractions
with unlike denominators.
(9-6)
will use models and
computational procedures
to add fractions with unlike
denominators. (9-7)
will use models and
computational procedures
to subtract fractions with
unlike denominators. (9-8)
will solve problems
involving addition and
subtraction of fractions. (9-
9)
will draw a picture and
write an equation to solve a
problem (9-10)
VOCABULARY RESOURCES/MATERIALS ASSESSMENT/PROJECT
Equivalent fractions
Simplest form
Benchmark fraction
Common multiple
Least common multiple (LCM)
Common denominator
Least common denominator (LCD)
Calendar Math:
Daily Depositor
Counting Tape and Daily
Decimal
A Fraction a Day
Sept & Mar. graphing
Jan. measurement
Exemplar:
Disappearing Cookies
Calculator
Fraction Models
Number lines
(Teaching Tool 5, 25, 26, 28)
Hundred Charts
Problem Solving Recording
Sheet
Optional:
Hands-On Standards: Number
and Operations: Lesson 1,2,3,
8,9,10
Formative
Daily Common core review
Informal observation
Differentiated activities
Leveled Homework
Center activities
Summative
Topic test
Quarterly benchmark
83
ROCHELLE PARK TOWNSHIP SCHOOL DISTRICT
Math 3-5 Curriculum Guide
Grade: 5 Unit: Topic 10- Adding and Subtracting Mixed Numbers Time Frame: 7 lessons
ENDURING UNDERSTANDINGS ESSENTIAL QUESTIONS
Any number, measure, numerical expression.
Algebraic expression, or equation can be
represented in an infinite number of ways that
have the same value.
There are multiple interpretations of addition,
subtraction, multiplication, and division of
rational numbers, and each operation is related
to other operations.
Numbers can be approximated by numbers that
are close. Numerical calculations can be
approximated by replacing numbers with other
numbers that are close and easy to compute
with.
The set of real numbers is infinite and ordered.
Whole numbers, fractions, and mixed numbers
are real numbers. Each real number can be
associated with a unique point on the number
line. .
Mathematics content and practices can be
applied to solve problems.
What does it mean to add and subtract mixed
numbers?
What is a standard procedure for adding and
subtracting mixed numbers
KNOWLEDGE SKILLS STANDARDS
Students will know:
fractional amounts greater than
1 can be represented using a
whole number and a fraction.
Whole number amounts can be
represented as fractions. When
the numerator and
denominator are equal, the
fraction equals 1. Fractions
greater than 1 can be named
using a whole number and a
fraction of an improper
fraction.(10-1)
sums and differences of mixed
numbers can be estimated by
rounding the mixed number to
the nearest whole number. .
(10-2)
Students will be able to:
write improper fractions as
mixed numbers and mixed
numbers as improper fractions
and they place them on a
number line. (10-1)
estimate sums and differences
of fractions and mixed
numbers by rounding to the
nearest whole number.(10-2)
will use models to add and
subtract mixed numbers. (10-
3)
will use models and
computational procedures to
add mixed numbers. (10-4)
will use models and
computational procedures to
subtract mixed numbers. (10-5)
5.NF.1
5.NF.2
84
models can be used to show
different ways of adding and
subtracting mixed numbers.
( 10-3)
one way to add mixed numbers
is to utilize a number line to
model and find common
denominators. Sometimes
whole numbers or fractions
need to be renamed. (10.4)
one way to subtract mixed
numbers is to utilize a number
line to model and find
common denominator.
Sometimes whole numbers or
fractions need to be renamed..
(10-5)
there is more than one way to
add or subtract mixed
numbers.(10-6)
information in a problem can
often be shown with a picture
or diagram, which can be used
to understand and solve the
problem. Some problems can
be solved by writing and
completing a number sentence
or equation.(10-7)
will solve more complex
problems involving the
addition and subtraction of
mixed numbers. (10-6)
draw a picture and write an
equation in order to accurately
solve a problem. (10-7)
VOCABULARY RESOURCES/MATERIALS ASSESSMENT/PROJECT
improper fraction
mixed number
proper fraction
Calendar Math:
Daily Depositor
Counting Tape and Daily Decimal
A Fraction a Day
Feb. measurement
Exemplar:
Galaxy Araca
fractional models (Teaching Tool
5)
Problem Solving recording sheet
( Teaching Tool 1)
Optional:
Hands-On Standards: Number and
Operations: Lesson 11,12
Formative
Daily Common core review
Informal observation
Differentiated activities
Leveled Homework
Center activities
Summative
Topic test
Quarterly benchmark
85
ROCHELLE PARK TOWNSHIP SCHOOL DISTRICT
Math 3-5 Curriculum Guide
Grade: 5 Unit: Topic 11- Multiplying and Dividing Fractions and Mixed Numbers
Time Frame: 11 lessons
ENDURING UNDERSTANDINGS ESSENTIAL QUESTIONS
Any number, measure, numerical expression.
Algebraic expression, or equation can be
represented in an infinite number of ways that
have the same value.
There are multiple interpretations of addition,
subtraction, multiplication, and division of
rational numbers, and each operation is related
to other operations.
Numbers can be approximated by numbers that
are close. Numerical calculations can be
approximated by replacing numbers with other
numbers that are close and easy to compute
with.
There is more than one algorithm for each of
the operations with rational numbers. Most
algorithms for operations with rational
numbers, both mental math and paper and
pencil, use equivalence to transform
calculations into simpler ones.
Mathematics content and practices can be
applied to solve problems.
What are standard procedures for estimating
and finding products and quotients of fractions
and mixed numbers?
KNOWLEDGE SKILLS STANDARDS
Students will know:
a fraction describes the division of
a whole into equal parts, and it can
be interpreted in more than one
way depending on the whole to be
divided. .(11-1)
the product of a whole number and
a fraction can be interpreted in
different ways. One interpretation
is repeated addition. Multiplying a
whole number by a fraction
involves division as well as
multiplication. The product is a
fraction of the whole number. (11-
2)
rounding and compatible numbers
can be used to estimate the product
of fractions or mixed numbers.
( 11-3)
Students will be able to:
write improper fractions as
mixed numbers and mixed
numbers as improper
fractions and they place
them on a number line. (10-
1)
estimate sums and
differences of fractions and
mixed numbers by rounding
to the nearest whole
number.(10-2)
will use models to add and
subtract mixed numbers.
(10-3)
will use models and
computational procedures to
add mixed numbers. (10-4)
5.NF.1
5.NF.2
86
a unit square can be used to show
the area of meaning fraction
multiplication. When you multiply
two fractions that are both less
than 1, the product is smaller than
either fraction. To multiply
fractions, write the product of the
denominators. (11-4;11-5))
one way to find the product of
mixed numbers is to change the
calculation to an equivalent one
involving improper fractions. (11-
6)
the relative size of factors can be
used to determine the relative size
of the product.(11-6)
the relative size of the factos can
be used to determine the relative
size of the product.(11-7)
some problems can be solved by
first finding and solving a sub-
problem(s) and then using that
answer(s) to solve the original
problem.( 11-8)
one way to find the quotient of a
whole number divided by a
fraction is to multiply the whole
number by the reciprocal of the
fraction (11-9)
the inverse relationship between
multiplication and division can be
used to divide with fractions.(11-
10)
information in a problem can often
be shown with a a diagram and
used to solve the problem. Some
problems can be solved by writing
and completing a number sentence
or equation. (11-11)
will use models and
computational procedures to
subtract mixed numbers.
(10-5)
will solve more complex
problems involving the
addition and subtraction of
mixed numbers. (10-6)
draw a picture and write an
equation in order to
accurately solve a problem.
(10-7)
87
VOCABULARY RESOURCES/MATERIALS ASSESSMENT/PROJECT
improper fraction
mixed number
proper fraction
Calendar Math:
Daily Depositor
Counting Tape and Daily
Decimal
A Fraction a Day
Feb. measurement
Exemplar:
Deluxe Birthday Cake
fractional models ( Teaching
Tool 5)
Problem Solving recording
sheet
( Teaching Tool 1)
Optional:
Hands-On Standards: Number
and Operations: Lesson 14,16
Formative
Daily Common core review
Informal observation
Differentiated activities
Leveled Homework
Center activities
Summative
Topic test
Quarterly benchmark
88
ROCHELLE PARK TOWNSHIP SCHOOL DISTRICT
Math 3-5 Curriculum Guide
Grade: 5 Unit: Topic 12- Volume of Solids Time Frame: 7 Lessons
ENDURING UNDERSTANDINGS ESSENTIAL QUESTIONS
Two- and three-dimensional objects with or
without curved surfaces can be described,
classified, and analyzed by their attributes. An
objects location in space can be described
quantitatively.
Mathematics content and practices can be
applied to solve problems.
How can three-dimensional shapes be
represented and analyzed?
What does the volume of a rectangular prism
mean and how can it be found?
KNOWLEDGE SKILLS STANDARDS
Students will know:
three-dimensional or solid figures
have length, width, and height.
Many can be described, classified,
and analyzed by their faces, edges,
and vertices. Many everyday
objects closely approximate
standard geometric solids. (12-1)
the shape of a solid can sometimes
be determined by analyzing
different views of the solid. (12-2)
some problems can be solved by
breaking apart or changing the
problem into simpler ones, solving
simpler ones, and using those
solutions to solve the original
problem (12-3)
volume is a measure of the amount
of space inside a solid figure.
Volume can be measured by
counting the number of cubic units
needed to fill a three –dimensional
object (12-4, 12-5)
the volume of some objects can be
found by breaking apart the object
of into other objects from which the
volume can be found. (12-6)
some problems can be solved by
using objects to act out the action in
the problem. Some problems can be
solved by reasoning about
conditions in the problem. (12-7)
Students will be able to:
will identify three
dimensional shapes
according to faces, edges,
and vertices. (12-1)
identify different views of
a solid. (12-2)
will use objects to act out
and break apart problems
into simpler ones in order
to reach a solution. (12-3)
will determine the volume
of regular solids. (12-4)
will count cubic units and
use formulas to find the
volume of rectangular
prisms. (12-5)
will find volumes of
irregular solids. (12-6)
will use objects and
reasoning to find volumes
of solid figures. (12-7)
5.MD.3
5.MD.3.a
5.MD.3.b
5.MD.4
5.MD.5
5.MD.5.a
5.MD.5.b
5.MD.5.c
89
VOCABULARY RESOURCES/MATERIALS ASSESSMENT/PROJECT
three-dimensional shape
cube
edge
face
vertex (pl: vertices)
cone
cylinder
prism
pyramid
volume
cubic unit
Calendar Math:
Daily Depositor
Counting Tape and Daily
Decimal
calendar for Sept., Oct., Nov.,
Jan, Feb,. Mar., Apr.
Whole day celebration Feb.
Measurement March
Exemplar:
Carpet Caper
Power Solids
Centimeter Cubes
Centimeter
Grid Paper
Unit Cubes
Folders
(Teaching Tool 1, 31, 32)
Optional:
Hands-On Standards:
Geometry: Lesson 16
Measurement: Lesson 5-9
Formative
Daily Common core review
Informal observation
Differentiated activities
Leveled Homework
Center activities
Summative
Topic test
Quarterly benchmark
90
ROCHELLE PARK TOWNSHIP SCHOOL DISTRICT
Math 3-5 Curriculum Guide
Grade: 5 Unit: Topic 13- Units of Measure Time Frame: 7 lessons
ENDURING UNDERSTANDINGS ESSENTIAL QUESTIONS
Some attributes of objects are measureable and
can be quantified using unit amounts.
Mathematics content and practices can be
applied to solve problems.
What are customary measurement units and
how are they related?
What are metric measurement units and how
are they related?
KNOWLEDGE SKILLS STANDARDS
Students will know:
relationships between measurement
units of the same length can be
expressed as an equation (e.g. 1
ft=12 in; 1 m = 100cm). (13-1)(13-
4)
relationships exist that enable you
to convert between units of length
by multiplying or dividing. (13-1)
(13-4)
relationships between measurement
units of the same capacity can be
expressed as a ratio (e.g. 1 qt. to 2
pt or 1 qt = 2 pt; 1 L to 1,000 mL or
1 L =1,000 mL) (13-2) (13-5)
relationships exist that enable you
to convert between units of capacity
by multiplying and dividing.
( 13-2)( 13-5)
relationships between measurement
units of weight/mass can be
expressed as a ratio (e.g 1 lb to 16
oz or 1 lb. = 16 oz; 1 kg to 1,000 g
or 1 kg= 1,000 g). (13-3) (13-6)
relationships exist that enable you
to convert between units of weight
or mass by multiplying or dividing.
(13-3) (13-6)
some problems can be solved by
first finding and solving a sub-
problem(s) and then using that
answer(s) to solve the original
problem.( 13-7)
Students will be able to:
convert from one unit of
customary length (inches,
feel, yards, and miles) to
another. (13-1)
convert from one unit of
customary capacity
(gallons, quarts, pints,
cups, and fluid ounces) to
another. (13-2)
convert from one
customary unit of weight
(ounces, pounds, and tons)
to another and apply this
skill to compare quantities.
( 13-3)
convert one metric unit of
length (kilometer, meter,
centimeter, and millimeter)
into another. (13-4)
convert from one metric
unit of capacity by
multiplying and dividing.
(13-5)
convert from one metric
unit of mass (milligrams,
grams, and kilograms) to
another. (13-6)
find the hidden question or
questions to solve multiple-
step problems. (13-7)
5.MD.1
91
VOCABULARY RESOURCES/MATERIALS ASSESSMENT/PROJECT
no new vocabulary introduced
Calendar Math:
Daily Depositor
Counting Tape and Daily
Decimal
A Fraction a Day
Measurement Jan. , Feb., April
Exemplar:
Ant in the Wall
Inch and yard rulers ( or
Teaching Tool 33)
2 different colored markers
Strips of paper 1 yard long( 1
per group)
Liquid measuring cup
Empty containers ( pint, quart,
½ gallon, and gallon size)
Water
Centimeter rulers marked in
millimeters ( Teaching Tool
35) (per group)
Problem solving recording
sheet
Optional:
Hands-On Standards:
Measurement: Lessons 1-4
Formative
Daily Common core review
Informal observation
Differentiated activities
Leveled Homework
Center activities
Summative
Topic test
Quarterly benchmark
92
ROCHELLE PARK TOWNSHIP SCHOOL DISTRICT
Math 3-5 Curriculum Guide
Grade: 5 Unit: Topic 14- Data Time Frame: 5 lessons
ENDURING UNDERSTANDINGS ESSENTIAL QUESTIONS
Some questions can be answered by collecting
and analyzing data, and the question to be
answered determines the data that needs to be
collected and how best to collect it. Data can
be represented visually using tables, charts, and
graphs. The type of data determines the best
choice of visual representation.
Mathematics content and practices can be
applied to solve problems.
How can line plots be used to represent data
and answer questions?
How can numbers be used to describe certain
data sets?
KNOWLEDGE SKILLS STANDARDS
Students will know:
each type of graph is most
appropriate for certain
kinds of data, A line plot
organized data on a
number line and is useful
for showing visually how a
set of data is distributed.
(14-1)(14-3)
some questions can be
answered using a survey.
An appropriate selected
sample can be used to
make predictions about a
population. Sample size is
one factor that determines
how close data from the
sample will mirror the
population. (14-2) (14-4)
mathematical explanations
can be given using words,
pictures, numbers, or
symbols. A good
explanation should be
correct, simple, complete,
and easy to understand.
(14-5)
Students will be able to:
learn and understand how to
draw line plots, interpret
points, and recognize outliers.
(14-1)
collect data and record data in
frequency tables and line
plots. Students then interpret
the results. (14-2)
learn how to make a line plot
from data in a frequency table.
(14-3)
how to use the information in
a line plot to solve problems
involving the data. (14-4)
write math explanation that
relate to line graphs that show
data changing over time. (14-
5)
5.MD.2
93
VOCABULARY RESOURCES/MATERIALS ASSESSMENT/PROJECT
data
frequency table
line plot
outlier
sample
survey
Calendar Math:
Daily Depositor
Counting Tape and Daily Decimal
A Fraction a Day
Graphing Sept., Nov., Jan., Mar.
& April
Exemplar:
Checkerboard Investigation
Problem-solving: Look for a
pattern ( Teaching Tool 8,
optional)
Optional:
Hands-On Standards: Data
Analysis: Lessons 1-8
Formative
Daily Common core review
Informal observation
Differentiated activities
Leveled Homework
Center activities
Summative
Topic test
Quarterly benchmark
94
ROCHELLE PARK TOWNSHIP SCHOOL DISTRICT
Math 3-5 Curriculum Guide
Grade: 5 Unit: Topic 15- Classifying Plane Figures Time Frame: 6 lessons
ENDURING UNDERSTANDINGS ESSENTIAL QUESTIONS
Two and three-dimensional objects with or without
curved surfaces can be described, classified, and
analyzed by their attributes. An object’s location
can be described quantitatively.
Mathematics content and practices can be applied
to solve problems.
How can angles be measured and
classified?
How can polygons, triangles, and
quadrilaterals be described, classified and
named?
KNOWLEDGE SKILLS STANDARDS
Students will know:
plane shapes have many
properties that make them
different from one another.
Polygons can be described
and classified by their sides
and angles. . (15-1)(15-
2)(15-3)
classify two-dimensional
shapes into categories
based on their properties.
(15-4)(15-5)
commonalities in attributes
of objects or situations can
be found and used to make
generalization about
relationships. (15-6))
Students will be able to:
identify and classify polygons. (15-
1)
place shapes have many properties
that make them different form one
another. (15-2)
polygons can be described and
classified by their sides and angles.
(15-2)(15-3)
classify two-dimensional shaped
into categories based on their
properties. (15-4)(15-5)
commonalities in attributes of
objects or situations can be found
and used to make generalizations
about relationships. (15-6)
5.G.3
5.G.4
VOCABULARY RESOURCES/MATERIALS ASSESSMENT/PROJECT
polygon, regular
polygon,triangle
quadrilateral, pentagon,
hexagon, octagon, equilateral
triangle, isosceles triangle,
scalene triangle
right triangle, acute triangle
obtuse triangle, parallelogram
trapezoid, rectangle, rhombus
square, generalization
Calendar Math:
Daily Depositor
Counting Tape and Daily Decimal
calendar for Sept., Oct., Nov., Jan,
Feb,. Mar., Apr.
Whole day celebration Feb.
Measurement March
Exemplar:
Who Owns the Most Land
Wooden sticks or straws
Teaching Tool 37
Teaching Tool 38
Scissors
Paper
Optional:
Hands-On Standards: Geometry:
Lessons 1-15
Formative
Daily Common core review
Informal observation
Differentiated activities
Leveled Homework
Center activities
Summative
Topic test
Quarterly benchmark
95
ROCHELLE PARK TOWNSHIP SCHOOL DISTRICT
Math 3-5 Curriculum Guide
Grade: 5 Unit: Topic 16- Coordinate Geometry Time Frame: 6 lessons
ENDURING UNDERSTANDINGS ESSENTIAL QUESTIONS
Two and three-dimensional objects with or
without curved surfaces can be described,
classified, and analyzed by their attributes. An
object’s location can be described
quantitatively.
Relationships can be described and
generalization made for mathematical situations
that have numbers or objects that repeat or are
arranged in predictable ways. For some
relationships, mathematical expressions and
equations can be used to describe how
members of one set are related to members of a
second set.
Mathematics content and practices can be
applied to solve problems.
How are points graphed?
How can we show the relationship between
sequences on a graph?
KNOWLEDGE SKILLS STANDARDS
Students will know:
the coordinate system is a scheme
that uses two perpendicular lines
intersecting at 0 to name the
location of points in the plane.
(16-1)
the ordered pairs of the end points
of vertical and horizontal line
segments can be used to find the
length of the segments. ( 16-2)
some problems can be solved by
breaking apart of changing the
problem into simpler ones. ( 16-
3)
a graph of a rule contains all of
the points on the coordinate grid
whose x- and y-coordinates
satisfy the rule. (16-4)
mathematical relationships
represented by rules can also be
represented by a graph of the rule.
Ordered pairs that satisfy the rule
can be used to graph the data. (16-
5)
Students will be able to:
identify and graph points on
a coordinate grid. (16-1)
find the distance between
two points by using ordered
pairs.. (16-2)
find the distance between
two points not on a straight
line by solving a simpler
problem. (16-3)
create and interpret
coordinate graph (16-4)
use coordinate graphs to
explore the relationship
between two rules. (16-5)
work backward to solve a
problem. (16-6)
5.G.1
5.G.2
96
some problems with the initial
data point unknown can be solved
by starting wit the end result and
reversing the steps and processes
to work backward to find the
initial data point. ( 16-6
VOCABULARY RESOURCES/MATERIALS ASSESSMENT/PROJECT
Coordinate grid
x-axis
y-axis
origin
ordered pair
x-coordinate
y-coordinate
Calendar Math:
Daily Depositor
Counting Tape and Daily
Decimal
Graphing Jan. and April
Exemplar:
Bulletin Board Border
Coordinate grids
10 x 10 grids ( Teaching Tool
40)
Grid paper
Optional:
Hands-On Standards: Algebra:
Lessons 10-16
Formative
Daily Common core review
Informal observation
Differentiated activities
Leveled Homework
Center activities
Summative
Topic test
Quarterly benchmark