AYER SHIRLEY REGIONAL SCHOOL DISTRICT
MATH CURRICULUM GUIDELINES
Grades 3­5
KEY SHIFTS IN NEW 2011 MATH STANDARDS
1. Focus strongly where the Standards focus
2. Coherence: Think across grades, and link to major topics within grades
3. Rigor: In major topics pursue conceptual understanding, procedural skill and
fluency, and application with equal intensity
Learn more about where the standards focus at achievethecore.org
Mathematical Practice Standards:
1 Make sense of problems and persevere in solving them
2 Reason abstractly and quantitatively
3 Construct viable arguments and critique the reasoning of others.
4 Model with mathematics.
5 Use appropriate tools strategically
6 Attend to precision.
7 Look for and make use of structure.
8 Look for and express regularity in repeated reasoning.
see p 15­17 of the 2011 MA Curriculum Frameworks for Math for descriptors of these behaviors
Grades 3­5 Focus Areas in Support of Rich Instruction and Expectations of Fluency
and Conceptual Understanding:
Multiplication and division of whole numbers and fractions ­ concepts, skills, and
problem solving
3
4
In grade three, students will
In grade four, students will use
continue to build their concept addition, subtraction,
of numbers, developing an
multiplication, and division to
5
In grade five, students will
build their understanding of
the place value system by
ASRSD MATH CURRICULUM GUIDELINES Grades 3­5 created August 2013
understanding of fractions as
numbers. They will learn the
concepts behind
multiplication and division and
apply problem­solving skills
and strategies for multiplying
and dividing numbers up
through 100 to solve word
problems. Students will use
place value to perform
operations. Students will also
make connections between
the concept of the area of a
rectangle and multiplication
and addition of whole
numbers.
solve word problems, including
problems involving
measurement of volume, mass,
and time. Students will continue
to build their understanding of
fractions ­creating equal
fractions, comparing the size of
fractions, adding and
subtracting fractions, and
multiplying fractions by whole
numbers. They will also start to
understand the relationship
between fractions and decimals.
working with decimals up
to the hundredths place.
Students will also add,
subtract, and multiply
fractions, including
fractions with unlike
denominators. They will
continue to expand their
geometry and
measurement skills,
learning the concept of
volume and measuring the
volume of a solid figure.
source:
Council of the Great City
Schools
source:
Council of the Great City Schools
source:
Council of the Great City
Schools
By the end of grade 3,
students will be able to...
By the end of grade 4,
students will be able to...
By the end of grade 5,
students will be able to...
• Understand and explain
what it means to multiply or
divide numbers
• Multiply all one­digit
numbers from memory
(knowing their times table)
• Multiply one­digit numbers
by multiples of 10 (such as
20, 30, 40)
• Solve two­step word
problems using addition,
subtraction, multiplication,
and division
• Measure and find length of
time
• Understand the concept of
area
• Relate the measurement of
area to multiplication and
division
• Relate the measurement of
perimeter to addition and/or
multiplication
• Understand fractions as
•Add and subtract whole
numbers up to 1 million quickly
and accurately
• Solve multi­step word
problems, including problems
involving measurement and
converting measurements from
larger to smaller units
• Multiply and divide multi­digit
numbers
• Extend understanding of
fractions by comparing the size
of two fractions with different
numerators (top numbers) and
different denominators (bottom
numbers)
• Create equal fractions (3
∕4 = 3x2∕4x2 = ∕8)
• Add and subtract fractions with
the same denominator
• Build fractions from smaller
fractions (3∕8 = 1∕8+∕18+∕18)
• Connect addition and
subtraction of whole numbers to
• Quickly and accurately
multiply multi­digit whole
numbers
• Divide numbers with up
to four digits by two digit
numbers
• Use exponents to
express powers of 10 (in
102, 2 is the exponent)
• Read, write, and
compare decimals to the
thousandths place
• Add, subtract, multiply,
and divide decimals to the
hundredths place
• Write and interpret
mathematical expressions
using symbols such
as parentheses. For
example, “add 8 and 7,
then multiply by 2” can be
written as 2×(8+7).
• Add and subtract
fractions with unlike
ASRSD MATH CURRICULUM GUIDELINES Grades 3­5 created August 2013
numbers
• Understand and identify a
fraction as a number on a
number line
• Compare the size of two
fractions
• Express whole numbers as
fractions and identify fractions
that are equal to whole
numbers (for example,
recognize that 3∕1 and 3 are
the same number)
• Measure weights and
volumes and solve word
problems involving
these measurements
• Describe, analyze and
classify 2­ dimensional
shapes
• Represent and interpret
data
source: Parents’ Guide to Student
Success (National PTA)
View the full standards at
http://www.doe.mass.edu/framewor
ks/current.html
multiply fractions by whole
numbers
• Connect addition of fractions to
the concept of angle
measurement
• Represent and interpret data
• Convert fractions with
denominators of 10 or 100 into
decimals
• Locate decimals on a number
line
• Compare decimals and
fractions using the symbols >
(more than), = (equal to), and <
(less than)
denominators
(bottom numbers) by
converting them to
fractions with matching
denominators
• Multiply fractions by
whole numbers and other
fractions
• Divide fractions by whole
numbers and whole
numbers by fractions
• Analyze and determine
relationships between
numerical patterns
• Measure volume using
multiplication and addition
source: Parents’ Guide to
Student Success (National PTA)
View the full standards at
http://www.doe.mass.edu/frame
works/current.html
source: Parents’ Guide to Student
Success (National PTA)
View the full standards at
http://www.doe.mass.edu/frameworks/c
urrent.html
Required Fluency by the
end of 3:
Required Fluency by the end
of 4:
Required Fluency by the
end of 5:
3.OA.7 Multiply/divide within
100
3.NBT.2 Add/subtract within
1000
4.NBT.4
Add/subtract within 1,000,000
5.NBT.5
Multi­digit multiplication
Curriculum Resources:
Pearson Envision Math­3
(2012)
Curriculum Resources:
Curriculum Resources:
Pearson Envision Math­4 (2012) Pearson Envision Math­5
(2012)
Accelerated Math Program
Resources/Links:
DESE 2011 Math Frameworks
http://www.doe.mass.edu/frameworks/math/0311.pdf
ASRSD MATH CURRICULUM GUIDELINES Grades 3­5 created August 2013
Central MA District and School Assistance Center
https://sites.google.com/a/dsacma.org/central­dsac/home
Common Core State Standards Initiative
http://www.corestandards.org/Math
Common Core Works­From the Page to the Classroom
http://www.commoncoreworks.org
Achieve The Core
http://www.achievethecore.org
Parent Roadmaps to the Common Core Standards­ Mathematics
http://www.cgcs.org/Page/244 (English)
http://www.cgcs.org/Page/263 (Spanish)
Tools for the Common Core Standards
http://commoncoretools.me/category/progressions/
Partnership for Advancement of College and Career Readiness (PARCC)
http://www.parcconline.org/about­parcc
Renaissance Learning (Accelerated Math, STAR Math)
http://www.renlearn.com//
ASRSD MATH CURRICULUM GUIDELINES Grades 3­5 created August 2013