2016-17 Manhattan-Ogden USD 383 – Math Year at a Glance – Grade 5
Grade 5
Welcome to math curriculum design maps for ManhattanOgden USD 383, striving to produce learners who are:
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Effective Communicators who clearly express ideas and effectively
communicate with diverse audiences,
Quality Producers who create intellectual, artistic and practical products
which reflect high standards
Complex Thinkers who identify, access, integrate, and use available
resources
Collaborative Workers who use effective leadership and group skills to
develop positive relationships within diverse settings.
Community Contributors who use time, energies and talents to improve
the welfare of others
Self-Directed Learners who create a positive vision for their future, set
priorities and assume responsibility for their actions. Click here for more.
Overview of Math Standards
Teams of teachers and administrators comprised the pK-12+ Vertical
Alignment Team to draft the maps below. The full set of Kansas College and
Career Standards (KCCRS) for Math, adopted in 2010, can be found here.
To reach these standards, teachers use Math in Focus curriculum, resources,
assessments and supplemented instructional interventions with Every Day
Counts Calendar Math, Compass Odyssey, Daily Spiral Reviews, Fact Fluency
Tests, additional websites and app for specific skills.
1
Standards of Mathematical Practice
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. Click here for more.
Additionally, educators strive to provide math instruction centered on:
1: Focus - Teachers significantly narrow and deepen the scope of how time
and energy is spent in the math classroom. They do so in order to focus
deeply on only the concepts that are prioritized in the standards.
2: Coherence - Principals and teachers carefully connect the learning within
and across grades so that students can build new understanding onto
foundations.
3: Fluency - Students are expected to have speed and accuracy with simple
calculations; teachers structure class time and/or homework time for
students to memorize, through repetition, core functions.
4: Deep Understanding - Students deeply understand and can operate
easily within a math concept before moving on. They learn more than the
trick to get the answer right. They learn the math.
5: Application - Students are expected to use math concepts and choose the
appropriate strategy for application even when they are not prompted.
6: Dual Intensity - Students are practicing and understanding. There is
more than a balance between these two things in the classroom – both are
occurring with intensity. Click here for more.
2016-17 Manhattan-Ogden USD 383 – Math Year at a Glance – Grade 5
Unit/CH
1. Whole
Numbers:
Numbers to
10,000,000,
Place Value,
Comparing
Numbers to
10,000,000,
Rounding and
Estimating
KCCRS Standards
Number and Operations in Base Ten
5.NBT.1. Understand the place value
system. Use and understand the
powers of ten in the place value
system.
5.NBT.2. Recognize and explain
patterns when multiplying and dividing
by the powers of 10, as it relates to the
place value system. Use whole number
exponents to express the powers of 10.
Vocabulary
powers of 10
decimal point
hundred thousand
periods
million
place value
estimate
front-end estimation
with adjustment
compatible numbers
Essential
Resources
How can whole
numbers be
written in
different ways?
180 Days (Reference
on last page)
NBT.1 Convert
between Place
Values
Questions
How can
numbers be
compared and
rounding,
according to
their place
value?
NBT.1 Place Values in
Decimals
NBT.2 Multiply
increasing Place
Value
NBT.2 Multiply a
decimal by powers of
10
NBT.1,2,5,6 Unit 1
Georgia Standards &
Lessons
(see page 12 for
lesson details list)
See EngageNY
resources/links at
bottom of document
MODULE 1
1
“I Can”
Sample Learning
Targets
NBT.1 I can understand and
explain the value of digits in
a larger number.
NBT.2 I can explain patterns
of zeroes in an answer when
multiplying a number by
powers of 10.
2016-17 Manhattan-Ogden USD 383 – Math Year at a Glance – Grade 5
2. Whole
Number
Multiplication
and Division:
Using a
Calculator,
Multiplying by
Tens/Hundreds/
Thousands,
Multiplying by 2Digit Numbers,
Dividing by
Tens/Hundreds/
Thousands,
Dividing by 2Digit Numbers,
Order of
Operation, RealWorld Problems
(3. Fractions and
Mixed Numbers:
Adding Unlike
Fractions,
Subtracting
Unlike Fractions,
Fractions/Mixed
2
Number and Operations in Base Ten
5.NBT.1 Understand the place value
system. Use and understand the
powers of ten in place value.
5.NBT.2. Recognize and explain
patterns when multiplying and dividing
by the powers of 10, as it relates to the
place value system.
5. NBT.5. Perform operations with
multi-digit whole numbers and with
decimals to hundredths. Fluently
multiply whole numbers.
5.NBT.6. Perform operations with
multi-digit whole numbers and with
decimals to hundredths. Divide up to
four digit dividends by two digit
divisors. Use various models to
represent division.
5.NBT.7. Multiply and divide decimals
to hundredths using various models
and relate the strategy to a written
method, being able to explain.
Operations and Algebraic Thinking
5.OA.1. Write and interpret numerical
expressions. Use parentheses,
brackets, or braces and solve.
5.OA.2. Write expressions that record
calculations with numbers and
interpret numerical expressions.
product
factor
quotient
dividend
divisor
remainder
numeric expression
order of operations
parentheses
brackets
braces
evaluate
Number and Operations—Fractions
5.NF.1. Use equivalent fractions as a
strategy to add and subtract fractions.
Add and subtract fractions with unlike
denominators.
5.NF.2. Solve real world problems
involving adding and subtracting
fractions with unlike denominators.
multiple
least common multiple
least common
denominator
equivalent fractions
benchmarks
division expression
How can
patterns be
used to help
you multiply
and divide
numbers?
How can
numeric
expressions be
simplified using
the order of
operations?
How can
multiplication
and division be
used to solve
real-world
problems?
NBT.1,2,5,6 & OA.1,2
Unit 1 Georgia
Standards & Lessons
(see page 12 for
lesson details list)
See EngageNY
resources/links at
bottom of document
MODULE 1.
NBT.5 Multiply larger
numbers
NBT.6 Divide by
increasing PV
NBT.7 VIDEO
(showing place value
to array to
multiplying decimals)
180 Days
OA.1 multiple
operations
OA.2 Write
Numerical
Expressions
How can you
add and
subtract unlike
fractions and
mixed numbers
by rewriting
them with like
denominators?
Scholastic materials
180 Days
NF.1-7 Unit 4 Georgia
Standards & Lessons
(see page 18 for
content details)
(see above)
* NBT.5 I can easily multiply
larger whole numbers.
* NBT.6 I can divide fourdigit numbers (dividends) by
two-digit numbers
(divisors).
* NBT.6 I can illustrate and
explain a division problem
using equations, arrays
and/or models.
* NBT.7 I can add, subtract,
multiply, and divide
decimals to hundredths
using what I have learned
about place value.
* OA.1 I can write and figure
out number sentences that
have parentheses, brackets
and/or braces.
* OA.2 I can understand
number sentences and
estimate their answers
without actually calculating
them.
* OA.2 I can correctly write
number sentences using
mathematic symbols and
the order of operations
correctly.
* NF.1 I can add and
subtract fractions with
unlike denominators.
* NF.2 I can solve word
problems that involve
addition and subtraction of
fractions.
2016-17 Manhattan-Ogden USD 383 – Math Year at a Glance – Grade 5
Numbers/and
Division
Expressions,
Expressing
Fractions/
Division
Expressions/and
Mixed Numbers
as Decimals,
Adding Mixed
Numbers,
Subtracting
Mixed Numbers,
Real-World
Problems
4. Multiplying
and Dividing
Fractions and
Mixed Numbers:
Multiplying
Proper Fractions,
Real-World
Problems,
Multiplying
Improper
Fractions by
Fractions,
Multiplying
Mixed Numbers
and Whole
Numbers,
Dividing a
3
5.NF.3. Apply and extend
understanding of multiplication and
division to multiply and divide
fractions. Interpret a fraction as
division of the numerator by the
denominator. Solve word problems
involving division of whole numbers
leading to answers in the form of mixed
numbers or fractions.
5.NF.4. Apply and extend
understanding of multiplication and
division to multiply and divide
fractions. Use strategy of multiplying
by a whole in fraction form, which
results in an equivalent fraction that
can be converted into a decimal.
Number and Operations—Fractions
5.NF.4. Apply and extend
understanding of multiplication and
division to multiply and divide
fractions. Apply knowledge of
multiplication to multiply a fraction or
whole number by a fraction.
5.NF.5. Interpret multiplication as
scaling.
5.NF.6. Solve real world problems
involving multiplication of fractions and
mixed numbers.
5.NF.7. Apply and extend
understanding of multiplication and
division to multiply and divide
fractions. Apply understanding of
division to divide unit fractions by
See EngageNY
resources/links at
bottom of document
MODULE 3-5
NF.1 Eq. Fractions
NF.1 Add unlike
denom.
NF.2 Word Problems
NF.3 Word Problems
None
How can whole
numbers,
fractions, and
mixed numbers
be multiplied
or divided in
any
combination?
K’NEX Lesson with
Multiplying and
Dividing Fractions
(with Chris Herald).
See EngageNY
resources/links at
bottom of document
MODULE 4 & 5
LEGO Mindstorm
lesson using
scaling/distance.
(with Chris Herald)
StarBase Activities
(map scale and flight)
* NF.2 I can use number
sense and fractions that I
know to estimate the
reasonableness of answers
to fraction problems.
* NF.3 I can understand that
fractions are really division
problems.
* NF.4 I can use what I know
about multiplication to
multiply fractions or whole
numbers by a fraction.
* NF.4 I can understand and
show with models that
multiplying a fraction by a
whole number is the same
as finding the product of the
numerator and whole
number and then dividing it
by the denominator.
(see above)
* NF.5 I can think of
multiplication as the scaling
of a number (similar to a
scale on a map)…Mentally
compare the size of a
product to the size of one of
the factors by thinking
about the other factor in the
problem…explain why
multiplying a number by a
fraction greater than 1 will
result in a bigger number
than the number I started
with…explain why
multiplying a number by a
fraction less than 1 will
result in a smaller number
2016-17 Manhattan-Ogden USD 383 – Math Year at a Glance – Grade 5
Fraction by a
Whole Number
whole numbers and whole numbers by
unit fractions.
180 Days
NF.5 Models
NF.7 Division Models
8. Decimals:
Understanding
Thousandths,
Comparing and
Rounding
Decimals,
Rewriting
Decimals as
Fractions and
Mixed Numbers
Numbers and Operations in Base Ten
5.NBT.3. Read write and compare
decimals to the thousandths place.
5.NBT.4. Use place value
understanding to round decimals to
any place.
thousandth
equivalent
9. Multiplying
and Dividing
Numbers and Operations in Base Ten
dividend
per unit
4
How can
thousandths be
represented
with three
decimal places
or as fractions?
How can
decimals be
* FDP Art Lesson
(intro/review)
* NBT.3, 4 Georgia
Standards & Lessons
Unit 3
(see page 10 for
content details)
* See EngageNY
resources/links at
bottom of document
MODULE 2
* NBT.3 Model
decimals and
Fractions
* NBT.3 Convert
Decimals
* NBT.3 Decimals on
#Line
* NBT.4 Rounding
Decimals
* NBT.4 Estimate
Decimals
NBT.7 +-x/ word
problems
than the number I started
with…relate the notion of
equivalent fractions to the
effect of multiplying a
fraction by 1.
* NF.6 I can solve real world
problems that involve
multiplication of fractions
and mixed numbers.
* NF.7 I can use what I know
about division to divide
fractions by whole numbers
or whole numbers by
fractions.
NBT.3 I can read, write, and
compare decimals to
thousandths.
NBT.4 I can use place value
understanding to round
decimals to any place.
(see above)
2016-17 Manhattan-Ogden USD 383 – Math Year at a Glance – Grade 5
Decimals:
Multiplying
Decimals,
Multiplying by
Tens/Hundreds/
Thousands,
Dividing
Decimals,
Dividing by T/H/
T, Estimating
Decimals
11. Graphs and
Probability:
Making and
Interpreting
Double Bar
Graphs,
Graphing an
Equation,
Combinations,
Theoretical
Probability and
Experimental
Probability
5.NBT.7. Perform operations with
multi-digit whole numbers and with
decimals to hundredths.
estimate
divisor
powers of 10
multiplied and
divided in the
same way as
whole
numbers?
Geometry
5.G.1. Graph points on the coordinate
place to solve real –world and
mathematical problems.
Coordinate grid
x-axis
y-axis
coordinate plane
coordinates
ordered pair
x-coordinate
y-coordinate
equation
origin
How can we
displaying data
in a graph to
highlight some
features of the
data?
Operations and Algebraic Thinking.
5.OA.3 Analyze patterns and
relationships.
How does
probability
measures the
likelihood of an
event
occurring?
NBT.7 Georgia
Standards & Lessons
(Unit 2)
(see page 15 for
lesson content)
Explorer Grid (use
UTM map to chart or
follow various
Explorers’ travels)
http://yhoo.it/1Y77q
zG (UTM)
Overlay with explorer
routes
http://yhoo.it/1XBGj
1l
G.1 Coordinate Grid
G.1; OA.3 Georgia
Standards & Lessons
Unit 7
(see page 10 for
lesson content)
See EngageNY
resources/links at
bottom of document
MODULE 6
Division Design
(similar to:
5
G.1 I can understand a
coordinate place and
ordered pairs of number
coordinates on that
plane…graph ordered pairs
of numbers on a coordinate
plane using what I have
learned about the x-axis and
y-axis coordinates.
OA.3 I can create two
number patterns using two
given rules…form ordered
pairs using the relationship
between two number
patterns and graph them on
a coordinate plane.
G.2 I can represent realworld and mathematical
problems by graphing points
in the first quadrant of a
coordinate plane.
2016-17 Manhattan-Ogden USD 383 – Math Year at a Glance – Grade 5
http://yhoo.it/1OaPr
H0
StarBase Lessons
180 Days
OA.3 IXL Practice
OA.3 IXL Practice
OA.3 IXL Practice
(Spiral concept with
chapter 8 & 9)
Number Tightrope :
http://www.mathmid
way.org/pdf/teachers
/guide/Number_Line
_Tightrope.pdf
13. Properties of
Triangles and
Four-sided
Figures:
Classifying
Triangles,
Measures of
Angles of a
Triangle, Right/
Isosceles/
Equilateral
Triangles,
Triangle
Inequalities,
Parallelogram/
6
Geometry
5.G.3. Classify two-dimensional figures
into categories based on their
properties.
parallelogram
rhombus
trapezoid
How do
properties of
geometric
figures state
relationships
among angles
or sides of the
figures?
How do
triangles and
four-sided
figures have
their own
special
properties?
Calendar Math
(shapes and patterns,
angles)
180 Days
See EngageNY
resources/links at
bottom of document
MODULE 5
(spiral with ch. 2; 14;
15)
Nets/foldable
http://yhoo.it/1tcSgO
r
G.3 I can understand how
attributes of 2-D shapes in a
category also belong to all
subcategories of those
shapes.
G.4 I can classify 2-D shapes
based on their properties.
2016-17 Manhattan-Ogden USD 383 – Math Year at a Glance – Grade 5
Rhombus/
Trapezoid
G.3 Georgia
Standards & Lessons
Unit 7
(see page 10 for
lesson content)
15. Surface Area
and Volume:
Building Solids
Using Unit
Cubes, Drawing
Cubes and
Rectangular
Prisms,
Nets/Surface
Area,
Understanding
and Measuring
Volume, Volume
of a Rectangular
Prism and Liquid
Measurement and Data.
5.MD.3 Geometric measurement:
understand concepts of volume and
relate volume to multiplication and to
addition. Measure using unit cubes,
using cubic cm, cubic in, cubic ft., and
improvised units.
5.MD.4 Relate volume to the
operations of multiplication and
addition and solve real world and
mathematical problems involving
volume.
Here are the 5th
grade Math in
Focus chapters not
emphasized with
KCCRS standards:
Chapters 5, 6, 7, 10, 12, 14
Here are the 5th
grade KCCRS not
emphasized by
MIF:
7
Unit cube
Surface area
volume
How can the
volume of
cubes and
rectangular
prisms be
expressed as
the number of
cubic units
they contain?
How is the
surface area of
a solid the sum
of the areas of
all its faces?
5.MD.1. Convert among different-sized standard measurement units when a given
measurement system and use these conversions solving a multistep, real world
problem.
G.3 Classify
Use lesson 14.1 focus
on prisms.
Unit Cubes video
(silly)
Video (comparing
area to volume)
See EngageNY
resources/links at
bottom of document
MODULE 4-5
MD.1-5 Georgia
Standards - Lessons
Unit 6
(See page 16 for
lesson standards
content)
MD.2 Georgia
Standards - Lessons
(pages 10; 16 for
MD3 I can recognize volume
as a characteristic of solid
figures and understand how
it can be measured…I can
understand a “unit cube” as
a cube with side lengths of 1
unit and can use it to
measure volume…I can
understand that a solid
figure filled with a number
of unit cubes is said to have
a volume of that many
cubes.
2016-17 Manhattan-Ogden USD 383 – Math Year at a Glance – Grade 5
5.MD.2. Make a line plot to display a data set of measurements in fractions of a unit.
Use operations on fractions for this grade to solve problems involving information
presented in line plots. [How can I use a line plot to compare fractions? What
strategies help when solving problems with line plots? ]
5.MD.5. Relate volume to the operations of multiplication and addition and solve
real world and mathematical problems involving volume.
5.NBT.5. Fluently multiply multi-digit whole numbers using the standard algorithm.
5.G.A.2. Represent real world and mathematical problems by graphing points in the
first quadrant of the coordinate plane, and interpret coordinate values of point in
the context of the situation.
content; 33-37; 3742 primarily)
See EngageNY
resources/links at
bottom of document
MODULE 4
MD.5 Georgia
Standards - Lessons
Unit 6
(See page 16 for
lesson standards
content)
5.G.B.4. Classify two dimensional figures in a hierarchy based on properties.
G.2 Map
G.2 Georgia
Standards – Lessons
Unit 7 (see page 10
for lesson standards
content)
G.4 Figure Sort
G.4 Georgia
Standards – Lessons
Unit 5 (see page 9 for
lesson standards
content)
8
2016-17 Manhattan-Ogden USD 383 – Math Year at a Glance – Grade 5
Additional Resources List:
Scholastic resources
Xtra math for math facts fluency
Odyssey Hybridge
Daily Math
180 Days of Math for Fifth Grade, Shell Education (Daily math skills by mathematical concepts)
The Common Core Mathematics Companion: The Standards Decoded. (Grades 3-5) Linda Gojak, Ruth Harbin Miles. ISBN# 978-1-4833-8160-2
Lots of practice opportunities online (beyond what is listed above):
IXL Links by Standard (for Practice): https://www.ixl.com/standards/georgia/math/grade-5
Georgia Dept. of Education (GADOE) home page for grade level standards and lessons.
New York State Common Core Mathematics Curriculum Map and Resources links (EngageNY)
-
Module 1: Place Value and Decimal Fractions (NBT.1-4, 7, MD.1)
Module 2: Multi Digit Whole number and Decimal Fraction Operations (OA.1-2, NBT.1-2, 5-7, MD.1)
Module 3: Addition and Subtraction of Fractions (NF.1-2)
Module 4: Multiplication and Division of Fractions and Decimal Fractions (OA.1-2, NBT.7, NF.3-7, MD.1-2)
Module 5: Addition and Multiplication with Volume and Area (NF.4, MD.3-5, G.3-4)
Module 6: Problem Solving with the Coordinate Plane (OA.2-3, G.1-2)
9