Manhattan-Ogden USD 383 – Math Curriculum Design Map – Grade 4
Grade 4
Welcome to math curriculum design maps for ManhattanOgden USD 383, striving to produce learners who are:
•
•
•
•
•
•
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 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 4
Unit/Chapter
KCCRS Standards
1.1 Numbers to
100,000
1.2 Comparing
Numbers to 100,000
Number and Operations in Base Ten
4.NBT.1 Recognize that in a multidigit whole number, a digit in one
place represents ten times what it
represents in the place to its right.
4.NBT.2 Read and write multi-digit
whole numbers using base-ten
numerals, number names, and
expanded form. Compare two multidigit numbers based on place values
of each digit using >, =, and <
symbols.
digit
place value
place value chart
table
compare
multiples
least common
multiple
compare
standard form
word form
expanded form
greater than (>)
less than (<)
greatest
least
order
Number and Operations in Base Ten
4.NBT.3 Use place value
understanding to round multi-digit
whole numbers to any place.
estimate
reasonable
front-end estimation
round
product
quotient
factor pairs
common factor
2.1 Estimation
2.2 Factors
2.3 Multiples pg. 63
Operations and Algebraic Thinking
1
Vocabulary
Essential Questions
Resources
I Can Learning
Targets
How can you read, compare,
and order numbers according
to the place value of their
digits?
How can I use place value to
compare numbers?
How do digit values change as
they are moved around in
large numbers?
What determines the value of a
digit?
How can you represent the
same number in different
ways?
What conclusions can I make
about the places within our
base-10 number system?
What effect does the location of
a digit have on the value of
the digit?
How can we compare large
numbers?
Why is it important for me to be
able to compare numbers?
What patterns do I notice?
When two factors are
multiplied, the product is a
multiple of both numbers.
How can knowing factors and
multiples of numbers help in
estimating products and
quantities?
Engage NY:
Module 1,
Topic A,
Lessons 1-4
NBT.1 I can recognize that in
a multi-digit whole number, a
digit in one place represents
ten times what it represents
in the place to its right.
NBT. 2 I can read and write
larger whole numbers using
numerals, words, and in
expanded form.
NBT. 2 I can compare two
larger numbers by using what
I know about the values in
each place, symbols to show
the comparison.
NBT. 2 I can compare two
larger numbers and use the
symbols <,>, and = to show
the comparison.
OA.5 I can create a number
or shape pattern that follows
a given rule.
OA.5 I can notice and point
out different features of a
pattern once it is created by
a rule.
NBT.3 I can round larger
whole numbers to any place.
NBT. 4 I can add and subtract
larger numbers.
OA. 1 I can understand that
multiplication equations can
be seen as comparisons of
groups.
Module 1,
Topic B,
Lessons 5-6
Engage NY:
Module 1,
Topic C,
Lessons 710
Module 3,
Topic F,
2016-17 Manhattan-Ogden USD 383 – Math Year at a Glance – Grade 4
Unit/Chapter
3.1 Multiplying by a
1-Digit Number
3.2 Estimate
Products
3.3 Modeling Division
with Regrouping
3.5 Real-World
Problems:
Multiplication &
Division
KCCRS Standards
Vocabulary
Essential Questions
Resources
I Can Learning
Targets
4.OA.1 Use four operations with
whole numbers and solve problems.
Multiplication equations as
comparisons of groups.
4.OA.4 Gain familiarity with factors
and multiples. Find all factor pairs
for a whole number within 1-10.
Recognize that a whole number is a
multiple of each of its factors.
greatest common
factor
least common factor
prime number
composite number
whole number
Lessons 2225
OA. 4 I can find all factor
pairs for a whole number
from 1 to 100.
OA. 4 I can recognize a whole
number as a multiple of each
of its factors.
OA. 4 I can determine
whether a whole number
from 1 to 100 is a multiple of
a given 1-digit number.
OA. 4 I can determine
whether a given whole
number up to 100 is a prime
or composite number.
Number and Operations in Base Ten
4.NBT.5 Multiply a whole number of
up to four digits by a one-digit
whole number and multiply two
two-digit numbers. Using strategies
based on place value and the
properties of operations illustrate
and explain how to multiply larger
numbers by using equations, arrays,
or models.
4.NBT.3 Use place value
understanding to round multi-digit
whole numbers to any place.
remainder
regroup
quotient
product
What is a sensible answer to a
real problem?
What information is needed in
order to round whole number
to any place?
How does estimation keep us
from having to count large
numbers individually?
When is estimation useful?
How can I ensure my answer is
reasonable?
How can rounding help me
compute numbers?
How can a remainder affect the
answer in a division problem?
How is place value used to
multiply and divide multidigit numbers?
How can estimation be used to
check the reasonableness of
an answer?
What strategies can I use to help
me make sense of a written
algorithm?
What effect does a remainder
have on my rounded answer?
How does the explanation of the
remainder depend on the
problem situation?
How can we use various
strategies to solve a word
problem?
Engage NY:
NBT. 5
Module 3,
Topic B,
Lessons 4-6
NBT. 5 I can multiply a whole
number up to 4 digits by a 1digit whole number.
NBT. 5 I can multiply two
two-digit.
NBT. 5 I can illustrate and
explain how to multiply
larger numbers by using
equations, arrays, or models.
NBT. 3 I can round larger
whole numbers to any place.
NBT. 6 I can find whole
number quotients and
remainders with up to 4 digit
dividends and 1 digit divisors.
NBT. 6 I can illustrate and
explain how to divide larger
Operations and Algebraic Thinking
2
NBT. 5
Module 3,
Topic C,
Lessons 711
NBT. 5
Module 3,
Topic H,
Lessons 3438
2016-17 Manhattan-Ogden USD 383 – Math Year at a Glance – Grade 4
Unit/Chapter
KCCRS Standards
Vocabulary
4.OA.2 Use four operations with
whole numbers and solve problems:
Multiply or divide to solve word
problems involving multiplicative
comparison.
Essential Questions
Resources
How can we use estimation to
check for the reasonability of
addition, subtraction,
multiplication, and division
solutions?
NBT. 6
Module 3,
Topic E,
Lessons 1421
4.OA.3 Use four operations with
whole numbers and solve problems
5.2 Mean, Median,
Mode, Range
3
Measurement and Data
4.MD.4 Make a line plot to display a
data set of measurements in
fractions of a unit (1/2, 1/4, 1/8).
Solve problems involving addition
and subtraction of fractions by using
information presented in line plots.
median*
mode*
range*
fractions
*Note: Terms are
found in 6th grade
standards but taught
in 4th grade MIF.
How can information be
analyzed to find a typical
value for a data set?
How can data be analyzed to
predict the likelihood of an
event happening?
How do we determine the most
appropriate graph to use to
display the data?
How do we make a line plot to
display a data set?
I Can Learning
Targets
numbers by using equations,
arrays, or models.
OA. 2 I can multiply and
divide to solve word
problems by using drawings
or writing equations and
solving for a missing number.
OA. 2 and
OA. 3 I can use what I know
OA. 3
about addition, subtraction,
Lessons
multiplication, and division to
referenced
at bottom of solve multi-step word
problems involving whole
document
numbers.
and used
OA. 3 I can represent word
with MD. 1
problems by using equations
and MD. 2
with a letter standing for the
unknown number.
OA. 3 I can determine how
reasonable my answers to
word problems are by using
estimation, mental math, and
rounding.
Engage NY: MD. 4 I can make a line plot
*Not
to show a data set of
covered in
measurements involving
Engage NY
fractions.
lessons
MD. 4 I can solve problems
involving addition and
subtractions of fractions by
using information shown in
line plots.
2016-17 Manhattan-Ogden USD 383 – Math Year at a Glance – Grade 4
Unit/Chapter
KCCRS Standards
6.1 Big Idea/Lesson
6.1 Adding Fractions
6.2 Subtraction
Fractions
6.3 Mixed Numbers
(*Recall Grd 2-Read
Fract. Grd 3: Equiv.
Fract.)
6.4 Improper
Fractions
6.6 Renaming Whole
Numbers with + and
– Fractions
6.7 Fraction of a Set
6.8 Real-World
Problems: Fractions
Number and Operations—Fractions
4.NF.1 Explain and show models for
why a fraction a/b is equivalent to a
fraction (n × a)/(n × b) with
attention to how the number and
size of the parts differ.
4.NF.3(a) Understand a fraction a/b
with a > 1 as a sum of fractions 1/b.
4.NF.2 Compare two fractions with
different numerators and different
denominators by creating common
denominators or numerators
4.NF.3(c) Add and subtract mixed
numbers with like denominators
4.NF.4 Understand a fraction a/b as
a multiple of 1/b. Understand a
multiple of a/b as a multiple of 1/b.
4.NF.3(d) Solve word problems
involving addition and subtraction of
fractions referring to the same
whole and having like denominators
4.NF.5 Express a fraction with a
denominator of 10 as an equivalent
fraction with a denominator 100 in
order to add the two fractions.
4
Vocabulary
numerator
denominator
equivalent fraction
unlike fraction
tenth
decimal point
expanded form
decimal
hundredth
mixed number
simplest form
numerator
denominator
improper fraction
Essential Questions
Resources
I Can Learning
Targets
How are fractions and mixed
numbers used to name
wholes and parts of a whole?
How can fractions and mixed
numbers be added and
subtracted?
What are examples of relative
sizes of measurement units
within one system including
km, m, cm; kg, g; lb, oz; l, ml;
hr, min, and sec?
How can we estimate and
measure capacity?
What is a fraction and how can
it be represented?
How can equivalent fractions be
identified?
How can we find equivalent
fractions?
In what ways can we model
equivalent fractions?
How can identifying factors and
multiples of denominators
help to identify equivalent
fractions?
How can we find equivalent
fractions?
In what ways can we model
equivalent fractions?
How do fractions relate to other
number concepts?
• Engage NY:
• NF.3(b) and
NF.4(a)
Module 5,
Topic A,
Lessons 1-6
• NF. 1
Module 5,
Topic B,
Lessons 711
• NF. 2
Module 5,
Topic C,
Lessons 1215
• NF. 3(a-d)
Module 5,
Topic D,
Lessons 1621
• NF. 2 and
NF. 3
Module 5,
Topic E,
Lessons 2228
• NF. 3(c)
Module 5,
Topic F,
Lessons 2934
NF. 1 I can explain why
multiplying a numerator and
denominator by the same
number does not change the
value of a fraction.
NF. 1 I can recognize and
generate equivalent fractions
based on my knowledge of
numerators and
denominators.
NF. 2 I can recognize that
comparisons of fractions are
valid only when the two
fractions refer to the same
whole.
NF. 2 I can compare fractions
using the symbols <, >, = and
justify the comparison using
models.
NF.3(a) I can understand
addition and subtraction of
fractions as joining and
separating parts referring to
the same whole.
NF.3(c) I can add and
subtract mixed numbers with
like denominators.
NF. 3 (d) I can solve word
problems involving addition
and subtraction of fractions
that refer to the same whole
2016-17 Manhattan-Ogden USD 383 – Math Year at a Glance – Grade 4
Unit/Chapter
KCCRS Standards
Vocabulary
Essential Questions
4.NF.6 Use decimal notation for
fractions with denominators of 10 or
100.
Operations and Algebraic Thinking
4.OA.5 Generate a number or shape
pattern that follows a given rule.
Identify apparent features of the
pattern once it has been created by
the rule.
7.1 Understanding
Tenths
7.2 Understanding
Hundredths
7.3 Comparing
Decimals
5
Number and Operations—Fractions
4.NF.5 Express a fraction with a
denominator of 10 as an equivalent
fraction with a denominator 100 in
order to add the two fractions.
4.NF.6 Use decimal notation for
fractions with denominators of 10 or
100.
4.NF.7 Compare two decimals to
hundredths by reasoning about their
size. Recognize that comparisons are
valid only when the two decimals
refer to the same whole. Compare
the results with the symbols >, =, or
<, and justify the conclusions by
using a visual models.
unlike fractions
equivalent fractions
tenth
decimal point
expanded form
decimal
unlike fraction
hundredth
fraction
decimal
hundredth
fraction
compare
How are decimals another way
to show amounts that are
parts of a whole?
How can we find equivalent
fractions and simplify
fractions?
What are benchmark fractions?
How are benchmark fractions
helpful when comparing
fractions?
How can we use fair sharing to
determine equivalent
fractions?
How are equivalent fractions
related?
How can you compare and order
fractions?
Resources
I Can Learning
Targets
• NF. 4
Module 5,
Topic G,
Lessons 3540
• OA. 5
Module 5,
Topic H,
Lesson 41
• NF. 5
Module 6,
Topic D,
Lesson 1214
Engage NY:
NF. 6
Module 6,
Topic A, L 13
and that have like
denominators.
NF. 4 I can apply my
understanding of
multiplication to multiply a
fraction by a whole number.
NF. 4 I can understand a
fraction a/b as a multiply of
1/b.
NF. 4 I can solve word
problems involving
multiplication of a fraction by
a whole number.
NF. 5 and
NF. 6,
Module 6,
Topic B, L 48
NF. 7
Module 6,
Topic C, L 911
NF. 5 I can show a fraction
with a denominator of 10 as
an equivalent fraction with a
denominator of 100 in order
to add the two fractions.
NF. 6 I can use decimals to
show fractions with
denominators of 10 and 100.
NF. 7 I can compare two
decimals to hundredths by
reasoning about their size
and realizing that the
comparison is only true if the
two decimals refer to the
same whole.
NF. 7 I can compare decimals
using the symbols <, >, = and
2016-17 Manhattan-Ogden USD 383 – Math Year at a Glance – Grade 4
Unit/Chapter
KCCRS Standards
Vocabulary
8.1 Adding Decimals
8.2 Subtracting
Decimals
8.3 Real-World
Problems: Decimals
4.MD.2 Use the four operations to
solve word problems involving
distances, intervals of time, liquid
volumes, masses of objects, and
money.
tenth
decimal point
decimal
hundredth
compare
9.1 Understanding
and Measuring
Angles
9.2 Drawing Angles
to 180 ⁰
9.3 Turns and Right
Angels
Measurement and Data
4.MD.5a An angle is measured with
reference to a 360° circle with its
center at the common endpoint
4.MD.5b An angle that turns
through n one-degree angles is said
to have an angle measure of n
degrees.
4.MD.6 Using a protractor to
measure and sketch angles in whole
number degrees.
4.MD.7 Recognize angle measure as
additive. When an angle is
decomposed, the angle measure of
the whole is the sum of the angles
measured parts.
ray
vertex
protractor
degree
endpoint
point
lines
line segments
inner scale
outer scale
acute angle
obtuse angle
straight angle
degree
protractor
turn
6
Essential Questions
How do we locate fractions on a
number line?
How can angles be seen and
measured when two rays or
sides of a shape meet?
What do we actually measure
when we measure an angle?
What do we know about the
measurement of angles in a
triangle?
What are benchmark angles and
how can they be useful in
estimating angle measures?
How are a circle and an angle
related?
Resources
Engage NY:
MD. 2
Module 6,
Topic E,
Lessons 1516
Engage NY:
MD.5 and
MD. 6
Module 4,
Topic B, L 58
MD. 7
Module 4,
Topic C, L 911
I Can Learning
Targets
justify the comparison by
using models.
MD. 2 I can use the four
operations to solve word
problems using
measurement.
MD. 2 I can solve
measurement problems
involving simple fractions and
decimals.
MD. 2 I can show
measurement quantities
using diagrams that involve a
measurement scale.
MD. 5 (a) I can understand
that angles are measured
with reference to a 360degree circle, with its center
at the common endpoint of
the rays.
MD.5 (b) I can understand
that an angle that turns
through n one-degree angles
is said to have an angle
measurement of n degrees.
MD. 6 I can use a protractor
to measure and sketch angles
in whole number degrees.
MD. 7 I can solve real world
and mathematical addition
and subtraction problems to
find unknown angles.
2016-17 Manhattan-Ogden USD 383 – Math Year at a Glance – Grade 4
Unit/Chapter
10.1 Drawing
Perpendicular Line
Segments
10.2 Drawing Parallel
Line Segments
10.3 Horizontal &
Vertical Lines
11.1 Squares and
Rectangles
11.2 Properties of
Squares and
Rectangles
12. 1 Area of a
Rectangle; 12.2
Rectangles and
Squares; 12.3
Composite Figures
12. 4 Using Formulas
for Area and
Perimeter
7
KCCRS Standards
Geometry
4.G.1 Draw points, lines, line
segments, rays, angles (right, acute,
obtuse), and perpendicular and
parallel lines. Identify these in twodimensional figures.
Geometry
4.G.1 Draw points, lines, line
segments, rays, angles (right, acute,
obtuse), and perpendicular and
parallel lines. Identify these in twodimensional figures.
Geometry
4.G.2 Classify two-dimensional
figures based on geometrical
attributes (acute, obtuse, and, right
angles and parallel/perpendicular
lines). Recognize right triangles as a
category and identify right triangles.
4.MD.3 Apply the area and
perimeter formulas in real world
and mathematical problems.
The team recommends following up
these standards with supportive
materials to ensure proficiency.
Vocabulary
Essential Questions
Resources
I Can Learning
Targets
G. 1 I can identify and draw
points, lines, line segments,
rays, angles, and
perpendicular and parallel
lines.
lines
line segments
parallel lines
perpendicular lines
right triangle
base
horizontal lines
vertical lines
right angle
angle
degrees
Area
Perimeter
Formula
How can line segments go up
and down, from side to side,
and in every direction?
Engage NY:
G. 1 Module
4, Topic A,
Lessons 1-4
G. 1 I can identify and draw
points, lines, line segments,
rays, angles, and
perpendicular and parallel
lines.
How are squares and rectangles
four-sided figures with
special properties?
How are the angles of a triangle
related?
Engage NY:
*Engage NY
Lessons in
Chapter 13
G. 2 I can classify two
dimensional shapes based on
what I know about their
geometrical attributes.
G. 2 I can recognize and
identify right triangles.
Engage NY:
MD. 3
Module 3,
Topic A,
Lessons 1-3
MD. 3 I can use what I know
about area and perimeter to
solve real world problems
involving rectangles
2016-17 Manhattan-Ogden USD 383 – Math Year at a Glance – Grade 4
Essential Questions
Resources
I Can Learning
Targets
line of symmetry
How can figures have line and
symmetric figure
rotational symmetry?
rotation
How do you identify if a shape
rotational symmetry
has a line or lines of
center of rotation
symmetry?
clockwise
counter-clockwise
pound
ounce
conversion
Most KCCRS standards have 1-2 (3 at the most) lessons each that can be used in 4th Grade MIF.
* The team would be very cautious in saying that students have mastered a skill in 1-2 lessons.
These KCCRS standards will require additional resources:
4.NF.3.b Decompose a fraction into a sum of fractions with the same denominator
4.MD.1 Know relative sizes of measurement units within one system of units. Within a single
system of measurement, express measurements in a larger unit in terms of a small unit.
4.MD.2 Use the four operations to solve word problems involving distances, intervals of time,
liquid volumes, masses of objects, and money.
4.NBT.4 Fluently add and subtract multi-digit whole numbers using the standard algorithm.
4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and onedigit divisors.
Suggested Supplemental Resources
● http://community.ksde.org/LinkClick.aspx?fileticket=iX3kWvXtgRY%3d&tabid=5276&mid=13
067 (keep KSDE math standards link)
● http://www.thecurriculumcorner.com/thecurriculumcorner456/i-can-standards-for-4th-5th6th-grades/ (keep “I can statements”)
● www.insidemathematics.org (performance tasks resources)
● www.engageny.org (common core resources that teachers can print immediately)
● https://www.georgiastandards.org (common core lessons)
https://grade4commoncoremath.wikispaces.hcpss.org/home (4th grade common core lessons)
Engage NY:
G.2 and G. 3
Module 4,
Topic D, L
12-16
G. 3 I can recognize, identify,
and draw lines of symmetry.
Unit/Chapter
KCCRS Standards
13.1 Identifying Lines
of Symmetry
Geometry
4.G.3 Recognize a line of symmetry
for a two-dimensional figure as a
line across the figure so that the
figure can be folded along that line
into matching parts. Identify linesymmetric figures and draw lines of
symmetry.
Team Notes:
The following KCCRS
standards are not
emphasized in 4th
Grade MIF.
8
Vocabulary
• NBT. 4 Module 1, Topic D, L 11-12
• NBT. 4 Module 1, Topic E, L 13-16
• NBT. 6 Module 3, Topic G, L 26-33
• MD. 1 and MD. 2 Module 2, Topic A, L 1-3
• MD. 1 and MD. 2 Module 2, Topic B, L 4-5
• MD. 1, OA. 1 and OA. 2
• Module 7, Topic A L 1-5
• OA. 2 and OA. 3, MD. 1 and MD. 2 Module
7, Topic B, l 6-11
• OA.3, MD. 1 and MD. 2 Module 7, Topic C,
L 12-14
• NF. 3(b) Engage NY lessons in chapter 6
2016-17 Manhattan-Ogden USD 383 – Math Year at a Glance – Grade 4
Unit/Chapter
The following chapters
are not emphasized
with the KCCRS math
standards in 4th Grade.
KCCRS Standards
Vocabulary
Essential Questions
Chapter 4 - How are graphs and tables visual tools for showing and analyzing data?
4th Grade Performance Standards
Standard
OA.1-OA.3
Tasks OA.1-OA.3
OA.4
Task OA.4
OA.5
Task OA.5
NBT.1-NBT.3
Tasks NBT.1 - NBT.3
NBT.4 - NBT.6
Tasks NBT.4 - NBT.6
NF.1 - NF.2
Tasks NF.1 - NF.2
NF.3 - NF.4
Tasks NF.3 - NF.4
NF.5 - NF.7
Tasks NF.5 - NF.7
MD.1 - MD.3
Tasks MD.1 - MD.3
MD.4
Task MD.4
MD.5 - MD.7
Tasks MD.5 - MD.7
G.1 - G.3
Tasks G.1 - G.3
9
Resources
Performance Tasks
I Can Learning
Targets