Operations and Algebraic Thinking
First Trimester
Second Trimester
Use the four operations with whole numbers to solve problems
4.OA.1 Interpret
N/A
-Multiply multi-digit
multiplication equation
numbers and compare
as a comparison (35 =
them (6)
5x7 is 35 is 5 times as
many as 7, and 7 times
as many as 5)

4.OA.2 Multiply or
divide to solve word
problems involving
multiplication
comparison
-Multiply single-digit
numbers and compare
them (50-Facts Test)
-Multiply multi-digit
numbers and compare
them (6)

4.OA.3 Solve multi-step
word problems posed
with whole numbers and
having whole-number
answers using the four
operations
-Solve addition and
subtraction facts (1)
-Solve addition and
subtraction number
stories (2)
- Add and subtract
decimals (4)
-Estimate sums (5)
-Add and subtract
decimals (5)
- Multiply multi-digit
whole numbers (5)
-Solve division number
stories; interpret
remainders (6)
-Divide multi-digit
numbers by 1-digit
divisors; express
remainders as fractions
(6)
- Multiply multi-digit
numbers (7)
-Divide multi-digit
numbers by one-digit
numbers (7)
Gain familiarity with factors and multiples
4.OA.4 Find all factor
-Name factors of a
pairs for a whole
given number (3)
number in the range 1- Write factors and
100. Recognize that a
multiples (4)
whole number is a
-Review through Math
Boxes
Third Trimester
-Explain how a multiplication equation (e.g. 35=5x7) can be interpreted as a
comparison (e.g. Johnny has 5 times as many cards as Bill who has 7 cards).
-Write an equation for a situation involving multiplicative comparison.
-Distinguish between multiplicative (as many times as) and additive (more)
comparisons.
-Determine when to multiply or divide in word problems.
-Solve a multiplication or division word problem involving multiplicative
comparisons using drawings and equations.
-Write an equation using a variable to represent the unknown.
-Choose the correct operation to perform at each step of a multi-step word
problem.
-Interpret remainders in word problems.
-Write equations using a variable to represent the unknown.
-Use mental math or estimation strategies to check if answers are reasonable.
-Find factors and factor pairs (12)
-Define factors and multiples.
-List all of the factor pairs for any whole number, in the range 1-100.
-Determine multiples of a given whole number.
-Define prime and composite.
multiple of each of its
factors.
-Determine if a number is prime or composite.
Generate and analyze patterns

4.OA.5 Generate a
number or shape
pattern that follows a
given rule.
- Solve “What’s My
Rule?” problems (3)
- Multiply using
“What’s My Rule?”
tables (5)
-Generate a pattern that follows a given rule.
-Identify and explain additional patterns or special behaviors in a pattern that go
beyond the given rule.
Number and Operations in Base Ten
First Trimester
Second Trimester
Third Trimester
Generalize place value understanding for multi-digit whole numbers
4.NBT.1 Recognize that
-Identify places in
- Compare large
-Explain the value of each digit in a multi-digit number as ten times the digit to
in a multi-digit whole
whole numbers and the numbers up to one
the right.
number, a digit in one
values of the digits in
billion (5)
place represents ten
those places (2)
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.
-Identify the values of
digits in numbers up to
one billion (2)
-Read and write large
-Read and write a multi-digit number in word form, base ten numerals, and
numbers using base-ten expanded form.
patterns (5)
-Compare two multi-digit numbers using place value and record the comparison
using symbols <, >, =

4.NBT.3 Use place value
understanding to round
multi-digit whole
numbers to any place.
-Round numbers to a
given place value (3)
- Round numbers to a
given place value (5)
-Explain how to use place value and what digits to look for in order to round a
multi-digit number.
-Use the value of the digit to the right of the place to be rounded to determine
whether to round up or down.
-Write a multi-digit number rounded to any given place.
Use place value understanding and properties of operations to perform multi-digit arithmetic.
4.NBT.4 Fluently add and -Solve addition and
-Review through Math
-Solve addition problems involving negative integers
subtract multi-digit
subtraction facts (1)
Boxes
-Add multi-digit whole numbers with ease by using the standard algorithm (e.g.
whole numbers using
-Add and subtract
add one column of numbers at a time starting with the ones digits, then the
the standard algorithm.
multi-digit numbers (2)
tens digits).
-Solve addition and
-Subtract multi-digit whole numbers with ease by using the standard algorithm
subtraction number
(e.g. subtract one column of numbers at a time starting with the ones digits,
stories (3)
then the tens digits).

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.
N/A
- Multiply multi-digit
numbers (5.1
enrichment, 5.3, 5.4,
5.5, 5.6) (7)
-Multiply a multi-digit number by a one-digit whole number.
-Demonstrate multiplication of two two-digit numbers using rectangular arrays,
place value, and the area model.
-Solve multiplication of two two-digit numbers using properties of operations
and equations.
-Explain my chosen strategy.

4.NBT.6 Find wholenumber quotients and
remainders with up to
four-digit dividends and
one-digit divisors, using
strategies based on
place value, the
properties of operations,
and/or the relationship
between multiplication
and division.
N/A
-Divide multi-digit
numbers by one-digit
numbers (7)
-Solve division number
stories; interpret
remainders (6)
-Divide multi-digit
numbers by 1-digit
divisors; express
remainders as fractions
(6)
-Demonstrate division of a multi-digit number by a one-digit number using place
value, rectangular arrays, and area model.
-Solve division of a multi-digit number by a one-digit number using properties of
operations and equations.
-Explain my chosen strategy
Number and Operations – Fractions
First Trimester
Second Trimester
Third Trimester
Extend understanding of fraction equivalence and ordering
4.NF.1. Explain why a N/A
- Write equivalent
-Explain why fractions are equivalent using models.
fraction a/b is
fractions (7)
-Generate equivalent fractions by multiplying or dividing the numerator and
equivalent to a fraction
denominator by the same number.
(n × a)/(n × b) by using
-Use visual models to justify why multiplying or dividing the numerator and
visual fraction models,
denominator by the same number generates equivalent fractions.
with attention to how
the number and size of
the parts differ even
though the two
fractions themselves
are the same size.



4.NF.2. Compare two
fractions with different
numerators and
different
denominators, e.g., by
creating common
denominators or
numerators, or by
comparing to a
benchmark fraction
such as 1/2.
N/A
-Compare fractions
(7.6)
-Order fractions (7)
-Equivalent fractions
(7.7)
-Explain the comparing two fractions is valid only when they refer to the same
whole.
-Compare two given fractions by generating equivalent fractions with common
denominators.
-Compare two given fractions by reasoning about their size or their location on
a number line, or comparing them to a benchmark fraction.
-Record the comparison using symbols (<, =, and >) and justify each comparison.
Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers
4.NF.3. Understand a
N/A
- Add and subtract
- Add and subtract fractions (10)
fraction a/b with a > 1
fractions (7.5, 8)
-Use visual models to add and subtract fractions within the same whole.
as a sum of fractions
- Name fractions of
-Use visual models to decompose a fraction in more than one way, including
1/b.
regions or collections;
decomposing a fraction into a sum of its unit fraction.
find the ONE (7)
-Record decomposition in an equation.
-Add or subtract a mixed fraction using equivalent fractions, properties of
operations, or the relationship between addition and subtraction.
-Solve addition and subtraction word problems using drawings, pictures, and
equations.
4. NF 4. Apply and
N/A
-Compare fractions
-Explain why a/b = a x 1/b by using visual models to show how to decompose
extend previous
(7.1)
fractions into unit fractions and represent it as a multiple of unit fractions (e.g.
understandings of
-Word problems with
3/4 = 1/4 + 1/4 + 1/4 = 3 x 1/4).
multiplication to
fractions (7.2, 7.4)
-Decompose a fraction (a/b) into a multiple of unit fractions (a x 1/b) in order to
multiply a fraction by a
show why multiplying a whole number by a fraction (n x (a/b)) results in (n x
whole number.
a)/b (e.g. 5 x 3/8 = 5 x (3 x 1/8) = (5 x 3) x 1/8 = 15 x 1/8 = 15/8).
- Solve word problems that involve multiplying a whole number and fraction
with visual models and equations.
(Need supplemental materials)
Understand decimal notation for fractions, and compare decimal fractions
4.NF.5. Express a
N/A
- Add and subtract
-Rewrite a fraction with a denominator 10 as an equivalent fraction with
fraction with
fractions (8)
denominator 100.
denominator 10 as an
-Add two fractions with denominators 10 and 100.
equivalent fraction with
denominator 100, and
use this technique to
add two fractions with
respective
denominators 10 and
100.

4.NF.6. Use decimal
notation for fractions
with denominators 10
or 100.
-Convert fractions to
decimals (4.2)
-Rename tenths and
hundredths as decimals
(7)

4.NF.7. Compare two
decimals to
hundredths by
reasoning about their
size.
- Order decimals (4.3)
- Write numbers
between two whole
numbers (4)
-Review through Math
Boxes
- Fill in a table of equivalent fractions, decimals, and percents (9)
-Use a calculator to rename fractions as decimals (9)
-Use a calculator to rename fractions as percents (9)
- Give fraction, decimal, and percent equivalents (10)
-Write a ratio as a fraction and a percent (9)
-Interpret a percent (9)
-Shade a percent of a region; write the percent as a fraction and a decimal (9)
-Explain the relationship between a fraction and the decimal representation.
(10.6)
-Represent fractions with denominators of 10 and 100 as a decimal.
-Identify the tenths and hundredths place of a decimal.
-Show the placement of a decimal on a number line.
-Explain that comparing two decimals is valid only when they refer to the same
whole.
-Justify the comparison by reasoning about the size of the decimals and by using
a visual model.
-Compare two decimals to the hundredths place and record the comparison
using symbols <, >, or =.
Measurement and Data
First Trimester
Second Trimester
Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit
Third Trimester


4.MD.1. Know relative
sizes of measurement
units within one
system of units
including km, m, cm;
kg, g; lb, oz.; l, ml; hr,
min, sec.
- Measure line
segments to the
nearest centimeter (4)
-Measure and draw line
segments to the
nearest ½ centimeter
(4)
- Measure to the
nearest ¼ inch and ½
centimeter (5)
- Find the volume of a stack of cm cubes (11)
- Calculate volume (12)
-Make reasonable weight estimates (11)
-Describe the relative size of measurement units (e.g. km, m, cm; kg, g; lb, oz; l,
ml; hr, min, sec).
-Represent a larger unit as a multiple of smaller units within the same system of
measurement and record the equivalent measures in a two-column table (e.g. 1
foot = 12 inches, 2 feet = 24 inches, 3 feet = 36 inches).
4.MD.2. Use the four
operations to solve
word problems
involving distances,
intervals of time, liquid
volumes, masses of
objects, and money,
including problems
involving simple
fractions or decimals,
and problems that
require expressing
measurements given
in a larger unit in terms
of a smaller unit.
-exchange rates (3.6)
-finding air distances
(3.7)
-Review through math
boxes
-Word problems with
fractions (7.2, 7.4)
-Review through math
boxes
- Find equivalent capacities (12)
-Represent measurements using diagrams and correct measurement scale.
-Use the four operations to solve measurement word problems.
-Solve word problems involving various measurements expressed by whole
numbers, fractions, and decimals.
-Convert a measurement given in a larger unit into an equivalent measurement
in smaller units in order to solve problems.
4.MD.3. Apply the
area and perimeter
formulas for rectangles
in real world and
mathematical
problems.
N/A
- Find the perimeter of
a polygon (8)
-Find the area of a
polygon drawn on a
grid (8)
-Draw a rectangle with
a given area and
perimeter (8)
-Solve number stories
involving area (8)
- Find the area and perimeter of a rectangle, parallelogram, and triangle (9)
-Explain the formulas for area and perimeter.
-Use the formulas for area and perimeter to solve real world problems.
-Create a line plot with
a given data set of
-Create a line plot with a given data set of measurements using fractions as a
unit. (Use science to incorporate fractions in standard- for example, from a line
Represent and interpret data
4.MD.4. Make a line
Line plots (2.6)
plot to display a data
-Create a line plot with
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.
a given data set of
measurements using
fractions as a unit. (Use
science to incorporate
fractions in standardfor example, from a line
plot find and interpret
the difference in length
between the longest
and shortest specimens
in an insect collection.)
measurements using
fractions as a unit. (Use
science to incorporate
fractions in standardfor example, from a line
plot find and interpret
the difference in length
between the longest
and shortest specimens
in an insect collection.)
plot find and interpret the difference in length between the longest and
shortest specimens in an insect collection.)
-Use the information on the line plot to solve addition and subtraction
problems.
Measurement and Data
First Trimester
Second Trimester
Third Trimester
Geometric measurement: understand concepts of angle and measure angles
4.MD.5. Recognize
-Construct angles (1)
-Classify and measure
-Identify the parts of an angle (vertex, common endpoint, rays) and define an
angles as geometric
angles (6)
angle.
shapes that are
-Explain that an angle is measured in degrees related to the 360 degrees in a
formed wherever two
circle.
rays share a common
endpoint, and
understand concepts
of angle
measurement.

4.MD.6. Measure
angles in wholenumber degrees using
a protractor. Sketch
angles of specified
measure.
N/A
- Classify and measure
angles (6)
-Measure an angle using a protractor in whole-number degrees.
-Sketch angles with a given measurement.
-Use a protractor to create a given angle measurement.
4.MD.7. Recognize
angle measure as
additive.
N/A
- Classify and measure
angles (6)
-Explain that the angle measurement of a larger angle is the sum of the angle
measures of its decomposed parts.
-Write an equation with an unknown angle measurement.
-Use addition and subtraction to solve for the missing angle measurements.
-Solve word problems involving unknown angles.
Geometry
First Trimester
Second Trimester
Third Trimester
Draw and identify lines and angles and classify shapes by properties of their lines and angles
4.G.1. Draw points,
-Draw parallel and
Review through Math
-Draw an example of a point, line, line segment, ray, right angle, acute angle,
lines, line segments,
intersecting lines and
Boxes
obtuse angle, perpendicular lines, and parallel lines.
rays, angles (right,
line segments (1)
-Look for and identify the following in a given two-dimensional figure: point,
acute, obtuse), and
-Name lines and rays
line, line segment, ray, right angle, acute angle, obtuse angle, perpendicular
perpendicular and
(1)
lines, and parallel lines.
parallel lines. Identify
these in twodimensional figures.

4.G.2. Classify twodimensional figures
based on the presence
or absence of parallel
or perpendicular lines,
or the presence or
absence of angles of a
specified size.
-Draw quadrangles (1)
-Name polygons (1)
-Identify properties of
polygons (1)
- Draw a polygon, mark
the right angles (2)
Explain whether or not
a given polygon is a
parallelogram (2)
Review through Math
Boxes
-Classify two-dimensional shapes into the following categories: those with
parallel lines, those with perpendicular lines, those with both parallel and
perpendicular lines, those with no parallel or perpendicular lines.
-Classify two-dimensional shapes into categories based on the presence or
absence of acute, obtuse, or right angles.
-Identify a right angle.
4.G.3. Recognize a
line of symmetry for a
two-dimensional figure
as a line across the
figure such that the
figure can be folded
along the line into
matching parts.
-Stand-Out Math
-Stand-Out Math
-Draw a shape with zero, one, two, or multiple lines of symmetry (10)
-Use a transparent mirror to draw the reflection of the preimage (10)
-Use a transparent mirror to draw the other half of the figure across the line of
symmetry (10)
-Identify line-symmetric figures.
-Define line of symmetry, explain how to identify it in a two-dimensional figure,
and explain how folding along the line of symmetry results in matching parts.
-Draw a line on a figure to create two symmetric figures.