Operations
and Algebraic Thinking (4.OA) 
Use the four operations with whole numbers to solve problems.

4.OA.1 
Interpret
a multiplication equation as a comparison, e.g., interpret 35 = 5
× 7 as a statement that 35 is 5 times as many as 7 and 7 times
as many as 5. Represent verbal statements of multiplicative comparisons
as multiplication equations. 

4.OA.2 
Multiply
or divide to solve word problems involving multiplicative comparison,
e.g., by using drawings and equations with a symbol for the unknown
number to represent the problem, distinguishing multiplicative comparison
from additive comparison. 
Farm
Stand
Number
Nut Activity

4.OA.3 
Solve
multistep word problems posed with whole numbers and having wholenumber
answers using the four operations, including problems in which remainders
must be interpreted. Represent these problems using equations with
a letter standing for the unknown quantity. Assess the reasonableness
of answers using mental computation and estimation strategies including
rounding. 
Number
Nut Word Problems
Play
Division MathO
Play
Grand Slam Math 
Gain
familiarity with factors and multiples. 

Find
all factor pairs for a whole number in the range 1–100. Recognize
that a whole number is a multiple of each of its factors. Determine
whether a given whole number in the range 1–100 is a multiple
of a given onedigit number. Determine whether a given whole number
in the range 1–100 is prime or composite. 
Interactive
Factor Chart
Interactive
Multiples Chart
Play
Finding Factors
Play
The Factor Game
Octopus
Factors
Multiple
Frenzy (Sheppard)
Visual
Factor Pairs (NCTM)
MultiMultiples
(EZ School)
Fruit
Shoot Primes (Numbers to 99)
Prime
Number Activity
Play
Number Cop (sign in and click
primes) 
Generate
and analyze patterns. 

Generate
a number or shape pattern that follows a given rule. Identify
apparent features of the pattern that were not explicit in the rule
itself.
For example, given the rule “Add 3” and the starting
number 1, generate terms in the resulting sequence and observe that
the terms appear to alternate between odd and even numbers. Explain
informally why the numbers will continue to alternate in this way. 
Mission
2110 
Number
and Operations in Base Ten (4.NBT) 
Generalize
place value understanding for multidigit whole numbers. 
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. For
example, recognize that 700 ÷ 70 = 10 by applying concepts
of place value and division.


4.NBT.2

Read
and write multidigit whole numbers using baseten numerals, number
names, and expanded form. Compare two multidigit numbers based
on meanings of the digits in each place, using >, =, and <
symbols to record the results of comparisons.

Expanded
Form Hangman
Online
Lesson (What's Your Name?)
Math.com
Activity 

Use
place value understanding to round multidigit whole numbers to any
place. 
thatquiz
Practice
Half
Court Rounding 
Use
place value understanding and properties of operations to perform
multidigit arithmetic. 

Fluently
add and subtract multidigit whole numbers using the standard algorithm. 
Draggable
Addition
Draggable
Subtraction
Play
Math Journey 

Multiply
a whole number of up to four digits by a onedigit whole number,
and multiply two twodigit numbers, using strategies based on place
value and the properties of operations. Illustrate and explain the
calculation by using equations, rectangular arrays, and/or area
models. 


Find
wholenumber quotients and remainders with up to fourdigit dividends
and onedigit divisors, using strategies based on place value, the
properties of operations, and/or the relationship between multiplication
and division. Illustrate and explain the calculation by using equations,
rectangular arrays, and/or area models. 

Number
and Operations  Fractions (4.NF) 
Extend
understanding of fraction equivalencies and ordering. 

Explain
why a fraction a/b is equivalent to a fraction (n × a)/(n ×
b) by using visual fraction models, with attention to how the number
and size of the parts differ even though the two fractions themselves
are the same size. Use this principle to recognize and generate equivalent
fractions. 
Equivalent
Fractions (thatquiz.com)
Matching
Equivalent Fractions
Targeting
Equivalent Fractions
Fraction
Vault Multiplier 

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. Recognize that comparisons
are valid only when the two fractions refer to the same whole. Record
the results of comparisons with symbols >, =, or <, and justify
the conclusions, e.g., by using a visual fraction model. 
Tony's
Pizza Shop 
Build
fractions from unit fractions by applying and extending previous
understandings of operations on whole numbers. 

Understand
a fraction a/b with a > 1 as a sum of fractions 1/b. 


Understand
addition and subtraction of fractions as joining and separating parts
referring to the same whole. 


Decompose
a fraction into a sum of fractions with the same denominator in more
than one way, recording each decomposition by an equation. Justify
decompositions, e.g., by using a visual fraction model. Examples:
3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8
+ 8/8 + 1/8. 


Add
and subtract mixed numbers with like denominators, e.g., by replacing
each mixed number with an equivalent fraction, and/or by using properties
of operations and the relationship between addition and subtraction. 


Solve
word problems involving addition and subtraction of fractions referring
to the same whole and having like denominators, e.g., by using visual
fraction models and equations to represent the problem. 


Apply
and extend previous understandings of multiplication to multiply
a fraction by a whole number.



Understand
a fraction a/b as a multiple of 1/b. For example, use a visual
fraction model to represent 5/4 as the product 5 × (1/4), recording
the conclusion by the equation 5/4 = 5 × (1/4). 


Understand
a multiple of a/b as a multiple of 1/b, and use this
understanding to multiply a fraction by a whole number. For
example, use a visual fraction model to express 3 × (2/5) as
6 × (1/5),
recognizing this product as 6/5. (In general, n × (a/b) = (n
× a)/b.) 


Solve
word problems involving multiplication of a fraction by a
whole number, e.g., by using visual fraction models and equations
to represent the problem. For example, if each person at a party
will
eat 3/8 of a pound of roast beef, and there will be 5 people at the
party, how many pounds of roast beef will be needed? Between what
two whole numbers does your answer lie? 

Understand
decimal notation for fractions, and compare decimal fractions. 

Express
a fraction with denominator 10 as an equivalent fraction with
denominator 100, and use this technique to add two fractions with
respective denominators 10 and 100. For example, express 3/10
as 30/100, and add 3/10 + 4/100 = 34/100.



Use
decimal notation for fractions with denominators 10 or 100. For
example, rewrite 0.62 as 62/100; describe a length as 0.62 meters;
locate 0.62 on a number line diagram. 
Convert
Fractions and Decimals (thatquiz)
Convert
Decimals and Fractions (freewebs)
Decimals
on a Number Line (thatquiz) 

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. Record the results of comparisons with the symbols >,
=, or <, and justify the conclusions, e.g., by using a visual model. 
Play
Decimals of the Caribbean
Compare
Decimals (thatquiz.com)
Ordering
Decimals with Builder Ted (Level
1)
Play
Beat the Clock
Play
Decimal Concentration
Play
Decimal Darts (Pick
Level 2) 
Measurement
and Data (4.MD) 
Solve
problems involving measurement and conversion of measurements from
a larger unit to a smaller unit. 

Know
relative sizes of measurement units within one system of units including
km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system
of measurement, express measurements in a larger unit in terms of
a smaller unit. Record measurement equivalents in a two column table.
For example, know that 1 ft is 12 times as long as 1 in. Express the
length of a 4 ft snake as 48 in. Generate a conversion table for feet
and inches listing the number pairs (1, 12), (2, 24), (3, 36), ... 
Inches
& Feet
Yards
& Feet
Ounces & Pounds 

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. Represent measurement quantities using diagrams such as number
line diagrams that feature a measurement scale. 


Apply
the area and perimeter formulas for rectangles in real world and
mathematical problems. For example, find the width of a rectangular
room given the area of the flooring and the length, by viewing the
area formula as a multiplication equation with an unknown factor. 
Calculate
Area
Compare
Area
Find
Missing Values
Online
Lesson and Activity 
Represent
and interpret 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. For
example, from a line plot find and interpret the difference in length
between the longest and shortest specimens in an insect collection. 

Geometric
measurement: understand concepts of angle and measure angles. 

Recognize
angles as geometric shapes that are formed wherever two rays share
a common endpoint, and understand concepts of angle measurement: 
AntiHomework
Elementary 

An
angle is measured with reference to a circle with its center at the
common endpoint of the rays, by considering the fraction of the circular
arc between the points where the two rays intersect the circle. An
angle that turns through 1/360 of a circle is called a “onedegree
angle,” and can be used to measure angles. 


An
angle that turns through n onedegree angles is said to have
an angle measure of n degrees. 
Interactie
Angle Degree Estimation Measurements 

Measure
angles in wholenumber degrees using a protractor. Sketch angles of
specified measure. 
Measure
Angles (thatquiz)
Create
Angles (mathplayground) 
4.MD.7 
Recognize
angle measure as additive. When an angle is decomposed
into nonoverlapping parts, the angle measure of the whole is the
sum
of the angle measures of the parts. Solve addition and subtraction
problems to find unknown angles on a diagram in real world and
mathematical problems, e.g., by using an equation with a symbol
for
the unknown angle measure. 


Draw
and identify lines and angles, and classify shapes by properties
of their lines and angles. 
4.G.1

Draw
points, lines, line segments, rays, angles (right, acute, obtuse),
and perpendicular and parallel lines. Identify these in twodimensional
figures. 
Sheppard
Software 
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. Recognize right triangles as a category, and identify
right triangles. 
thatquiz.com
mathplay.com


Recognize
a line of symmetry for a twodimensional figure as a line across the
figure such that the figure can be folded along the line into matching
parts. Identify linesymmetric figures and draw lines of symmetry. 
Symmetry
Sort
Symmetry
Game
Draw
Lines of Symmetry
Online
Lesson (then practice)
hbschool.com
Demonstration
