# data[].attributes.body
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.

# data[].attributes.body
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 one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite.

# data[].attributes.body
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.

# data[].attributes.body
Count to 100 by ones and by tens.

# data[].attributes.body
Write numbers from 0 to 20. Represent a number of objects with written numeral 0-20 with 0 representing no objects.

# data[].attributes.body
Understand that each successive number name refers to a quantity that is one larger.

# data[].attributes.body
Use addition and subtraction within 100 to solve one-step and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing with unknowns in all positions.

# data[].attributes.body
Identify whether the number of objects in one group is greater than less than, or equal to the number of objects in another group

# data[].attributes.body
Represent addition and subtraction with objects, fingers, mental
images, drawings2, sounds (e.g., claps), acting out situations, verbal
explanations, expressions, or equations

# data[].attributes.body
Decompose numbers less than or equal to 10 into pairs in more
than one way, e.g., by using objects or drawings, and record each
decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).

# data[].attributes.body
Compose and decompose numbers from 11 to 19 into ten ones and
some further ones, e.g., by using objects or drawings, and record each
composition or decomposition by a drawing or equation (e.g., 18 = 10 +
8); understand that these numbers are composed of ten ones and one,
two, three, four, five, six, seven, eight, or nine ones.

# data[].attributes.body
Use addition to find the total number of objects arranged inrectangular arrays with up to 5 rows and up to 5 columns; write anequation to express the total as a sum of equal addends.

# data[].attributes.body
Describe objects in the environment using names of shapes, and
describe the relative positions of these objects using terms such as
above, below, beside, in front of, behind, and next to.

# data[].attributes.body
Use addition and subtraction within 20 to solve word problems involving
situations of adding to, taking from, putting together, taking apart,
and comparing, with unknowns in all positions, e.g., by using objects,
drawings, and equations with a symbol for the unknown number to
represent the problem.2

# data[].attributes.body
Apply properties of operations as strategies to add and subtract.3 Examples:
If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of
addition.) To add 2 + 6 + 4, the second two numbers can be added to make
a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.)

# data[].attributes.body
Measure the length of an object twice, using length units ofdifferent lengths for the two measurements; describe how the twomeasurements relate to the size of the unit chosen.

# data[].attributes.body
Add and subtract within 20, demonstrating fluency for addition and
subtraction within 10. Use strategies such as counting on; making ten
(e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to
a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between
addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8
= 4); and creating equivalent but easier or known sums (e.g., adding 6 +
7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).

# data[].attributes.body
Determine the unknown whole number in an addition or subtraction
equation relating three whole numbers. For example, determine the
unknown number that makes the equation true in each of the equations 8 +
? = 11, 5 = � – 3, 6 + 6 = �.

# data[].attributes.body
Represent whole numbers as lengths from 0 on a number line diagram
with equally spaced points corresponding to the numbers 0, 1, 2, ..., and
represent whole-number sums and differences within 100 on a number
line diagram

# data[].attributes.body
Count to 120, starting at any number less than 120. In this range, read
and write numerals and represent a number of objects with a written
numeral.

# data[].attributes.body
Understand that the two digits of a two-digit number represent amounts
of tens and ones. Understand the following as special cases:
a. 10 can be thought of as a bundle of ten ones — called a “ten.”
b. The numbers from 11 to 19 are composed of a ten and one, two,
three, four, five, six, seven, eight, or nine ones.
c. The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two,
three, four, five, six, seven, eight, or nine tens (and 0 ones).

# data[].attributes.body
Add within 100, including adding a two-digit number and a one-digit
number, and adding a two-digit number and a multiple of 10, using concrete
models or drawings and strategies based on place value, properties of
operations, and/or the relationship between addition and subtraction;
relate the strategy to a written method and explain the reasoning used.
Understand that in adding two-digit numbers, one adds tens and tens, ones
and ones; and sometimes it is necessary to compose a ten

# data[].attributes.body
Tell and write time from analog and digital clocks to the nearest five
minutes, using a.m. and p.m.

# data[].attributes.body
Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and (c) symbols appropriately

# data[].attributes.body
Understand that the three digits of a three-digit number represent
amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0
tens, and 6 ones.

# data[].attributes.body
Fluently add and subtract within 100 using strategies based on place
value, properties of operations, and/or the relationship between
addition and subtraction.

# data[].attributes.body
Add and subtract within 1000, using concrete models or drawings
and strategies based on place value, properties of operations, and/or
the relationship between addition and subtraction; relate the strategy
to a written method. Understand that in adding or subtracting threedigit numbers, one adds or subtracts hundreds and hundreds, tens
and tens, ones and ones; and sometimes it is necessary to compose or
decompose tens or hundreds

# data[].attributes.body
Recognize and draw shapes having specified attributes, such as a given
number of angles or a given number of equal faces.5 Identify triangles,
quadrilaterals, pentagons, hexagons, and cubes.

# data[].attributes.body
Tell and write time in hours and half-hours using analog and digital
clocks

# data[].attributes.body
Use multiplication and division within 100 to solve word problems in
situations involving equal groups, arrays, and measurement quantities,
e.g., by using drawings and equations with a symbol for the unknown
number to represent the problem.1

# data[].attributes.body
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.

# data[].attributes.body
Organize, represent, and interpret data with up to three categories; ask
and answer questions about the total number of data points, how many
in each category, and how many more or less are in one category than in
another.

# data[].attributes.body
Apply properties of operations as strategies to multiply and
divide

# data[].attributes.body
Analyze and compare two- and three-dimensional shapes, in
different sizes and orientations, using informal language to describe
their similarities, differences, parts (e.g., number of sides and
vertices/“corners”) and other attributes (e.g., having sides of equal
length).

# data[].attributes.body
Fluently multiply and divide within 100, using strategies such as the
relationship between multiplication and division (e.g., knowing that 8 ×
5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end
of Grade 3, know from memory all products of two one-digit numbers.

# data[].attributes.body
Solve two-step word problems using the four operations. 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

# data[].attributes.body
Tell and write time to the nearest minute and measure time intervals
in minutes. Solve word problems involving addition and subtraction
of time intervals in minutes, e.g., by representing the problem on a
number line diagram.

# data[].attributes.body
Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols

# data[].attributes.body
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.

# data[].attributes.body
Measure and estimate liquid volumes and masses of objects using
standard units of grams (g), kilograms (kg), and liters (l).6 Add,
subtract, multiply, or divide to solve one-step word problems involving
masses or volumes that are given in the same units, e.g., by using
drawings (such as a beaker with a measurement scale) to represent
the problem

# data[].attributes.body
Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10

# data[].attributes.body
Relate area to the operations of multiplication and addition

# data[].attributes.body
Fluently add and subtract within 1000 using strategies and algorithms
based on place value, properties of operations, and/or the relationship
between addition and subtraction.

# data[].attributes.body
Distinguish between defining attributes (e.g., triangles are closed and
three-sided) versus non-defining attributes (e.g., color, orientation,
overall size); build and draw shapes to possess defining attributes.

# data[].attributes.body
Fluently multiply multi-digit whole numbers using the standard algorithm

# data[].attributes.body
Partition shapes into parts with equal areas. Express the area of each
part as a unit fraction of the whole. For example, partition a shape into 4
parts with equal area, and describe the area of each part as 1/4 of the area
of the shape.

# data[].attributes.body
Find whole-number quotients of whole numbers with ip to four-digit dividends and two-digit 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.

# data[].attributes.body
Understand a fraction 1/b as the quantity formed by 1 part when a
whole is partitioned into b equal parts; understand a fraction a/b as
the quantity formed by a parts of size 1/b.

# data[].attributes.body
Add, subtract, multiply and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

# data[].attributes.body
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.

# data[].attributes.body
Relate volume to the operations of multiplication and addition and
solve real world and mathematical problems involving volume.

# data[].attributes.body
Recognize volume as an attribute of solid figures and understand
concepts of volume measurement.

# data[].attributes.body
Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

# data[].attributes.body
Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem

# data[].attributes.body
Compare two fractions with different numerators and different
denominators

# data[].attributes.body
Use place value understanding to round multi-digit whole numbers to
any place.

# data[].attributes.body
Fluently add and subtract multi-digit whole numbers using the
standard algorithm.

# data[].attributes.body
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
the calculation by using equations, rectangular arrays, and/or area
models.