# data[].attributes.body
Use decimal notation for fractions with denominators 10 or 100.

# 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.

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Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.

# 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
Compose and decompose numbers from 11 to 19 using quantities (numbers with units) of ten ones and some further ones.  Understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones.

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

# data[].attributes.body
Convert and add fractions with denominators of 10 and 100.  a. Convert a fraction with a denominator of 10 as an equivalent fraction with denominator 100.
b. Add two fractions with respective denominators 10 and 100.

# data[].attributes.body
Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900.

# data[].attributes.body
Operations with decimals to hundredths.
a. Add, subtract, multiply, and divide decimals to hundredths using…

concrete models or drawings

strategies based on place value

properties of operations

the relationship between addition and subtraction

b. Relate the strategy to a written method and explain the reasoning used.

# data[].attributes.body
Understand 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
Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes, using appropriate range and intervals, to represent points on the line and in the plane that include negative numbers and coordinates.
a. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize 0 is its own opposite and the opposite of a negative number is a positive, and the opposite of a negative number is the number itself, such as  –(–3) = 3.
b. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.
c. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize the similarity between whole numbers, their negative opposites and their positions on a number line, ordered pairs differ only by signs and their locations on one or both axes.

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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
Count
a. Count to 100 by ones and tens.
b. Count backwards from 30 by ones.

# data[].attributes.body
Fluently divide multi-digit numbers using an algorithm.
a. Convert a rational number to a decimal using long division.
b. Know that the decimal form of a rational number terminates in 0s or eventually repeats.

# data[].attributes.body
Recognize in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right.

# data[].attributes.body
Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.

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Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0 and use rate language in the context of a ratio relationship.

# data[].attributes.body
Use place value understanding to round decimals to any place.

# data[].attributes.body
Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.

# data[].attributes.body
Understand and generate equivalent fractions.
a. Use visual fraction models to recognize and generate equivalent fraction that have different numerators/denominators even though they are the same size.
b. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b).

# data[].attributes.body
Divide up to four-digit dividends by one-digit divisors. Find whole number quotients and remainders using

strategies based on place value

the properties of operations

the relationship between multiplication and division

Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

# data[].attributes.body
Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.

# data[].attributes.body
Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, = and < symbols to record the results of comparisons.

# data[].attributes.body
Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones. Understand the following as special cases:
a. 100 can be thought of as a bundle of ten tens — called a “hundred.”
b. The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones).

# data[].attributes.body
Understand the relationship between numbers and quantities; connect counting to cardinality.
a. When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object.
b. Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted.
c. Understand that each successive number name refers to a quantity that is one larger.

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Understand ordering and absolute value of rational numbers.
a. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram.
b. Write, interpret, and explain statements of order for rational numbers in real-world contexts.
c. Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation.
d. Distinguish comparisons of absolute value from statements about order.

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

# data[].attributes.body
Efficiently add and subtract fractions with unlike denominators (including mixed numbers) by…

using reasoning strategies, such as counting up on a number line or creating visual fraction models

finding common denominators

# data[].attributes.body
Understand a fraction as a number on the number line; represent fractions on a number line diagram.
a. Represent a fraction 1/b (unit fraction) on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts.

Recognize that each part has size 1/b.

a unit fraction, 1/b is located 1/b whole unit from 0 on the number line.

b. Represent a non-unit fraction a/b on a number line by marking off a lengths of 1/b (unit fractions) from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the non-unit fraction a/b on the number line.

# data[].attributes.body
Compare two fractions with different numerators and different denominators using the symbols >, = or <.  Recognize comparisons are valid only when the two fractions refer to the same whole. Justify the conclusions.

# data[].attributes.body
Read, write, and compare decimals to thousandths.
a. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form.
b. Compare two decimals to thousandths based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons.

# data[].attributes.body
Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences).
a. Subtract using

concrete models or drawings;

strategies based on place value;

properties of operations;

the relationship between addition and subtraction

b. Relate the subtraction strategy to a written method and explain the reasoning used.

# 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
Apply and extend previous understandings of multiplication to multiply a fraction by a whole number
a. Understand a fraction a/b as a multiple of 1/b.
b. Understand a multiple of a/b as a multiple of 1/b and use this understanding to multiply a fraction by a whole number.
c. Solve word problems involving multiplication of a fraction by a whole number.

# data[].attributes.body
Use place value understanding to round whole numbers to the nearest 10 or 100.

# data[].attributes.body
Divide up to four-digit dividends by two-digit divisors.
a. Find whole-number quotients of whole numbers with up to four-dividends and two-digit divisors using…

strategies based on place value

the properties of operations

the relationship between multiplication and division

b. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

# data[].attributes.body
Explain why addition and subtraction strategies work, using place value and the properties of operations.

# data[].attributes.body
Add within 100 including adding a two-digit number and a one digit number. Add a two-digit number and a multiple of 10
a. Add within 100 using…

concrete models or drawings;

strategies based on place value;

properties of operations;

the relationship between addition and subtraction.

b. 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
Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions.

# data[].attributes.body
Multiply whole numbers

up to four digits by a one-digit whole number

two-digit number by two-digit number

Multiply 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.

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

# data[].attributes.body
Solve word problems involving addition and subtraction of fractions.
a. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators.
b. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers.

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Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.

# data[].attributes.body
Represent and compare multi-digit whole numbers
a. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form.
b. Compare two multi-digit numbers based on meanings of the digit in each place, using >, = and < symbols to record the results of comparisons.

# data[].attributes.body
Multiply one-digit whole numbers by multiples of 10 in the range 10–90 using strategies based on place value and properties of operations.

# data[].attributes.body
Understand division as an unknown-factor problem.

# data[].attributes.body
Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions by using drawings and equations with a symbol for the unknown number to represent the problem.

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Determine the unknown whole number in a multiplication or division equation relating three whole numbers.

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Find factors and multiples of numbers in the range 1-100.
a. Find all factor pairs for a given whole number.
b. Recognize that a whole number is a multiple of each of its factors.
c. Determine whether a given whole number is a multiple of a given one-digit number.
d. Determine whether a given whole number is prime or composite.

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

# data[].attributes.body
For any number from 1 to 9, find the number that makes 10 when added to the given number by using objects or drawings, and record the answer with a drawing or equation.

# data[].attributes.body
Fluently add and subtract within 5.

# data[].attributes.body
Write simple expressions with numbers and interpret numerical expressions without evaluating them.

# data[].attributes.body
Interpret and demonstrate products of whole numbers.

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Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, by using objects, drawings, and equations with a symbol for one unknown number to represent the problem.

# data[].attributes.body
Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false.

# data[].attributes.body
Relate counting to addition and subtraction.

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

# data[].attributes.body
Solve addition and subtraction word problems and add and subtract within 10 by using objects or drawings to represent the problem.

# data[].attributes.body
Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.

# data[].attributes.body
Write, read and evaluate expressions in which letters stand for numbers.
a. Write expressions that record operations with numbers and with letters standing for numbers.
b. Identify parts of an expression using mathematical terms (sums, term, product, factor, quotient, coefficient); view one or more parts of an expression in a single entity.
c. Evaluate expressions for specific values of their variables, including values that are non-negative rational numbers. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).

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Add and subtract within 20.
a. Fluently add and subtract within 10.
b. Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making 10; decomposing a number leading to a ten; using the relationship between addition and subtraction; and creating equivalent but easier or known sums.

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Determine the unknown whole number in an addition or subtraction equation relating three whole numbers.

# data[].attributes.body
Decompose numbers less than or equal to 10.
a. Decompose numbers into two groups in more than one way by using objects or drawings and record each decomposition by a drawing or equation.
b. Use objects or drawings to demonstrate equality as the balancing of quantities.

# data[].attributes.body
Fluently add and subtract within 20 using mental strategies.

# data[].attributes.body
Write and evaluate numerical expressions involving whole-number exponents.

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Apply the properties of operations to generate equivalent expressions.

# data[].attributes.body
Interpret a multiplication equation as a comparison.  Represent verbal statements of multiplicative comparisons as multiplication equations.

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Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.

# 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.

# data[].attributes.body
Generate numerical patterns for situations.
a. Generate a rule for growing patterns, identifying the relationship between corresponding terms (x, y).
b. Generate patterns using one or two given rules (x, y).
c. Use tables, ordered pairs, and graphs to represent the relationship between the quantities.

# data[].attributes.body
Identify when two expressions are equivalent, when the two expressions name the same number regardless of which value is substituted into them.

# data[].attributes.body
Use various strategies to solve two-step word problems using the four operations (involving only whole numbers with whole number answers). 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
Solve multistep problems.
a. Perform operations in the conventional order when there are no parentheses to specify a particular order.
b. Solve multistep word problems posed with whole numbers and having whole number 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.

# data[].attributes.body
Use variables to represent two quantities in a real-world problem that change in relationship to one another;
a. Appropriately recognize one quantity as the dependent variable and the other as the independent variable.
b. Write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable.
c. Analyze the relationship between the dependent and independent variables using graphs and tables and relate these to the equation.

# data[].attributes.body
Represent addition and subtraction with objects, fingers, mental images, drawings, sounds, acting out situations, verbal explanations, expressions or equations.

# data[].attributes.body
Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern not explicit in the rule itself.

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

# data[].attributes.body
Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations.

# data[].attributes.body
Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division or properties of operations.

# data[].attributes.body
Determine whether a group of objects (up to 20) has an odd or even number of members; write an equation to express an even number as a sum of two equal addends.

# data[].attributes.body
Multiply or divide to solve word problems involving multiplicative comparisons, 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
Apply properties of operations as strategies to add and subtract.

# data[].attributes.body
Interpret and demonstrate whole-number quotients of whole numbers, where objects are partitioned into equal shares.

# data[].attributes.body
Write an inequality of the form x > c, x < c, x ≥ c, or x ≤ c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of these forms have infinitely many solutions; represent solutions of such inequalities on vertical and horizontal number lines.

# data[].attributes.body
Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.

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

# data[].attributes.body
Understand subtraction as an unknown-addend problem.

# data[].attributes.body
Measure and solve problems involving mass and liquid volume.
a. Measure and estimate masses and liquid volumes of objects using standard units of grams (g), kilograms (kg) and liters (L).
b. Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units.

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Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers.

# data[].attributes.body
Apply the area and perimeter formulas for rectangles in real world and mathematical problems.

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Order three objects by length; compare the lengths of two objects indirectly by using a third object.

# data[].attributes.body
Recognize and identify coins by name (penny, nickel, dime, quarter).

# data[].attributes.body
Summarize numerical data sets in relation to their context, such as by:
a. Reporting the number of observations.
b. Describing the nature of the attribute under
investigation, including how it was measured and its units of
measurement.
c. Determining quantitative measures of center (median and/or mean) to describe distribution of numerical data.

d. Describing distributions of numerical data qualitatively relating to shape (using terms such as cluster, mode(s), gap, symmetric, uniform, skewed-left, skewed-right and the presence of outliers)and quantitatively relating to spread/variability (using terms such as range and interquartile range).
e. Relating the choice of measures of center and variability
to the shape of the data distribution.

# data[].attributes.body
Assign values to time and money.
a. Tell and write time in hours and half-hours using analog and digital clocks.
b. Identify the coins by values (penny, nickel, dime, quarter).

# data[].attributes.body
Solve real world and mathematical problems involving perimeters of polygons.
a. Find the perimeter given the side lengths of a polygon.
b. Find an unknown side length, given the perimeter and some lengths.
c. Draw rectangles with the same perimeter and different areas or with the same area and different perimeters.

# data[].attributes.body
Tell and write time to the nearest minute and measure elapsed time intervals in minutes. Solve word problems involving addition and subtraction of time intervals within and across the hour in minutes.

# data[].attributes.body
Recognize volume as an attribute of solid figures and understand concepts of volume measurement.
a. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume and can be used to measure volume.
b. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units.

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

# data[].attributes.body
Recognize that a measure of center for a numerical data set summarizes all of its values with a single number to describe a typical value, while a measure of variation describes how the values in the distribution vary.