Kindergarten

23 atomsView all →

NUM

Numbers

(8 atoms)

• Extend oral counting from 51 through 100

  Continues the oral counting sequence from 51 through 100, crossing each decade boundary without restarting, skipping, or inventing number names.

• Perceptually subitize quantities through five

  Names a briefly shown quantity from zero through five without counting, across both structured and unstructured arrangements.

• Maintain one-to-one correspondence while counting

  Pairs exactly one number word with each object in a collection so no object is skipped or counted more than once.

• Use the final count word to state how many

  After counting a collection, states that the final number word gives the total quantity without treating it only as a label for the last object.

• Conserve number across order and arrangement

  Recognizes that a set has the same number of objects when it is counted in a different order or rearranged without adding or removing anything.

• Relate each successive number to one more

  Explains and represents that the next number in the counting sequence names a quantity containing exactly one more object.

• Compare concrete groups through 10

  Compares two groups containing up to 10 objects and identifies one as greater than, less than, or equal to the other without requiring comparison symbols.

• Compare written numerals from 1 through 10

  Given two written numerals from 1 through 10, identifies which names the greater quantity or that the quantities are equal without requiring comparison symbols.

GEO

Shapes

(8 atoms)

• Describe positions as above or below

  Describes one object's vertical position relative to another object using above or below correctly in either direction.

• Describe positions as beside or next to

  Identifies and describes when one object is beside or next to another object across varied arrangements.

• Describe positions as in front of or behind

  Describes one object's position as in front of or behind another object when the observer frame is visually or verbally established.

• Name common two-dimensional shapes across size and orientation

  Names circles, triangles, squares, rectangles, and hexagons when their size, proportion, or orientation varies.

• Informally analyze and compare two-dimensional shapes

  Compares two flat shapes by observable parts and attributes such as sides, corners, and equal side lengths without requiring a formal classification proof.

• Model a named or real-world shape by building or drawing

  Builds or draws a recognizable model of a named two-dimensional or three-dimensional shape, including shapes observed in the environment.

• Distinguish two-dimensional from three-dimensional shapes

  Classifies shapes as flat two-dimensional figures or solid three-dimensional objects while distinguishing a pictured representation from the object it represents.

• Informally analyze and compare three-dimensional shapes

  Compares two solid shapes by observable parts and behavior, such as flat or curved surfaces and whether they roll, stack, or slide.

MD

Measurement

(3 atoms)

• Identify and describe linear attributes

  Identifies length, height, or width as the relevant measurable attribute of an object and describes it with appropriate comparative language.

• Identify a penny as one cent and value up to 20 pennies

  Recognizes a penny as a coin worth one cent and determines the total value of a collection of up to 20 pennies.

• Directly compare weights as heavier or lighter

  Directly compares the weight of two objects and describes the result as heavier, lighter, or the same weight.

OA

Operations

(1 atoms)

• Decompose numbers through 10 in multiple ways

  Breaks a total through 10 into two or more parts and produces multiple valid decompositions while preserving the original total.

FLU

Fluency

(3 atoms)

• Add accurately within 10

  Finds sums with addends and totals within 10 accurately, using any mathematically valid strategy without a fluency requirement.

• Find the part needed to make 10 using a model

  Given a number from 1 through 9, uses objects or a drawing to find the missing part that makes 10 and records the result with a drawing or equation.

• Subtract accurately within 10

  Finds differences with starting quantities within 10 accurately, using any mathematically valid strategy without a fluency requirement.

1st Grade

126 atomsView all →

NUM

Numbers

(15 atoms)

• Count forward by ones to 20

  Says the counting sequence from 1 to 20 in order, unaided, without skipping or repeating numbers.

• Count forward by ones starting from any number within 20

  Continues the counting sequence from a given starting number within 20 without restarting at 1.

• Count forward by ones to 50

  Extends the oral counting sequence to 50, handling each decade transition correctly.

• Extend oral counting from 101 through 120

  Continues the learned oral counting sequence past 100 through 120, handling the transition from 100 to 101 correctly.

• Continue counting from any number in a learned sequence

  Continues counting for at least 10 numbers from an arbitrary entry point in the currently learned oral sequence without needing a running start from one or a decade.

• Read numerals to 20

  Says the number name for any written numeral from 0 to 20 on sight.

• Write numerals to 20

  Writes the correct numeral for a spoken number word from 0 to 20, correctly formed and ordered.

• Read numerals to 120

  Says the number name for any written two- or three-digit numeral up to 120.

• Write numerals to 120

  Writes the correct numeral for any spoken number up to 120, including numbers with a zero in the ones place.

• Subitize larger quantities using five and ten structures

  Recognizes six through 10 without counting when a structured arrangement can be composed from a known group of five or ten and a smaller part.

• Count a set of objects and record the count as a numeral within 20

  Coordinates a correct count of up to 20 objects with writing the numeral that records the resulting total.

• Count a set of objects and record the count as a numeral within 120

  Counts a collection of up to 120 objects, organizing the count, often into groups of ten, and records the numeral.

• Count backward by ones from any number within 20

  Says the counting sequence in reverse from a given number within 20 down to 0.

• Count forward by tens within a known sequence

  Says the decade sequence through the currently learned range and continues the tens pattern from a given decade without restarting at 10.

• Order numerals within 120 on a number path or line

  Places numbers in order and identifies what comes before, after, or between given numbers within 120.

GEO

Shapes

(8 atoms)

• Distinguish defining from non-defining attributes of shapes

  Separates attributes that determine what a shape is—sides, corners, and closure—from color, size, and orientation.

• Identify and name two-dimensional shapes by their defining attributes

  Names circles, triangles, squares, rectangles, trapezoids, and hexagons and justifies each by its attributes.

• Build or draw a shape with given defining attributes

  Produces a shape meeting a stated set of attributes, including non-prototypical examples.

• Compose two-dimensional shapes to create a composite shape

  Joins two or more flat shapes to form a larger named shape.

• Decompose a composite two-dimensional shape into its parts

  Identifies smaller shapes inside a larger figure, including when boundaries are not drawn.

• Recognize that a composite shape can be built in more than one way

  Finds multiple distinct ways to compose the same target shape.

• Identify and name three-dimensional shapes

  Names cubes, rectangular prisms, cones, cylinders, and spheres across varied sizes, orientations, and real-world examples.

• Compose three-dimensional shapes to build a composite solid

  Combines solid figures into a larger structure and names the solids used.

MD

Measurement

(12 atoms)

• Directly compare two objects by a linear dimension

  Compares the length, height, or width of two objects by aligning the relevant endpoints and states which is longer, shorter, taller, or wider.

• Order three objects by length

  Arranges three objects from shortest to longest and describes the order.

• Compare lengths indirectly using a third object

  Compares objects that cannot be placed together by using a third object as a go-between.

• Identify the hour and minute hands and what each shows

  Distinguishes the two clock hands and states what each one indicates.

• Tell time to the hour on an analog clock

  Reads an analog clock showing an exact hour and says the time.

• Tell time to the half hour on an analog clock

  Reads a half-hour time while accounting for the hour hand sitting between two numbers.

• Understand length as a count of same-size units

  Understands a length measurement as the number of identical units fitting end to end.

• Measure a length by iterating units with no gaps or overlaps

  Lays same-size units end to end along an object, starting at one end, without gaps or overlaps.

• Report and compare measurements expressed in units

  States a measurement as a number of units and uses two measurements to compare lengths.

• Write time in digital notation for hours and half hours

  Records a time digitally with the colon and minutes correctly placed.

• Match analog and digital clock representations

  Pairs an analog clock face with its digital equivalent and explains the correspondence.

• Identify dimes and count mixed penny-and-dime collections

  Identifies a dime as 10 cents and determines the value of mixed penny-and-dime collections up to 100 cents.

DAT

Data

(5 atoms)

• Sort objects into up to three categories

  Groups a collection consistently by a stated attribute into as many as three categories.

• Represent categorical data in a chart or picture graph

  Organizes sorted data into a labeled tally chart, picture graph, or simple bar-style chart.

• Interpret how many are in each category

  Reads a data display to report the count for a named category.

• Determine the total number of data points

  Adds the category counts to find how many items or responses are represented in all.

• Answer comparison questions about categories

  Uses a data display to answer how-many-more and how-many-fewer questions.

OA

Operations

(28 atoms)

• Count on from a number to add within 10

  Adds by starting at one addend and counting forward by the second addend instead of counting all from one.

• Count on from a number to add within 20

  Extends counting on to sums within 20, including crossing ten.

• Count back to subtract within 10

  Subtracts by starting at the total and counting backward the number being taken away.

• Count back to subtract within 20

  Extends counting back to differences within 20, including crossing ten.

• Interpret addition as putting together or adding to

  Recognizes joined or increased quantities as addition situations and explains why.

• Interpret subtraction as taking from or taking apart

  Recognizes removal and decomposition situations as subtraction situations and explains what quantity is being taken away or separated.

• Represent an addition situation with an equation

  Writes an addition equation with a symbol for the unknown that matches the structure of a given situation.

• Represent a subtraction situation with an equation

  Writes a subtraction equation with a symbol for the unknown that matches the structure of a given situation.

• Understand subtraction as an unknown-addend problem

  Rewrites a subtraction as a missing-addend addition and solves it by thinking addition.

• Write the related addition and subtraction facts for a part-part-whole triple

  Given three related numbers, writes all four equations in the fact family.

• Interpret subtraction as comparing two quantities

  Recognizes a comparison asking how many more or fewer as a subtraction situation and identifies the difference between the two quantities.

• Solve add-to, result-unknown word problems

  Given a start amount and an amount added, finds the resulting total.

• Solve add-to, change-unknown word problems within 20

  Given a start amount and a resulting total, finds how many were added.

• Solve add-to, start-unknown word problems within 20

  Given an amount added and a resulting total, finds the original starting amount.

• Solve take-from, result-unknown word problems

  Given a start amount and an amount removed, finds how many remain.

• Solve take-from, change-unknown word problems within 20

  Given a start amount and what remains, finds how many were removed.

• Solve take-from, start-unknown word problems within 20

  Given an amount removed and what remains, finds the original amount.

• Solve put-together, total-unknown word problems

  Given two parts that exist at the same time, finds the whole.

• Solve put-together, addend-unknown word problems within 20

  Given a whole and one part, finds the other part.

• Solve put-together, both-addends-unknown word problems

  Given a total in a put-together or take-apart situation, finds two unknown parts that compose the stated whole.

• Solve compare, difference-unknown word problems within 20

  Given two amounts, finds how many more or how many fewer one is than the other.

• Solve compare, bigger-unknown word problems within 20

  Given a smaller amount and the difference, finds the larger amount.

• Solve compare, smaller-unknown word problems within 20

  Given a larger amount and the difference, finds the smaller amount — including inconsistent-language versions.

• Add three whole numbers with a sum within 20

  Adds three addends by choosing an efficient order or grouping, not strictly left to right.

• Solve three-addend word problems within 20

  Solves a situation combining three quantities and writes a matching equation.

• Recognize that addition can be done in any order (commutative property)

  Knows that changing the order of two addends does not change the sum, and can show why with a model.

• Use the commutative property to count on from the larger addend

  Reorders an addition so counting on starts from the larger number, reducing the number of steps.

• Group addends to make a ten (associative property)

  Regroups three addends so that two of them combine to ten, then adds the remaining addend.

FRA

Fractions

(6 atoms)

• Recognize equal versus unequal shares

  Judges whether a shape has been divided into parts of the same size regardless of arrangement.

• Partition a circle or rectangle into two equal shares

  Divides a whole into two equal parts and identifies each part as a half.

• Partition a circle or rectangle into four equal shares

  Divides a whole into four equal parts and identifies each as a fourth or quarter.

• Use the words halves, fourths, and quarters to describe shares

  Names partitioned parts with correct fraction vocabulary, including half of and quarter of.

• Describe the whole as two of two shares or four of four shares

  States that the whole shape is made of all its equal parts together.

• Understand that more equal shares make smaller shares

  Knows that dividing the same whole into more parts produces smaller parts, and compares halves to fourths.

FLU

Fluency

(20 atoms)

• Add zero to any number within 20

  Knows that adding zero leaves a quantity unchanged, without counting.

• Add one or two to any number within 20

  Adds 1 or 2 using immediate sequence knowledge rather than recounting from one.

• Fluently add within 5

  Recalls all sums with addends and totals within 5 accurately and quickly.

• Recall doubles facts within 10

  Instantly recalls one plus one through five plus five and recognizes them as a special set.

• Recall doubles facts to 20

  Instantly recalls 6+6 through 10+10 as anchor facts for larger sums.

• Use near-doubles to add within 20

  Solves facts one or two away from a known double by adjusting the double.

• Fluently add within 10

  Recalls all addition facts with totals within 10 accurately and quickly, by any secure strategy.

• Recall the combinations that make ten

  Instantly produces the partner that completes ten for any number 0-10, in both directions.

• Decompose an addend to make ten

  Splits one addend so part of it completes a ten, then adds the remainder to ten.

• Add ten to a single-digit number

  Knows that 10 + n produces the teen number with n ones, without counting.

• Add within 20 crossing the ten

  Computes sums between 10 and 20 where the ones digits total more than ten, using a secure strategy.

• Subtract zero and subtract all

  Knows that subtracting zero leaves a number unchanged and subtracting a number from itself leaves zero.

• Fluently subtract within 5

  Recalls all subtraction facts with minuends within 5 accurately and quickly.

• Fluently subtract within 10

  Recalls all subtraction facts with minuends within 10 accurately and quickly.

• Subtract from ten

  Instantly produces the difference when subtracting any number from 10, using ten-partner knowledge.

• Decompose to subtract across the ten

  Subtracts a teen number by first going down to ten, then removing the rest.

• Use think-addition to subtract within 20

  Solves a subtraction within 20 by recalling the related addition fact.

• Subtract within 20 accurately across all fact types

  Solves any subtraction with a minuend within 20 correctly, selecting among counting back, down-to-ten, and think-addition.

• Create an equivalent but easier sum by compensation

  Adjusts both addends in compensating directions to make an easier problem with the same total.

• Select an efficient strategy for a given fact

  Given an addition or subtraction fact within 20, names and applies a sensible strategy rather than defaulting to counting.

NBT

Place Value

(21 atoms)

• Bundle ten ones as one ten

  Understands that ten individual ones can be grouped into one unit called a ten without changing the quantity.

• Compose teen numbers as one ten and some ones

  Builds or represents 11–19 as one group of ten and one to nine additional ones.

• Decompose a teen number into a ten and ones

  Decomposes a teen number into one ten and additional ones using objects, a drawing, or an equation and identifies each part.

• Identify the tens and ones digits in a two-digit number

  Names how many tens and how many ones any two-digit number contains.

• Represent a two-digit number with tens-and-ones models

  Builds or draws any two-digit number within 120 using ten-rods and unit cubes.

• Write the numeral for a given number of tens and ones

  Converts a spoken or modeled tens-and-ones description into the correct two-digit numeral.

• Understand decade numbers as tens with zero ones

  Knows that 10, 20, 30 ... 90 name whole numbers of tens with no leftover ones.

• Write a two-digit number in expanded form

  Writes a two-digit number as the sum of its tens value and ones value.

• Compare two-digit numbers by the tens digit

  Decides which of two numbers is greater when the tens digits differ.

• Compare two-digit numbers with the same tens digit

  Decides which of two numbers is greater when the tens digits match, using the ones digit.

• Record a comparison of two-digit numbers using >, <, or =

  Writes the correct comparison symbol between two two-digit numbers and reads the statement correctly.

• Compare numbers presented as models or expanded forms

  Compares two-digit quantities when they are shown as base-ten models or expanded forms rather than as numerals.

• Find 10 more than a two-digit number mentally

  Adds ten to any two-digit number within 100 without counting, explaining that only the tens digit changes.

• Find 10 less than a two-digit number mentally

  Subtracts ten from any two-digit number within 100 without counting.

• Add a multiple of ten to a multiple of ten within 100

  Adds two decade numbers by reasoning about counts of tens.

• Add a multiple of ten to a two-digit number

  Adds a decade number to any two-digit number, changing only the tens.

• Subtract a multiple of ten from a multiple of ten

  Subtracts decade numbers within 100 by reasoning about counts of tens.

• Add a two-digit and a one-digit number without composing a ten

  Adds a single-digit number to a two-digit number when the ones digits sum to nine or less.

• Add a two-digit and a one-digit number composing a ten

  Adds a single-digit number to a two-digit number when the ones exceed ten, forming a new ten.

• Explain that tens add to tens and ones add to ones

  Articulates the place-value principle underlying two-digit addition and uses it to check a result.

• Justify a within-100 addition with a model, drawing, or strategy

  Explains and defends the reasoning used for a two-digit addition, connecting a written method to a concrete or drawn representation.

EQ

Equations

(11 atoms)

• Understand the equal sign as meaning the same amount as

  Interprets the equal sign as a statement that both sides have the same value, not as a signal to write an answer.

• Judge whether an identity equation is true or false

  Evaluates equations of the form a equals a and a equals b with no operation present.

• Judge whether an equation in the form a + b = c is true or false

  Evaluates a standard-form addition equation and decides whether it holds.

• Judge whether an equation with the total first is true or false

  Evaluates equations written in the form c = a + b, where the sum appears on the left.

• Judge whether an equation with operations on both sides is true or false

  Evaluates equations of the form a + b = c + d by computing and comparing both sides.

• Judge whether an equation involving subtraction is true or false

  Evaluates true/false equations containing subtraction on one or both sides.

• Find the unknown addend in a + ☐ = c

  Determines the missing second addend in an addition equation.

• Find the unknown addend in ☐ + b = c

  Determines the missing first addend in an addition equation.

• Find the unknown in a − ☐ = c

  Determines the missing subtrahend in a subtraction equation.

• Find the unknown in ☐ − b = c

  Determines the missing starting amount in a subtraction equation.

• Find the unknown in equations with the unknown after the equal sign or on either side

  Solves equations such as c = ☐ + b and a + b = ☐ + d, where the unknown is not in a standard position.

2nd Grade

101 atomsView all →

NUM

Numbers

(9 atoms)

• Count within 1000 by ones from any starting number

  Continues the counting sequence by ones from any number under 1000, handling decade and hundred transitions.

• Read three-digit number names

  Says the number name for any written three-digit numeral, including numbers with internal zeros.

• Write three-digit numerals from number names

  Writes the correct numeral for any spoken or written three-digit number name.

• Count backward by ones within 1000

  Says the reverse counting sequence from a given number under 1000, crossing decade and hundred boundaries.

• Skip-count by fives within 1000

  Counts by fives from a multiple of five, forward and from any entry point.

• Skip-count by tens within 1000

  Counts by tens from any multiple of ten through 1000, including across hundreds.

• Skip-count by hundreds within 1000

  Counts by hundreds from any multiple of one hundred up to 1000.

• Identify numbers before, after, and between within 1000

  Names neighbors of a given three-digit number and fills gaps in a sequence.

• Order a set of three-digit numbers

  Arranges several three-digit numbers from least to greatest using place-value reasoning.

GEO

Shapes

(6 atoms)

• Identify shapes by number of sides and angles

  Names triangles, quadrilaterals, pentagons, and hexagons by counting sides and angles.

• Draw a shape with specified attributes

  Produces a shape meeting a stated number of sides or angles, including non-prototypical forms.

• Describe solids by faces, edges, and vertices

  Identifies solids and counts their faces, edges, and vertices.

• Partition a rectangle into rows and columns of same-size squares

  Divides a rectangle into a grid of equal squares matching a given number of rows and columns.

• Count the total squares in a partitioned rectangle

  Finds the total number of same-size squares tiling a rectangle, using the row-and-column structure.

• Relate the rows-and-columns structure to repeated addition

  Writes a repeated-addition equation for a partitioned rectangle and connects it to array reasoning.

MD

Measurement

(19 atoms)

• Determine how much longer one object is than another

  Measures two objects and finds the difference in length, expressed in the unit used.

• Solve length word problems within 100

  Uses addition and subtraction within 100 to solve problems involving lengths in the same units.

• Tell time to the nearest five minutes on an analog clock

  Reads an analog clock at five-minute intervals, coordinating both hands.

• Measure length in inches with a ruler

  Measures an object to the nearest inch using a standard ruler, aligning the object with the zero mark.

• Measure length in centimeters with a ruler

  Measures an object to the nearest centimeter using a metric ruler.

• Select an appropriate measuring tool for a given length

  Chooses among ruler, yardstick, meter stick, and measuring tape based on what is being measured.

• Write time to the nearest five minutes

  Records a clock time in digital notation with correct minutes, including times past the half hour.

• Use a.m. and p.m. appropriately

  Applies a.m. and p.m. to a time based on the activity or part of the day described.

• Identify the values of coins and bills

  Names each coin and bill and states its value.

• Count a collection of like coins

  Totals a group of identical coins by skip counting.

• Count a mixed collection of coins

  Totals a mixed group of coins by sorting from largest value and skip counting on.

• Solve money word problems using $ and ¢ notation

  Solves problems involving money amounts and records them with the correct symbol.

• Measure the same object in two different units

  Measures one object twice using different units and reports both numbers.

• Explain why smaller units give larger measurement numbers

  Articulates the inverse relationship between the size of the unit and the count of units.

• Estimate lengths in inches and feet

  Gives a reasonable estimate of an object's length in customary units before measuring.

• Estimate lengths in centimeters and meters

  Gives a reasonable estimate of an object's length in metric units before measuring.

• Represent whole numbers as lengths on a number line diagram

  Places numbers on a number line with equally spaced points, understanding position as distance from zero.

• Represent sums and differences on a number line diagram

  Shows an addition or subtraction as a jump or series of jumps on a number line.

• Describe relationships among standard units of time

  States relationships among minutes, hours, days, weeks, months, and years and uses them in simple questions.

DAT

Data

(8 atoms)

• Collect data through surveys, interviews, and observations

  Plans and carries out a simple survey, interview, or observation, recording each response exactly once.

• Draw a picture graph with a single-unit scale

  Represents a categorical data set as a picture graph with one symbol per item, a title, and labels.

• Draw a bar graph with a single-unit scale

  Represents a categorical data set as a bar graph with a labeled axis and consistent scale.

• Solve put-together and take-apart problems using a bar graph

  Uses values read from a bar graph to find totals and remaining amounts.

• Solve compare problems using a bar graph

  Uses a bar graph to answer how-many-more and how-many-fewer questions, including multi-category comparisons.

• Generate measurement data by measuring several objects

  Measures a set of objects in the same unit and records the results as a data set.

• Represent measurement data on a line plot

  Builds a line plot with a whole-number horizontal scale and one mark per measurement.

• Interpret a line plot

  Answers questions about how many, most common, and range from a line plot.

OA

Operations

(15 atoms)

• Find the total in a rectangular array using repeated addition

  Counts the objects in an array up to 5 by 5 by adding equal rows.

• Write an equation expressing an array as a sum of equal addends

  Records the total of a rectangular array as a repeated-addition equation.

• Relate rows and columns in an array to the same total

  Recognizes that adding by rows and adding by columns give the same total for the same array.

• Determine whether a group of up to 20 objects is even or odd

  Decides evenness by pairing objects or by counting by twos.

• Express an even number as a sum of two equal addends

  Writes an equation showing an even number as a double.

• Explain why a number is odd using pairing

  Justifies oddness by showing one object without a partner, and knows an odd number cannot be a double.

• Solve one-step result-unknown word problems within 100

  Solves add-to and take-from situations within 100 where the result is unknown.

• Solve one-step change-unknown word problems within 100

  Finds the amount added or removed given the start and the result, within 100.

• Solve one-step start-unknown word problems within 100

  Finds the original amount given the change and the result, within 100.

• Solve put-together and take-apart problems with an unknown addend within 100

  Finds a missing part when the whole and one part are known.

• Solve compare, difference-unknown word problems within 100

  Finds how many more or fewer one quantity is than another, within 100.

• Solve compare, bigger-unknown word problems within 100

  Finds the larger quantity given the smaller and the difference.

• Solve compare, smaller-unknown word problems within 100

  Finds the smaller quantity given the larger and the difference, including inconsistent-language versions.

• Solve two-step word problems within 100

  Solves problems requiring two operations, tracking the intermediate result.

• Represent a two-step problem with equations

  Writes equations capturing both steps of a two-step problem, using a symbol for each unknown.

FRA

Fractions

(5 atoms)

• Partition a circle or rectangle into two, three, or four equal shares

  Divides a whole into halves, thirds, or fourths with genuinely equal parts.

• Recognize that equal shares of identical wholes need not have the same shape

  Accepts that two halves of congruent wholes can look different while representing the same amount.

• Name shares as halves, thirds, and fourths

  Uses the correct share vocabulary for a partitioned whole, including a third of and a fourth of.

• Describe the whole as two halves, three thirds, or four fourths

  States that all the equal parts together reconstitute the whole.

• Compare the sizes of halves, thirds, and fourths of the same whole

  Orders unit shares of one whole and explains why more shares means smaller shares.

FLU

Fluency

(5 atoms)

• Recall all related differences within 20 from memory

  Produces any subtraction fact with a minuend within 20 from memory.

• Recall all sums of two one-digit numbers from memory

  Produces any single-digit addition fact from memory without computation or strategy work.

• Select and apply mental strategies flexibly within 20

  Chooses an efficient mental route for any within-20 computation when retrieval does not fire.

• Derive multiples-of-ten computations from known facts

  Uses a known single-digit fact to compute the matching tens or hundreds fact instantly.

• Recall ten-partners and doubles as anchor facts

  Retrieves the combinations that make ten and the doubles to 20 instantly, as anchors for derived computation.

NBT

Place Value

(30 atoms)

• Add two two-digit numbers without composing a ten

  Adds two two-digit numbers when the ones digits sum to nine or less.

• Add two two-digit numbers composing a ten

  Adds two two-digit numbers when the ones exceed ten, regrouping to form a new ten.

• Add up to four two-digit numbers

  Adds three or four two-digit numbers, grouping strategically and managing multiple regroups.

• Subtract two-digit numbers without decomposing a ten

  Subtracts two two-digit numbers when each ones digit in the minuend is large enough.

• Subtract two-digit numbers decomposing a ten

  Subtracts two two-digit numbers when the ones digit of the minuend is too small, regrouping a ten into ones.

• Fluently add and subtract within 100

  Computes any addition or subtraction within 100 accurately and efficiently, selecting among place-value, compensation, and regrouping strategies.

• Bundle ten tens as one hundred

  Understands that ten tens can be grouped into a single unit called a hundred, and that the bundle and the loose tens are the same quantity.

• Identify hundreds, tens, and ones in a three-digit number

  Names how many hundreds, tens, and ones any three-digit number contains.

• Understand multiples of one hundred as hundreds with zero tens and ones

  Knows that 100, 200 ... 900 name whole numbers of hundreds with no leftover tens or ones.

• Represent three-digit numbers with base-ten models

  Builds or draws any number within 1000 using hundreds flats, ten rods, and unit cubes.

• Write a three-digit number in expanded form

  Writes a three-digit number as the sum of its hundreds, tens, and ones values.

• Write the numeral from an expanded form or place-value description

  Converts an expanded form or a spoken hundreds-tens-ones description into the correct numeral.

• Interpret non-standard base-ten representations

  Determines the value of a collection where one place holds ten or more, such as 3 hundreds and 14 ones.

• Compare three-digit numbers using place value

  Decides which of two three-digit numbers is greater by comparing hundreds, then tens, then ones.

• Record three-digit comparisons using >, <, or =

  Writes the correct comparison symbol between two three-digit numbers and reads the statement.

• Mentally add 10 to a number within 1000

  Adds ten to any three-digit number without counting, including when the tens digit rolls over.

• Mentally subtract 10 from a number within 1000

  Subtracts ten from any three-digit number without counting, including when the tens digit rolls back.

• Mentally add 100 to a number within 1000

  Adds one hundred to any three-digit number without counting, changing only the hundreds digit.

• Mentally subtract 100 from a number within 1000

  Subtracts one hundred from any three-digit number without counting.

• Add within 1000 without regrouping

  Adds two three-digit numbers when no place requires composing.

• Add within 1000 composing a ten

  Adds three-digit numbers where the ones exceed ten, regrouping into the tens place.

• Add within 1000 composing a hundred

  Adds three-digit numbers where the tens exceed ten, regrouping into the hundreds place, including double regroups.

• Subtract within 1000 without regrouping

  Subtracts two three-digit numbers when no place requires decomposing.

• Subtract within 1000 decomposing a ten

  Subtracts three-digit numbers where the ones place requires trading a ten.

• Subtract within 1000 decomposing a hundred

  Subtracts three-digit numbers where the tens place requires trading a hundred, including double decompositions.

• Subtract across a zero within 1000

  Subtracts when the minuend contains a zero requiring a trade through an empty place.

• Relate a concrete or drawn strategy to the written method

  Connects each step of a base-ten model or drawing to the corresponding step in the recorded algorithm.

• Explain why an addition or subtraction strategy works

  Justifies a computation strategy using place value and the properties of operations.

• Add and subtract on an open number line

  Uses an open number line to compute within 1000 by jumping hundreds, tens, and ones.

• Judge the reasonableness of a sum or difference

  Estimates a result before or after computing and decides whether the answer is plausible.

EQ

Equations

(4 atoms)

• Judge whether an equation within 100 is true or false

  Evaluates equations with operations on one or both sides using numbers within 100.

• Write an equation with a symbol for the unknown in any position within 100

  Represents a situation with an equation placing the unknown wherever the problem structure requires.

• Solve for an unknown in any position within 100

  Finds the unknown in an addition or subtraction equation within 100, whatever its position.

• Write and solve equations for a two-step situation

  Represents a two-step problem with equations and solves for the final unknown.

3rd Grade

112 atomsView all →

GEO

Shapes

(7 atoms)

• Classify quadrilaterals by their attributes

  Identifies rhombuses, rectangles, squares, and other quadrilaterals by side and angle properties.

• Understand that shared attributes define a larger category

  Recognizes that shapes from different subcategories can belong to the same larger category because they share defining attributes.

• Recognize a square as both a rectangle and a rhombus

  Applies attribute reasoning to see that a square satisfies the definitions of several categories at once.

• Recognize examples that do not belong to a category

  Identifies a shape that fails a defining attribute and names the attribute it lacks.

• Draw a shape that does not belong to a named subcategory

  Produces a shape meeting a broad category but deliberately failing a narrower one.

• Partition a shape into parts with equal areas

  Divides a shape into a given number of parts that each cover the same area, including parts of different shapes.

• Express the area of each part as a unit fraction of the whole

  Names each equal-area part of a partitioned shape with the correct unit fraction.

MD

Measurement

(22 atoms)

• Tell time to the nearest minute

  Reads an analog clock to the exact minute, coordinating the hour hand and a minute count.

• Measure lengths to the nearest half and quarter inch

  Reads a ruler marked in halves and fourths and reports a fractional measurement.

• Write time to the nearest minute

  Records a to-the-minute time in digital notation.

• Measure a time interval in minutes

  Finds the number of minutes between two times within the same hour or across an hour boundary.

• Solve word problems involving time intervals

  Solves start, elapsed, and end-time problems in context, including finding an unknown start time.

• Estimate and measure liquid volume in liters

  Estimates and measures the volume of liquids using liters, with a sense of benchmark quantities.

• Estimate and measure mass in grams and kilograms

  Estimates and measures mass, choosing between grams and kilograms appropriately.

• Solve one-step problems involving mass and volume

  Uses the four operations to solve problems about masses or liquid volumes given in the same units.

• Recognize area as an attribute of plane figures

  Understands area as the amount of surface a flat figure covers, distinct from its outline.

• Understand a unit square as the unit of area

  Knows that area is measured in squares of a given side length, with no gaps or overlaps.

• Measure area by counting unit squares

  Finds the area of a figure drawn on a grid by counting the unit squares that cover it.

• Relate tiling a rectangle to multiplying side lengths

  Shows that the number of unit squares tiling a rectangle equals the product of its side lengths.

• Find the area of a rectangle by multiplying side lengths

  Computes the area of a rectangle from its dimensions and labels the answer in square units.

• Solve area word problems

  Applies area computation inside a real-world context, including finding an unknown side length.

• Use tiling to show the distributive property

  Decomposes a rectangle into two smaller rectangles and shows the areas sum to the whole.

• Recognize area as additive

  Knows the area of a figure equals the sum of the areas of its non-overlapping parts.

• Find the area of a rectilinear figure by decomposing it

  Splits an L-shaped or composite figure into rectangles, finds each area, and sums them.

• Find the perimeter of a polygon given its side lengths

  Adds all side lengths to find the distance around a polygon.

• Find an unknown side length given the perimeter

  Works backward from a known perimeter and some side lengths to find a missing one.

• Distinguish area from perimeter

  Selects the right measure for a question and uses the correct units for each.

• Compare rectangles with the same perimeter and different areas

  Finds multiple rectangles sharing a perimeter and shows their areas differ.

• Compare rectangles with the same area and different perimeters

  Finds multiple rectangles sharing an area and shows their perimeters differ.

DAT

Data

(8 atoms)

• Read a scaled picture graph

  Interprets a picture graph where each symbol represents more than one item, using the key.

• Draw a scaled picture graph

  Builds a picture graph with a chosen scale, including a key and partial symbols where needed.

• Read a scaled bar graph

  Reads values from a bar graph whose axis increases in intervals greater than one, including values between gridlines.

• Draw a scaled bar graph

  Builds a bar graph with an appropriate scale, labeled axes, and accurately drawn bars.

• Solve one-step problems using a scaled graph

  Answers how-many-more and how-many-fewer questions from a scaled picture or bar graph.

• Solve two-step problems using a scaled graph

  Combines two readings from a scaled graph before comparing or totalling.

• Generate measurement data using fractional units

  Measures a set of objects to the nearest half or quarter inch and records the results.

• Show measurement data on a line plot with halves and fourths

  Builds a line plot whose horizontal scale is marked in halves and fourths of a unit.

OA

Operations

(24 atoms)

• Interpret a product as a number of equal groups

  Reads 5 × 7 as five groups of seven objects and states the total the expression describes.

• Interpret a product as an array or area

  Reads a product as the total in a rectangular arrangement of rows and columns.

• Write a multiplication equation for an equal-groups situation

  Records a situation involving equal groups as a multiplication equation with the factors in a defensible order.

• Apply the commutative property of multiplication

  Knows that changing the order of two factors does not change the product, and uses it to halve the facts to be learned.

• Apply the associative property of multiplication

  Regroups three factors to make a computation easier without changing the product.

• Apply the distributive property to decompose a fact

  Breaks a hard fact into two easier known facts and adds the partial products.

• Interpret a quotient as the size of each share

  Reads 56 ÷ 8 as the number in each group when 56 objects are shared equally among 8 groups.

• Interpret a quotient as the number of shares

  Reads 56 ÷ 8 as the number of groups when 56 objects are split into groups of 8.

• Distinguish sharing division from grouping division

  Identifies which quantity the divisor represents in a given situation and explains why the same equation can model both.

• Write a division equation for a situation

  Records a sharing or grouping situation as a division equation with the quantities in the correct roles.

• Understand division as an unknown-factor problem

  Rewrites a division as a multiplication with a missing factor and solves it that way.

• Write the multiplication and division fact family for a triple

  Given three related numbers, writes all four multiplication and division equations.

• Solve equal-groups multiplication word problems within 100

  Solves multiplication situations involving equal groups and answers with a unit.

• Solve array and area multiplication word problems

  Solves multiplication situations described as rows and columns or as a rectangular region.

• Solve measurement-quantity multiplication word problems

  Solves multiplication situations involving lengths, masses, volumes, or money rather than discrete objects.

• Solve sharing division word problems within 100

  Solves division situations where a total is shared among a known number of groups.

• Solve grouping division word problems within 100

  Solves division situations where a total is split into groups of a known size.

• Solve problems with equal groups where the group size or count is unknown

  Solves situations requiring division even though the story emphasizes the total and one factor.

• Identify arithmetic patterns in the multiplication table

  Notices regularities such as even products, column patterns, and repeated results in a multiplication table.

• Explain an arithmetic pattern using properties of operations

  Justifies why an observed pattern must hold, referring to the structure of the operation.

• Identify patterns in even and odd products and sums

  Predicts whether a product or sum will be even or odd based on the parity of the numbers involved.

• Solve two-step word problems using the four operations

  Solves problems requiring two operations, tracking the intermediate result and choosing operations correctly.

• Represent a two-step problem with an equation using a letter for the unknown

  Writes one or more equations using a letter to stand for the unknown quantity in a multi-step problem.

• Assess the reasonableness of an answer using estimation

  Uses rounding and mental computation to judge whether a computed answer is plausible.

FRA

Fractions

(22 atoms)

• Partition a whole into b equal parts and name one part as a unit fraction

  Divides a shape into equal parts and names one part with the correct unit-fraction notation.

• Understand the numerator as a count of unit fractions

  Reads a/b as a copies of the unit fraction 1/b.

• Identify the whole in a fraction context

  Determines what counts as one whole in a given situation and recognizes that a fraction is meaningless without it.

• Recognize non-examples of fractional partitioning

  Rejects partitions with unequal parts as valid representations of a fraction.

• Partition a number line from 0 to 1 into b equal parts

  Divides the unit interval into equal segments and understands each segment as length 1/b.

• Locate a unit fraction on a number line

  Places 1/b at the endpoint of the first segment when 0 to 1 is partitioned into b equal parts.

• Locate a non-unit fraction on a number line

  Places a/b by iterating a copies of the unit fraction from zero.

• Locate fractions greater than one on a number line

  Places fractions such as 5/4 or 7/3 by continuing to iterate the unit fraction past one.

• Understand a fraction as a single number

  Treats a fraction as one quantity with a location, not as a pair of unrelated whole numbers.

• Express whole numbers as fractions

  Writes a whole number as a fraction with denominator one, and as a fraction with other denominators.

• Recognize fractions equivalent to one whole

  Identifies fractions where the numerator equals the denominator as equal to one.

• Recognize equivalent fractions using area models

  Identifies two fractions as equivalent when they cover the same amount of the same whole.

• Recognize equivalent fractions on a number line

  Identifies two fractions as equivalent when they land on the same point of a number line.

• Generate simple equivalent fractions

  Produces a fraction equivalent to a given one by splitting each part into the same number of smaller parts.

• Compare fractions with the same denominator

  Decides which of two fractions with a common denominator is greater by comparing numerators.

• Compare fractions with the same numerator

  Decides which of two fractions with the same numerator is greater by reasoning about piece size.

• Justify a fraction comparison with a model or number line

  Backs a comparison with a drawing, fraction strip, or number line rather than a rule alone.

• Recognize that comparisons require the same whole

  Knows a fraction comparison is only valid when both fractions refer to identically sized wholes.

• Record fraction comparisons using >, <, or =

  Writes the correct comparison symbol between two fractions and reads the statement.

• Compare a fraction to one half as a benchmark

  Judges whether a fraction is more or less than one half without finding a common denominator.

• Order a set of fractions

  Arranges three or more fractions from least to greatest using models, benchmarks, or common denominators.

• Solve word problems involving fractions of a whole

  Applies fraction understanding inside a context, naming the whole and interpreting the answer.

FLU

Fluency

(17 atoms)

• Multiply by zero

  Knows any number of groups of zero, or zero groups of anything, totals zero.

• Multiply by one

  Knows that multiplying by one leaves a number unchanged.

• Multiply by two

  Recalls the twos facts by connecting them to known doubles.

• Multiply by ten

  Recalls the tens facts and explains the place-value pattern behind them.

• Multiply by five

  Recalls the fives facts, using skip counting and the half-of-ten relationship as backup.

• Multiply by three

  Recalls the threes facts, deriving from doubles-plus-one-group when retrieval does not fire.

• Multiply by four

  Recalls the fours facts, using double-double as the derivation strategy.

• Multiply by six

  Recalls the sixes facts, deriving from fives-plus-one-group when needed.

• Multiply by nine

  Recalls the nines facts, using the tens-minus-one-group relationship and the digit pattern.

• Multiply by seven

  Recalls the sevens facts, the set with the fewest supporting patterns.

• Multiply by eight

  Recalls the eights facts, using double-double-double as the derivation strategy.

• Multiply by eleven and twelve

  Recalls the elevens and twelves facts, beyond the grade-3 core but included in the authored course.

• Recall all products of two one-digit numbers from memory

  Produces any single-digit product from memory, unaided and without derivation.

• Derive an unknown product from a known one

  Reconstructs a fact that does not come to mind by adjusting a nearby known fact.

• Divide by two, five, and ten

  Recalls the easiest division facts by connecting them to the corresponding multiplication sets.

• Divide using known multiplication facts

  Solves any division within 100 by retrieving the related multiplication fact.

• Fluently divide within 100

  Computes any division within 100 accurately and quickly across all fact families.

NBT

Place Value

(7 atoms)

• Fluently add within 1000

  Adds three-digit numbers accurately and efficiently, with any needed regrouping.

• Fluently subtract within 1000

  Subtracts three-digit numbers accurately and efficiently, including across zeros.

• Round a whole number to the nearest ten

  Rounds a two- or three-digit number to the nearest ten using place-value reasoning, including the halfway case.

• Round a whole number to the nearest hundred

  Rounds a three-digit number to the nearest hundred using place-value reasoning.

• Use rounding to estimate a sum or difference

  Rounds the numbers in a computation to produce a quick estimate before or after computing exactly.

• Multiply a one-digit number by a multiple of ten

  Computes products such as 7 × 40 by scaling a known basic fact.

• Explain the multiples-of-ten strategy using place value

  Justifies why 7 × 40 equals 7 × 4 tens, connecting the shortcut to quantity.

EQ

Equations

(5 atoms)

• Find the unknown in a multiplication equation

  Determines the missing factor or product in a multiplication equation, whatever its position.

• Find the unknown in a division equation

  Determines the missing dividend, divisor, or quotient in a division equation.

• Solve one-step equations mixing the four operations

  Finds the unknown in a one-step equation using any of the four operations, with the unknown in any position.

• Use a letter to represent the unknown in an equation

  Writes and solves equations using a letter rather than a box, treating the letter as a number.

• Solve two-step equations by undoing operations

  Finds the unknown in equations combining two operations by undoing them in reverse order. Stretch content: two-step unknowns reach beyond the grade-3 core toward order-of-operations work — a miss here is not evidence of a grade-3 gap.