Common Core

Counting & Cardinality

• Counting in order and naming numbers
• K.CC.A.1Say the numbers in order up to 100, counting by 1s and also by 10s.14
• K.CC.A.2Keep counting upward from a number other than 1, within the numbers already known.5
• K.CC.A.3Write the numerals 0 to 20 and use a numeral to show how many objects are in a group, with 0 meaning none.25
• K.CC.B.4Link numbers to amounts and understand that counting tells how many.24
• K.CC.B.4aCount objects by saying numbers in order and matching exactly one number to each object, none skipped or counted twice.20
• K.CC.B.4bKnow the final number in a count gives the total, and the total stays the same however the objects are arranged or counted.20
• K.CC.B.4cKnow that each next number in the count stands for a group with one more object.4
• Counting to find how many
• K.CC.B.5Tell how many: up to 20 objects in a line, array or circle, or 10 scattered. Also count out a requested number up to 20.20
• Comparing groups and numerals
• K.CC.C.6Decide whether one group of up to 10 objects has more, fewer or the same as another, by matching or counting.7
• K.CC.C.7Tell which of two written numerals from 1 to 10 is greater or less.8

Operations & Algebraic Thinking

• What adding and subtracting mean: joining and separating
• K.OA.A.1Show adding and taking away in many ways: fingers, objects, pictures, sounds, acting out, words, or number sentences.12
• K.OA.A.2Solve story problems and add or subtract with totals up to 10, modeling them with objects or drawings.37
• K.OA.A.3Break a number up to 10 into two parts several ways, recording each as a picture or equation (7 = 3 + 4).9
• K.OA.A.4For a number from 1 to 9, find the partner that adds with it to 10, and show it in a picture or number sentence.10
• K.OA.A.5Add and subtract quickly and accurately with numbers up to 5.29

Number & Operations in Base Ten

• Teen numbers as a first step toward place value
• K.NBT.A.1Build and break apart 11 to 19 as ten ones plus more ones, recording with drawings or equations like 14 = 10 + 4.5

Measurement & Data

• Measurable features of objects
• K.MD.A.1Name the features of an object that can be measured, such as how long or how heavy it is, including several for one object.1
• K.MD.A.2Put two objects side by side to see which is longer, taller, heavier and so on, and describe the difference.1
• Sorting objects and counting each group
• K.MD.B.3Sort objects into named groups, count each group (up to 10), and order the groups by how many they hold.4

Geometry

• Naming and describing shapes
• K.G.A.1Use shape names for everyday objects, and tell where things are with position words like over, under, next to and behind.5
• K.G.A.2Name shapes correctly even when they are turned, tilted, bigger or smaller.5
• K.G.A.3Tell whether a shape is flat (two-dimensional) or solid (three-dimensional).5
• Comparing, building and combining shapes
• K.G.B.4Compare flat and solid shapes of any size or position, using everyday words for their sides, corners and other features.2
• K.G.B.5Make shapes seen in the world by drawing them or building them from parts such as straws and clay.1
• K.G.B.6Put small shapes together to make bigger ones, such as joining triangles to make a square.1

Operations & Algebraic Thinking

• Addition and subtraction problem solving
• 1.OA.A.1Solve story problems up to 20 that join, separate, combine or compare amounts, with the missing number in any spot, using objects, drawings or equations.7
• 1.OA.A.2Solve story problems where three numbers are added together for a total of 20 or less.12
• Properties of addition and how subtraction relates to it
• 1.OA.B.3Use the order and grouping rules of addition as shortcuts, for example knowing 5 + 9 gives the same answer as 9 + 5.1
• 1.OA.B.4Treat subtraction as finding a missing addend: to solve 12 - 9, ask what added to 9 makes 12.13
• Sums and differences up to 20
• 1.OA.C.5Connect counting with adding and subtracting, such as adding 4 by counting on four more.9
• 1.OA.C.6Add and subtract to 20, working fluently within 10, with strategies like counting on, making ten, fact families and doubles plus one.52
• Equations with addition and subtraction
• 1.OA.D.7Know the equal sign means both sides have the same value, and decide whether addition and subtraction equations hold true.2
• 1.OA.D.8Solve for the missing number in adding or subtracting equations like 9 + ? = 15 or ? - 4 = 6.27

Number & Operations in Base Ten

• Counting further, up to 120
• 1.NBT.A.1Count up to 120 from any starting number, and read, write and use numerals up to 120 to show how many objects.11
• 1.NBT.B.2In a two-digit number, the left digit counts tens and the right digit counts ones.16
• 1.NBT.B.2aSee a group of ten ones as one unit called a ten.12
• 1.NBT.B.2bKnow that 11 through 19 are each made of one ten plus 1 to 9 ones.8
• 1.NBT.B.2cKnow that 10, 20, 30 and so on up to 90 mean 1 to 9 tens with no ones.12
• Place value: tens and ones
• 1.NBT.B.3Compare two-digit numbers by looking at their tens and ones, and write the result with >, = or <.15
• Adding and subtracting with place value
• 1.NBT.C.4Find sums up to 100 (two-digit plus one-digit, or plus a multiple of 10) with models and place value, making a new ten when needed.12
• 1.NBT.C.5Without counting, find the number 10 greater or 10 smaller than any two-digit number, doing it mentally and explaining why.3
• 1.NBT.C.6Subtract one multiple of 10 from another (between 10 and 90, answer zero or more), such as 70 - 40, using models or place value.12

Measurement & Data

• Comparing lengths and measuring with repeated units
• 1.MD.A.1Put three objects in order from longest to shortest, and compare two lengths by checking each against a third object.1
• 1.MD.A.2Measure an object by lining up equal-size units (like cubes) along it without spaces or overlapping, and give the whole-number count.1
• Reading clocks
• 1.MD.B.3Read and record times to the hour and half hour on clock faces and digital displays.15
• Showing and reading data
• 1.MD.C.4Sort and show data in up to three groups, then answer questions about the total, each group's count, and how groups differ.8

Geometry

• Thinking about shapes and their features
• 1.G.A.1Separate the features that define a shape (three sides) from ones that do not (color, size, turn), and build or draw shapes with them.3
• 1.G.A.2Combine flat shapes (such as trapezoids and half-circles) or solids (such as cubes and cones) into a new shape, then build more shapes from it.1
• 1.G.A.3Split circles and rectangles into 2 or 4 equal parts, name them halves, fourths or quarters, and see that more parts means smaller parts.6

Operations & Algebraic Thinking

• Addition and subtraction problem solving
• 2.OA.A.1Solve one- and two-step story problems with sums and differences up to 100, with the unknown in any position, using drawings and equations.3
• Sums and differences up to 20
• 2.OA.B.2Add and subtract to 20 quickly using strategies done in the head, and by year's end instantly recall every sum of two single-digit numbers.36
• Equal groups as groundwork for multiplication
• 2.OA.C.3Decide if up to 20 objects are odd or even (match them in twos or skip count by 2s); write evens as doubles.20
• 2.OA.C.4Use adding to find the total in an array with at most 5 rows and 5 columns, and write it as repeated addition.8

Number & Operations in Base Ten

• 2.NBT.A.1In a three-digit number, the digits count hundreds, tens and ones, so 482 is 4 hundreds, 8 tens and 2 ones.14
• 2.NBT.A.1aSee ten tens grouped together as one unit called a hundred.14
• 2.NBT.A.1bKnow that 100, 200 and so on up to 900 mean 1 to 9 hundreds with no tens or ones.14
• Place value: hundreds, tens and ones
• 2.NBT.A.2Count up to 1,000, and count by fives, tens and hundreds.11
• 2.NBT.A.3Read and write numbers up to 1,000 as digits, in words, and in expanded form (like 300 + 40 + 7).7
• 2.NBT.A.4Compare three-digit numbers by looking at the value of each place, and record the result with >, = or <.2
• Adding and subtracting with place value
• 2.NBT.B.5Add and subtract to 100 fluently with place-value strategies, properties of addition, or the link between adding and subtracting.19
• 2.NBT.B.6Find the sum of two, three or four two-digit numbers using place value and properties of addition.14
• 2.NBT.B.7Add and subtract to 1,000 with models and place-value strategies, working hundreds, tens and ones separately and regrouping tens or hundreds as needed.10
• 2.NBT.B.8Mentally find the number 10 or 100 greater or smaller than any number from 100 to 900.2
• 2.NBT.B.9Tell why an adding or subtracting method gives the right answer, reasoning from place value and number properties.8

Measurement & Data

• Length in standard units: measuring and estimating
• 2.MD.A.1Choose a suitable tool, such as a ruler, yardstick, meter stick or tape measure, and use it to measure length.1
• 2.MD.A.2Measure one object with two different units, such as inches and centimeters, and explain why a smaller unit gives a bigger number.1
• 2.MD.A.3Make sensible guesses of lengths in inches, feet, centimeters and meters.1
• 2.MD.A.4Measure two objects and find the difference in their lengths in a standard unit.1
• Length, number lines and adding or subtracting
• 2.MD.B.5Solve story problems about lengths in the same unit, adding or subtracting within 100, with drawings like rulers and equations.1
• 2.MD.B.6Show whole numbers as distances from 0 on an evenly marked number line, and show sums and differences up to 100 as jumps on it.6
• Time and money
• 2.MD.C.7Read and record clock times in 5-minute steps on clock faces and digital displays, and use a.m. and p.m. correctly.10
• 2.MD.C.8Solve story problems with pennies, nickels, dimes, quarters and dollar bills, writing amounts with the $ and ¢ signs.5
• Showing and reading data
• 2.MD.D.9Measure several objects, or one object several times, in whole units and display the results on a line plot.1
• 2.MD.D.10Make picture and bar graphs (one unit per square or picture) for up to four categories, and answer joining, separating and comparing questions from them.6

Geometry

• Thinking about shapes and their features
• 2.G.A.1Draw and spot shapes with given features, like a number of angles or faces, and name triangles, quadrilaterals, pentagons, hexagons and cubes.2
• 2.G.A.2Cut a rectangle into a grid of equal squares and count how many squares it holds.6
• 2.G.A.3Cut circles and rectangles into 2, 3 or 4 equal parts called halves, thirds or fourths; equal parts of one whole can look different.7

Operations & Algebraic Thinking

• Multiplication and division problem solving
• 3.OA.A.1Understand a product as the total in equal groups, such as 4 × 6 meaning 4 groups with 6 in each.9
• 3.OA.A.2Understand a quotient as either the size of each equal share or the number of equal groups, such as 24 ÷ 6.4
• 3.OA.A.3Solve story problems about equal groups, arrays and measurements by multiplying or dividing within 100, using drawings and equations.1
• 3.OA.A.4Solve for the missing number in multiplying or dividing equations, such as 7 × ? = 42 or ? ÷ 3 = 6.5
• Properties of multiplication and how division relates to it
• 3.OA.B.5Use the commutative, associative and distributive properties to multiply and divide, such as finding 7 × 8 from 7 × 5 and 7 × 3.1
• 3.OA.B.6Treat division as finding a missing factor: solve 35 ÷ 5 by asking what times 5 equals 35.4
• Products and quotients up to 100
• 3.OA.C.7Multiply and divide to 100 fluently with strategies, and by year's end instantly recall every product of two single-digit numbers.15
• Problems with all four operations; patterns in arithmetic
• 3.OA.D.8Solve two-step story problems with +, −, × and ÷, using a letter for the missing amount, and check answers by estimating or rounding.1
• 3.OA.D.9Spot patterns in addition tables, times tables and other arithmetic, and explain them with properties, like why multiples of 5 end in 0 or 5.16

Number & Operations in Base Ten

• Place value in multi-digit arithmetic
• 3.NBT.A.1Use place value to decide which ten or hundred a whole number is closest to, and round to it.4
• 3.NBT.A.2Add and subtract to 1,000 fluently using place-value strategies and written methods, properties of addition, and fact-family relationships.4
• 3.NBT.A.3Multiply a single-digit number by a multiple of ten from 10 to 90, such as 4 × 70, using place value and properties.1

Number & Operations—Fractions

• What fractions are and how they compare
• 3.NF.A.1Know 1/b is one of b equal parts of a whole, and a/b is a of those parts (denominators 2, 3, 4, 6 and 8).7
• 3.NF.A.2Fractions are numbers with their own places on a number line, and can be shown there.–
• 3.NF.A.2aMark 1/b on a number line by splitting the space from 0 to 1 into b equal parts; the first part ends at 1/b.–
• 3.NF.A.2bPlace a/b on a number line by counting a jumps of size 1/b from 0; where the jumps end is a/b.–
• 3.NF.A.3Reason about fraction size to compare fractions and to explain when two simple fractions are equal.2
• 3.NF.A.3aKnow that two fractions are equal when they cover the same amount of a whole or land at the same spot on a number line.2
• 3.NF.A.3bFind and make simple equal fractions, such as 3/6 = 1/2, and use a picture or model to show why they match.2
• 3.NF.A.3cShow a whole number in fraction form and notice when a fraction names a whole number, such as 2 = 2/1 or 8/4 = 2.2
• 3.NF.A.3dCompare fractions of the same whole that have equal numerators or equal denominators, thinking about part size; record with >, = or < and explain.2

Measurement & Data

• Time, liquid volume and mass problems
• 3.MD.A.1Read and record time to the exact minute, find how many minutes pass between times, and solve story problems adding or subtracting minutes.2
• 3.MD.A.2Estimate and measure mass in grams and kilograms and liquid volume in liters, and solve one-step story problems about them with any operation.–
• Showing and reading data
• 3.MD.B.3Make picture and bar graphs where each symbol or square stands for several items, and answer one- and two-step comparison questions from them.–
• 3.MD.B.4Measure lengths to the nearest half or quarter inch and show the measurements on a line plot marked in wholes, halves or quarters.–
• 3.MD.C.5Area is a measurable feature of flat shapes, measured in square units.2
• 3.MD.C.5aKnow that a square with 1-unit sides has an area of one square unit and can be used to measure area.2
• 3.MD.C.5bKnow that a flat shape exactly covered by some number of unit squares, with no spaces or overlapping, has that many square units of area.2
• Area and how it connects to multiplication and addition
• 3.MD.C.6Find an area by counting how many unit squares cover it, in square centimeters, meters, inches, feet or made-up units.2
• 3.MD.C.7Connect finding area with multiplying and adding.3
• 3.MD.C.7aTile a rectangle with whole-number sides and show that the number of tiles matches multiplying its length by its width.3
• 3.MD.C.7bMultiply length by width to get the area of whole-number rectangles in story and math problems, and picture products as rectangles.3
• 3.MD.C.7cUse tiles or area models to show that splitting a rectangle's side into two parts splits its area into two products (the distributive property).3
• 3.MD.C.7dFind the area of shapes made of rectangles by splitting them into separate rectangles and adding their areas, including in real problems.1
• Perimeter, and how it differs from area
• 3.MD.D.8Solve perimeter problems for polygons: add side lengths, find a missing side, and compare rectangles with equal perimeters but different areas, or the reverse.2

Geometry

• Thinking about shapes and their features
• 3.G.A.1See that shapes like rhombuses, rectangles and squares share features, such as four sides, that make them all quadrilaterals; draw quadrilaterals outside those groups.1
• 3.G.A.2Divide shapes into parts of equal area and describe each part with a unit fraction, such as 1/6 of the shape.7