allenai/achieve-the-core huggingface dataset:
K.CC.A.1 (Standard, major cluster): Count to 100 by ones and by tens.
K.CC.A.2 (Standard, major cluster): Count forward beginning from a given number within the known sequence (instead of having to begin at 1).
K.CC.A.3 (Standard, major cluster): Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects).
K.CC.B.4 (Standard, major cluster): Understand the relationship between numbers and quantities; connect counting to cardinality.
K.CC.B.4a (Sub-standard, major cluster): 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.
K.CC.B.4b (Sub-standard, major cluster): 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.
K.CC.B.4c (Sub-standard, major cluster): Understand that each successive number name refers to a quantity that is one larger.
K.CC.B.5 (Standard, major cluster): Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1–20, count out that many objects.
K.CC.C.6 (Standard, major cluster): Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies (include groups with up to ten objects).
K.CC.C.7 (Standard, major cluster): Compare two numbers between 1 and 10 presented as written numerals.
K.OA.A (Cluster, major cluster): Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.
K.OA.A.1 (Standard, major cluster): Represent addition and subtraction with objects, fingers, mental images, drawings (Drawings need not show details, but should show the mathematics in the problem. (This applies wherever drawings are mentioned in the Standards.)), sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.
Aspects: conceptual understanding
K.OA.A.2 (Standard, major cluster): Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.
Aspects: Application
K.OA.A.3 (Standard, major cluster): Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).
K.OA.A.4 (Standard, major cluster): For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation.
K.OA.A.5 (Standard, major cluster): Fluently add and subtract within 5.
Aspects: Procedural Skill and Fluency
K.NBT.A (Cluster, major cluster): Work with numbers 11–19 to gain foundations for place value.
K.NBT.A.1 (Standard, major cluster): Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones.
K.MD.A.1 (Standard, additional cluster): Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object.
K.MD.A.2 (Standard, additional cluster): Directly compare two objects with a measurable attribute in common, to see which object has “more of”/“less of” the attribute, and describe the difference. For example, directly compare the heights of two children and describe one child as taller/shorter.
K.MD.B (Cluster, supporting cluster): Classify objects and count the number of objects in each category.
K.MD.B.3 (Standard, supporting cluster): Classify objects into given categories; count the numbers of objects in each category and sort the categories by count. (Limit category counts to be less than or equal to 10.)
K.G.A (Cluster, additional cluster): Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres).
K.G.A.1 (Standard, additional cluster): Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to.
K.G.A.2 (Standard, additional cluster): Correctly name shapes regardless of their orientations or overall size.
K.G.A.3 (Standard, additional cluster): Identify shapes as two-dimensional (lying in a plane, “flat”) or three-dimensional (“solid”).
K.G.B (Cluster, supporting cluster): Analyze, compare, create, and compose shapes.
K.G.B.4 (Standard, supporting cluster): Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/“corners”) and other attributes (e.g., having sides of equal length).
K.G.B.5 (Standard, supporting cluster): Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes.
K.G.B.6 (Standard, supporting cluster): Compose simple shapes to form larger shapes. For example, “Can you join these two triangles with full sides touching to make a rectangle?”
1.OA.A (Cluster, major cluster): Represent and solve problems involving addition and subtraction.
Aspects: Application
1.OA.A.1 (Standard, major cluster): Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.
Aspects: Application
1.OA.A.2 (Standard, major cluster): Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.
Aspects: Application
1.OA.B (Cluster, major cluster): Understand and apply properties of operations and the relationship between addition and subtraction.
1.OA.B.3 (Standard, major cluster): Apply properties of operations as strategies to add and subtract. (Students need not use formal terms for these properties.) Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.)
1.OA.B.4 (Standard, major cluster): Understand subtraction as an unknown-addend problem. For example, subtract 10 – 8 by finding the number that makes 10 when added to 8.
1.OA.C.5 (Standard, major cluster): Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).
1.OA.C.6 (Standard, major cluster): Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).
Aspects: Procedural Skill and Fluency
1.OA.D (Cluster, major cluster): Work with addition and subtraction equations.
1.OA.D.7 (Standard, major cluster): Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 – 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2.
1.OA.D.8 (Standard, major cluster): Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = �� – 3, 6 + 6 = ��.
1.NBT.A.1 (Standard, major cluster): Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral.
1.NBT.B (Cluster, major cluster): Understand place value.
Aspects: conceptual understanding
1.NBT.B.2 (Standard, major cluster): Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases:
- The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones.
- 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).
- 10 can be thought of as a bundle of ten ones — called a “ten.”
Aspects: conceptual understanding
1.NBT.B.2a (Sub-standard, major cluster): 10 can be thought of as a bundle of ten ones — called a “ten.”
Aspects: conceptual understanding
1.NBT.B.2b (Sub-standard, major cluster): The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones.
Aspects: conceptual understanding
1.NBT.B.2c (Sub-standard, major cluster): 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).
Aspects: conceptual understanding
1.NBT.B.3 (Standard, major cluster): Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.
Aspects: conceptual understanding
1.NBT.C (Cluster, major cluster): Use place value understanding and properties of operations to add and subtract.
Aspects: conceptual understanding
1.NBT.C.4 (Standard, major cluster): Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.
Aspects: conceptual understanding
1.NBT.C.5 (Standard, major cluster): Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.
Aspects: conceptual understanding
1.NBT.C.6 (Standard, major cluster): Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.
Aspects: conceptual understanding
1.MD.A (Cluster, major cluster): Measure lengths indirectly and by iterating length units.
1.MD.A.1 (Standard, major cluster): Order three objects by length; compare the lengths of two objects indirectly by using a third object.
1.MD.A.2 (Standard, major cluster): Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps.
1.MD.B.3 (Standard, additional cluster): Tell and write time in hours and half-hours using analog and digital clocks.
1.MD.C.4 (Standard, supporting cluster): Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another.
1.G.A.1 (Standard, additional cluster): Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes.
1.G.A.2 (Standard, additional cluster): Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape. (Students do not need to learn formal names such as “right rectangular prism.”)
1.G.A.3 (Standard, additional cluster): Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares.
2.OA.A (Cluster, major cluster): Represent and solve problems involving addition and subtraction.
Aspects: Application
2.OA.A.1 (Standard, major cluster): 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, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.
Aspects: Application
2.OA.B.2 (Standard, major cluster): Fluently add and subtract within 20 using mental strategies. (See standard 1.OA.6 for a list of mental strategies.) By end of Grade 2, know from memory all sums of two one-digit numbers.
Aspects: Procedural Skill and Fluency
2.OA.C (Cluster, supporting cluster): Work with equal groups of objects to gain foundations for multiplication.
2.OA.C.3 (Standard, supporting cluster): Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends.
2.OA.C.4 (Standard, supporting cluster): 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.
2.NBT.A (Cluster, major cluster): Understand place value.
Aspects: conceptual understanding
2.NBT.A.1 (Standard, major cluster): Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:
- 100 can be thought of as a bundle of ten tens — called a “hundred.”
- 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).
Aspects: conceptual understanding
2.NBT.A.1a (Sub-standard, major cluster): 100 can be thought of as a bundle of ten tens — called a “hundred.”
Aspects: conceptual understanding
2.NBT.A.1b (Sub-standard, major cluster): 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).
Aspects: conceptual understanding
2.NBT.A.2 (Standard, major cluster): Count within 1000; skip-count by 5s, 10s, and 100s.
Aspects: conceptual understanding
2.NBT.A.3 (Standard, major cluster): Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.
Aspects: conceptual understanding
2.NBT.A.4 (Standard, major cluster): Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons.
Aspects: conceptual understanding
2.NBT.B (Cluster, major cluster): Use place value understanding and properties of operations to add and subtract.
Aspects: conceptual understanding
2.NBT.B.5 (Standard, major cluster): Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.
Aspects: conceptual understanding, Procedural Skill and Fluency
2.NBT.B.6 (Standard, major cluster): Add up to four two-digit numbers using strategies based on place value and properties of operations.
Aspects: conceptual understanding
2.NBT.B.7 (Standard, major cluster): Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.
Aspects: conceptual understanding
2.NBT.B.8 (Standard, major cluster): Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900.
Aspects: conceptual understanding
2.NBT.B.9 (Standard, major cluster): Explain why addition and subtraction strategies work, using place value and the properties of operations. (Explanations may be supported by drawings or objects.)
Aspects: conceptual understanding
2.MD.A (Cluster, major cluster): Measure and estimate lengths in standard units.
2.MD.A.1 (Standard, major cluster): Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes.
2.MD.A.2 (Standard, major cluster): Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen.
2.MD.A.3 (Standard, major cluster): Estimate lengths using units of inches, feet, centimeters, and meters.
2.MD.A.4 (Standard, major cluster): Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit.
2.MD.B (Cluster, major cluster): Relate addition and subtraction to length.
2.MD.B.5 (Standard, major cluster): Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem.
2.MD.B.6 (Standard, major cluster): Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, ..., and represent whole-number sums and differences within 100 on a number line diagram.
2.MD.C.7 (Standard, supporting cluster): Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.
2.MD.C.8 (Standard, supporting cluster): Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. Example: If you have 2 dimes and 3 pennies, how many cents do you have?
2.MD.D.9 (Standard, supporting cluster): Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units.
2.MD.D.10 (Standard, supporting cluster): Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put together, take-apart, and compare problems  using information presented in a bar graph.
2.G.A.1 (Standard, additional cluster): Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. (Sizes are compared directly or visually, not compared by measuring.) Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.
2.G.A.2 (Standard, additional cluster): Partition a rectangle into rows and columns of same-size squares and count to find the total number of them.
2.G.A.3 (Standard, additional cluster): Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.
3.OA.A (Cluster, major cluster): Represent and solve problems involving multiplication and division.
3.OA.A.1 (Standard, major cluster): Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7.
Aspects: conceptual understanding
3.OA.A.2 (Standard, major cluster): Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8.
Aspects: conceptual understanding
3.OA.A.3 (Standard, major cluster): Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.
Aspects: Application
3.OA.A.4 (Standard, major cluster): Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = �� ÷ 3, 6 × 6 = ?.
3.OA.B (Cluster, major cluster): Understand properties of multiplication and the relationship between multiplication and division.
3.OA.B.5 (Standard, major cluster): Apply properties of operations as strategies to multiply and divide. (Students need not use formal terms for these properties.) ^( )Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.)
3.OA.B.6 (Standard, major cluster): Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.
3.OA.C (Cluster, major cluster): Multiply and divide within 100.
3.OA.C.7 (Standard, major cluster): Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.
Aspects: Procedural Skill and Fluency
3.OA.D (Cluster, major cluster): Solve problems involving the four operations, and identify and explain patterns in arithmetic.
3.OA.D.8 (Standard, major cluster): Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. (This standard is limited to problems posed with whole numbers and having whole number answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order (Order of Operations).)
Aspects: Application
3.OA.D.9 (Standard, major cluster): Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.