allenai/achieve-the-core huggingface dataset:
3.NBT.A (Cluster, additional cluster): Use place value understanding and properties of operations to perform multi-digit arithmetic. (A range of algorithms may be used.)
3.NBT.A.1 (Standard, additional cluster): Use place value understanding to round whole numbers to the nearest 10 or 100.
3.NBT.A.2 (Standard, additional cluster): Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.
Aspects: Procedural Skill and Fluency
3.NBT.A.3 (Standard, additional cluster): Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations.
3.NF.A (Cluster, major cluster): Develop Understanding of fractions as numbers.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.
3.NF.A.1 (Standard, major cluster): Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.
3.NF.A.2 (Standard, major cluster): Understand a fraction as a number on the number line; represent fractions on a number line diagram.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.
3.NF.A.2a (Sub-standard, major cluster): Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.
3.NF.A.2b (Sub-standard, major cluster): Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.
3.NF.A.3 (Standard, major cluster): Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.
3.NF.A.3a (Sub-standard, major cluster): Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.
3.NF.A.3b (Sub-standard, major cluster): Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., by using a visual fraction model.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.
3.NF.A.3c (Sub-standard, major cluster): Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.
3.NF.A.3d (Sub-standard, major cluster): Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.
3.MD.A (Cluster, major cluster): Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.
3.MD.A.1 (Standard, major cluster): Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram.
3.MD.A.2 (Standard, major cluster): Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). (Excludes compound units such as cm^(3) and finding the geometric volume of a container.) Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem. [Excludes multiplicative comparison problems (problems involving notions of “times as much”)]
3.MD.B.3 (Standard, supporting cluster): Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets.
3.MD.B.4 (Standard, supporting cluster): Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units— whole numbers, halves, or quarters.
3.MD.C (Cluster, major cluster): Geometric measurement: understand concepts of area and relate area to multiplication and to addition.
3.MD.C.5 (Standard, major cluster): Recognize area as an attribute of plane figures and understand concepts of area measurement.
3.MD.C.5a (Sub-standard, major cluster): A square with side length 1 unit, called “a unit square,” is said to have “one square unit” of area, and can be used to measure area.
3.MD.C.5b (Sub-standard, major cluster): A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units.
3.MD.C.6 (Standard, major cluster): Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).
3.MD.C.7 (Standard, major cluster): Relate area to the operations of multiplication and addition.
3.MD.C.7a (Sub-standard, major cluster): Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths.
3.MD.C.7b (Sub-standard, major cluster): Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning.
3.MD.C.7c (Sub-standard, major cluster): Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a × b and a × c. Use area models to represent the distributive property in mathematical reasoning.
3.MD.C.7d (Sub-standard, major cluster): Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems.
3.MD.D (Cluster, additional cluster): Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.
3.MD.D.8 (Standard, additional cluster): Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.
3.G.A.1 (Standard, supporting cluster): Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.
3.G.A.2 (Standard, supporting cluster): Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape.
4.OA.A (Cluster, major cluster): Use the four operations with whole numbers to solve problems.
4.OA.A.1 (Standard, major cluster): Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.
4.OA.A.2 (Standard, major cluster): Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.
4.OA.A.3 (Standard, major cluster): Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
Aspects: Application
4.OA.B (Cluster, supporting cluster): Gain familiarity with factors and multiples.
4.OA.B.4 (Standard, supporting cluster): Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite.
4.OA.C.5 (Standard, additional cluster): Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.
4.NBT.A (Cluster, major cluster): Generalize place value understanding for multi-digit whole numbers.
Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.
Aspects: conceptual understanding
4.NBT.A.1 (Standard, major cluster): Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.
Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.
Aspects: conceptual understanding
4.NBT.A.2 (Standard, major cluster): Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.
Aspects: conceptual understanding
4.NBT.A.3 (Standard, major cluster): Use place value understanding to round multi-digit whole numbers to any place.
Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.
Aspects: conceptual understanding
4.NBT.B (Cluster, major cluster): Use place value understanding and properties of operations to perform multi-digit arithmetic.
Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.
Aspects: conceptual understanding
4.NBT.B.4 (Standard, major cluster): Fluently add and subtract multi-digit whole numbers using the standard algorithm.
Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.
Aspects: conceptual understanding, Procedural Skill and Fluency
4.NBT.B.5 (Standard, major cluster): Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.
Aspects: conceptual understanding
4.NBT.B.6 (Standard, major cluster): Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.
Aspects: conceptual understanding
4.NF.A (Cluster, major cluster): Extend understanding of fraction equivalence and ordering.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
Aspects: conceptual understanding
4.NF.A.1 (Standard, major cluster): Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
Aspects: conceptual understanding
4.NF.A.2 (Standard, major cluster): Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
Aspects: conceptual understanding
4.NF.B (Cluster, major cluster): Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
4.NF.B.3 (Standard, major cluster): Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
4.NF.B.3a (Sub-standard, major cluster): Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
4.NF.B.3b (Sub-standard, major cluster): Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
4.NF.B.3c (Sub-standard, major cluster): Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
4.NF.B.3d (Sub-standard, major cluster): Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
Aspects: Application
4.NF.B.4 (Standard, major cluster): Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
4.NF.B.4a (Sub-standard, major cluster): Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4).
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
4.NF.B.4b (Sub-standard, major cluster): Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. (In general, n × (a/b) = (n × a)/b.)
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
4.NF.B.4c (Sub-standard, major cluster): Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
Aspects: Application
4.NF.C (Cluster, major cluster): Understand decimal notation for fractions, and compare decimal fractions.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
4.NF.C.5 (Standard, major cluster): Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. (Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade.) For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
4.NF.C.6 (Standard, major cluster): Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
4.NF.C.7 (Standard, major cluster): Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
4.MD.A (Cluster, supporting cluster): Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.
4.MD.A.1 (Standard, supporting cluster): Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...
4.MD.A.2 (Standard, supporting cluster): Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.
4.MD.A.3 (Standard, supporting cluster): Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.
4.MD.B.4 (Standard, supporting cluster): Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection.
4.MD.C (Cluster, additional cluster): Geometric measurement: understand concepts of angle and measure angles.
4.MD.C.5 (Standard, additional cluster): Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:
- An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles.
- An angle that turns through n one-degree angles is said to have an angle measure of n degrees.
4.MD.C.5a (Sub-standard, additional cluster): An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles.
4.MD.C.5b (Sub-standard, additional cluster): An angle that turns through n one-degree angles is said to have an angle measure of n degrees.
4.MD.C.6 (Standard, additional cluster): Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.
4.MD.C.7 (Standard, additional cluster): Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.
4.G.A (Cluster, additional cluster): Draw and identify lines and angles, and classify shapes by properties of their lines and angles.
4.G.A.1 (Standard, additional cluster): Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.
4.G.A.2 (Standard, additional cluster): Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.
4.G.A.3 (Standard, additional cluster): Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry.
5.OA.A.1 (Standard, additional cluster): Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.