Grades
Standard
Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, [...]
Classify two-dimensional figures into categories based on their properties. Classify two-dimensional figures in a hierarchy based on properties.
Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a [...]
Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., [...]
Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving [...]
Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition [...]
Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by [...]
Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by [...]
Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. (Grade 4 expectations in this [...]
Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as [...]
Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a [...]
Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations [...]
Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two [...]
Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100 ; describe a length [...]
Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons comparisons are valid only when two decimals [...]
Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.
Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation [...]
Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding [...]
Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in [...]
Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain [...]
Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 [...]
Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols [...]
Understand the place value system. Use place value understanding to round decimals to any place.
Fluently multiply multi-digit whole numbers using the standard algorithm.
Use place value understanding to round multi-digit whole numbers to any place. (Grade 4 expectations in this domain are limited [...]
Fluently add and subtract multi-digit whole numbers using the standard algorithm. (Grade 4 expectations in this domain are limited to [...]
Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using [...]
Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the [...]
Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, [...]
Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, [...]
Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of [...]
Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve [...]
Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle [...]
An angle is measured with reference to a circle with its center at the common endpoint of the rays, by [...]
An angle that turns through n one-degree angles is said to have an angle measure of n degrees.
Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.
Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is [...]
Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.
Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of [...]
Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can [...]
Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, [...]
Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to [...]
Understand a fraction a/b with a > 1 as a sum of fractions 1/b. (Grade 4 expectations in this domain [...]
Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of [...]
Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an [...]
Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that [...]
Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. [...]
Grades
Standard
Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, [...]
Classify two-dimensional figures into categories based on their properties. Classify two-dimensional figures in a hierarchy based on properties.
Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a [...]
Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., [...]
Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving [...]
Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition [...]
Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by [...]
Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by [...]
Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. (Grade 4 expectations in this [...]
Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as [...]
Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a [...]
Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations [...]
Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two [...]
Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100 ; describe a length [...]
Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons comparisons are valid only when two decimals [...]
Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.
Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation [...]
Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding [...]
Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in [...]
Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain [...]
Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 [...]
Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols [...]
Understand the place value system. Use place value understanding to round decimals to any place.
Fluently multiply multi-digit whole numbers using the standard algorithm.
Use place value understanding to round multi-digit whole numbers to any place. (Grade 4 expectations in this domain are limited [...]
Fluently add and subtract multi-digit whole numbers using the standard algorithm. (Grade 4 expectations in this domain are limited to [...]
Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using [...]
Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the [...]
Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, [...]
Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, [...]
Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of [...]
Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve [...]
Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle [...]
An angle is measured with reference to a circle with its center at the common endpoint of the rays, by [...]
An angle that turns through n one-degree angles is said to have an angle measure of n degrees.
Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.
Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is [...]
Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.
Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of [...]
Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can [...]
Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, [...]
Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to [...]
Understand a fraction a/b with a > 1 as a sum of fractions 1/b. (Grade 4 expectations in this domain [...]
Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of [...]
Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an [...]
Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that [...]
Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. [...]
