Standards
Interpret a multiplication situation 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.
Generate resourceMultiply or divide to solve multiplicative comparison problems in context by using drawings and equations with a symbol for the unknown number to represent the problem
Generate resourceSolve multistep problems in context involving whole numbers and having whole number answers using the four operations, including problems in which remainders must be interpreted.
Generate resourceRepresent these problems using equations with a letter standing for the unknown quantity.
Generate resourceAssess the reasonableness of answers in terms of context, including interpreting remainders.
Generate resourceAsk and answer questions by collecting, organizing and summarizing data, recognizing the importance of context when analyzing data.
Generate resourceCreate scaled data visualization (e.g. bar graphs for categorical data; line plots with fraction units of halves, fourths, and eighths for numerical data) to display data to communicate an idea.
Generate resourceSummarize data presented in scaled data visualizations (e.g. bar graphs, line plots) and draw conclusions about the data.
Generate resourceCompare and contrast different data visualizations of the same data by varying attributes (e.g., reordering bars, changing the scale) and explain how changing the attributes affects the interpretation.
Generate resourceDraw and identify lines and angles, and classify shape by properties of their lines and angles.
Generate resourceDraw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.
Generate resourceClassify 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.
Generate resourceRecognize 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.
Generate resourceApply the relationship between measurement units within a given measurement system (customary: in, ft, yd, oz, lb, sec, min, hr; metric: cm, m, km, g, kg, mL, L) to convert measurements from a larger unit to smaller unit.
Generate resourceUse the four operations to solve problems in context involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving common fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit.
Generate resourceApply the area and perimeter formulas for rectangles in context, including rectangles with missing dimensions.
Generate resourceRelate the area of a triangle to the area of a rectangle using decomposition and visual models. Derive and apply the formula to solve problems in contexts involving triangles positioned within or formed from the decomposition of rectangles
Generate resourceIdentify angles as geometric figures formed by two rays that share a common endpoint and describe angle size as the amount of rotation between the two rays measured in degrees with reference to a circle.
Generate resourceMeasure angles in whole-number degrees using a protractor. Estimate and sketch angles of specified measures.
Generate resourceExplain that when an angle is decomposed into nonoverlapping 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 context (e.g., by using an equation with a symbol for the unknown angle measure).
Generate resourceDRAW AND IDENTIFY LINES AND ANGLES AND CLASSIFY SHAPES BY PROPERTIES OF THEIR LINES AND ANGLES.
Generate resourceDraw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.
Generate resourceClassify 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.
Generate resourceSolve problems involving measurement and conversion of measurements for a larger unit to a smaller unit.
Generate resourceKnow 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.
Generate resourceUse 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.
Generate resourceApply 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 formulas as a multiplication equation with an unknown factor.
Generate resourceMake a line plot to display a data set of measurements in fractions of a unit (½, ¼, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots.
Generate resourceRecognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement.
Generate resourceAn 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 the circle is called a "one-degree angle," and can be used to measure angles.
Generate resourceAn angle that turns through <em>n</em> one-degree angles is said to have an angle measure of <em>n</em> degrees.
Generate resourceMeasure angles in whole-number degrees using a protractor. Sketch angles of specified measure.
Generate resourceRecognize 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.
Generate resourceRecognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right.
Generate resourceRead 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.
Generate resourceUse place value understanding to round multi- digit whole numbers to any place.
Generate resourceUse place value understanding and properties of operations to perform multi-digit arithmetic.
Generate resourceFluently add and subtract multi-digit whole numbers using the standard algorithm.
Generate resourceMultiply 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.
Generate resourceFind 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.
Generate resourceExplain why a fraction a/b is equivalent to a fraction (n x a)/(n x 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.
Generate resourceCompare 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 ½. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, <, and justify the conclusions, e.g., by using a visual fraction model.
Generate resourceBuild fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
Generate resourceUnderstand addition and subtraction of fractions as joining and separating parts referring to the same whole.
Generate resourceDecompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition as an equation. Justify decompositions, e.g., by using a visual fraction model.
Generate resourceAdd 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.
Generate resourceSolve 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.
Generate resourceApply and extend previous understandings of multiplication to multiply a fraction by a whole number.
Generate resourceUnderstand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number.
Generate resourceSolve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem.
Generate resourceExpress 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.
Generate resourceCompare 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 >, =, <, and justify the conclusions, e.g., by using a visual model.
Generate resourceApply and extend place value understanding to multidigit whole numbers within 1,000,000.
Generate resourceRead and write multi-digit whole numbers using base-ten numerals, number names, and expanded form.
Generate resourceEstimate quantities by reasoning about their location on a number line, their relationship to benchmark numbers, and rounding to any place.
Generate resourceCompare two multi-digit numbers by reasoning about the values of the digits and the location of the numbers on a number line. Record the results of comparisons with the symbols , =, and .
Generate resourceExplain that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right (e.g., recognize that 700 ÷ 70 = 10 by applying concepts of place value and division).
Generate resourceUSE PLACE VALUE UNDERSTANDING AND PROPERTIES OF OPERATIONS TO PERFORM MULTI-DIGIT ARITHMETIC.
Generate resourceUse computational strategies (e.g., decomposition, partials sums) efficiently.
Generate resourceExtend place value understanding and basic facts to multiply a multi-digit whole number by a multiple of ten.
Generate resourceMultiply a whole number of up to four digits by a onedigit whole number, and multiply two two-digit numbers.
Generate resourceUse strategies based on place value (e.g., partial products) to multiply.
Generate resourceUse properties of operations (e.g., use doubling and halving strategy to think of 12 × 32 as 6 × 64) to multiply.
Generate resourceRepresent and explain the computation by connecting rectangular arrays, area models, and/or equations to the meaning of multiplication.
Generate resourceDivide whole numbers with up to four-digit dividends and one-digit divisors with and without remainders.
Generate resourceUse strategies based on place value (e.g., partial quotients) to divide.
Generate resourceUse properties of operations and/or the inverse relationship between multiplication and division to divide.
Generate resourceRepresent and explain the computation by connecting rectangular arrays, area models, and/or equations to the meaning of division.
Generate resourceRecall or quickly derive multiplication and division facts within 100 (e.g., factors less than or equal to 10 and quotients less than are equal to 10).
Generate resourceSkip count (2s, 5s, 10s) and apply properties of operations (0s, 1s) to derive foundational facts.
Generate resourceDerive unknown facts from known facts using double facts (e.g., to solve 4 × 3, double 3 to get 6 and double 6 to get 12) to multiply and divide.
Generate resourceUse properties of operations (e.g., to solve 8 × 7, think of (5 × 7 + (3 × 7)) to multiply.
Generate resourceUse the inverse relationship between multiplication and division (e.g., think of to solve ) to multiply and divide.
Generate resourceExplain and apply concepts of factors, multiples, and prime and composite numbers for whole numbers in the range of 1-100.
Generate resourceDetermine whether a given whole number in the range of 1–100 is a multiple of a one-digit number.
Generate resourceDistinguish between factors and multiples and explain how they relate to a given number.
Generate resourceDetermine whether a given whole number in the range of 1–100 is prime, composite, or neither.
Generate resourceCompare two fractions with different numerators and different denominators, understanding that comparisons are valid only when the two fractions refer to the same whole.
Generate resourceUse benchmark numbers (e.g., , 1), common numerators, and common denominators to compare.
Generate resourceIdentify and generate equivalent fractions using representations and the Identity Property of Multiplication.
Generate resourceBUILD FRACTIONS FROM UNIT FRACTIONS BY APPLYING AND EXTENDING PREVIOUS UNDERSTANDINGS OF OPERATIONS ON WHOLE NUMBERS.
Generate resourceApply understanding of a fraction with d >1 as a sum of unit fractions ( ) to decompose a fraction (including fractions greater than 1) into a sum of fractions with the same denominator in more than one way, recording each decomposition as an equation. Justify decompositions using visual fraction models and equations (e.g., or or or ).
Generate resourceApply and extend previous understanding of addition and subtraction of whole numbers to add and subtract fractions with like denominators.
Generate resourceUnderstand addition and subtraction of fractions as joining and separating parts referring to the same whole.
Generate resourceEstimate sums and differences by reasoning about benchmark numbers and assess reasonableness of answers (e.g., will be greater than 1 because both fractions are greater than ).
Generate resourceApply and extend whole number addition and subtraction strategies (e.g. counting on, making a whole, partial sums, compensation, properties of operations, the inverse relationship between addition and subtraction) to add and subtract fractions.
Generate resourceSolve problems in context involving addition and subtraction of fractions using visual fraction models and equations to represent the problem.
Generate resourceApply and extend previous understandings of multiplication to multiply a fraction by a whole number ( ).
Generate resourceEstimate products by reasoning about benchmark numbers and assess reasonableness of answers (e.g., will be less than 4 because I have 4 groups of something less than 1).
Generate resourceUse understanding of multiplication as equal groups to multiply a unit fraction by whole number (e.g., interpret as b groups of ).
Generate resourceUse understanding of multiplication as equal groups to multiply a fraction by whole number (e.g., interpret as b groups of when is greater than or less than 1).
Generate resourceSolve problems in context involving multiplication of a fraction by a whole number, using visual fraction models and equations to represent the problem.
Generate resourceExpress a fraction with a denominator of 10 as an equivalent fraction with a denominator of 100 to add two fractions with respective denominators of 10 and 100.
Generate resourceUse decimal notation for fractions with denominators 10 and 100 (e.g., rewrite 0.62 as or describe a length as 0.62 meters or locate 0.62 on a number line).
Generate resourceCompare 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 , =, , and justify the conclusions, (e.g. using a visual model).
Generate resourceInterpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 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.
Generate resourceMultiply 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.
Generate resourceSolve 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.
Generate resourceFind 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 of 1-100 is prime or composite.
Generate resourceGenerate 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.
Generate resource