Standards
Generate data-based questions of interest to the students, generate ideas based on the questions, and refine the question as necessary.
Generate resourceDetermine strategies for collecting and considering data in a variety of ways including with the use of technology, evaluate whether additional data that should be collected to completely address the investigative question.
Generate resourceCritically analyze data visualizations, including tables, bar graphs, line plots, or spreadsheets to support a claim related to the investigative question. Ask whether the data collected sufficiently addresses the investigative question.
Generate resourceInterpret and communicate results, describing difference between groups, with teacher guidance. Make a statement(s) about the data collected to support the answer to the investigative question.
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 resourceKnow relative sizes of measurement units within one system of units including . and 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 flexibly, efficiently, and accurately 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 multiple visual models.
Generate resourceApply the area and perimeter formulas for rectangles in real world and mathematical problems.
Generate resourceMake a line plot to display a data set of measurements in fractions of a unit. Flexibly, efficiently, and accurately solve problems involving addition and subtraction of fractions by using information presented in line plots.
Generate resourceDemonstrate understanding of angles as geometric shapes that are formed wherever two rays share a common endpoint and understand concepts of angle measure.
Generate resourceMeasure angles in whole-number degrees using a protractor. Sketch angles of specified measure.
Generate resourceDemonstrate understanding that 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. Flexibly, efficiently, and accurately solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems.
Generate resourceUnderstand 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 and compare multi-digit whole numbers using base-ten numerals, number names, and expanded form using the meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
Generate resourceUse place value understanding of multi-digit whole numbers to generate estimates to any place less than or equal to 1,000,000 using a variety of estimation strategies.
Generate resourceFind whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using multiple 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 resourceFlexibly, efficiently, and accurately 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.
Generate resourceFlexibly, efficiently, and accurately add and subtract multi-digit whole numbers using strategies or algorithms.
Generate resourceExplain why a fraction is equivalent to another fraction by using visual fraction models (e.g., tape diagrams and number lines), with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Understand and use general principles 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 . Understand 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.
Generate resourceFlexibly, efficiently, and accurately compose and decompose fractions with a numerator greater than 1 into unit fractions, including fractions greater than one or mixed numbers, to solve situations in context with addition and subtraction of fractions with like denominators.
Generate resourceFlexibly apply and extend previous understandings of multiplication to multiply a fraction by a whole number using visual models in the context of word problems.
Generate resourceExplore and explain using models, words, and numbers that a fraction with a denominator of 10 is an equivalent fraction with denominator of 100, and use this technique to add two fractions with respective denominators of 10 and 100.
Generate resourceExplore and explain decimal notation for fractions with denominators of 10 and 100 using models, words, and numbers.
Generate resourceCompare two decimals to hundredths by reasoning about their size. Understand 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 by using multiple strategies or visual models.
Generate resourceInterpret 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 these verbal comparison statements as multiplication equations.
Generate resourceMultiply or divide to flexibly, efficiently, and accurately 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 resourceFlexibly, efficiently, and accurately 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 visual models and equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental and estimation strategies.
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 1–100 is prime or composite.
Generate resourceGenerate a number or shape pattern that follows a given rule. Identify and explain apparent features of the pattern that were not explicit in the rule itself. Explain informally why the numbers will continue to alternate in this way.
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 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 resourceSolve problems involving measurement and conversion of measurements from 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.
Generate resourceMake 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.
Generate resourceGeometric measurement: understand concepts of angle and measure angles.
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 a circle is called a "one-degree angle," and can be used to measure angles.
Generate resourceAn angle that turns through n one-degree angles is said to have an angle measure of n 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 resourceGeneralize place value understanding for multi-digit whole numbers.
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 × 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.
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 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.
Generate resourceBuild fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
Generate resourceUnderstand a fraction a/b with a > 1 as a sum of fractions 1/b.
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 by 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 resourceUnderstand decimal notation for fractions, and compare decimal fractions.
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 resourceUse decimal notation for fractions with denominators 10 or 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 >, =, or <, and justify the conclusions, e.g., by using a visual model.
Generate resourceUse the four operations with whole numbers to solve problems.
Generate resourceInterpret 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.
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 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.
Generate resourceConstruct viable arguments and critique the reasoning of others.
Generate resourceBuild fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
Generate resourceUse place value understanding and properties of operations to perform multidigit arithmetic.
Generate resourceDraw and identify lines and angles and classify shapes by properties of their lines and angles.
Generate resourceSolve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.
Generate resource