Mathematics Standards
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Expressing Geometric Properties with Equations
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Reasoning with Equations and Inequalities
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Showing 71 - 80 of 123 Standards
Standard Identifier: 5.NF.5.b
Grade:
5
Domain:
Number and Operations—Fractions
Cluster:
Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
Standard:
Interpret multiplication as scaling (resizing), by: Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1.
Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
Standard:
Interpret multiplication as scaling (resizing), by: Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1.
Standard Identifier: 5.NF.6
Grade:
5
Domain:
Number and Operations—Fractions
Cluster:
Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
Standard:
Solve real-world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.
Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
Standard:
Solve real-world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.
Standard Identifier: 5.NF.7.a
Grade:
5
Domain:
Number and Operations—Fractions
Cluster:
Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
Standard:
Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3.
Footnote:
Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division. But division of a fraction by a fraction is not a requirement at this grade.
Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
Standard:
Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3.
Footnote:
Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division. But division of a fraction by a fraction is not a requirement at this grade.
Standard Identifier: 5.NF.7.b
Grade:
5
Domain:
Number and Operations—Fractions
Cluster:
Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
Standard:
Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4.
Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
Standard:
Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4.
Standard Identifier: 5.NF.7.c
Grade:
5
Domain:
Number and Operations—Fractions
Cluster:
Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
Standard:
Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Solve real-world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins?
Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
Standard:
Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Solve real-world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins?
Standard Identifier: A-REI.1
Grade Range:
7–12
Domain:
Reasoning with Equations and Inequalities
Discipline:
Algebra I
Conceptual Category:
Algebra
Cluster:
Understand solving equations as a process of reasoning and explain the reasoning. [Master linear; learn as general principle.]
Standard:
Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
Understand solving equations as a process of reasoning and explain the reasoning. [Master linear; learn as general principle.]
Standard:
Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
Standard Identifier: A-REI.1
Grade Range:
7–12
Domain:
Reasoning with Equations and Inequalities
Discipline:
Math I
Conceptual Category:
Algebra
Cluster:
Understand solving equations as a process of reasoning and explain the reasoning. [Master linear; learn as general principle.]
Standard:
Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
Understand solving equations as a process of reasoning and explain the reasoning. [Master linear; learn as general principle.]
Standard:
Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
Standard Identifier: A-REI.10
Grade Range:
7–12
Domain:
Reasoning with Equations and Inequalities
Discipline:
Math I
Conceptual Category:
Algebra
Cluster:
Represent and solve equations and inequalities graphically. [Linear and exponential; learn as general principle.]
Standard:
Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).
Represent and solve equations and inequalities graphically. [Linear and exponential; learn as general principle.]
Standard:
Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).
Standard Identifier: A-REI.10
Grade Range:
7–12
Domain:
Reasoning with Equations and Inequalities
Discipline:
Algebra I
Conceptual Category:
Algebra
Cluster:
Represent and solve equations and inequalities graphically. [Linear and exponential; learn as general principle.]
Standard:
Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).
Represent and solve equations and inequalities graphically. [Linear and exponential; learn as general principle.]
Standard:
Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).
Standard Identifier: A-REI.11
Grade Range:
7–12
Domain:
Reasoning with Equations and Inequalities
Discipline:
Algebra I
Conceptual Category:
Algebra
Cluster:
Represent and solve equations and inequalities graphically. [Linear and exponential; learn as general principle.]
Standard:
Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. *
Represent and solve equations and inequalities graphically. [Linear and exponential; learn as general principle.]
Standard:
Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. *
Showing 71 - 80 of 123 Standards
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