Mathematics Standards
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Showing 71 - 80 of 80 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: 8.F.1
Grade:
8
Domain:
Functions
Cluster:
Define, evaluate, and compare functions.
Standard:
Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.
Footnote:
Function notation is not required in grade 8.
Define, evaluate, and compare functions.
Standard:
Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.
Footnote:
Function notation is not required in grade 8.
Standard Identifier: 8.F.2
Grade:
8
Domain:
Functions
Cluster:
Define, evaluate, and compare functions.
Standard:
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.
Define, evaluate, and compare functions.
Standard:
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.
Standard Identifier: 8.F.3
Grade:
8
Domain:
Functions
Cluster:
Define, evaluate, and compare functions.
Standard:
Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s^2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.
Define, evaluate, and compare functions.
Standard:
Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s^2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.
Standard Identifier: 8.F.4
Grade:
8
Domain:
Functions
Cluster:
Use functions to model relationships between quantities.
Standard:
Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.
Use functions to model relationships between quantities.
Standard:
Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.
Standard Identifier: 8.F.5
Grade:
8
Domain:
Functions
Cluster:
Use functions to model relationships between quantities.
Standard:
Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.
Use functions to model relationships between quantities.
Standard:
Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.
Showing 71 - 80 of 80 Standards
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