Learning Domain: Expressions and Equations

Standard: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations as strategies to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Expressions and Equations

Standard: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Expressions and Equations

Standard: Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, The perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?

Degree of Alignment: Not Rated (0 users)

Learning Domain: Expressions and Equations

Standard: Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example, As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.

Degree of Alignment: Not Rated (0 users)

Learning Domain: The Number System

Standard: Understand subtraction of rational numbers as adding the additive inverse, p - q = p + (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.

Degree of Alignment: Not Rated (0 users)

Learning Domain: The Number System

Standard: Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

Degree of Alignment: Not Rated (0 users)

Learning Domain: The Number System

Standard: Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.

Degree of Alignment: Not Rated (0 users)

Learning Domain: The Number System

Standard: Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real-world contexts.

Degree of Alignment: Not Rated (0 users)

Learning Domain: The Number System

Standard: Apply properties of operations as strategies to multiply and divide rational numbers.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Expressions and Equations

Standard: Solve linear equations in one variable.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Expressions and Equations

Standard: Analyze and solve pairs of simultaneous linear equations.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Expressions and Equations

Standard: Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.

Degree of Alignment: Not Rated (0 users)

Cluster: Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers

Standard: Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.

Degree of Alignment: 3 Superior (1 user)

Cluster: Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers

Standard: Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

Degree of Alignment: 3 Superior (1 user)

Cluster: Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers

Standard: Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.

Degree of Alignment: 3 Superior (1 user)

Cluster: Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers

Standard: Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers then –(p/q) = (–p)/q = p/(–q). Interpret quotients of rational numbers by describing real-world contexts.

Degree of Alignment: 3 Superior (1 user)

Cluster: Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers

Standard: Apply properties of operations as strategies to multiply and divide rational numbers.

Degree of Alignment: 3 Superior (1 user)

Cluster: Use properties of operations to generate equivalent expressions

Standard: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

Degree of Alignment: 3 Superior (1 user)

Cluster: Solve real-life and mathematical problems using numerical and algebraic expressions and equations

Standard: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations as strategies to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.

Degree of Alignment: 3 Superior (1 user)

Cluster: Solve real-life and mathematical problems using numerical and algebraic expressions and equations

Standard: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.

Degree of Alignment: 3 Superior (1 user)

Cluster: Solve real-life and mathematical problems using numerical and algebraic expressions and equations

Standard: Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, The perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?

Degree of Alignment: 3 Superior (1 user)

Cluster: Solve real-life and mathematical problems using numerical and algebraic expressions and equations

Standard: Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example, As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.

Degree of Alignment: 3 Superior (1 user)

Cluster: Analyze and solve linear equations and pairs of simultaneous linear equations

Standard: Solve linear equations in one variable.

Degree of Alignment: 3 Superior (1 user)

Cluster: Analyze and solve linear equations and pairs of simultaneous linear equations

Standard: Analyze and solve pairs of simultaneous linear equations.

Degree of Alignment: 3 Superior (1 user)

Cluster: Analyze and solve linear equations and pairs of simultaneous linear equations

Standard: Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.

Degree of Alignment: 3 Superior (1 user)