Use multiplication (up to and including 10 × 10) and/or division (limit dividends through 50 and limit divisors and quotients through 10) to solve word problems in situations involving equal groups, arrays, and/or measurement quantities.


When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content

Determine the unknown whole number in a multiplication (up to and including 10 × 10) or division (limit dividends through 50 and limit divisors and quotients through 10) equation relating three whole numbers. Example: Determine the unknown number that makes an equation true.


When grade appropriate instruction pertaining to an eligible content should begin

Determine the unknown whole number in a multiplication (up to and including 10 × 10) or division (limit dividends through 50 and limit divisors and quotients through 10) equation relating three whole numbers. Example: Determine the unknown number that makes an equation true.


When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content

Solve two-step equations using order of operations (equation is explicitly stated with no grouping symbols).


When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content

Solve two-step word problems using the four operations (expressions are not explicitly stated). Limit to problems with whole numbers and having whole-number answers.


When grade appropriate instruction pertaining to an eligible content should begin

Solve two-step word problems using the four operations (expressions are not explicitly stated). Limit to problems with whole numbers and having whole-number answers.


When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content

Interpret and/or model division as a multiplication equation with an unknown factor. Example: Find 32 ÷ 8 by solving 8 × ? = 32.


When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content

Identify the missing symbol (+, –, ×, ÷, <, >, and =) that makes a number sentence true.


When grade appropriate instruction pertaining to an eligible content should begin

Identify the missing symbol (+, –, ×, ÷, <, >, and =) that makes a number sentence true.


When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content

Create or match a story to a given combination of symbols (+, –, ×, ÷, <, >, and =) and numbers.


When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content

Represent two-step word problems using equations with a symbol standing for the unknown quantity. Limit to problems with whole numbers and having whole-number answers.


When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content

Assess the reasonableness of answers. Limit problems posed with whole numbers and having whole-number answers.


When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content

Interpret a multiplication equation as a comparison. Represent verbal statements of multiplicative comparisons as multiplication equations. Example 1: Interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Example 2: Know that the statement 24 is 3 times as many as 8 can be represented by the equation 24 = 3 × 8 or 24 = 8 × 3.


When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content

Multiply or divide to solve word problems involving multiplicative comparison, distinguishing multiplicative comparison from additive comparison. Example: Know that 3 × 4 can be used to represent that Student A has 4 objects and Student B has 3 times as many objects not just 3 more objects.


When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content

Solve multi-step word problems posed with whole numbers using the four operations. Answers will be either whole numbers or have remainders that must be interpreted yielding a final answer that is a whole number. Represent these problems using equations with a symbol or letter standing for the unknown quantity.


When grade appropriate instruction pertaining to an eligible content should begin

Solve multi-step word problems posed with whole numbers using the four operations. Answers will be either whole numbers or have remainders that must be interpreted yielding a final answer that is a whole number. Represent these problems using equations with a symbol or letter standing for the unknown quantity.


When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content

Identify the missing symbol (+, –, ×, ÷, =, <, and >) that makes a number sentence true (single-digit divisor only).


When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content

Use substitution to determine whether a given number in a specified set makes an equation or inequality true.


When grade appropriate instruction pertaining to an eligible content should begin

Use substitution to determine whether a given number in a specified set makes an equation or inequality true.


When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content

Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q, and x are all non-negative rational numbers.


When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content

Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem and/or represent solutions of such inequalities on number lines.


When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content

Write an equation to express the relationship between the dependent and independent variables. Example: In a problem involving motion at a constant speed of 65 units, write the equation d = 65t to represent the relationship between distance and time.


When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content

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. Example: The perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?


When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content

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, and graph the solution set of the inequality. Example: A salesperson is paid $50 per week plus $3 per sale. This week she wants her pay to be at least $100. Write an inequality for the number of sales the salesperson needs to make and describe the solutions.


When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content

Determine the reasonableness of answer(s) or interpret the solution(s) in the context of the problem. Example: If you want to place a towel bar that is 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.


When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content

Write or solve compound inequalities and/or graph their solution sets on a number line (may include absolute value inequalities).


When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content

Identify or graph the solution set to a linear inequality on a number line.


When grade appropriate instruction pertaining to an eligible content should begin

Identify or graph the solution set to a linear inequality on a number line.


When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content

Interpret solutions to problems in the context of the problem situation (limit to linear inequalities).


When grade appropriate instruction pertaining to an eligible content should begin

Interpret solutions to problems in the context of the problem situation (limit to linear inequalities).


When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content

Write and identify linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).


When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content

Solve linear equations that have rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.


When grade appropriate instruction pertaining to an eligible content should begin

Solve linear equations that have rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.


When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content

Use algebraic processes to solve a formula for a given variable (e.g., solve d = rt for r).


When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content

Write, solve and/or apply a linear equation (including problem situations).


When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content

Interpret solutions to problems in the context of the problem situation (linear equations only).


When grade appropriate instruction pertaining to an eligible content should begin

Interpret solutions to problems in the context of the problem situation (linear equations only).


When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content

Interpret solutions to a system of two linear equations in two variables as points of intersection of their graphs because points of intersection satisfy both equations simultaneously.


When grade appropriate instruction pertaining to an eligible content should begin

Interpret solutions to a system of two linear equations in two variables as points of intersection of their graphs because points of intersection satisfy both equations simultaneously.


When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content

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


When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content

Write and/or solve a system of linear equations (including problem situations) using graphing, substitution and/or elimination (limit systems to 2 linear equations).


When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content

Solve real-world and mathematical problems leading to two linear equations in two variables. Example: Given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.


When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content

Interpret solutions to problems in the context of the problem situation (systems of 2 linear equations only).


When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content

Write and/or solve a system of linear inequalities using graphing (limit systems to 2 linear inequalities).


When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content

Interpret solutions to problems in the context of the problem situation (systems of 2 linear inequalities only).


When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content

Write and/or solve quadratic equations (including factoring and using the Quadratic Formula).


When grade appropriate instruction pertaining to an eligible content should begin

Write and/or solve quadratic equations (including factoring and using the Quadratic Formula).


When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content

Write and/or solve a simple exponential or logarithmic equation (including common and natural logarithms).


When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content

Write, solve and/or apply linear or exponential growth or decay (including problem situations).


When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content