ALEX Classroom Resource

Students:
Given situations that have been modeled with equations or inequalities:

• Substitute given specified values for the variables and the evaluate expressions.
• Determine if the resulting numerical sentence is true when the specified values are substituted for the variables.
• Explain with mathematical reasoning why a specified value is or is not a solution to a given equation or inequality.

Students know:

• Conventions of order of operations.
• The solution is the value of the variable that will make the equation or inequality true.
• That using various processes to identify the value(s) that when substituted for the variable will make the equation true.

Students are able to:

• Substitute specific values into algebraic equation or inequality and accurately perform operations of addition, subtraction, multiplication, division and exponentiation using order of operation.

Students understand that:

• Solving an equation or inequality means finding the value or values (if any) that make the mathematical sentence true.
• The solution to an inequality is often a range of values rather than a specific value.

Learning Objectives:
M.6.18.1: Define exponent, numerical expression, algebraic expression, variable, base, power, square of a number, and cube of a number.
M.6.18.2: Compute a numerical expression with exponents, with or without a calculator.
M.6.18.3: Restate exponential numbers as repeated multiplication.
M.6.18.4: Choose the correct value to replace each variable in the expression (Substitution).
M.6.18.5: Calculate the multiplication of single or multi-digit whole numbers, with or without a calculator.

Students:

• Write and solve mathematical equations (or inequalities) to model real-world problems.
• Interpret the solution to an equation in the context of a problem
• Interpret the solution set of an inequality in the context of a problem.
• Graph the solution to an inequality on a number line.

Students know:

• p(x + q) = px + pq, where p and q are specific rational numbers.
• When multiplying or dividing both sides of an inequality by a negative number, every term must change signs and the inequality symbol reversed.
• In the graph of an inequality, the endpoint will be a closed circle indicating the number is included in the solution set (≤ or ≥) or an open circle indicating the number is not included in the solution set ( < or >).

Students are able to:

• use variables to represent quantities in a real-world or mathematical problem.
• Construct equations (px + q = r and p(x + q) = r) to solve problems by reasoning about the quantities.
• Construct simple inequalities (px + q > r or px + q < r) to solve problems by reasoning about the quantities.
• Graph the solution set of an inequality.

Students understand that:

• Real-world problems can be represented through algebraic expressions, equations, and inequalities.
• Why the inequality symbol reverses when multiplying or dividing both sides of an inequality by a negative number.

Learning Objectives:
M.7.9.1: Define equation, inequality, and variable.
M.7.9.2: Set up equations and inequalities to represent the given situation, using correct mathematical operations and variables.
M.7.9.3: Calculate a solution or solution set by combining like terms, isolating the variable, and/or using inverse operations.
M.7.9.4: Test the found number or number set for accuracy by substitution.
M.7.9.5: Recall solving one step equations and inequalities.
M.7.9.6: Recognize properties of numbers (Distributive, Associative, Commutative).
M.7.9.7: Define equation and variable.
M.7.9.8: Set up an equation to represent the given situation, using correct mathematical operations and variables.
M.7.9.9: Calculate a solution to an equation by combining like terms, isolating the variable, and/or using inverse operations.
M.7.9.10: Test the found number for accuracy by substitution.
Example: Is 5 an accurate solution of 2(x + 5)=12?.
M.7.9.11: Identify the unknown, in a given situation, as the variable.
M.7.9.12: List given information from the problem.
M.7.9.13: Recalling one-step equations.
M.7.9.14: Explain the distributive property.
M.7.9.15: Define inequality and variable.
M.7.9.16: Set up an inequality to represent the given situation, using correct mathematical operations and variables.
M.7.9.17: Calculate a solution set to an inequality by combining like terms, isolating the variable, and/or using inverse operations.
M.7.9.18: Test the solution set for accuracy.
M.7.9.19: Identify the unknown, of a given situation, as the variable.
M.7.9.20: List information from the problem.
M.7.9.21: Recall how to graph inequalities on a number line.
M.7.9.22: Recall how to solve one step inequalities.

Students:

• Write and solve mathematical equations (or inequalities) to model real-world problems.
• Interpret the solution to an equation in the context of a problem.
• Interpret the solution set of an inequality in the context of a problem.

Students know:

• p(x + q) = px + pq, where p and q are specific rational numbers.
• When multiplying or dividing both sides of an inequality by a negative number, every term must change signs and the inequality symbol reversed.
• In the graph of an inequality, the endpoint will be a closed circle indicating the number is included in the solution set (≤ or ≥) or an open circle indicating the number is not included in the solution set ( < or >).

Students are able to:

• Use variables to represent quantities in a real-world or mathematical problem.
• Construct equations (px + q = r and p(x + q) = r) to solve problems by reasoning about the quantities.
• Construct simple inequalities (px + q > r or px + q < r) to solve problems by reasoning about the quantities.
• Graph the solution set of an inequality.

Students understand that:

• Real-world problems can be represented through algebraic expressions, equations, and inequalities.
• The inequality symbol reverses when multiplying or dividing both sides of an inequality by a negative number, and why.