Properties

Whole Number Equations

Fraction and Decimal Equations

Inequalities

Unit Objectives:

• Translate mathematical sentences into algebraic expressions.
• Identify parts of an expressions.
• Evaluate algebraic expressions and express real-world problems algebraically.
• Apply the properties of operations to simplify and rewrite algebraic expressions.
• Define, identify and combine like terms in an algebraic expression.
• Apply the properties of operations to identify equivalent algebraic expressions.
• Prove true solutions to equations through substitution.
• Construct equations in relation to real world problems.
• Solve one-step equations with positive numbers, fractions, and decimals.
• Apply equations to problem-solve.
• Use equations to express the relationship between dependent and independent variables.
• Relate a written inequality to the position of numbers on the number line.
• Compare and interpret rational numbers in real-world contexts.
• Represent and write inequalities.

New Jersey Student Learning Standards for this Unit:

CCSS.Math.Content.6.EE.A.2

Write, read, and evaluate expressions in which letters stand for numbers.

• 6.EE.A.2a Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y.
• 6.EE.A.2b Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms.
• 6.EE.A.2c Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas V = s3 and A = 6 s2 to find the volume and surface area of a cube with sides of length s = 1/2.

CCSS.Math.Content.6.EE.A.3

Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.

CCSS.Math.Content.6.EE.A.4 Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.

CCSS.Math.Content.6.EE.B.5 Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.

CCSS.Math.Content.6.EE.B.6 Use variables to represent numbers and write equations when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.

CCSS.Math.Content.6.EE.B.7 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 nonnegative rational numbers.

CCSS.Math.Content.6.EE.C.9 Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the

independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.

CCSS.Math.Content.6.NS.C.7

Understand ordering and absolute value of rational numbers.

• 6.NS.C.7a Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right.
• 6.NS.C.7b Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write –3 C > –7 C to express the fact that –3 C is warmer than –7 C.

CCSS.Math.Content.6.EE.B.8 Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.