Understand rational numbers as points on the number line and as ordered pairs on a coordinate plane.
On a number line:
Recognize opposite signs of numbers as indicating locations on opposite sides of 0 and that the opposite of the opposite of a number is the number itself.
Find and position rational numbers on a horizontal or vertical number line.
Understand ordering of rational numbers.
Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram.
Write, interpret, and explain statements of order for rational numbers in real-world contexts.
Apply and extend previous understandings of addition and subtraction.
β’ Describe situations in which opposite quantities combine to make 0.
β’ Understand π + π as the number located a distance q from p, in the positive or negative direction depending on the sign of q. Show that a number and its additive inverse create a zero pair.
β’ Understand subtraction of integers as adding the additive inverse, π β π = π +(β π). Show that the distance between two integers on the number line is the absolute value of their difference.
β’ Use models to add and subtract integers from -20 to 20 and describe real-world contexts using sums and differences.
Understand rational numbers as points on the number line and as ordered pairs on a coordinate plane.
On a coordinate plane: o Understand signs of numbers in ordered pairs as indicating locations in quadrants. o Recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.
Find and position pairs of rational numbers on a coordinate plane.
Write, read, and evaluate algebraic expressions.
β’ Write expressions that record operations with numbers and with letters standing for numbers.
β’ Identify parts of an expression using mathematical terms and view one or more of those parts as a single entity.
β’ Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems.
Apply the properties of operations to generate equivalent expressions without exponents.
Identify when two expressions are equivalent and justify with mathematical reasoning.
Use variables to represent numbers and write expressions when solving a real-world or mathematical problem.
Use substitution to determine whether a given number in a specified set makes an equation true.
Solve real-world and mathematical problems by writing and solving equations of the form: β’ π₯ + π = π in which p, q and x are all nonnegative rational numbers; and, β’ π β π₯ = π for cases in which p, q and x are all non negative rational numbers.
Reason about inequalities by:
β’ Using substitution to determine whether a given number in a specified set makes an inequality true.
β’ Writing an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem.
β’ Recognizing that inequalities of the form x > c or x < c have infinitely many solutions.
β’ Representing solutions of inequalities on number line diagrams.
Represent and analyze quantitative relationships by:
β’ Using variables to represent two quantities in a real-world or mathematical context that change in relationship to one another.
β’ Analyze the relationship between quantities in different representations (context, equations, tables, and graphs).