Section	Teacher-facing learning goals
Negative Numbers and Absolute Value	Lesson 1 Comprehend the words “positive” and “negative” (in spoken and written language) and the symbol “-” (in written language). Say “negative” when reading numbers written with the “-” symbol. Interpret positive and negative numbers that represent temperature or elevation, and understand the convention of what “below zero” typically means in each of these contexts. Recognize that the number line can be extended to represent negative numbers. Lesson 2 Comprehend that two numbers are called “opposites” when they are the same distance from zero, but on different sides of the number line. Interpret a point on the number line that represents a positive or negative rational number. Plot a point on a number line to represent a positive or negative rational number. Lesson 3 Compare rational numbers in the context of temperature or elevation, and express the comparisons (in writing) using the symbols > and <. Comprehend the word “sign” (in spoken language) to refer to whether a number is positive or negative. Critique (orally and in writing) statements comparing rational numbers, including claims about relative position and claims about distance from zero. Lesson 4 Compare rational numbers without a context and express the comparisons using the terms “greater than,” “less than,” and “opposite” (orally and in writing). Comprehend that all negative numbers are less than all positive numbers. Order rational numbers from least to greatest, and explain (orally and through other representations) the reasoning. Lesson 5 Interpret a table of signed numbers that represent how a quantity changed. Recognize that signed numbers can be useful to represent changes in a quantity in opposite directions, e.g., money received and money paid, inventory bought and inventory sold, etc. Lesson 6 Compare rational numbers and their absolute values, and explain (orally and in writing) the reasoning. Comprehend the phrase “absolute value” and the symbol \(\|\|\) to refer to a number’s distance from zero on the number line. Interpret rational numbers and their absolute values in the context of elevation or temperature. Lesson 7 Critique comparisons (expressed using words or symbols) of rational numbers and their absolute values. Generate values that meet given conditions for their relative position and absolute value, and justify the comparisons (using words and symbols). Recognize that the value of \(\text-a\) can be positive or negative, depending on the value of \(a\).
Inequalities	Lesson 8 Coordinate verbal, algebraic, and number line representations of inequalities. Critique (orally and in writing) possible values given for a situation with a constraint, including determining whether the boundary value is included and making sense of situations with discrete quantities. Interpret phrases that describe a quantity constrained by a maximum or minimum acceptable value, e.g. “at least,” “at most,” “up to,” “more than,” “less than”, etc., and write an inequality statement to represent the constraint. Lesson 9 Draw and label a number line diagram to represent the solutions to an inequality. Recognize and explain (orally and in writing) that an inequality may have infinitely many solutions. Use substitution to justify (orally) whether a given value is a “solution” to a given inequality. Lesson 10 Critique (orally and in writing) possible values given for a situation with more than one constraint, including whether fractional or negative values are reasonable. Interpret unbalanced hanger diagrams (orally and in writing) and write inequality statements to represent relationships between the weights on an unbalanced hanger diagram. Write and interpret inequality statements that include more than one variable.
The Coordinate Plane	Lesson 11 Generalize about the signs of coordinates that represent locations in each “quadrant” of the coordinate plane. Plot a point given its coordinates or identify the coordinates of a given point on the coordinate plane. Recognize that the axes of the coordinate plane can be extended to represent negative numbers. Lesson 12 Choose and label appropriate scales for the axes of the coordinate plane, based on the coordinates to be plotted, and explain (orally and in writing) the choice. Compare and contrast different scales for the axes of the coordinate plane. Lesson 13 Compare points on a graph, including statements about relative position and the vertical distance between points. Describe (using words and inequality symbols) and interpret the range of coordinates on a graph, including the meaning of \(y\)-values that are negative. Identify and interpret points on a graph to answer questions about situations involving temperature or money. Lesson 14 Compare and contrast (orally and in writing) the coordinates for points in different locations on the coordinate plane. Determine the vertical or horizontal distance between two points on the coordinate plane that share the same \(x\)- or \(y\)-coordinate. Generalize (orally) about the coordinates of points that are reflected across the \(x\)- or \(y\)-axis. Lesson 15 Determine the total length of multiple horizontal and vertical segments in the coordinate plane that are connected end-to-end. Draw a polygon in the coordinate plane given the coordinates for its vertices. Explain (orally) that coordinates can be a useful way of describing geometric figures or modeling real-world locations.
Common Factors and Common Multiples	Lesson 16 Comprehend (orally and in writing) the terms “factor,” “common factor,” and “greatest common factor.” Explain (orally and in writing) how to determine the greatest common factor of two whole numbers less than 100. List the factors of a number and identify common factors for two numbers in a real-world situation. Lesson 17 Comprehend (orally and in writing) the terms “multiple,” “common multiple,” and “least common multiple.” Explain (orally and in writing) how to calculate the least common multiple of 2 whole numbers. List the multiples of a number and identify common multiples for two numbers in a real-world situation. Lesson 18 Choose to calculate the greatest common factor or least common multiple to solve a problem about a real-world situation, and justify (orally) the choice. Present (orally, in writing, and using other representations) the solution method for a problem involving greatest common factor or least common multiple. Lesson 19 Generate a list of ordered pairs to create an image in the coordinate plane, and explain (orally) the reasoning.

6.7 Rational Numbers