In this unit students deepen and extend their understanding of addition and subtraction with rational numbers, as they operate with both positive and negative numbers. Students bring their solid understanding of integers and other rational numbers as both locations on the number line and a distance from zero, and use the ideas of distance and direction to add and subtract with all types and forms of rational numbers. Absolute value as a distance, as described in 6.NS.C, and properties of operations help students make and defend claims about sums, differences, and comparisons of rational numbers.
Key Concepts:
 Thinking about positive and negative directions helps to understand that the number (p + q) is a distance from p equal to the absolute value of q. For instance, 14 is a distance of 5 from 9, and 4 is also a distance of 5 from 9, but in the opposite direction.
 Using distance and direction on the number line, we can understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q).
 The relationship between addition and subtraction (i.e., if a + b = c, then c  b = a and c  a = b) holds for the set of rational numbers, and this relationship can be used to derive "rules" for operating with positive and negative numbers.
Prior Knowledge Needed:
 Numbers have distance and direction on the number line; (Grade 6, Unit 6; 6.NS.6).
 The properties of operations can be used to generate equivalent expressions; (Grade 6, Unit 8; 6.EE.3).
Units on the Horizon:
 Simplifying expressions, solving equations, and solving inequalities; (Grade 7, Unit 6, and Unit 7)
 Rational and irrational numbers; (Grade 8, Unit 4)
Lessons

Lesson objective: Understand that sums of integers can be found using distance and direction on the number line. Students bring prior knowledge of distance and direction on the number line, including the relationship of opposites from 6.NS.C. This prior...

Lesson objective: Add integers using the idea of distance and direction. This lesson helps to build procedural skill with adding integers. The number line is used here because it supports students in thinking about the sign of a number indicating direct...

Lesson objective: Add rational numbers using the idea of distance and direction. This lesson helps to build procedural skill with adding rational numbers, including both positive and negative numbers written as fractions or decimals. The number line is ...

Lesson objective: Apply understanding of distance, direction, and locations on the number line to justify sums of integers. This lesson provides an opportunity for students to apply their knowledge and understanding of the location of signed numbers on ...

Lesson objective: Understand that for every expression that includes subtraction, there is an equivalent expression using addition of the opposite of the number being subtracted. Students bring prior knowledge of finding sums of rational numbers. This p...

Lesson objective: Practice subtracting integers by writing equivalent expressions using addition. This lesson helps to build procedural skill with adding and subtracting integers. The number line is used here because students are working with the connec...

Lesson objective: Apply and extend understanding of adding and subtracting with integers to the set of rational numbers. This lesson provides an opportunity for students to apply their knowledge and understanding of adding and subtracting integers to th...

Lesson objective: Extend the understanding that there are rules for adding and subtracting rational numbers. Students bring prior knowledge of adding and subtracting integers from 7.NS.A.1.B. This prior knowledge is extended to adding and subtracting ra...

Lesson objective: Fluently use the rules for adding and subtracting rational numbers. This lesson helps to build fluency with adding subtracting rational numbers. Equations are used here because they support students' understanding of how to interpret t...

Lesson objective: Apply the understanding of the relationships between rational numbers. This lesson provides an opportunity for students to apply their knowledge and understanding of adding and subtracting rational numbers to a reallife situation. Stu...