In this unit, students will extend their understanding of numbers to include all rational numbers. They will use rational numbers in realworld contexts and understand the meaning of 0 in any situation. Students will discover integers and rational numbers, how to determine their value, and where those numbers live on the number line in relation to other, more familiar numbers. Students are likely to struggle with comparing the values of negative integers and creating meaningful context for interpreting the values of integers.
Key Concepts:
 The number line can show both distance and direction; the sets of positive and negative numbers exist in opposite directions from 0.
 The set of integers includes whole numbers, their opposites, and zero, and live on the number line with the other types of numbers students know.
 There are three possible relationships between any two numbers, a and b (namely, a<b, a>b, or a=b) for the set of integers.
 Because the number line can show both distance and direction, we can locate the opposite of any rational number on the number line. The absolute values of the rational number and its opposite are equivalent.
 There are three possible relationships between any two numbers, a and b (namely, a<b, a>b, or a=b) for the set of rational numbers.
Prior Knowledge Needed:
 Exploring the coordinate plane; (Grade 5, Unit 14; 5.G.1, 5.G.2)
 Comparing two fractions; (Grade 4, Unit 5; 4.NF.2)
 Comparing decimal fractions; (Grade 4, Unit 12; 4.NF.5, 4.NF.7)
Units on the Horizon:
 Relationships in the coordinate plane; (Grade 6, Unit 7; 6.NS.6)
 Understanding, writing,and solving equations and inequalities; (Grade 6, Unit 9; 6.EE.8)
 Rational number operationsaddition and subtraction; (Grade 7, Unit 4; 7.NS.1)
Lessons

Lesson objective: Understand that a number's value is determined by its distance and direction from zero. Students bring prior knowledge of decimal fractions on a number line from 4.NF.5 and 4.NF.7. This prior knowledge is extended to integers on a numb...

Lesson objective: Fluently use integers to represent real life situations. This lesson helps to build fluency with integers. Number lines are used here because it allows students to look at an integers distance and direction from zero. This work develop...

Lesson objective: Fluenty use a number line to represent negative numbers. This lesson helps to build fluency with using a number line to plot negative numbers. Number lines are used here because it supports student's understanding of a number's distanc...

Lesson objective: Solve problems using positive and negative numbers in real life situations. This lesson provides an opportunity for students to apply their knowledge and understanding of integers to a reallife situation. Students are asked to determi...

Lesson objective: Understand that the set of integers includes whole numbers, their opposites, and zero. Students bring prior knowledge of plotting points on a number line from 6.NS.C.5. This prior knowledge is extended to plotting whole numbers, their ...

Lesson objective: Fluently determine opposites and the meaning of zero in real life situations. This lesson helps to build fluency with determining the opposite of integers and the meaning of zero. Number lines are used here because they highlight an in...

Lesson objective: Connect what we know about opposites to determine the opposite of the opposite of a number. This lesson provides an opportunity for students to apply their knowledge and understanding of integer opposites to a mathematical situation. S...

Lesson objective: Compare integers by looking at their distance and direction from zero and each other. Students bring prior knowledge of integers from 6.NS.5. This prior knowledge is extended to comparing integers as students reason about an integers l...

Lesson objective: Fluently compare integers using inequalities in real life situations. This lesson helps to build fluency with integer comparison. A number line is used here because it highlights an integer's distance and direction from other integers ...

Lesson objective: Solve problems by ordering and comparing integers based on their distance and direction from zero. This lesson provides an opportunity for students to apply their knowledge and understanding of integers to a reallife situation. Studen...

Lesson objective: Understand that rational numbers have opposites and that the absolute value of those rational numbers is equivalent. Students bring prior knowledge that the set of integers includes whole numbers, their opposites, and zero, and live on...

Lesson objective: Fluently locate opposite numbers on a number line. This lesson helps to build fluency with opposite numbers. Number lines are used because they show, visually, the relationship opposite numbers have to 0 and to each other. This work de...

Lesson objective: Fluently locate and compare rational numbers on a number line based on absolute value. This lesson helps to build fluency with absolute value. Number lines are used here because they provide visual cues for understanding rational numbe...

Lesson objective: Apply the concepts of absolute value and opposite numbers. This lesson provides an opportunity for students to apply their knowledge and understanding of absolute value and opposite numbers to a mathematical situation. Students are ask...

Lesson objective: Understand that relationships between two rational numbers result in three possibilities for a and b: a < b, a > b, or a = b. Students bring prior knowledge of integer relationships and opposite numbers from 6.NS.C.5 and 6.NS.C.6...

Lesson objective: Fluently compare the inequality of rational numbers. This lesson helps to build fluency with comparing rational numbers. Inequality symbols are used here because they specifically denote the relationship between rational numbers. This ...

Lesson objective: Compare rational numbers by determining their values. This lesson provides an opportunity for students to apply their knowledge and understanding of rational numbers to a reallife situation. Students are asked to help a teacher match ...