Students will use a large number line to understand rational numbers and to position positive and negative numbers correctly.

**Class:** Sixth Grade

**Duration:** 1 class period, ~45-50 minutes

**Materials:**

- long strips of paper (adding machine tape works well)
- display model of a number line
- rulers

**Key Vocabulary:** positive, negative, number line, rational numbers

**Objectives:** Students will construct and use a large number line to develop an understanding of rational numbers.

**Standards Met:** 6.NS.6a. Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line.

**Lesson Introduction:**
Discuss the lesson target with students. Today, they will be learning about rational numbers. Rational numbers are numbers that can be used as fractions or ratios. Ask students to list any examples of those numbers that they can think of.

**Step-by Step Procedure:**

- Lay out the long strips of paper on tables, with small groups; have your own strip at the board to model what students should be doing.
- Have students measure two inch markings all the way to both ends of the paper strip.
- Somewhere in the middle, model for students that this is zero. If this is their first experience with rational numbers below zero, they’ll be confused that the zero isn’t located on the far left end.
- Have them mark the positive numbers to the right of zero. Every marking should be one whole number - 1, 2, 3, etc.
- Paste your number strip on the board, or have a number line started on the overhead machine.
- If this is your students’ first attempt at understanding negative numbers, you’ll want to begin slowly by explaining the concept in general. One good way, especially with this age group, is by discussing money owed. For example, you owe me $1. You don’t have any money, so your money status can’t be anywhere along the right (positive) side of zero. You need to get a dollar in order to pay me back and be right at zero again. So you could be said to have -$1. Depending on your location, temperature is also a frequently discussed negative number. If it needs to warm up considerably in order to be 0 degrees, we are in the negative temperatures.
- Once students have the beginning understanding of this, have them begin marking their number lines. Again, it will be hard for them to understand that they are writing their negative numbers -1, -2, -3, -4 from right to left, as opposed to left to right. Model this carefully for them, and if necessary, use examples such as the ones described in Step 6 to increase their understanding.
- Once students have their number lines created, see if some of them can create their own stories to go along with their rational numbers. For example, Sandy owes Joe 5 dollars. She only has 2 dollars. If she gives him her $2, she could be said to have how much money? (-$3.00) Most students may not be ready for problems like this, but for those that are, they can keep a record of them and they could become a classroom learning center.

**Homework/Assessment:** Let students take their number lines home and have them practice some simple addition problems with the number strip. This isn’t an assignment to be graded, but one that will give you an idea of your students' understanding of negative numbers. You can also use these number lines to assist you as students learn about negative fractions and decimals.

- -3 + 8
- -1 + 5
- -4 + 4

**Evaluation:** Take notes during the class discussion and the individual and group work on the number lines. Don’t assign any grades during this lesson, but keep track of who is seriously struggling, and who is ready to move on.