Positive (or natural) and negative numbers can confuse students with disabilities. Special education students face special challenges when confronted with math after 5th grade. They need to have an intellectual foundation built using manipulatives and visuals in order to be prepared to do operations with negative numbers or apply algebraic understanding of integers to algebraic equations. Meeting these challenges will make the difference for children who might have the potential to attend college.

Integers are whole numbers, but can be whole numbers both greater than or less than zero. Integers are easiest to understand with a number line. Whole numbers that are greater than zero are called natural, or positive numbers. They increase as they move to the right away from the zero. Negative numbers are below or to the right of the zero. Number names grow bigger (with a minus for "negative" in front of them) as they move away from the zero to the right. Numbers growing larger, move to the left. Numbers growing smaller (as in subtraction) move to the right.

### Common Core Standards for Integers and Rational Numbers

Grade 6, the Numbers System (NS6)Students will apply and extend previous understandings of numbers to the system of rational numbers.

**NS6.5.**Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.

**NS6.6.**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.**NS6.6.a.**Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., (-3) = 3, and that 0 is its own opposite.

**NS6.6.b.**Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.**NS6.6.c.**Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.

### Understanding Direction and Natural (positive) and Negative Numbers.

I emphasize the use of the number line rather than counters or fingers when students are learning operations so that practice with the number line will make understanding natural and negative numbers much easier. Counters and fingers are fine to establish one to one correspondence but will become crutches rather than supports for higher level math.

The pdf number line here is for positive and negative integers. Run the end of the number line with positive numbers on one color, and the negative numbers on another. After students have cut them out and glued them together, have them laminated. You overhead or write on board markers (though they often stain the laminate) to model problems like 5 - 11 = -6 on the number line.

I also have a pointer made with a glove and a dowel, and a larger laminated number line on the board, and I call one student to the board to demonstrate the numbers and jumps.

Provide lots of practice. You "Integer Number Line" should be part of your daily warm up until you really feel that students have mastered the skill.

### Understanding the Applications of Negative Integers.

Common Core Standard NS6.5 offers some great examples for applications of negative numbers: Below sea level, debt, debits and credits, temperatures below zero and positive and negative charges can help students understand the application of negative numbers. The positive and negative poles on magnets will help students understand the relationships: how a positive plus a negative moves to the right, how two negatives make a positive.

Assign students in groups the task of making a visual chart to illustrate the point being made: perhaps for altitude, a cross cut showing Death Valley or the Dead Sea next and it's surroundings, or a thermostat with pictures to show whether people are hot or cold above or below zero.

### Coordinates on an XY Graph

Students with disabilities need lots of concrete instruction on locating coordinates on a chart. Introducing ordered pairs (x,y) i.e. (4, -3) and locating them on a chart is a great activity to do with a smart board and a digital projector. If you don't have access to a digital projector or EMO, you might just create a xy coordinates chart on a transparency and have students locate the dots.