OPERATIONS

GOALS

1. Draw and describe patterns using positive and negative numbers.

2. Compare and order positive and negative numbers.

3. Perform operations with positive and negative numbers (add, subtract, multiply, & divide).

4. Name and plot ordered pairs on a coordinate system.

5. Recognize and use the property of opposites (canceling out positive and negative numbers)

6. Understand the similarities of using integers in algebraic and in geometric contexts.

7. Explore transformations of geometric figures on a coordinate system {(reflections – flips), (translations – slides),(rotations –

turns),(dilations – shrinking & enlarging)}.

8. Reason about and predict transformations of geometric figures in a coordinate system.

9. Generalize rules for operating with positive and negative numbers (integers).

10. Use a model or an illustrative context to help solve problems about integers.

11. Model situations involving positive and negative numbers by using concrete manipulatives.

SECTION SUMMARIES

SECTION A: GRAPHING FIGURES

1. Veda designs were drawn using repeated movements of right, up, left, and down. A “+” meant to move up or right while a “-“ meant to move down or left; the numbers indicated the length of each move.

SECTION B: TIME ZONES

1. To solve problems about time zones and time differences, you can calculate with positive & negative numbers.

2. Traveling to the east, add one hour for each time zone difference; traveling west, subtract one hour for each.

SECTION C: PLUS AND MINUS CHIPS

1. The Property of Opposites allows you to say that –5 and +5 combined would be zero.

2. Rules for Integer addition:

a. A positive number added to a positive number results in a positive number.

b. A negative number added to a negative number results in a negative number.

c. To add a negative number to a positive number, let as many negatives and positives cancel each other out as

possible and your sum is whatever is left over with the sign of whatever is left.

3. Rules for Integer subtraction: (to subtract, add the opposite)

a. Subtracting a negative is the same thing as adding a positive.

b. Subtracting a positive is the same thing as adding a negative.

SECTION D: ALTITUDES AND TEMPERATURES

1. There are different ways to add a group of positive and negative numbers.

a. You can add them in their given order.

b. You can add all of the positives, add all of the negatives, then add the two results.

c. You can first add the numbers that are easily combined, such as 65 and 35, or 24 and –24.

2. The symbols < and > can be used to compare two numbers: b > a means that b is greater than a, while a < b

means that a is less than b.

SECTION E: ALL OPERATIONS

1. If you are multiplying or dividing two numbers with the same signs, the product or quotient will be positive.

2. If you are multiplying or dividing two numbers with different signs, the product or quotient will be negative.
3. Addition & Multiplication is commutative - you can add or multiply in any order. (The answer will not be affected).

SECTION F: OPERATIONS AND COORDINATES

1. To locate points on a grid, you use a coordinate system. The origin is the point at the intersection of the x (the

horizontal) and y (the vertical) axes. Every point can be located using two coordinates telling what direction

and how far the point is from the origin. You can change the position of a figure drawn in a coordinate

system by adding a number to or subtracting a number from each coordinate, or by multiplying or dividing the

coordinates by some number.