Math - 2019-20
6.6ab - Integer Operations (No Calc)
6.6 The student will
a) add, subtract, multiply, and divide integers;* (NO CALCULATOR)
b) solve practical problems involving operations with integers;
- I can determine yard line after each play of a football game, calculate amount of force required to stop a drag racer, figure golf score in relation to par, and track my finances over time.
- I will understand numbers and their opposites are equal distance from zero on a number line and the role of negative values in practical situations.
UNDERSTANDING THE STANDARD
· The set of integers is the set of whole numbers and their opposites (e.g., …-3, -2, -1, 0, 1, 2, 3…). Zero has no opposite and is neither positive nor negative.
· Integers are used in practical situations, such as temperature changes (above/below zero), balance in a checking account (deposits/withdrawals), golf, time lines, football yardage, and changes in altitude (above/below sea level).
· Concrete experiences in formulating rules for adding, subtracting, multiplying, and dividing integers should be explored by examining patterns using calculators, using a number line, and using manipulatives, such as two-color counters, drawings, or by using algebra tiles.
· Sums, differences, products and quotients of integers are either positive, negative, undefined or zero. This may be demonstrated through the use of patterns and models.
· The order of operations is a convention that defines the computation order to follow in simplifying an expression. Having an established convention ensures that there is only one correct result when simplifying an expression.
· The order of operations is as follows:
– First, complete all operations within grouping symbols.1 If there are grouping symbols within other grouping symbols, do the innermost operation first.
– Second, evaluate all exponential expressions.
– Third, multiply and/or divide in order from left to right.
– Fourth, add and/or subtract in order from left to right.
1Parentheses , absolute value (e.g., ), and the division bar (e.g., ) should be treated as grouping symbols.
· Expressions are simplified using the order of operations and applying the properties of real numbers. Students should use the following properties, where appropriate, to further develop flexibility and fluency in problem solving (limitations may exist for the values of a, b, or c in this standard):
- Commutative property of addition:
- Commutative property of multiplication:
- Associative property of addition:
- Associative property of multiplication:
- Subtraction and division are neither commutative nor associative.
- Distributive property (over addition/subtraction): and
- Identity property of addition (additive identity property):
- Identity property of multiplication (multiplicative identity property):
- The additive identity is zero (0) because any number added to zero is the number. The multiplicative identity is one (1) because any number multiplied by one is the number. There are no identity elements for subtraction and division.
- Inverse property of addition (additive inverse property):
- Multiplicative property of zero:
- Substitution property: If then b can be substituted for a in any expression, equation or inequality.
· The power of a number represents repeated multiplication of the number (e.g., 83 = 8 · 8 · 8). The base is the number that is multiplied, and the exponent represents the number of times the base is used as a factor. In the example, 8 is the base, and 3 is the exponent.Any number, except zero, raised to the zero power is 1. Zero to the zero power (is undefined.
· 6.6a1 Model addition, subtraction, multiplication and division of integers using pictorial representations or concrete manipulatives.
· 6.6a2 Add, subtract, multiply, and divide two integers.
· 6.6b1 Solve practical problems involving addition, subtraction, multiplication, and division with integers.