Chapter 1 Decimals Patterns and Algebra

Lesson 1-1 A Plan for Problem Solving 1. Understand the Problem (Explore) – What is the question being asked? 2. Plan – What strategy will you use? 3. Solve – Carry out the plan. Explain in words how you did so. 4. Look Back (Examine) – Verify your answer by solving another way. Is your answer reasonable?

Lesson 1-2 Powers and Exponents Factors – two or more numbers multiplied together. Powers – Numbers expressed using exponents Exponent – tells how many times a base is used as a factor. Base – the common or repeated factor.

Lesson 1-2 Powers and Exponents (cont.) Squared – a number raised to the second power Cubed – a number raised to the third power Evaluate – to find the answer or value of Standard Form – a number written without exponents Exponential Form – a number written with exponents

Lesson 1-3 Order of Operations Numerical Expressions – expressions that use only numbers Order of operations – 1. Do all operations within grouping symbols first 2. Evaluate all powers 3. Multiply and divide in order from left to right 4. Add and subtract in order from left to right

Lesson 1-4 Algebra: Variables and Expressions Algebraic Expression – an expression that contains numbers, variables, and at least one operation Term- the parts of an expression separated by plus or minus signs Coefficient – A number multiplied by a variable Constant – a term that does not contain a variable.

4x (4 is the coefficient) 6x + y – 10 (6 is the coefficient; 10 is the constant; the coefficient of y is one because 1 * y = y)

Lesson 1-5 Algebra: Equations Equation – a mathematical sentence that contains an equal sign Solution – the value that makes an equation true Solving an Equation – the process of finding a solution Defining a variable – choosing a variable to represent an unknown

Lesson 1-6 Algebra: Properties Equivalent Expressions – expressions that have the same value. 8(250) = 8(200) + 8(50) Properties – statements that are true for any number or variable. Distributive Property – To multiply a sum by a number, multiply each addend of the sum by the number outside parentheses. See example above Commutative Property – the order in which two numbers are added or multiplied does not change the sum or product. 5 x 11 = 11 x 5

Associative Property – The way in which three numbers are grouped when they are added or multiplied does not change their sum or product. (5 + 4) + 6 = 5 + (4 + 6) Identity Property – The sum of an addend and 0 is the addend. The product of a factor and 1 is the factor = 5; 5 x 1 = 5

Lesson 1-7 Sequences Sequence – an ordered list of numbers. Term – The number or shape in a sequence. Arithmetic Sequence – each term is found by adding the same number to the previous term. 3, 5, 7, 9… (+2) Geometric Sequence – Each term is found by multiplying the previous term by the same number. 4, 12, 36, 108… (x3)

Lesson 1-8 Measurement: The Metric System Kilo – thousand Centi – hundredth Milli - thousandth Units of Length 1 km = 1000 meters 1 m = 100 cm 1 cm = 10 mm 1 mm = 0.1 cm 1cm = 0.01 m 1m = km Larger > Smaller (multiply by a power of 10). Units of Mass 1 kilogram = 1000g 1 gram = 1000mg 1 mg = g 1 g = kg Smaller > Larger (divide by a power of 10). Units of Capacity 1 kiloLiter = 1000L 1L = 1000 mL 1 mL = L 1 L = kL

Lesson 1-9 Scientific Notation Scientific Notation – used to express very large or very small numbers. A number between 1 and 10 times a power of ten x 10 2 is written in scientific notation. 483 is written in standard form. When changing from scientific notation to standard form, the exponent tells you how far to move the decimal point.