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?

Presentation on theme: "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?"— Presentation transcript:

1 Chapter 1 Decimals Patterns and Algebra

2 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?

3 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.

4 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

5 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

6 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.

7 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)

8 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

9 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

10 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 + 0 = 5; 5 x 1 = 5

11 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)

12 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 = 0.001 km Larger > Smaller (multiply by a power of 10). Units of Mass 1 kilogram = 1000g 1 gram = 1000mg 1 mg = 0.001 g 1 g = 0.001 kg Smaller > Larger (divide by a power of 10). Units of Capacity 1 kiloLiter = 1000L 1L = 1000 mL 1 mL = 0.001 L 1 L = 0.001 kL

13 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. 4.83 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.