Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Interactive Study Guide for Students: Pre-Algebra Chapter 1: The Tools of Algebra Section 1: Using a Problem-Solving Plan Four-Step Problem Solving Plan Examples E______________: Read problem, ask questions Weight(oz) Cost P______________: Reread, determine, make plan, estimate 1 $0.34 S______________: Use plan, revise 2 $0.55 E______________: Check solution, try again if necessary 3 $0.76 A ____________________ is an educated guess. When you make a conjecture based on a pattern of examples or past events, you are using _____________ ________________. 4 $0.97 5 $1.18 1. How much would it cost to mail a 9ounce letter? 2. Find the next term in 1,3,9,27,81,_____ 3. Draw the next figure in the pattern: Choose the Method of Computation This is an _________________ step in solving _________________. Do you need an exact answer? Do you see a pattern or number fact? Use mental math no no Estimate Are there simple calculations to do? 4. Ryan needs to save $125 for a ski trip. He has $68 in his bank. He receives $15 allowance and earns $25 delivering newspapers and $16 shoveling snow. Does he have enough money for the trip? Use paper and pencil Interactive Study Guide for Students: Pre-Algebra Chapter 1: The Tools of Algebra Section 2: Numbers and Expressions Order of Operations P E M D A S Examples 1. 3 + 4 5 = 2. 18 3 2 = ____________: symbols, usually letters, used to represent unknown quantities. 3. 6(2 + 9) – 3 8 = ________________ Expressions: mathematical expressions that contain at least one variable. 4. [(15 – 9) + 8(2)] = 5. 53 15 = 17 13 Translate Verbal Phrases into Numerical Expressions Translate into expressions: It is sometimes necessary to change a ____________ phrase into a ________________ expression. This is actually how ________ is used in _____________. 6. The product of eight and seven 7. The difference of nine and three Interactive Study Guide for Students: Pre-Algebra Chapter 1: The Tools of Algebra Section 3: Variables and Expressions Evaluate Expressions A ________________ is a placeholder for any value. This variable represents some _____________ number. An ____________________ expression contains sums and/or products of variables and numbers. Example: x + 3 Replacing a variable with a number demonstrates the _____________________ Property of Equality Examples 1. Evaluate x + y – 9 if x=15 and y=26. Evaluate each expression if k=2, m-7, and n=4 2. 6m – 3k 3. mn 2 4. n + (k + 5m) Translate Verbal Phrases The first step in translating verbal phrases into algebraic phrases is to ____________ a ___________. Translate each phrase into an algebraic expression: 5. twelve points more than the Dolphins scored 6. four times a number decreased by six Interactive Study Guide for Students: Pre-Algebra Chapter 1: The Tools of Algebra Section 4: Properties Properties of Addition and Multiplication In algebra, _______________ are statements that are true for any numbers. Property Addition Multiplication C_______________ a+b=b+a ab = ba A_______________ (a+b)+c=a+(b+c) (ab)c = a(bc) I________________ a+0=a=0+a a1 = a = 1a I________________ a+(-a)=0=(-a)+a If a≠0, a1/a=1=1/aa a(b+c)=ab+ac and (b+c)a=ba+ca One way to show that something is not true is to provide a _____________________. 2. (a 6) 5 = a (6 5) 3. 0 12 = 0 4. Find 4 (25 11) mentally 5. Is the statement “Subtraction of whole numbers is associative” true or false? If it is false, provide a counterexample. Simplify each expression: 6. (k + 2) + 7 Simplify Algebraic Expressions When you are asked to _________________ an algebraic expression, that means to write it in a simpler form. You can use all of the properties to help you. Interactive Study Guide for Students: Pre-Algebra Chapter 1: The Tools of Algebra Name the property shown by each statement: 1. 3 + 7 + 9 = 7 + 3 + 9 For any real numbers a, b, and c: D_______________ Examples 7. 5 (d 9) Section 5: Variables and Equations Equations and Open Sentences A mathematical sentence that contains an _________ sign is called an equation. Examples: 3 + 5 = 8 x – 7 = 14 2m = 6 An equation that contains a variable is an _______________ ______________. An open sentence is neither ________ nor _____________. Examples Solve: 1. If 12 – m = 8. does m=2, 4, or 7? 2. Which value is the solution of 2x+1=7? a. 6 b. 5 c. 4 d. 3 A value for the variable that makes the equation true is called the ____________. The process of finding a solution is called ____________ the _____________. Solve each equation mentally: 3. 5x = 30 S________________ T________________ If a=b then b=a If a=b and b=c then a=c If 10=4+6 then 4+6=10 If 3+5=8 and 8=24 then 3+5=24 4. 72 9 d Name the property of equality shown: 5. If 5=x+2 then x+2=5 6. If y+8=15 and 15=7+8 then y+8=7+8 Translate Verbal Sentences into Equations Just as verbal phrases can be translated into algebraic expressions, verbal sentences can be translated into ___________ and then _______________. Interactive Study Guide for Students: Pre-Algebra Translate the sentence into an equation then solve. 7. The difference of a number and ten is seven. Find the number. Chapter 1: The Tools of Algebra Section 6: Ordered Pairs and Relations Ordered Pairs Examples In mathematics, a ________________ ______________ is used to locate points. It is sometimes call the _________ ________. Graph each ordered pair on the coordinate system to the left. Draw arrows to the correct part: 1. (4, 1) y-axis origin x-axis M N P 2. (3, 0) Write the ordered pair that names the points on the graph at the left. 3. M 4. N 5. P An ______________ __________ of numbers is used to locate any point of a coordinate plane. The first number is called the _______________ and the second is called the ________________. It is written like this ( ___, ___). To ______________ and ordered pair, draw a _____ at the point that corresponds to the ordered pair. The _____________ are you directions to locate that point. Relations A set of ordered pairs such as {(1, 2), (3, 4), (4, 5)} is a _________________. The ______________ of the relation is the set of all of the numbers in the __-_____________. The ______________ of the relation is the set of all of the numbers in the _______________. A relation can be shown as ordered _______, in a ___________, or on a ______________. 6. Express the relation {(0,0),(2,1),(1,3),(5,2)}as a table and as a graph. x y