6th Grade Mathematics. STAAR Study Guide. This Study Guide belongs to:

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1 This Study Guide belongs to: TABLE OF CONTENTS Absolute Value & Opposite of a Number Page 7 Additive & Multiplicative Relationships Page 3 Area & Volume (Rec, Parallelogram) Page 1 Area & Volume (Trapezoid & Triangle) Page 1 Box Plots, & Interquartile Range Page 10 Comparing Rational Numbers Page Convert Units within Measurement Sys Page 6 Credit Reports & Check Register Page 8 Debit Cards vs Credit Cards Page 13 Dependent & Independent Variables Page 1 Division in Notation Page Dot Plots, Stem & Leaf, & Bar Graphs Page 11 Equations (One-Step, One Variable) Page 1 Equations (Verbal, Tables, & Graphs) Page 1 Expressions vs Equations Page 14 Inequalities Page 1 Integer Operations with Models Page 5 Mode, Median, Mean, Range Page 10 Multiplying & Dividing s Page 4 Mult & Div Positive Rational Numbers Page 5 Multiply & Divide Decimals Page 5 Operations with Integers (+, -, x, ) Page 13 Operation Properties Page 14 Ordering Rational Numbers Page Order of Operations Page 1 Ordered Pairs on the Coordinate Plane Page 11 Part, Whole and Percent of a Number Page 6 Prime Factorization Page 1 Ratios & Rates Page 3 Rational Numbers Venn Diagram Page 7 Ratios & Percent Models Page 3 Triangles Page 9 6th Grade Mathematics STAAR Study Guide

2 Rational Numbers s, decimals, mixed numbers, integers, whole numbers, and counting numbers Integers Whole numbers and their opposites Whole Numbers Counting numbers and zero Natural Numbers Counting Numbers {1,, 3 } {0, 1,, 3 } { -3, -, -,1 0, 1,, 3 } { -1.33, -1, -1/, 0, 1/3, 1.75, } Deposit credit (+) putting money in Withdrawal take money out (-) payment/fee (-) Transfer - take money out and put in another account Important because it shows your financial responsibility and: Lenders will decide whether you can get a loan and the terms of the loan For insurance (whether you can get insurance and the rates you will pay Employment (employers may use your credit report) to see if they would like to hire you Telephone and utility companies may use the information to determine if they should provide services to you Landlords may use information to determine whether or not to rent an apartment to you What s in a credit report? Identification information (address, social, date of birth and employment history) Credit accounts Negative information remains Credit inquiries on your credit report for 7 Public record and collections Factors that affect your credit: years and bankruptcies can be Types of credit reported for 10 years. New credit Length of credit history Amounts owed Payment history Important factors to consider when choosing a career path: Salary (pay per year) Level of education or training required (skills needed, college, trade school, on the job training) Job outlook in the future and personal job interests * ALWAYS POSITIVE! Grants Scholarships Work-study Savings Loans Free money Need-based Free money Merit-based Part-time jobs for undergrad students Your own money you saved Money bor- rowed, paid back with interest

3 Be sure to convert all #s to the same form (ex: change all #s to decimal form) *The bigger the negative #, the smaller the value Same Signs Different Signs Pos x or Pos = Pos. Pos x or Neg = Neg 6 > > - -3 > < - Pacman eats Same = Sum Add & Keep the Sign Different = Difference Subtract & Keep the sign of the larger number Neg x or Pos = Neg Neg x or Neg = Pos Debit card deducts money from your own account from money that you have available. You use a pin. Credit card is not your own money, you will owe the money you spend in the future, you are required to pay back what you use at a later date. Credit cards are interest free if you pay the entire balance prior to the due date. Dividing by is the same as multiplying by Dividing by 3 is the same as multiplying by Dividing by 4 is the same as multiply by When multiplying by a fraction GREATER than 1, the # will INCREASE When multiplying by a fraction LESS than 1, the # will DECREASE

4 - Zero Pairs - +5 = = = -7 Solution is where the line stops (4) = 8 Multiplying Decimals Step 1: Multiply normally, ignoring the decimal points Step : Put the decimal point in the answer as many decimal places as the two original #s combined 1.85 x 0.5 = x places 1 place.95 3 places total x 0.5 Dividing Decimals Step 1: If the divisor is not a whole #, move the decimal pt to the right as many times necessary to make it a whole #. Move the decimal pt in the dividend the same # of places Step : Divide as usual... Step 3: Put decimal pt directly above decimal pt in dividend Step 4: Check your answer (by multiplying) = x 15 = 9.75

5 Multiplying s WEST EAST Step 1: Make sure you have a numerator and denominator with both numbers. Whole #s put a one as the denominator Mixed #s change into improper fraction (around the world) Step : Multiply the numerators. numerator x numerator x Whole # x Mixed # x Fractio n 8 + x Step 3: Multiply the denominators. denominator x denominator SOUTH *cluster *outliers *symmetrical *peak Step 4: Simplify, if possible. Step 1: Make sure you have a numerator and denominator with both numbers. Whole #s put a one as the denominator Mixed #s change into improper fraction (around the world) Step : K-C-F (Keep, Change, Flip) Multiply by the Reciprocal Step 3: Multiply the numerators. numerator x numerator Step 4: Multiply the denominators. denominator x denominator Dividing s Whole # Mixed # 8+ K C F K C F K C F x Step 5: Simplify, if possible.

6 x y x y x + 4 x x 6 RECTANGLE h b TRAPEZIOD b1 PARALLELOGRAM b TRIANGLE h x 8 b b b y results from being added to x, y = x + y results from being multiplied to x, y = x RECTANGULAR PRISM V = area of base x height V = (b x h) x h V = l x w x h When predicting, setup a proportion *surveys *scales *traveling *expectations *Pay attention to the order the question wants the ratio On map, the scale is 1 inch to 1 miles. How many inches represent 60 miles on the map? $18 = /3 Mark had $7. He spent /3 of his money at the store. Then he spent 1/4 of the remaining money on a drink. How much money does he have left? $.5 = 1/4 $7 = 100% $9 $9 $9 He has 3/4 of the remaining money left = $6.75 Isolate variable by performing the opposite operation! X - 4 = 10 x X =

7 How many ounces are in 0 pounds? How many feet are in a mile? How many cups are in a gallon? 16 Find the whole given a part and percent Mary spent $1 on a ticket to the county fair. She now has 60% of her original amount of money remaining. How much money did Mary originally have? Find the part given the whole and percent Find the percent given the part and the whole At an animal shelter, 1% of the dogs are Chihuahuas. If there are 75 dogs at the shelter, how many Dan has 50 songs on his MPS player. Ninety- five of the songs are by the same singer. What percent of Dan s songs are by that one singer? * move decimal point two times to the right (x 100)

8 EX: The amount of money you make depends on the amount of time you work Dependent variable (y): amount of money you make Independent variable (x): amount of time worked Number(s) (has an equal sign) =9 An equation represents a relationship between two values (expressions) An expression represents a single value Single Value Variable(s) SUBSTITUTE Equation: y = x + 5 (has no equal sign) a number plus 4 a number plus 4 is 9 n+4 n+4=9 (in words) Verbal: Sam has x apples and 3 more oranges. Oranges (y) Equation Numerical Verbal Table: Apples (x) Expression Algebraic Multiple Values Graph: Y 5 Oranges Commutative: = X x4=4x Apples PRIME FACTORIZATION Finding the factors of a number that are all prime (3 + 11) (9 + 11) = 3 11 same as ( x 4) x 3 = x (4 x 3) 13 Distributive: 6( + 4) = 6() + 6(4) 3(4 - ) = 3(4) - 3() Identity: 7+0=7 7x1=7 Inverse: = = 0