6th Grade Test Prep Number Sense

6.N.1 Read & Write whole numbers to trillions Write 268,745,320,709 in expanded form. Write 7,185,403,629 in word form. Write 53,602,015,008 in short word form.

6.N.2 6.N.3 6.N.4 6.N.5 Commutative, Associative, Distributive, Identity, Inverse, and Zero properties Commutative Property of Addition Commutative Property of Multiplication Associative Property of Addition Associative Property of Multiplication Distributive Property Identity Property of Addition Identity Property of Multiplication Inverse Property of Addition Inverse Property of Multiplication Zero Property a + b = b + a a * b = b * a (a + b) + c = a + (b + c) (a * b) * c = a * (b * c) a(b + c) = a(b) + a(c) a + 0 = a a × 1 = a a + (-a) = 0 a * (1/a) = a a × 0 = 0

6.N.6 6.N.7 6.N.8 6.N.9 6.N.10 Rate, Ratio, & Proportion Compares two numbers. 2 to 3, 5:4 UNIT RATE A ratio that compares one unit 24 miles per gallon, 24 miles / gal RATE A ratio that compares quantities of different units PROPORTION Compares two different ratios and determines if they are equal, by using cross-multiplication.

6.N.6 6.N.7 6.N.8 6.N.9 6.N.10 Rate, Ratio, & Proportion What is the ratio of red triangles to green triangles? What is the ratio of green triangles to red triangles? Julia traveled 426 miles in 8 hours. What is the unit rate for the number of miles Julia traveled? Mrs. Winters bought 8 pounds of ham for $18.88. What was the cost per pound of the ham? Pencils are on sale, 3 for 36 cents. How much money does Allie need to buy 8 pencils?

6.N.11 6.N.12 Percent Determine the percent of the grid that is shaded? Shade in 88% of the given grid. Write 45% as a decimal and a simplified fraction.

6.N.11 6.N.12 Percent What is 53% of 114? = .53 * 114 Method 1: Translate 60.42 Rate * base = Part Method 2: Formula .53 * 114 = 60.42 . 53 * 114 = 100x 6,042 = 100x 60.42 = x Method 3: Proportion

6.N.26 Estimating Percent A recent survey found that 41% of the 300 people surveyed forgot to turn off their cell phones before boarding an airplane. About how many people forgot to turn off their cell phones? Step 1: Round 41% to the nearest 10 percent. 41% rounds to 40% Step 2: Use mental math to find 10% of 300. 10% of 300 is 30 Step 3: Find 40% of 300. 40% of 300 is 4 times 10% of 300. 4 * 30 = 120 About 120 people forgot to turn off their cell phones.

6.N.26 Estimating Percent The Harris family wants to leave a 15% tip for their waiter. The cost of their meal is about $45.85. About how much tip should the Harris family leave for the waiter? For the premier of a new movie, 745 people lined up to buy tickets. 67% of those in line were able to purchase a ticket for the movie. About how many tickets were sold to the movie? Sally had to answer 93% of the test questions correctly to earn an A. About how many of the 80 questions on the test did she need to answer correctly to earn an A?

6.N.11 6.N.12 Percent What is 40% of 30? 123 is what percent of 150? What percent of 1,000 is 5? New York is the 27th largest state in the United States. What percent of the 50 states in the U.S. are larger than New York? Of the 36 students in Florence’s class, 27 have been inside the Empire State Building. What percent of the class has not been inside the Empire State Building?

6.N.13 Absolute Value What does |-22| mean? The absolute value of a number is the distance from 0 to the number on a number line. |4| means a distance of 4 units from 0 on the number line. |-8| means a distance of 8 units from 0 on the number line. What does |-22| mean? Which of the following has the least value? |-50| |5| |-1| |10| Which of the following has a value equal to the value of |-12|? -12 |-1.20| |1.20| |12|

6.N.20 6.N.21 Convert fractions to repeating / terminating decimals Terminating decimals are decimals that end. Non -Terminating decimals are decimals that go on forever. Repeating decimals are decimals where the decimal digits repeat forever in order. Non-Repeating decimals are decimals where the decimal digits repeat forever without any order. What kind of a decimal is 0.36? Express 0.36 as a fraction in simplest form? Represent 3/11 as a decimal. What kind of a decimal does 3/11 convert into? When written in decimal form, which of the following is a terminating decimal? 1/8 2/9 3/7

6.N.14 6.N.15 Locate and order Rational numbers Which of the following shows the integers in order from least to greatest? a) -4, -5, -7, 3 b) 3, -4, -5, -7 c) -7, -5, -4, 3 d) 3, -7, -5, -4 Place the following numbers in order from greatest to least. -8 80% 8/50 8.6012

6.N.19 Multiplicative Inverse of a number To find the multiplicative inverse (reciprocal) of a fraction, “flip” the fraction. The numerator takes the denominators place and the denominator takes the numerators place. Fraction Reciprocal 2/5 3 -3/4 Complete the following table:

6.N.16 6.N.17 6.N.18 Add, subtract, multiply & divide fractions and mixed numbers To Add or Subtract Fractions: - Convert all fractions to equivalent fractions with the same denominator Add or subtract the numerator - Simplify the fraction or turn it into a mixed number if possible.

6.N.16 6.N.17 6.N.18 Add, subtract, multiply & divide fractions and mixed numbers To Add or Subtract Mixed Numbers: - Convert the mixed numbers into improper fractions - Convert all fractions to equivalent fractions with the same denominator Add or subtract the numerator - Simplify the fraction or turn it into a mixed number if possible.

6.N.16 6.N.17 6.N.18 Add, subtract, multiply & divide fractions and mixed numbers To Multiply Fractions / Mixed Numbers: - Convert the mixed numbers into improper fractions - Multiply the two numerators Multiply the denominators - Simplify the fraction or turn it into a mixed number if possible.

6.N.16 6.N.17 6.N.18 Add, subtract, multiply & divide fractions and mixed numbers To Divide Fractions / Mixed Numbers: - Convert the mixed numbers into improper fractions - Find the reciprocal of the second fraction Rewrite the problem by changing the division sign into multiplication Multiply the numerator by the numerator. Multiply the denominator by the denominator - Simplify the fraction or turn it into a mixed number if possible.

6.N.23 6.N.24 Exponents & Repeated multiplication To write the numbers in exponential form - The base in exponential form is the number itself. - Count the number of times the number is repeated. Write the four as an exponent. 6 × 6 × 6 × 6 6 4 64

6.N.23 6.N.24 Exponents & Repeated multiplication To write the numbers in repeated multiplication form - Write the base, followed by a multiplication sign - Repeat the number as many times as the exponent Simplify (if the question asks for it) 35 3 × 3 × 3 × 3 × 3 × 3 243

6.N.22 6.N.25 Order of Operations To simplify, using order of operations - Do the operations inside the parentheses first and bring everything else down - Simplify any exponents, and bring everything else down Multiply /divide in order from left to right, and bring everything else down Add / Subtract in order from left to right, and bring everything else down 62 - (17 · 5) ÷ 5 + 3² 62 - 85 ÷ 5 + 3² 62 – 85 ÷ 5 + 9 62 – 17 + 9 45 + 9 54 20 – 5 + (13 – 3) 96 ÷ (4 × 4) ÷ 3 3 * 15 ÷ 5² 72 · 6 ÷ 3 + 48 - 29

6.N.27 Justify reasonableness using estimation Jenny spent $39.90 for a pair of shoes, $26.95 for a dress, and $4.15 for a bottle of shampoo. She estimates, that she spent $60. Is $60 a reasonable estimate for the amount of money she spent? To estimate an answer: Round each amount to the nearest dollar - Complete the indicated operation to estimate Write your answer $39.90 rounds to $40 $26.95 rounds to $27 $4.15 rounds to $4 40 + 27 + 4 = $71 Jenny spent about $71, thus her estimate of $60 is incorrect.