#1 MATH 6 SOL PRACTICE PACKET #1 Number Sense

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1 NAME: BLOCK: Due date: #1 MATH 6 SOL PRACTICE PACKET #1 Number Sense do not lose this packet!!! You MUST do EVERY problem. Page 1 of 14

2 Reporting Category: Number and Number Sense Number of Items: 10 Standards of Learning: 6.1 The student will describe and compare data, using ratios, and will use appropriate notations, such as a, a to b, and a:b. b 6.2 The student will a) investigate and describe fractions, decimals and percents as ratios; b) identify a given fraction, decimal or percent from a representation; c) (complete items without the use of a calculator) demonstrate equivalent relationships among fractions, decimals, and percents; and d) (complete items without the use of a calculator) compare and order fractions, decimals, and percents. 6.3 The student will a) identify and represent integers; b) order and compare integers; and c) identify and describe absolute value of integers. 6.4 The student will demonstrate multiple representations of multiplication and division of fractions. 6.5 The student will investigate and describe concepts of positive exponents and perfect squares. Page 2 of 14

3 6.1 RATIOS (Calculator use permitted.) Ratios compare 2 numbers. Ratios can be written as a fraction a, with a colon a:b, or with words ( a to b or a b out of b ). Since ratios compare TWO numbers, never simplify the fraction form to a whole number or mixed number. Leave it improper. Read VERY carefully. ORDER COUNTS. Make sure you are giving the number asked for (look for the word total ). (1) Directions: Circle each box to choose a ratio. You must select the three correct ratios. There are 24 fiction books and 36 nonfiction books on a shelf. Select the three ratios that represent the number of fiction books to the total number of books on the shelf to 3 2 : 5 2 to 5 2 : 3 3 to 5 3 : (2) (3) 2 3 Page 3 of 14

4 6.2a FRACTS/DECS/% AS RATIOS Decimal to Fraction: Use the PLACE VALUE. 0.3 = = Percent to Fraction: Percent means OUT OF % = or 1 20 (1) Lola made 23 out of 100 free throw attempts. How is this expressed as a percent? (2) A 0.23% B 23% C 100% D 230% (Calculator use permitted.) (3) (4) Page 4 of 14

5 6.2b FRACTS/DECS/% MODELS Fraction: PART TOTAL Decimal: Pay attention to PLACE VALUE. The place value is the TOTAL. Percent means OUT OF 100. (1) This model represents 1 whole and is divided into equal parts. Shade this model to represent 3 of this whole. 8 (Calculator use permitted.) (2) Page 5 of 14

6 (3) (Calculator use permitted.) A 60 : 100 B 60% C D 3 5 (4) (5) A 6.45 B 6.5 C 6.55 D 6.75 Page 6 of 14

7 6.2c FRACTS/DECS/% EQUIVALENTS ***NO CALCULATOR*** Fraction to Decimal: DIVIDE. Top number goes inside house. Decimal to Fraction: Pay attention to PLACE VALUE. The place value is the denominator. Percent to Decimal: Divide by 100, or just move the decimal point 2 places left ( hiphop away or PeDaL ). Decimal to Percent: Multiply by 100, or just move the decimal point 2 places right ( tiptoe or DeePeR ). Fraction to Percent: If the denominator goes evenly into 100 (2, 4, 5, 10, 20, 25, 50), make an equivalent fraction then write it as a %. If it does not (3, 6, 8, 9, 12), divide and move the decimal 2 places right ( tip-toe or DeePeR ). Percent to Fraction: Write it over 100 & simplify. (1) Directions: Circle each number you want to select. You must select all correct numbers. Do not use a calculator for this problem. Select each number that can be placed in the blank to make this statement true. 3 5 = 35% % (2) ((3) Page 7 of 14

8 6.2d COMPARE & ORDER FRACTS/DECS/% ***NO CALCULATOR*** Change them all to PERCENTS. Fraction to Percent: If the denominator goes evenly into 100 (2, 4, 5, 10, 20, 25, 50), make an equivalent fraction then write it as a %. If it does not (3, 6, 8, 9, 12), divide and move the decimal 2 places right ( tip-toe or DeePeR ). Decimal to Percent: Multiply by 100, or just move the decimal point 2 places right ( tiptoe or DeePeR ). (1) Directions: Write each number into the correct box. Do not use a calculator to solve this problem. Arrange the numbers in order from greatest to least. greatest least 10% (2) Do not use a calculator to solve this problem. Which is a true statement? A 1 3 > 0.3 > % B 1 3 = 0.33 = 33.3 % C 1 3 = 0.3 = % D 1 3 < 0.33 < 33.3 % (3) Do not use a calculator to solve this problem. Which numbers are arranged in order from least to greatest? A B C D Page 8 of 14

9 (4) Do not use a calculator to solve this problem. (5) Do not use a calculator to solve this problem. Beverly has 10 boxes of cookies to sell. She needs to sell more than 80% of the boxes of cookies today. How many boxes of cookies will Beverly need to sell? A 5 B 7 C 8 D 9 (6) Page 9 of 14

10 6.3 INTEGERS (Calculator use permitted.) Integers are all whole numbers and their opposites, including zero. Number Line: negative is LEFT of zero; positive is RIGHT; zero has no sign. LEFT is LESS. -5 < -4. Absolute value: how many steps away from zero a number is. -3 = 3 and 3 = 3. Opposite: same distance from zero. -3 and 3 are opposites. Positive situations include: profit, earning, ascend, gain, above, deposit, over, increase, forward, up. Negative situations include: loss, debt, owe, descend, below, withdraw, under, decrease, backward. (1) Directions: Circle each number you want to select. You must select all correct numbers. Identify each number that has an absolute value of (2) Directions: Circle each number you want to select. You must select all correct numbers. Select each number that represents an integer (3) Which number is less than -8? (a) -10 (b) -3 (c) 6 (d) 14 (4) Page 10 of 14

11 (Calculator use permitted.) (5) (6) (7) (8) (9) Page 11 of 14

12 6.4 FRACTION MULT/DIV MODELS (Calculator use permitted.) A fraction OF a number means multiplication. Fraction Fraction means a part of a part. Fraction Whole means a part of a whole. Whole Fraction means groups of a part. Division means how many groups of Total groups = size of groups. (1) Which expression is represented by this model? (a) 1 7 x 1 4 (b) 3 7 x 1 4 (c) 1 7 x 3 4 (d) 3 7 x 3 4 (2) Each hexagon represents 1 whole. Which product is represented by the shading shown on this model? (a) 3 x 6 (b) 3 x 1 6 (c) 1 3 x 1 6 (d) 1 3 x 6 Page 12 of 14

13 (Calculator use permitted.) (3) (4) Page 13 of 14

14 6.5 EXPONENTS & SQUARES Base (big) number is the number being multiplied. Exponent (little) is the number of times the base is multiplied. n 0 = 1 (always) squared means to the power of 2. A PERFECT SQUARE is a number that you get when you multiply a number by itself. (1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 361, 400) A power of 10 will be a 1 followed by the number of zeros indicated by the exponent. (10 4 = 10,000) (1) Which of these is equivalent to 14 x 14 x 14? (a) 3 x 42 (b) 14 x 42 (c) 3 14 (d) 14 3 (2) (3) (Calculator use permitted.) (4) (5) (6) (7) Page 14 of 14

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