6th Grade Math Study Guide for Final Exam Exam: Week of May 20th Prepared for you by: Mrs. Hunger Riverdale Middle School

Prepared for you by: Mrs. Hunger Riverdale Middle School Overview of Skills to be tested: Numbers in parenthesis represent pretest numbers. 1. Adding and Subtracting Fractions (1) Workbook pages 61 – 64 Chapter 4 Lessons 3 and 4 Decimals (27) Chapter 1 Lesson 2 Workbook p. 3-4 (35) Ch. 1 Lesson 3 Work book p. 5-6 (41) Not in workbook (44) Multiplying and Dividing Decimals Workbook p 13 – 18 Ch. 1 Les 7 (48) Adding and Subtracting Decimals Ch. 1 Lesson 5 Workbook pages 9 - 10 Prepared for you by: Mrs. Hunger Riverdale Middle School

Prepared for you by: Mrs. Hunger Riverdale Middle School Study Guide for Final Exams Geometry (66) Classify Angles: Workbook: ch 8 Les 2 p. 125 - 128 (69) Classifying Triangles: Workbook ch. 8 Les 4 p. 129 – 130 (75) Classifying Polygons: Workbook ch. 8 Les 5 p. 131 – 132 (79 ) Area and Perimeter: Wb. 145 – 148 Ch. 9 Les 3 Prepared for you by: Mrs. Hunger Riverdale Middle School

Prepared for you by: Mrs. Hunger Riverdale Middle School Study Guide for Final Exams: Integers (91) Operations with integers Wb. P. 161 – 175 (141) Perfect Squares Ch. 12 Les 5 Wb. P. 201 – 202 Prepared for you by: Mrs. Hunger Riverdale Middle School

Prepared for you by: Mrs. Hunger Riverdale Middle School Study Guide for Final Exam (151) Solving One – Step Equations Ch. 2 Les. 5 p. 29 – 30 (156) Exponents Ch. 2 Les 8 p 35 – 36 (157) Number Patterns Ch. 2 Les. 4 (160 – 172) Order of Operations Not in workbook Prepared for you by: Mrs. Hunger Riverdale Middle School

Prepared for you by: Mrs. Hunger Riverdale Middle School Study Guide for Final Exam ( 173 – 178) Evaluate Expressions Not in Workbook means to solve them or compare them. (179 – 187) Graphing Coordinate Pairs Ch. 10 Lesson 6 p. 171 - 172 Prepared for you by: Mrs. Hunger Riverdale Middle School

Prepared for you by: Mrs. Hunger Riverdale Middle School Practice Activities from Workbook: Fractions: See Workbook p. 61 – 64 for extra practice. To add or subtract fractions with unlike denominators, you can use equivalent fractions Example 1 : Find 5/6 + ½ Find the least common denominator of 6 and 2. Count by 2’s 2 4 6 Six is the first number 6 can go into. So the LCD is 6 Write equivalent fractions using the LCD 5/6 = 5/6 ½ = 1 x 3 = 3, 2 X 3 = 6, so ½ = 3/6 Add. Write the sum in simplest form. 5/6 + 3/6 = 8/6 = 1 2/6 = 1 1/3 Example 2: Find 4/5 - 1/3 Find the least common denominator of 5 and 3 Count by 3’s 3 6 9 12 15 15 is the first number the 5 can go into. So the LCD is 15 Write equivalent fractions using the LCD 4/5 = 4 X 3 = 12, 5 X 3 = 15 4/5 = 12/15 1/3 = 1X 5 = 5, 3 X 5 = 15 so 1/3 = 5/15 Subtract:. Write the difference in simplest form. 12/15 - 5/15 = 7/15 Practice: ½ + ¾ = _____ 11/16 - 5/16 = _____ 7/12 - 1/3 = ______ Prepared for you by: Mrs. Hunger Riverdale Middle School

Prepared for you by: Mrs. Hunger Riverdale Middle School Practice Activities from Workbook: Decimals Chapter 1 Reading and Writing Decimals: See Workbook p. 3-6 for extra practice. Standard form: 2.369 To find the value of a digit, multiply the digit by its place value. 9 stands for 9 X .001 or .009 Expanded form: 2.369 = 2 + 0.3 + 0.06 + 0.009 Comparing and Ordering Decimals: Use >, <, or = to compare Write the numbers on grid paper with the decimal points lined up. Compare digits in the greatest place. Move to the right until you find digits that are not the same. 4 ones = 4 ones 0 tenths = 0 tenths 9 hundredths > 8 hundredths So, 4.092 > 4.089 4.09 4.092 4.089 To order from least to greatest: Write the numbers on grid paper (decimal points lined up) and compare. Then arrange the numbers from least to greatest. 4 . 9 2 8 Prepared for you by: Mrs. Hunger Riverdale Middle School

Prepared for you by: Mrs. Hunger Riverdale Middle School Practice Activities: Decimals Adding and Subtracting Decimals See Wb p. 9-10 for extra practice. Add 3.25 + 12.6 + 18.93 First Estimate: 3.25 3 12.6 13 18.93 19 35 Then follow these steps. Line up the decimal points. 2. Add as you would add 3. Place the Write in any needed zeros. whole numbers. Decimal 3.25 3.25 3.25 12.60 12.60 12.60 + 18.93 + 18.93 + 18.93 34 78 34.78 Prepared for you by: Mrs. Hunger Riverdale Middle School

Prepared for you by: Mrs. Hunger Riverdale Middle School Practice Activities: Multiplying and Dividing Decimals See Workbook pages 13 – 18 for extra practice. When multiplying or dividing decimals, simply perform the operation pretending the decimals are not there. Then count the total digits to the right of all of the decimals. That is the number of digits you need after the decimal in your answer. You may have to add a zero to hold the place open. Example: 34.123 34123 X .02 X 02 68246 1 2 3 4 5 5 digits are after So place the decimal the decimals. in front of the six. Prepared for you by: Mrs. Hunger Riverdale Middle School

Prepared for you by: Mrs. Hunger Riverdale Middle School Study Guide for Final Exam 6th Grade Math Classifying Angles: Wb p. 125 – 128 Ch. 8 Les 2 When two lines cross perpendicularly, they form right angles. Any angle that opens wider than a right angle is called obtuse. Any angle that opens smaller than that is called acute. An angle that is 180 degrees is a straight angle. Complementary Angles: the sum of two angles measures 90 degrees Supplementary Angles: the sum of two angles measures 180 degrees. Congruent Angles: two angles that have the same measures. Prepared for you by: Mrs. Hunger Riverdale Middle School

Prepared for you by: Mrs. Hunger Riverdale Middle School Study Guide for Final Exam: Classifying Triangles: Chapter 8 Lesson 4 See Workbook p 129 – 130 for extra practice. The sum of all angles in any triangle is 180 degrees. Triangles can be classified by the measures of their angles. Acute: has 3 acute angles Right: has 1 right angle Obtuse: has 1 obtuse angle Triangles can be classified by the number of congruent sides. Equilateral: all congruent sides Isosceles: 2 congruent sides Scalene: no congruent sides Prepared for you by: Mrs. Hunger Riverdale Middle School

Prepared for you by: Mrs. Hunger Riverdale Middle School Study Guide for Final Exam: 6th Grade Math Classifying Polygons: Ch. 8 Les 5 See Workbook p. 131-132 for extra practice A polygon is a closed figure formed by three or more line segments that do not cross. Polygons can be named according to the number of sides: 3: Triangle 4: Quadrilateral 5: Pentagon 6: Hexagon 7: Septagon 8: Octagon 9: Nonagon 10: Decagon 12: Dodecagon Prepared for you by: Mrs. Hunger Riverdale Middle School

Prepared for you by: Mrs. Hunger Riverdale Middle School Study Guide for Final Exam: 6th Grade Math Area and Perimeter: Ch. 9 Les 3 Wb. p. 145- 148 Perimeter: The perimeter of a figure is the sum of the lengths of Its sides. Opposite sides of a rectangle are equal. To Find the perimeter, add the 2 lengths ( L) and the 2 widths (W). 4 inches 10 inches 4 + 4 + 10 + 10 = 28 inches Area: The area of a figure is the number of square units Needed to cover the figure. To find the area of a Rectangle, multiply the length (L) and the width (W) The area of the rectangle above is 4inches X 10 inches = 40 inches squared Prepared for you by: Mrs. Hunger Riverdale Middle School

Prepared for you by: Mrs. Hunger Riverdale Middle School Study Guide for Final Exam Operations with Integers See Workbook p. 161 – 175 for extra practice. Using a number line: -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 The absolute value of a number is its distance from zero. Written l -4 l = 4 or l 4 l = 4 Opposite integers like -4 and 4 are the same distance from 0. For two integers on a number line, the greater integer is farther to the right. Prepared for you by: Mrs. Hunger Riverdale Middle School

Prepared for you by: Mrs. Hunger Riverdale Middle School Study Guide for the Final Exam Adding Integers See Workbook p. 163 – 164 for extra practice. You can add integers on a number line. Example 1: Find 4 + 3 Start at zero and move 4 digits to the right, then 3 digits to the right. 4 + 3 = 7 Example 2: Find -3 + -2 Start at zero and move 3 digits to the left, then 2 digits to the left. -3 + -2 = - 5 Example 3: Find 5 + (-3) Start at zero and move 5 digits to the right, and then 3 digits left. 5 + (-3) = 2 Example 4: Find -4 + 1 Start at zero and move 4 digits to the left, and then 1 digit to the right. -4 + 1 = -3 Prepared for you by: Mrs. Hunger Riverdale Middle School

Prepared for you by: Mrs. Hunger Riverdale Middle School Study Guide for Final Exam Subtracting Integers: See Workbook pages 165 – 166 for extra practice. To subtract an integer, add the opposite. Example 1: Subtract 5 – 8 Add the opposite: 5 + (-8) 5 -8 = -3 Example 2: Subtract 2 - (-4) Add the opposite: 2 + 4 2 + 4 = 6 Prepared for you by: Mrs. Hunger Riverdale Middle School

Prepared for you by: Mrs. Hunger Riverdale Middle School Study Guide for Final Exam Multiplying Integers: See Workbook pages 167 - 168 for extra practice. When two integers have like signs, the product will always be positive. Examples: Both integers are positive: 3 X 4 = 12 Both integers are negative: -3 X ( -4) = 12 When two integers have unlike signs, the product will always be negative. One integer positive, one negative 3 X (-4) = -12 One integer negative, one positive -3 X 4 = -12 Prepared for you by: Mrs. Hunger Riverdale Middle School

Prepared for you by: Mrs. Hunger Riverdale Middle School Study Guide for Final Exam: Dividing Integers: See workbook p. 169 – 179 for extra practice. When two integers have like signs, the quotient will always be positive. Examples: Both integers are positive: 8 ÷ 2 = 4 Both integers are negative: -8 ÷ -2 = 4 When two integers have unlike signs, the quotient will always be negative. One integer positive, one negative: 8 ÷ (-2) = -4 One integer negative, one positive: -8 ÷ 2 = -4 Prepared for you by: Mrs. Hunger Riverdale Middle School

Prepared for you by: Mrs. Hunger Riverdale Middle School Study Guide for Final Exam: Graphing in the Coordinate Plane: See Workbook p. 171 -172 for extra practice. The X axis is the horizontal line on a coordinate plane. The first number in a coordinate pair tells its position on the X axis. The Y axis is the vertical line on a coordinate plane. The second number in a coordinate pair tells its position on the Y axis. The origin is the 0 point where the X and Y axis cross. Positive numbers move to the right of 0 on the X axis, or up on the Y axis. Negative numbers move to the left of 0 on the X axis, or down on the Y axis. Prepared for you by: Mrs. Hunger Riverdale Middle School

Prepared for you by: Mrs. Hunger Riverdale Middle School Study Guide for the Final Exam: Graphing Functions. See Workbook p. 175 – 176 for extra practice. A table or a graph can show how the input and output of a function are related. An input / output chart can give you the values for plotting points on a graph. Think of the input as the first coordinate, ( X axis) and the output as the second coordinate, ( Y axis). This data can show a trend in your data. Practice plotting coordinate points from Workbook p. 175. Prepared for you by: Mrs. Hunger Riverdale Middle School

Prepared for you by: Mrs. Hunger Riverdale Middle School Study Guide for Final Exam: Perfect Squares: See Workbook pages 201 -202 for extra practice. A perfect square is the square of a whole number. The number 81 is a perfect square because it is the square of 9. You could also say that 9 is the square root of 81, or 81 = 9 The square root of a given number is a number that, when multiplied by itself, is the given number. Prepared for you by: Mrs. Hunger Riverdale Middle School

Prepared for you by: Mrs. Hunger Riverdale Middle School Study Guide for Final Exam: (151) Solving One – Step Equations See Workbook p. 29 – 30 for extra practice. One way to solve some equations is to use mental math. Example 1: Find the solution to the equation a + 5 = 10 What you think: If I add 5 to 5, the sum is 10 5 + 5 = 10 So, a = 5 Example 2: Find the solution to the equation. Y - 9 = 15 If I subtract 9 from 24, the answer is 15, 24 - 9 = 15 So, y = 24 Example 3: Find the solution to the equation. W ÷ 5 = 100 W ÷ 5 means w divided by 5. I know that 500 ÷ 5 = 100 So, w = 500 Example 4: Find the solution to the equation. 4w = 24 4w means 4 times w. I know that 4 X 6 = 24 So, w = 6 Prepared for you by: Mrs. Hunger Riverdale Middle School

Prepared for you by: Mrs. Hunger Riverdale Middle School Study Guide for Final Exam: Exponents See Workbook page 35 -36 for extra practice. An exponent tells how many times a number is used as a factor. 3 X 3 X 3 X 3 shows the number 3 is used as a factor 4 times. 3 X 3 X 3 X 3 can be written 3 ⁴. In 3 ⁴, 3 is the base and 4 is the exponent. To simplify a power, first write it as a product. 2⁵ = 2 X 2 X 2 X 2 X 2 = 32 When you simplify expressions with exponents, do all operations inside parentheses first. Then simplify the powers. Example: 30 – (2 + 3) = 30 - 5 = 30 - 25 = 5 Prepared for you by: Mrs. Hunger Riverdale Middle School

Prepared for you by: Mrs. Hunger Riverdale Middle School Study Guide for Final Exam: (157)Number Patterns See Workbook page 27 for extra practice. Stony Hollow School District has a softball playoff Each spring for its 8 schools. Each school plays 1 game against every other school. The winner Is the school with the greatest number of victories. How many playoff games are played in all? Problem Solving: Make a table and look for a pattern. Read and Understand: Plan and Solve Make a table. Look for a pattern. Look back and Check. Prepared for you by: Mrs. Hunger Riverdale Middle School

Prepared for you by: Mrs. Hunger Riverdale Middle School # of schools # of games 2 1 3 4 6 5 10 15 7 21 8 28 +2 +3 +4 +5 +6 +7 Prepared for you by: Mrs. Hunger Riverdale Middle School

Prepared for you by: Mrs. Hunger Riverdale Middle School Study Guide for Final Exam: (160 – 172) Order of Operations Not in Workbook Operations need to be performed in this order: 1. Addition 2. Subtraction 3. Multiplication 4. Division When you need to solve an equation that does not have parentheses, you must first complete the addition or subtraction, then do the multiplication or division. Example 1: 2 X 3 + 5 = ________ First add 3 + 5 = 8 Then multiply 8 X 2 = 16 Example 2: 6 + 4 ÷ 2 = _________ First add 6 + 4 = 10, Then divide 10 ÷ 2 = 5 Now try a few on your own: 23 + 7 ÷ 2 = _______ 2. 5 + 4 X 3 = ____________ 3. 5 X ( 3 + 1) X 4 = _______ 4. 16 - 6 ÷ 2 = ___________ Prepared for you by: Mrs. Hunger Riverdale Middle School

Prepared for you by: Mrs. Hunger Riverdale Middle School Study Guide for Final Exam: Evaluate Expressions not in work book (173 – 178) Evaluate Expressions simply means to solve them. Graphing Coordinate Pairs See Workbook p. 171 – 172 Coordinate Pairs are always written in this order: 1st number is the number that is placed on the graph first. It is placed on the X axis. If it is positive, you start at zero and move to the right. If it is negative you start at zero and move to the left. 2nd number is the number that is placed on the graph second. It is placed on the Y axis. If it is positive, you start at the 1st number’s place and move up. If it is negative, you start at first number’s place and move down. Prepared for you by: Mrs. Hunger Riverdale Middle School

Prepared for you by: Mrs. Hunger Riverdale Middle School Study Guide for Final Exam: Prepared for you by: Mrs. Hunger Riverdale Middle School

Prepared for you by: Mrs. Hunger Riverdale Middle School Study Guide for Final Exam: Prepared for you by: Mrs. Hunger Riverdale Middle School