RAVEN S GUIDE TO BRITISH COLUMBIA LINKED DIRECTLY TO NEW CURRICULUM REQUIREMENTS FROM THE WESTERN PROTOCOLS FOR 2008 AND BEYOND


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1 RAVEN S GUIDE TO BRITISH COLUMBIA MATHEMATICS GRADE 6 LINKED DIRECTLY TO NEW CURRICULUM REQUIREMENTS FROM THE WESTERN PROTOCOLS FOR 2008 AND BEYOND STUDENT GUIDE AND RESOURCE BOOK Key to Student Success with Grade 6 Mathematics One of a series of publications by Raven Research Associates for Secondary and Elementary Mathematics Alan R. Taylor, Ed. D. Raven Research Associates, Inc. June 2008
2 Table of Contents Page Chapter 1 Number Concepts 1.1 Place Value Rounding Numbers Solving Problems with Large Numbers Factors and Multiples Greatest Common Factor and Least Common Multiple Improper Fractions and Mixed Numbers Ordering and Comparing Fractions and Decimals 32 Chapter 2 Ratio, Percent, Integers and Decimals 2.1 Ratio Percent Integers Multiplying and Dividing Decimals Problem Solving with Decimals Order of Operations 69 Chapter 3 Patterns 3.1 Number and Symbol Patterns Relationships with Tables of Values Patterns in Tables and Graphs Rules to Describe Relations and Predict Patterns 91 Chapter 4 Variables and Equations 4.1 Placeholders and Variables placeholders  variables 4.2 Representing Generalizations perimeter of a rectangle  area of a rectangle  tables and equations 4.3 Preserving Equality equality under + and   equality under x and  equivalent form of an equation Chapter 5 Measurement 5.1 Types of Angles and Estimating Measures Measuring and Drawing Angles Interior Angles in Triangles and Quadrilaterals Perimeter of Polygons Area of Rectangles Volume of Rectangular Prisms 140 Chapter 6 Triangles, Polygons, Shapes and Transformations 6.1 Types of Triangles Sorting and Drawing Triangles Regular and Irregular Polygons Congruent Polygons Transformations of 2D Shapes Plotting Points and Transformations in the First Quadrant 168 Chapter 7 Statistics and Probability Data Analysis 7.1 Collecting Data Line Graphs Displaying, Graphing and Interpreting Data 197 Probability 7.4 Possible Outcomes and Experimental Probability Theoretical Probability 207 Appendix  Answers to Exercises and Chapter Tests 218
3 2.6 Order of Operations SAMPLE FROM RAVEN GRADE 6 MATH Rules for Order of Number Operations In order to find the correct answer when number expressions have more than one operation, we have to use the following rules. 1. First do all operations that lie inside parentheses (brackets). 2. Working from left to right, do all multiplication and division in the order it occurs. 3. Finally, working from left to right, do all addition and subtraction in the order it occurs. If there are no brackets (parentheses), perform all multiplication and division in the order they appear, before any addition or subtraction x = x = = x 4 = x 4 = = 26 If there are brackets (parentheses) perform all operations inside the brackets before any other operations. 1. (5 + 6) x 3 = 11 x 3 = (82) x 4 = x 4 = = (2 + 4) + 7 = = = (4 + 7) = = = 17 Several examples follow: 1. Do things in Parenthesis First (i) 5 x ( 4 + 7) = 5 x 11 = 55 (ii) 6 x (8 5 ) = 6 x 3 = 18 (iii) 9 + (3 x 2) = = Multiply or Divide before you Add or Subtract. 3. Combinations (Remember to clear parentheses first, perform multiplication and division next and then addition and subtraction. Always work left to right.) (i) 2 x = = 18 (ii) x 3 = = 21 (iii) x 2 = = 14 (iv) = 15 3 = 12 (i) 7(4 + 9) 8 = 7x13 8=91 8 = 83 (ii) 5 x 3+(8 2) 2=5 x = = 18 (iii) 12 4 x 5 3 = 3 x 5 3 = 153 = 12
4 Examples with Solutions 1. Simplify x 4 2. Simplify (2 + 3) x 4 3. Simplify (3 x 2) 4. Simplify ( ) Simplify ( ) since there are no brackets, perform the multiplication first x 4 = now add = perform operations inside of the brackets first (2 + 3 ) x 4 = 5 x 4 2. now multiply 5 x 4 = perform operations inside of brackets first (3 x 2) = next perform division before adding or subtracting = now subtract 86 = 2 1. perform operations inside of brackets first 1.3+2( ) 4 =1.3+ 2(5.25) next perform multiplication before adding or subtracting now add and subtract perform operations inside of brackets first (3.5) next perform multiplication and division before subtracting now subtract 2
5 Exercises 2.6 Order of Operations Simplify each of the following statements. Show your work for each step. Work 1. 4 x x ( 7 + 5) 3. 5 x x (15 + 5) x x x (2 3) 8. 5 x 2 x 3 x (3 + 2) (4 + 5) x x (6 + 1) x x
6 Extra for Experts ( 2 + 1) Work (2.5) ( ) ( ) (1.5 x 2) 19. (7 2 x 1.4) + (4 2 x 0.5) 20. Find the missing number in each number sentence. a. 2 x 5 + = 4 b. 3 x + 1 = 10 c = 7 d. 5 x = 19 e. 8 + x 2 = 16
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