British Columbia Curriculum

Transcription

1 Supported by independent evidence-based research practice. Follows provincial curricula Powerful reporting Student centred

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3 BC Content BC Kindergarten 02 BC Apprenticeship Workplace BC Grade 1 03 BC Foundations Pre-calculus BC Grade 2 05 BC Grade 3 08 BC Foundations of Mathematics BC Grade 4 11 BC Pre-calculus BC Grade 5 15 BC Apprenticeship Workplace BC Grade 6 19 BC Foundations of Mathematics BC Grade 7 22 BC Apprenticeship Workplace BC Grade 8 26 BC Pre-calculus BC 29

4 Mathletics the British Columbia Curriculum The education team at Mathletics is committed to providing a resource that is powerful, targeted,, most importantly, relevant to all students. Mathletics includes well over 1200 individual adaptive practice activities ebooks available for all grades. Our team of educational publishers has created a course that specifically follows the British Columbia curriculum. You can be assured that students have access to relevant targeted content. Strs, sub-strs, learning outcomes of the curriculum are supported with activities, each with pre post assessment. What s more, Mathletics contains an extensive library of ebooks for use on screen or as a printable resource that are also mapped to the requirements of the British Columbia Curriculum. This document outlines this mapping acts as a useful guide when using Mathletics in your school. Rene Burke CEO, 3P Learning Canada Engage Target Diagnose Assess Report Fluency Mobile 1 3P Learning

5 BC Kindergarten Str Substr Outcome Outcome Description Activities ebooks Number Number BC.K.A1 Number Number BC.K.A2 Number Number BC.K.A3 Number Number BC.K.A4 Number Number BC.K.A5 Patterns hips Shape Shape Shape Patterns Measurement 3-D Objects 2-D Shapes 3-D Objects 2-D Shapes BC.K.B1 BC.K.C1 BC.K.C2 BC.K.C3 Say the number sequence by 1s starting anywhere from 1 to 10 from 10 to 1. Recognize, at a glance, name familiar arrangements of 1 to 5 objects or dots. Relate a numeral, 1 to 10, to its respective quantity. Represent describe numbers 2 to 10, concretely pictorially. Compare quantities, 1 to 10, using one-to-one correspondence. Demonstrate an understing of repeating patterns. Use direct comparison to compare two objects based on a single attribute such as length (height), mass (weight), volume (capacity). Sort 3-D objects using a single attribute. Build describe 3-D objects. Order Numbers to 10 Count to 5 How many dots? How Many? Who has the Goods? Matching Numbers to 10 Balance Numbers to 10 More or Less? More, Less or the Same to 10 Complete the Pattern Missing it! Share the Treasure Compare Length Everyday Mass How Full? Which Holds More? Match the Solid 1 Sort it Collect the Shapes Match the Solid 1 Sort it Kindergarten Number Patterns Kindergarten Number Patterns Kindergarten Number Patterns Kindergarten Number Patterns Kindergarten Number Patterns Kindergarten Number Patterns Kindergarten Measurement Kindergarten Shape Kindergarten Shape 3P Learning 2

6 BC Grade 1 Str Substr Outcome Outcome Description Activities ebooks Number Number BC.1.A1 Number Number BC.1.A2 Number Number BC.1.A3 Number Number BC.1.A4 Number Number BC.1.A5 Number Number BC.1.A6 Number Number BC.1.A7 Number Number BC.1.A8 Number Number BC.1.A9 Say the number sequence, 0 to 100. Recognize, at a glance, name familiar arrangements of 1 to 10 objects or dots. Demonstrate an understing of counting. Represent describe numbers to 20 concretely, pictorially, symbolically. Compare sets containing up to 20 elements to solve problems. Estimate quantities to 20 by using referents. Demonstrate, concretely pictorially, how a given number can be represented by a variety of equal groups with without singles. Identify the number, up to 20, that is one more, two more, one less, two less than a given number. Demonstrate an understing of addition of numbers with answers to 20 their corresponding subtraction facts, concretely, pictorially, symbolically. Going Up Counting Backwards Count by Twos Counting by Fives Count by Tens 1 to 30 How many dots? How Many? Reading numbers to 30 Ordinal Numbers Making Teen Numbers More, Less or the Same to 20 Compare Numbers to 20 1 more, 2 less Order Numbers to 20 Model Addition Model Subtraction Add Subtract Using Graphs Addition Facts to 18 Subtraction Facts to 18 Fact Families: Add Subtract Balance Numbers to 10 Adding to Ten Subtracting from Ten Adding to 10 word problems Grade 1 Numbers Grade 1 Numbers Grade 1 Numbers Grade 1 Numbers Grade 1 Numbers Grade 1 Numbers Grade 1 Numbers Grade 1 Numbers Grade 1 Operations with Numbers 3 3P Learning

7 BC Grade 1 Str Substr Outcome Outcome Description Activities ebooks Number Number BC.1.A10 Describe use mental mathematics strategies. Adding to make 5 10 Doubles Near Doubles Related Facts 1 All about Ten Grade 1 Operations with Numbers Patterns hips Patterns hips Patterns hips Patterns hips Shape Shape Shape Shape Patterns Patterns Variables Equations Variables Equations Measurement 3-D Objects 2-D Shapes 3-D Objects 2-D Shapes 3-D Objects 2-D Shapes BC.1.B1 BC.1.B2 BC.1.B3 BC.1.B4 BC.1.C1 BC.1.C2 BC.1.C3 BC.1.C4 Demonstrate an understing of repeating patterns (two to four elements). Translate repeating patterns from one representation to another. Describe equality as a balance inequality as an imbalance, concretely, pictorially. Record equalities using the equal symbol. Demonstrate an understing of measurement as a process of comparing. Sort 3-D objects 2-D shapes using one attribute, explain the sorting rule. Replicate composite 2-D shapes 3-D objects. Compare 2-D shapes to parts of 3-D objects in the environment. Simple Patterns Missing it! Pattern Error Balancing Act Balance Numbers to 10 Balance Numbers to 20 Everyday Length Which Holds More? Filling Fast! Biggest Shape Sort It Collect the Shapes Match the Object Collect the Objects Grade 1 Patterns hips Grade 1 Patterns hips Grade 1 Measurement Grade 1 Shape Grade 1 Shape Grade 1 Shape 3P Learning 4

8 BC Grade 2 Str Substr Outcome Outcome Description Activities ebooks Number Number BC.2.A1 Number Number BC.2.A2 Number Number BC.2.A3 Number Number BC.2.A4 Say the number sequence from 0 to 100 by 2s, 5s 10s, forward backward, using starting points that are multiples of 2, 5, 10 respectively. Demonstrate if a number (up to 100) is even or odd. Describe order or relative position using ordinal numbers (up to tenth). Represent describe numbers to 100, concretely, pictorially, symbolically. Number Number BC.2.A5 Compare order numbers up to 100. Number Number BC.2.A6 Number Number BC.2.A7 Number Number BC.2.A8 Number Number BC.2.A9 Estimate quantities to 100 using referents. Illustrate, concretely pictorially, the meaning of place value for numerals to 100. Demonstrate explain the effect of adding zero to or subtracting zero from any number. Demonstrate an understing of addition (limited to 1 2-digit numerals) with answers to 100 the corresponding subtraction by using personal strategies for adding subtracting with without the support of manipulatives; creating solving problems that involve addition subtraction; explaining that the order in which numbers are added does not affect the sum; explaining that the order in which numbers are subtracted may affect the difference. Counting by Twos Counting by Fives Counting by Tens Count by 2s, 5s 10s Skip counting with coins Odd Even Numbers 1 Odd or Even 1st to 31st Ordinal Numbers Making Big Numbers Count Place Value 1 Arranging Numbers Compare Numbers to 100 Number Line Order Going Up Going Down Before, After & Between to 100 Repartition two digit numbers Place Value 1 Making Big Numbers Count Concept of Zero Addictive Addition Simple Subtraction Add Two 2-Digit Numbers Balance Numbers to 20 Add Subtract Problems Bar Model Problems 1 Bar Model Problems 2 10 More, 10 Less Add 3 numbers using bonds to 10 Add 3 Single Digit Numbers Grade 2 Numbers Grade 2 Numbers Grade 2 Numbers Grade 2 Numbers Grade 2 Numbers Grade 2 Numbers Grade 2 Operations with Number 5 3P Learning

9 BC Grade 2 Str Substr Outcome Outcome Description Activities ebooks Number Number BC.2.A10 Patterns Patterns Patterns Patterns Shape Shape Shape Shape Shape Shape Patterns Patterns Variations Equations Variations Equations BC.2.B1 BC.2.B2 BC.2.B3 BC.2.B4 Measurement BC.2.C1 Measurement BC.2.C2 Measurement BC.2.C3 Measurement BC.2.C4 Measurement BC.2.C5 3-D Objects 2-D Shapes BC.2.C6 Apply mental mathematics strategies to determine basic addition facts to 18 related subtraction facts. Demonstrate an understing of repeating patterns. Demonstrate an understing of increasing patterns. Demonstrate explain the meaning of equality inequality by using manipulatives diagrams (0 to 100). Record equalities inequalities symbolically using the equal symbol or the not equal symbol. Relate the number of days to a week the number of months to a year in a problem-solving context. Relate the size of a unit of measure to the number of units (limited to non-stard units) used to measure length mass (weight). Compare order objects by length, height, distance around, mass (weight) using nonstard units, make statements of comparison. Measure length to the nearest non-stard unit. Demonstrate that changing the orientation of an object does not alter the measurements of its attributes. Sort 2-D shapes 3-D objects using two attributes explain the sorting rule. Related Facts 1 Repartition to Subtract All about Ten Doubles Near Doubles Add to 18 Adding in Any Order 1 more, 2 less 1 more, 10 less Simple Patterns Pattern Error Colour Patterns Count Forward Patterns Count Backward Patterns Greater or less to 100 Compare Numbers to 100 Balance Numbers to 20 Days of the Week Months of the Year Everyday Length Comparing Length Everyday Mass Measuring Length with Blocks Sort It Grade 2 Operations with Number Grade 2 Patterns hips Grade 2 Patterns hips Grade 2 Time Grade 2 Measurement Grade 2 Measurement Grade 2 Shape 3P Learning 6

10 BC Grade 2 Str Substr Outcome Outcome Description Activities ebooks Shape 3-D Objects 2-D Shapes BC.2.C7 Describe, compare, construct 3-D objects. Collect the Objects Match the Solid 1 Grade 2 Shape Shape 3-D Objects 2-D Shapes BC.2.C8 Describe, compare, construct 2-D shapes. Collect Simple Shapes Grade 2 Shape Shape 3-D Objects 2-D Shapes BC.2.C9 Identify 2-D shapes as parts of 3-D objects in the environment. Relate Shapes Solids Grade 2 Shape Statistics Data Analysis BC.2.D1 Gather record data about self others to answer questions. Grade 2 Chance Data Statistics Data Analysis BC.2.D2 Construct interpret concrete graphs pictographs to solve problems. Pictographs Making Graphs Add Subtract Using Graphs Sorting Data Grade 2 Chance Data 7 3P Learning

11 BC Grade 3 Str Substr Outcome Outcome Description Activities ebooks Number Number BC.3.A1 Number Number BC.3.A2 Number Number BC.3.A3 Number Number BC.3.A4 Number Number BC.3.A5 Number Number BC.3.A6 Number Number BC.3.A7 Number Number BC.3.A8 Say the number sequence forward backward from 0 to Represent describe numbers to 1000, concretely, pictorially, symbolically. Compare order numbers to Estimate quantities less than 1000 using referents. Illustrate, concretely pictorially, the meaning of place value for numerals to Describe apply mental mathematics strategies for adding two 2-digit numerals. Describe apply mental mathematics strategies for subtracting two 2-digit numerals, apply estimation strategies to predict sums differences of two 2-digit numerals in a problem-solving context demonstrate an understing of addition subtraction of numbers with answers to Apply mental mathematics strategies number properties. Counting on a 100 grid Counting by Fives Counting by Tens Count Forward Patterns Count Backward Patterns Model Numbers Place Value 2 Which is Smaller? Which is Bigger? Nearest 10? Nearest 100? Place Value 2 Model Numbers Place Value Partitioning Add Two 2-Digit Numbers Add Two 2-Digit Numbers: Regroup Magic Mental Addition Adding to 2-digit numbers Pyramid Puzzles 1 Magic Mental Subtraction Subtract Numbers Subtract Numbers: Regroup Repartition to Subtract Subtract tens Basic Fact Families Complements to 10, Complements to Commutative Property of Addition Doubles Halves to 20 Grade 3 Reading Understing Whole Numbers Grade 3 Reading Understing Whole Numbers Grade 3 Reading Understing Whole Numbers Grade 3 Reading Understing Whole Numbers Grade 3 Addition Subtraction Grade 3 Addition Subtraction Grade 3 Addition Subtraction 3P Learning 8

12 BC Grade 3 Str Substr Outcome Outcome Description Activities ebooks Number Number BC.3.A11 Number Number BC.3.A12 Number Number BC.3.A13 Patterns hips Patterns hips Patterns hips Shape Shape Shape Shape Patterns Patterns Variations Equations Measurement Measurement Measurement Measurement BC.3.B1 BC.3.B2 BC.3.B3 BC.3.C1 BC.3.C2 BC.3.C3 BC.3.C4 Demonstrate an understing of multiplication to 5 5. Demonstrate an understing of division. Demonstrate an understing of fractions. Demonstrate an understing of increasing patterns. Demonstrate an understing of decreasing patterns. Solve one-step addition subtraction equations involving symbols representing an unknown number. Relate the passage of time to common activities using nonstard stard units. Relate the number of seconds to a minute, the number of minutes to an hour, the number of days to a month in a problem-solving context. Demonstrate an understing of measuring length (cm, m). Demonstrate an understing of measuring mass (g, kg). Groups of Two Groups of Three Groups of Four Groups of Five Model Multiplication to 5 x 5 Fill the Jars Dividing Twos Dividing Threes Dividing Fours Dividing Fives Making Equal Groups Halves Quarters Model Fractions Part-whole rods 1 Thirds Sixths What Fraction Is Shaded? Identifying Fractions on a Number Line Shape Fractions Increasing Patterns Decreasing Patterns Missing Values Hour Times Half Hour Times What is the Time? Measuring Length How Long is That? How Heavy? Grade 3 Multiplication Division Grade 3 Multiplication Division Grade 3 Fractions Grade 3 Patterns hips Grade 3 Patterns hips Grade 3 Patterns hips Grade 3 Time Grade 3 Measurement Grade 3 Measurement 9 3P Learning

13 BC Grade 3 Str Substr Outcome Outcome Description Activities ebooks Shape Shape Shape Statistics Statistics Measurement 3-D Objects 2-D Shapes 3-D Objects 2-D Shapes Data Analysis Data Analysis BC.3.C5 BC.3.C6 BC.3.C7 BC.3.D1 BC.3.D2 Demonstrate an understing of perimeter of regular irregular shapes. Describe 3-D objects according to the shape of the faces, the number of edges vertices. Sort regular irregular polygons. Collect first-h data organize it. Construct, label interpret bar graphs to solve problems. Perimeter of Shapes How many Corners? How many Edges? How many Faces? Collect the Shapes 2 Collect the Polygons Triangles: Acute, Right, Obtuse Tallies Bar Graphs 1 Pictographs Grade 3 Measurement Grade 3 Measurement Grade 3, Shape Position Grade 3 Chance Data Grade 3 Chance Data 3P Learning 10

14 BC Grade 4 Str Substr Outcome Outcome Description Activities ebooks Number Number BC.4.A1 Number Number BC.4.A2 Number Number BC.4.A3 Number Number BC.4.A4 Number Number BC.4.A5 Represent describe whole numbers to , pictorially symbolically. Compare order numbers to Demonstrate an understing of addition of numbers with answers to their corresponding subtractions (limited to 3 4-digit numerals) by using personal strategies for adding subtracting estimating sums differences solving problems involving addition subtraction. Explain the properties of 0 1 for multiplication, the property of 1 for division. Describe apply mental mathematics strategies, such as skip counting from a known fact using doubling or halving using doubling or halving adding or subtracting one more group using patterns in the 9s facts using repeated doubling to determine basic multiplication facts to 9=9 related division facts. Exped Notation Exping Numbers Understing Place Value 2 Numbers in Words Place Value 3 Place Value to Thouss Ascending Order Descending Order Put in Order 1 Estimate Sums Estimate Differences Compensation - Add Compensation - Subtract Split Add Subtract Bump Add Subtract Jump Add Subtract 3-Digit Differences: 1 Regrouping 3-Digit Differences: 2 Regrouping Add 3-Digit Numbers Add 3-Digit Numbers: Regroup 3 Digit Differences 3 Digit Differences with Zeros Problems: Add Subtract 2 Add Multi-Digit Numbers 1 Adding Colossal Columns Subtracting Colossal Columns Adding in Any Order Pyramid Puzzles 2 Strategies for Column Addition Mental Methods Multiplication Mental Methods Division Double halve to multiply Grade 4 Reading Understing Whole Numbers Grade 4 Patterns Algebra Grade 4 Addition Subtraction Grade 4 Multiplication Division 11 3P Learning

15 BC Grade 4 Str Substr Outcome Outcome Description Activities ebooks Number Number BC.4.A6 Number Number BC.4.A7 Number Number BC.4.A8 Demonstrate an understing of multiplication (2- or 3-digit by 1-digit) to solve problems by using personal strategies for multiplication with without concrete materials using arrays to represent multiplication connecting concrete representations to symbolic epresentations estimating products. Demonstrate an understing of division (1-digit divisor up to 2-digit dividend) to solve problems by using personal strategies for dividing with without concrete materials estimating quotients relating division to multiplication. Demonstrate an understing of fractions less than or equal to one by using concrete pictorial representations to name record fractions for the parts of a whole or a set compare order fractions model explain that for different wholes, two identical fractions may not represent the same quantity provide examples of where fractions are used. Multiply: 1-Digit Number, Regroup Multiply: 2-Digit Number, Regroup Multiplication Facts Multiplication Arrays Multiply: 2-Digit by 1-Digit Multiply Multiples of 10 Multiply More Multiples of 10 Times Tables Multiplication Properties Arrays 1 Multiplication Grids Missing Numbers: x Equivalent Facts; Multiply Multiplication Problems 1 Multiply 3 single-digit numbers Estimation: Multiply Divide Problems: Multiply Divide Multiply Divide Problems 1 Dividing Tens Fact Families: Multiply Divide Division Facts Remainders by Arrays Divide: 1-Digit Divisor 1 Divide: 1-Digit Divisor 2 Divide: 1-Digit Divisor, Remainder Dividing Sixes Dividing Sevens Dividing Eights Dividing Nines Model Fractions Comparing Fractions 1 Counting with Fractions on a Number Line Part-whole rods 2 Shading Equivalent Fractions Shape Fractions Partition into equal parts Fraction Fruit Sets 1 Equivalent Fraction Wall 1 Grade 4 Multiplication Division Grade 4 Multiplication Division Grade 4 Fractions 3P Learning 12

16 BC Grade 4 Str Substr Outcome Outcome Description Activities ebooks Number Number BC.4.A9 Number Number BC.4.A10 Number Number BC.4.A11 Patterns Patterns Patterns Patterns Patterns Patterns Patterns Patterns Patterns Patterns Variables Equations Variables Equations BC.4.B1 BC.4.B2 BC.4.B3 BC.4.B4 BC.4.B5 BC.4.B6 Describe represent decimals (tenths hundredths) concretely, pictorially, symbolically. Relate decimals to fractions (to hundredths). Demonstrate an understing of addition subtraction of decimals (limited to hundredths) by using compatible numbers estimating sums differences using mental math strategies to solve problems. Identify describe patterns found in tables charts, including a multiplication chart. Reproduce a pattern shown in a table or chart using concrete materials. Represent describe patterns relationships using charts tables to solve problems. Identify explain mathematical relationships using charts diagrams to solve problems. Express a given problem as an equation in which a symbol is used to represent an unknown number. Solve one-step equations involving a symbol to represent an unknown number. Comparing Decimals 1 Decimals on the Number Line Decimals from Words to Digits 1 Decimal Place Value Decimals to Fractions 2 Decimal Complements Rounding Decimals 1 Add Decimals 1 Subtract Decimals 1 Caroll Diagram Pick the Next Number Pattern Error Describing Patterns Decreasing Patterns Increasing Patterns Find the Missing Number 1 Missing Values Missing Values: Decimals Missing Numbers Missing Numbers: Variables I am Thinking of a Number! Bar Model Problem 2 Grade 4 Fractions Grade 4 Fractions Grade 4 Fractions Grade 4 Patterns Algebra Grade 4 Patterns Algebra Grade 4 Patterns Algebra 13 3P Learning

17 BC Grade 4 Str Substr Outcome Outcome Description Activities ebooks Shape Shape Shape Shape Shape Statistics Statistics Measurement Measurement Measurement 3-D Objects 2-D Shapes Transformations Data Analysis Data Analysis BC.4.C1 BC.4.C2 BC.4.C3 BC.4.C4 BC.4.C5 BC.4.D1 BC.4.D2 Read record time using digital analog clocks, including 24- hour clocks. Read record calendar dates in a variety of formats. Demonstrate an understing of area of regular irregular 2-D shapes by recognizing that area is measured in square units selecting justifying referents for the units cm 2 or m 2 estimating area by using referents for cm 2 or m 2 determining recording area (cm 2 or m 2 ) constructing different rectangles for a given area (cm 2 or m 2 ) in order to demonstrate that many different rectangles may have the same area. Describe construct rectangular triangular prisms. Demonstrate an understing of line symmetry by identifying symmetrical 2-D shapes creating symmetrical 2-D shapes drawing one or more lines of symmetry in a 2-D shape. Demonstrate an understing of many-to-one correspondence. Construct interpret pictographs bar graphs involving manyto-one correspondence to draw conclusions. What is the Time? 24 Hour Time Elapsed Time Time Mentals Using a Calendar Area: Squares Rectangles Area of Shapes Equal Areas Symmetry or Not? Symmetry Making Graphs Pictographs Bar Graphs 1 Bar Graphs 2 Grade 4 Time Grade 4 Time Grade 4 Length, Area Perimeter Grade 4, Shape Position Grade 4, Shape Position Grade 4 Chance Data 3P Learning 14

18 BC Grade 5 Str Substr Outcome Outcome Description Activities ebooks Number Number BC.5.A1 Represent describe whole numbers to Place value 3 Place Value to Millions Place Value 1 (x 10 10) Numbers from Words to Digits 2 Numbers from Words to Digits 3 Exping Numbers Exped Notation Rounding Numbers Nearest Thous Nearest Whole Number Estimation: Add Subtract Estimation: Multiply Divide Estimate Products Estimate Quotients Compatible Numbers Estimate Sums Estimate Differences Grade 5 Reading Understing Whole Numbers Number Number BC.5.A2 Use estimation strategies including front-end rounding compensation compatible numbers in problem-solving contexts. Grade 5 Addition Subtraction Grade 5 Multiplication Division Number Number BC.5.A3 Apply mental mathematics strategies number properties, such as skip counting from a known fact using doubling or halving using patterns in the 9s facts using repeated doubling or halving to determine answers for basic multiplication facts to 81 related division facts. Apply mental mathematics strategies for multiplication, such as annexing then adding zero halving doubling using the distributive property. Mental Methods Multiplication 1 Mental Methods Division Fact Families: Multiply Divide Grade 5 Multiplication Division Number Number BC.5.A4 Halve it! Doubles Near Doubles Grade 5 Multiplication Division Number Number BC.5.A5 Demonstrate an understing of multiplication (2-digit by 2-digit) to solve problems. Mental Methods Multiplication 1 Mental Methods Multiplication 2 Fact Families: Multiply Divide Multiply Multiples of 10 Multiply More Multiples of 10 Multiply: 2-Digit by 1-Digit Multiply: 2-Digit Number, Regroup Multiply 2 Digits Area Model Grade 5 Multiplication Division 15 3P Learning

19 BC Grade 5 Str Substr Outcome Outcome Description Activities ebooks Number Number BC.5.A6 Number Number BC.5.A7 Number Number BC.5.A8 Number Number BC.5.A9 Number Number BC.5.A10 Number Number BC.5.A11 Demonstrate, with without concrete materials, an understing of division (3-digit by 1-digit) interpret remainders to solve problems. Demonstrate an understing of fractions by using concrete pictorial representations to create sets of equivalent fractions compare fractions with like unlike denominators. Describe represent decimals (tenths, hundredths, thousths) concretely, pictorially, symbolically. Relate decimals to fractions (to thousths). Compare order decimals (to thousths) by using benchmarks place value equivalent decimals. Demonstrate an understing of addition subtraction of decimals (limited to thousths). Divisibility Tests Divisibility Tests (3, 4, 9) Divisibility Tests (2, 5, 10) Tests of Divisibility 1 Divide: 1-Digit Divisor, Remainder Divide: 1-Digit Divisor 1 Divide: 1-Digit Divisor 2 Mental Methods Division Remainders by Array Short Division Rounding Numbers for Division Partition into equal parts Equivalent Fractions on a Number Line 2 Equivalent Fraction Wall 1 Equivalent Fraction Wall 2 Ordering Fractions Simplifying Fractions Shading Equivalent Fractions Compare Fractions 2 Comparing Fractions 2 Equivalent Fractions Comparing Fractions 1 Decimal Place Value Rounding Decimals Rounding Decimals 1 Rounding Decimals 2 Decimals to Fractions 1 Decimals to Fractions 2 Fractions to Decimals Fractions to Decimals 2 Decimals on the Number Line Comparing Decimals 2 Adding Subtracting Decimals Adding Decimals Subtracting Decimals Decimal Complements Estimate Decimal Differences 1 Estimate Decimal Differences 2 Estimate Decimal Sums 1 Estimate Decimal Sums 2 Add Decimals 2 Missing Values: Decimals Grade 5 Multiplication Division Grade 5 Fractions, Decimals Percentages Grade 5 Fractions, Decimals Percentages Grade 5 Fractions, Decimals Percentages Grade 5 Reading Understing Whole Numbers Grade 5 Fractions, Decimals Percentages 3P Learning 16

20 BC Grade 5 Str Substr Outcome Outcome Description Activities ebooks Patterns Patterns Shape Shape Shape Shape Patterns Patterns Measurement Measurement Measurement Measurement BC.5.B1 BC.5.B2 BC.5.C1 BC.5.C2 BC.5.C3 BC.5.C4 Determine the pattern rule to make predictions about subsequent elements. Solve problems involving single-variable, one-step equations with whole number coefficients whole number solutions. Design construct different rectangles given either perimeter or area, or both (whole numbers) draw conclusions. Demonstrate an understing of measuring length (mm) by - selecting justifying referents for the unit mm - modelling describing the relationship between mm cm units, between mm m units. Demonstrate an understing of volume by - selecting justifying referents for cm 3 or m 3 units - estimating volume by using referents for cm 3 or m 3 - measuring recording volume (cm 3 or m 3 ) - constructing rectangular prisms for a given volume. Demonstrate an understing of capacity by - describing the relationship between ml L - selecting justifying referents for ml or L units - estimating capacity by using referents for ml or L - measuring recording. Magic Symbols 1 Pick the Next Number Describing Patterns I am Thinking of a Number! Solve Equations: Add, Subtract 1 Solve Equations: Multiply, Divide 1 Word Problems with Letters Perimeter of Shapes Perimeter: Squares Rectangles Perimeter Detectives 1 Perimeter Detectives 2 Area of Squares Rectangles Converting cm mm Converting Units of Length Volume: Cuboid 1 Volume: Rectangular Prisms 1 Volume: Rectangular Prisms 2 Millilitres Litres Grade 5 Patterns Algebra Grade 5 Patterns Algebra Grade 5 Length, Perimeter Area Grade 5 Length, Perimeter Area Grade 5 Volume, Capacity Mass Grade 5 Volume, Capacity Mass 17 3P Learning

21 BC Grade 5 Str Substr Outcome Outcome Description Activities ebooks Shape Shape Shape Shape Statistics Statistics Statistics Statistics 3-D Objects 2-D Shapes 3-D Objects 2-D Shapes Transformations Transformations Data Analysis Data Analysis Data Analysis Data Analysis BC.5.C5 BC.5.C6 BC.5.C7 BC.5.C8 BC.5.D1 BC.5.D2 BC.5.D3 BC.5.D4 Describe provide examples of edges faces of 3-D objects, sides of 2-D shapes that are parallel, intersecting, perpendicular, vertical horizontal. Identify sort quadrilaterals, including rectangles, squares, trapezoids, parallelograms rhombuses according to their attributes. Perform a single transformation (translation, rotation, or reflection) of a 2-D shape (with without technology) draw describe the image. Identify a single transformation, including a translation, rotation, reflection of 2-D shapes. Differentiate between firsth second-h data. Construct interpret double bar graphs to draw conclusions. Describe the likelihood of a single outcome occurring using words such as impossible, possible certain. Compare the likelihood of two possible outcomes occurring using words such as - less likely - equally likely - more likely. Faces, Edges, Vertices Faces, Edges, Vertices 1 Faces, Edges, Vertices 2 Collect the Shapes 2 Collect the Polygons Collect the Shapes 2 Shapes Grade 5 Geometry Grade 5 Geometry Grade 5 Position Transformations Grade 5 Position What are the chances? scale Grade 5 Data Representation Grade 5 Chance Data Grade 5 Chance Data 3P Learning 18

22 BC Grade 6 Str Substr Outcome Outcome Description Activities ebooks Number Number BC.6.A1 Number Number BC.6.A2 Number Number BC.6.A3 Number Number BC.6.A4 Number Number BC.6.A5 Number Number BC.6.A6 Number Number BC.6.A7 Number Number BC.6.A8 Number Number BC.6.A9 Demonstrate an understing of place value for numbers - greater than one million - less than one thousth. Solve problems involving large numbers, using technology. Demonstrate an understing of factors multiples by - determining multiples factors of numbers less than identifying prime composite numbers - solving problems involving multiples. Relate improper fractions to mixed numbers. Demonstrate an understing of ratio, concretely, pictorially, symbolically. Demonstrate an understing of percent (limited to whole numbers) concretely, pictorially, symbolically. Demonstrate an understing of integers, concretely, pictorially, symbolically. Demonstrate an understing of multiplication division of decimals (1-digit whole number multipliers 1-digit natural number divisors). Explain apply the order of operations, excluding exponents, with without technology (limited to whole numbers). Comparing Numbers Rounding Decimals 2 Decimal Order Place Value to Millions Numbers from Words to Digits 3 Place Value 2 (x10 10) Prime or Composite? Multiples Factors Find the Factor Prime Factorization Fit the conditions 1 Identifying Fractions Beyond 1 Mixed to Improper Improper to Mixed Mixed Improper Fractions on a Number Line Ratios Ratio Word Problems Percent of a Number Calculating Percentages Modelling Percentages Comparing Integers Ordering Integers Integers on a number line Money Problems: Four Operations Decimal by Whole Number Divide Decimal by Whole Number Order of Operations 1 (BEDMAS) Grade 6 Reading Understing Whole Numbers Grade 6 Fractions, Decimals Percentages Grade 6 Fractions, Decimals Percentages Grade 7 Directed Numbers Grade 6 Fractions, Decimals Percentages 19 3P Learning

23 BC Grade 6 Str Substr Outcome Outcome Description Activities ebooks Patterns Patterns Patterns Patterns Patterns Patterns Patterns Patterns BC.6.B1 BC.6.B2 BC.6.B3 BC.6.B4 Shape Measurement BC.6.C1 Shape Measurement BC.6.C2 Shape Shape 3-D Objects 2-D Shapes 3-D Objects 2-D Shapes BC.6.C3 BC.6.C4 Demonstrate an understing of the relationships within tables of values to solve problems. Represent describe patterns relationships using graphs tables. Represent generalizations arising from number relationships using equations with letter variables. Demonstrate explain the meaning of preservation of equality concretely, pictorially, symbolically. Demonstrate an understing of angles. Demonstrate that the sum of interior angles is: 180 in a triangle 360 in a quadrilateral. Develop apply a formula for determining the perimeter of polygons, area of rectangles, volume of right rectangular prisms. Construct compare triangles, including scalene, isosceles, equilateral, right, obtuse, acute in different orientations. Find the Pattern Rule Pattern Rules Tables Table of Values Find the Pattern Rule Pattern Rules Tables Table of Values Describing Patterns Find the Pattern Rule Pattern Rules Tables Table of Values Write an Equation: Word Problems Find the Missing Number 2 Missing Values: Decimals Magic Symbols 2 Solve Equations: Add, Subtract 1 Solve Equations: Add, Subtract 2 Solve Equations: Multiply, Divide 1 Solve Equations: Multiply, Divide 2 Solving Simple Equations Classifying Angles Estimating Angles Labelling Angles Measuring Angles Angle Measures in a Triangle Angle sum of a quadrilateral Perimeter: Squares Rectangles Perimeter Detectives 2 Area: Squares Rectangles Perimeter: Triangles Volume: Rectangular Prisms 1 Triangle Tasters Triangles: Acute, Right, Obtuse Grade 6 Patterns Algebra Grade 6 Patterns Algebra Grade 6 Patterns Algebra Grade 6 Patterns Algebra Grade 6 Geometry Grade 6 Geometry Grade 6 Length, Perimeter Area Grade 6 Geometry 3P Learning 20

24 BC Grade 6 Str Substr Outcome Outcome Description Activities ebooks Shape Shape Shape Shape Shape Statistics Statistics Statistics Statistics 3-D Objects 2-D Shapes Transformations Transformations Transformations Transformations Data Analysis Data Analysis Data Analysis Data Analysis BC.6.C5 BC.6.C6 BC.6.C7 BC.6.C8 BC.6.C9 BC.6.D1 BC.6.D2 BC.6.D3 BC.6.D4 Describe compare the sides angles of regular irregular polygons. Perform a combination of translation(s), rotation(s) / or reflection(s) on a single 2-D shape, with without technology, draw describe the image. Perform a combination of successive transformations of 2-D shapes to create a design, identify describe the transformations. Identify plot points in the first quadrant of a Cartesian plane using whole number ordered pairs. Perform describe single transformations of a 2-D shape in the first quadrant of a Cartesian plane (limited to whole number vertices). Create, label, interpret line graphs to draw conclusions. Select, justify, use appropriate methods of collecting data. Graph collected data analyze the graph to solve problems. Demonstrate an understing of probability. Collect the Polygons Count Sides Corners Coordinate Graphs: 1st Quadrant Transformations: Coordinate Plane Line Graphs: Interpretation Data Types Circle Graphs Stem Leaf Plots Counting Principle Find the Complementary events with replacement without replacement Grade 6 Geometry Grade 6 Geometry Grade 6 Geometry Grade 7 The Number Plane Grade 7 The Number Plane Grade 6 Data Representation Grade 6 Data Representation Grade 6 Data Representation Grade 6 Chance 21 3P Learning

25 BC Grade 7 Str Substr Outcome Outcome Description Activities ebooks Number Number BC.7.A1 Number Number BC.7.A2 Number Number BC.7.A3 Number Number BC.7.A4 Number Number BC.7.A5 Determine explain why a number is divisible by 2, 3, 4, 5, 6, 8, 9, or 10 why a number cannot be divided by 0. Demonstrate an understing of the addition, subtraction, multiplication, division of decimals (for more than 1-digit divisors or 2-digit multipliers, the use of technology is expected) to solve problems. Solve problems involving percents from 1% to 100%. Demonstrate an understing of the relationship between positive repeating decimals positive fractions, positive terminating decimals positive fractions. Demonstrate an understing of adding subtracting positive fractions mixed numbers, with like unlike denominators, concretely, pictorially, symbolically (limited to positive sums differences). Divisibility Tests Divisibility Tests (2, 5, 10) Divisibility Tests (3, 4, 9) Adding Decimals Subtracting Decimals Adding Subtracting Decimals Decimal by Whole Number Decimal by Decimal Divide Decimal by Decimal Significant Figures Divide Decimal by Whole Number Percents to Fractions Percentage of a Quantity Calculating Percentages Percentage Word Problems Percent Increase Decrease Percentage Composition Percents Decimals Recurring Decimals Fractions to Decimals Decimals to Fractions 1 Decimals to Fractions 2 Rounding Significant Figures Add Like Fractions Subtract Like Fractions Add: Common Denominator Add Unlike Fractions Least Common Multiple Add: No Common Denominator Add Like Mixed Numbers Add Unlike Mixed Numbers Subtract: Common Denominator Subtract: No Common Denominator Subtract Like Mixed Numbers Subtract Unlike Mixed Numbers Subtract Mixed Numbers: Renaming Subtract Unlike Fractions Converting Mixed Improper Grade 7 Whole Numbers Grade 7 Decimals Grade 7 Percentage Basics Grade 7 Decimals Grade 7 Fractions 3P Learning 22

26 BC Grade 7 Str Substr Outcome Outcome Description Activities ebooks Number Number BC.7.A6 Number Number BC.7.A7 Patterns hips Patterns hips Patterns hips Patterns hips Patterns hips Patterns Patterns Variables Equations Variables Equations Variables Equations BC.7.B1 BC.7.B2 BC.7.B3 BC.7.B4 BC.7.B5 Demonstrate an understing of addition subtraction of integers, concretely, pictorially, symbolically. Compare order positive fractions, positive decimals (to thousths) whole numbers. Demonstrate an understing of oral written patterns their equivalent linear relations. Create a table of values from a linear relation, graph the table of values, analyze the graph to draw conclusions solve problems. Demonstrate an understing of preservation of equality. Explain the difference between an expression an equation. Evaluate an expression given the value of the variable(s). Integers: Add Subtract More with Integers Integers: Subtraction Add Integers Subtract Integers Integers: Order of Operations (BEDMAS) Integers on a Number Line Ordering Integers Ordering Fractions Comparing Fractions 2 Comparing Decimals 1 Decimals on the Number Line Decimal Order 1 Decimal Order 2 Absolute Value Rounding Significant Figures Find the Pattern Rule Pattern Rules Tables Table of Values Pattern Rules Tables Graphing from a Table of Values Find the Function Rule Determining the Rule for a Line Recognising Like Terms Like Terms: Add Subtract Solving Simple Equations Solve Equations: Add, Subtract 2 Algebraic Multiplication Solve Equations: Multiply, Divide 2 Algebraic Fractions 1 Dividing Expressions Algebra Tiles Like Terms: Add Subtract Algebraic Multiplication Algebraic Fractions 1 Dividing Expressions Algebra Tiles Simple Substitution 1 Simple Substitution 2 Complex Substitution Grade 7 Directed Numbers Grade 7 Fractions Grade 8 Linear hips Grade 8 Linear hips Grade 7 Algebra Basics Grade 8 Equations Grade 7 Algebra Basics 23 3P Learning

27 BC Grade 7 Str Substr Outcome Outcome Description Activities ebooks Patterns hips Patterns hips Shape Shape Shape Variables Equations Variables Equations Measurement Measurement 3-D Objects 2-D Shapes BC.7.B6 BC.7.B7 BC.7.C1 BC.7.C2 BC.7.C3 Model solve problems that can be represented by one-step linear equations of the form x + a=b, concretely, pictorially, symbolically, where a b are integers. Model solve problems that can be represented by linear equations or equations with fractions. Demonstrate an understing of circles by describing the relationships among radius, diameter, circumference of circles, relating circumference to pi, determining the sum of the central angles, constructing circles with a given radius or diameter, solving roblems involving the radii, diameters, circumferences of circles. Develop apply a formula for determining the area of triangles, parallelograms circles. Perform geometric constructions, including -perpendicular line segments -parallel line segments -perpendicular bisectors -angle bisectors. Writing Equations Solve Equations: Add, Subtract 1 Solve Equations: Add, Subtract 2 Solving Simple Equations Solving More Equations Equations with Grouping Symbols Solve Multi-Step Equations Equations with Decimals Equations: Variables, Both Sides Equations with Fractions Equations to Solve Problems Writing Equations Solve Equations: Add, Subtract 1 Solve Equations: Add, Subtract 2 Solving Simple Equations Solving Simple Equations Solving More Equations Equations with Grouping Symbols Solve Multi-Step Equations Equations with Decimals Equations: Variables, Both Sides Equations with Fractions Equations to Solve Problems Circumference: Circles Angles in a Revolution Circle Terms Area: Squares Rectangle Area: Right Angled Triangles Area: Quadrilaterals Area: Circles Area: Triangles Grade 8 Equations Grade 8 Equations Grade 8 Area Perimeter Grade 8 Constructions 3P Learning 24

28 BC Grade 7 Str Substr Outcome Outcome Description Activities ebooks Shape Shape Transformations Transformations BC.7.C4 BC.7.C5 Identify plot points in the four quadrants of a Cartesian plane using integral ordered pairs. Perform describe transformations (translations, rotations or reflections) of a 2-D shape in all four quadrants of a Cartesian plane (limited to integral number vertices). Vertical horizontal shift Ordered Pairs Graphing from a Table of Values Transformations: Coordinate Plane Rotations: Coordinate Plane Flip, Slide, Turn Transformations Rotational Symmetry Symmetry or Not? Grade 7 The Number Plane Grade 7 The Number Plane Statistics Data Analysis BC.7.D1 Demonstrate an understing of central tendency range by - determining the measures of central tendency (mean, median, mode) range - determining the most appropriate measures of central tendency to report findings. Mean Median Mode Line Graphs: Interpretation Data Extremes Range Data Statistics Statistics Statistics Statistics Statistics 25 3P Learning Data Analysis Data Analysis Chance Uncertainty Chance Uncertainty Chance Uncertainty BC.7.D2 BC.7.D3 BC.7.D4 BC.7.D5 BC.7.D6 Determine the effect on the mean, median, mode when an outlier is included in a data set. Construct, label, interpret circle graphs to solve problems. Express probabilities as ratios, fractions, percents. Identify the sample space (where the combined sample space has 36 or fewer elements) for a probability experiment involving two independent events. Conduct a probability experiment to compare the theoretical probability (determined using a tree diagram, table or another graphic organizer) experimental probability of two independent events. Mean Median Mode Line Graphs: Interpretation Data Extremes Range Circle Graphs Pie Charts Sector Graph Calculations Pie Chart Calculations Simple Scale Find the Possible Outcomes Dice Coins Two-Way Table with Replacement without Replacement Tree Diagrams Venn Diagrams Dice Coins Two-Way Table with Replacement without Replacement Data Data Grade 7 Chance Grade 7 Chance Grade 7 Chance

29 BC Grade 8 Str Substr Outcome Outcome Description Activities ebooks Number Number BC.8.A1 Number Number BC.8.A2 Number Number BC.8.A3 Number Number BC.8.A4 Number Number BC.8.A5 Demonstrate an understing of perfect squares square roots, concretely, pictorially, symbolically (limited to whole numbers). Determine the approximate square root of numbers that are not perfect squares (limited to whole numbers). Demonstrate an understing of percents greater than or equal to 0%. Demonstrate an understing of ratio rate. Solve problems that involve rates, ratios, proportional reasoning. Square Roots Square Roots 1 Estimating Square Roots Decimal to Percentage Profit Loss Solve Percent Equations Percentage Word Problems Percent Increase Decrease Percentage Composition Percentage of a Quantity Sector Graphs Ratio Simplify Ratios: 2 Whole Numbers Unitary Method Dividing a Quantity in a Ratio Ratio Word Problems Equivalent Ratios Ratio Proportion Rates Rate Word Problems Ratio Unitary Method Dividing a Quantity in a Ratio Ratio Word Problems Equivalent Ratios Rates Rate Word Problems Time Taken Average Speed Distance Travelled Using Similar Triangle Exponents Grade 8 Percentage Calculations Decimals Decimals 3P Learning 26

30 BC Grade 8 Str Substr Outcome Outcome Description Activities ebooks Number Number BC.8.A6 Number Number BC.8.A7 Patterns Patterns Patterns Variables Equations BC.8.B1 BC.8.B2 Demonstrate an understing of multiplying dividing positive fractions mixed numbers, concretely, pictorially, symbolically. Demonstrate an understing of multiplication division of integers, concretely, pictorially, symbolically. Graph analyse twovariable linear relations. Model solve problems using linear equations. Fraction of an Amount Model Fractions to Multiply Multiply Two Fractions 1 Multiplying Fractions Multiply Mixed Numbers Divide Whole Number by Fraction Divide Fractions by Fractions 1 Divide by a Unit Fraction Divide Fractions Visual Model Divide Mixed Numbers Dividing Fractions Ordering Integers Comparing Integers More with Integers Integers: Multiply Divide Multiplying Dividing Integers Determining a Rule for a Line Graphing from a Table of Values Find the Pattern Rule Find the Function Rule Function Rules Tables Number Plane y=ax Which Straight Line? Equation of a Line 1 Equation of a Line 2 Equation of a Line 3 Equation from Point Gradient Equation from Two Points Writing Algebraic Expressions Equations to Solve Problems Solve Equations: Add, Subtract 2 Solving Simple Equations Algebraic Multiplication Solve Equations: Multiply, Divide 2 Equations with Grouping Symbols Recognising Like Terms Factoring Simplifying Expressions Like Terms: Add Subtract Find Slant Height Perimeter Pythagoras Grade 7 Fractions Grade 7 Directed Numbers Grade 8 Linear hips Grade 8 Straight Lines Grade 8 Simplifying Algebra Grade 8 Equations 27 3P Learning

31 BC Grade 8 Str Substr Outcome Outcome Description Activities ebooks Shape Measurement Shape Measurement Shape Measurement Shape Measurement Shape 3-D Objects 2-D Shapes Shape Transformations Statistics Statistics Data Analysis Chance Uncertainty BC.8.C1 BC.8.C2 BC.8.C3 BC.8.C4 BC.8.C5 BC.8.C6 BC.8.D1 BC.8.D2 Develop apply the Pythagorean theorem to solve problems. Draw construct nets for 3-D objects. Determine the surface area of right rectangular prisms, right triangular prisms right cylinders. Develop apply formulas for determining the volume of right prisms right cylinders. Draw interpret top, front, side views of 3-D objects composed of right rectangular prisms. Demonstrate an understing of tessellation. Critique ways in which data is presented. Solve problems involving the probability of independent events. Hypotenuse, Adjacent, Opposite Pythagoras' Theorem Pythagorean Triads Nets Surface Area: Rectangular Prisms Surface Area: Triangular Prisms Surface Area: Cylinders Volume: Rectangular Prisms 1 Volume: Triangular Prisms Volume: Prisms Volume: Cylinders Simple With Replacement Find the Dice Coins Two-Way Table without replacement Grade 8 Pythagoras Theorem Measuring Solids Measuring Solids Grade 7 Chance 3P Learning 28

32 BC Str Substr Outcome Outcome Description Activities ebooks Number Number BC.9.A1 Demonstrate an understing of powers with integral bases (excluding base 0) whole number exponents by representing repeated multiplication using powers using patterns to show that a power with an exponent of zero is equal to one solving problems involving powers. Exponents Exponent Form to Numbers The Zero Exponent Negative Exponents Highest Common Algebraic Factor Factoring Expressions Simplifying Expressions Factoring with Negatives Factoring with Exponents Real Formulae Properties of Exponents Simplifying with Exponent Laws 1 Exponent Form to Numbers Exponent Notation Algebra Zero Exponent Algebra Exponent Laws Algebra Exponent Laws with Brackets Exponents Number Number BC.9.A2 Demonstrate an understing of operations on powers with integral bases (excluding base 0) whole number exponents. Exponents 29 3P Learning

33 BC Str Substr Outcome Outcome Description Activities ebooks Number Number BC.9.A3 Number Number BC.9.A4 Number Number BC.9.A5 Number Number BC.9.A6 Demonstrate an understing of rational numbers by comparing ordering rational numbers solving problems that involve arithmetic operations on rational numbers. Explain apply the order of operations, including exponents, with without technology. Determine the square root of positive rational numbers that are perfect squares. Determine an approximate square root of positive rational numbers that are non-perfect squares. Equivalent Fractions Simplifying Fractions Converting Mixed Improper Mixed to Improper Improper to Mixed Comparing Fractions with Signs Add Unlike Fractions Subtract: No Common Denominator Multiply Fraction by Whole Number Unit Fractions Fractions to Decimals Decimals to Fractions 1 Decimal Order Decimals on the Number Line Add Decimals 2 Subtracting Decimals Subtract Decimals 1 Multiply Decimals: 10, 100, 1000 Divide Decimals: 10, 100, 1000 Decimal by Whole Number Calculating Percentages Percent of a Number Multiplying Fractions Multiply Two Fractions 1 Dividing Fractions Divide Fractions by Fractions 1 Decimals to Fractions 2 Percents to Fractions Percentage Increase Decrease Fraction Word Problems Ordering Fractions Multiplication with Exponents Integers: Order of Operations (BEDMAS) Square Roots Estimating Square Roots Estimating Square Roots Grade 7 Fractions Exponents Exponents Exponents 3P Learning 30

34 BC Str Substr Outcome Outcome Description Activities ebooks Patterns Realtionships Patterns Realtionships Patterns Realtionships Patterns Realtionships Patterns Realtionships Patterns Patterns Variables Equations Variables Equations Variables Equations BC.9.B1 BC.9.B2 BC.9.B3 BC.9.B4 BC.9.B5 Generalize a pattern arising from a problem-solving context using linear equations verify by substitution. Graph linear relations, analyse the graph, interpolate or extrapolate to solve problems. Model solve problems using linear equations. Explain illustrate strategies to solve single variable linear inequalities with rational coefficients within a problem-solving context. Demonstrate an understing of polynomials (limited to polynomials of degree less than or equal to 2). Find the Pattern Rule y=ax Direct Variation Pattern Rules Tables Which Straight Line? Determining a Rule for a Line Equation of a Line 1 Horizontal Vertical Lines y=ax Intercepts Gradient Slope of a Line Algebraic Fractions 1 Dividing Expressions Equations with Grouping Symbols Solving Simple Equations Solving More Equations Solve Equations: Multiply, Divide 2 Equations with Fractions Equations with Fractions 2 Solve Multi-Step Equations Checking Solutions Find the Mistake Solve Equations: Add, Subtract 2 Equations with Decimals Solving Inequalities 1 Solving Inequalities 2 Linear hips Linear hips Grade 8 Equations Equations Inequalities Equations Inequalities Grade 8 Exping Factorising Grade 8 Simplifying Algebra Simplifying Algebra 31 3P Learning

35 BC Str Substr Outcome Outcome Description Activities ebooks Patterns Realtionships Patterns Realtionships Shape Shape Shape Shape Variables Equations Variables Equations Measurement 3-D Objects 2-D Shapes 3-D Objects 2-D Shapes BC.9.B6 BC.9.B7 BC.9.C1 BC.9.C2 BC.9.C3 Transformations BC.9.C4 Model, record, explain the operations of addition subtraction of polynomial expressions, concretely, pictorially, symbolically (limited to polynomials of degree less than or equal to 2). Model, record, explain the operations of multiplication division of polynomial expressions (limited to polynomials of degree less than or equal to 2) by monomials, concretely, pictorially, symbolically. Solve problems justify the solution strategy using circle properties. Determine the surface area of composite 3-D objects to solve problems. Demonstrate an understing of similarity of polygons. Draw interpret scale diagrams of 2-D shapes. Recognising Like Terms Like Terms: Add Subtract Exping with Negatives Exping Brackets Exping Binomial Products Special Binomial Products Exp then Simplify Exping with Negatives Exping Brackets Exping Binomial Products Special Binomial Products Circle Theorem Surface Area: Rearrange Formula Surface Area: Rectangular Pyramids Surface Area: Rectangular Prisms Surface Area: Cuboids Surface Area: Cylinders Surface Area: Triangular Prisms Surface Area: Square Pyramids Surface Area: Spheres Surface Area: Cones Similar Figures Using Similar Triangles Similar Areas Volumes Scale Factor Scale Measurement Grade 8 Exping Factorising Grade 8 Simplifying Algebra Simplifying Algebra Grade 8 Exping Factorising Grade 8 Simplifying Algebra Simplifying Algebra Grade 10 Chords Angles Grade 10 Tangents Secants Measuring Solids Similarity Congruence 3P Learning 32

36 BC Str Substr Outcome Outcome Description Activities ebooks Shape Transformations BC.9.C5 Demonstrate an understing of line rotation symmetry. Symmetry or Not? Rotational Symmetry Statistics Data Analysis BC.9.D1 Describe the effect of bias use of language ethics cost time timing privacy cultural sensitivity on the collection of data. Statistics Data Analysis BC.9.D2 Select defend the choice of using either a population or a sample of a population to answer a question. Statistics Data Analysis BC.9.D3 Develop implement a project plan for the collection, display, analysis of data by formulating a question for investigation choosing a data collection method that includes social considerations selecting a population or a sample collecting the data displaying the collected data in an appropriate manner drawing conclusions to answer the question. Statistics Chance Uncertainty BC.9.D4 Demonstrate an understing of the role of probability in society. Without Replacement Two-way Table - 'And' 'Or' Simple Scale Tables With Replacement Find the 33 3P Learning

37 BC Apprenticeship Workplace 10 Str Outcome Outcome Description Activities ebooks Measurement BC.10.AW.M.1a Describing the relationships of the units for length, area, volume, capacity, mass temperature using SI units. Centimetres Metres Converting cm mm Kilometre Conversions Metres Kilometres Converting Units of Length Nautical Mile, Kilometre, Knot Measuring Length Operations with Length Converting Units of Area Perimeter: Composite Shapes Perimeter Circles Perimeter: Triangles Perimeter Perimeter of Shapes Perimeter: Squares Rectangles Area: Squares Rectangles Area: Triangles Area: Right Triangles Area: Circles 1 Area: Circles 2 Area: Quadrilaterals Volume: Prisms Volume: Pyramids Volume: Rectangular Prisms 1 Volume: Cylinders Surface Area: Rectangular Prisms Surface Area: Rectangular Pyramids Surface Area: Square Pyramids Surface Area: Spheres Surface Area: Cylinders Surface Area: Cones Nets Grams Kilograms Kilogram Conversions Grams Milligrams Converting Units of Mass Millilitres Litres Temperature Grade 7 Converting Units Grade 7 Area Perimeter Measuring Solids 3P Learning 34

38 BC Apprenticeship Workplace 10 Str Outcome Outcome Description Activities ebooks Measurement BC.10.AW.M.1b Applying strategies to convert SI units to imperial units. Centimetres Metres Converting cm mm Kilometre Conversions Metres Kilometres Converting Units of Length Nautical Mile, Kilometre, Knot Measuring Length Operations with Length Converting Units of Area Perimeter: Composite Shapes Perimeter Circles Perimeter: Triangles Perimeter Perimeter of Shapes Perimeter: Squares Rectangles Area: Squares Rectangles Area: Triangles Area: Right Triangles Area: Circles 1 Area: Circles 2 Area: Quadrilaterals Volume: Prisms Volume: Pyramids Volume: Rectangular Prisms 1 Volume: Cylinders Grams Kilograms Kilogram Conversions Grams Milligrams Converting Units of Mass Millilitres Litres Temperature 35 3P Learning

39 BC Apprenticeship Workplace 10 Str Outcome Outcome Description Activities ebooks Measurement BC.10.AW.M.2a Describing the relationships of the units for length, area, volume, capacity, mass temperature in Imperial units. Centimetres Metres Converting cm mm Kilometre Conversions Metres Kilometres Converting Units of Length Nautical Mile, Kilometre, Knot Measuring Length Converting Units of Area Operations with Length Perimeter: Composite Shapes Perimeter Circles Perimeter: Triangles Perimeter Perimeter of Shapes Perimeter: Squares Rectangles Area: Squares Rectangles Area: Triangles Area: Right Angled Triangles Area: Circles 1 Area: Circles 2 Area: Quadrilaterals Volume: Prisms Volume: Pyramids Volume: Rectangular Prisms 1 Volume: Cylinders Grams Kilograms Kilogram Conversions Grams Milligrams Converting Units of Mass Millilitres Litres Temperature 3P Learning 36

40 BC Apprenticeship Workplace 10 Str Outcome Outcome Description Activities ebooks Measurement BC.10.AW.M.2b Comparing the American British imperial units for capacity. Centimetres Metres Converting cm mm Kilometre Conversions Metres Kilometres Converting Units of Length Nautical Mile, Kilometre, Knot Measuring Length Converting Units of Area Operations with Length Perimeter: Composite Shapes Perimeter Circles Perimeter: Triangles Perimeter Perimeter of Shapes Perimeter: Squares Rectangles Area: Squares Rectangles Area: Triangles Area: Right Triangles Area: Circles 1 Area: Circles 2 Area: Quadrilaterals Volume: Prisms Volume: Pyramids Volume: Rectangular Prisms 1 Volume: Cylinders Grams Kilograms Kilogram Conversions Grams Milligrams Converting Units of Mass Millilitres Litres Temperature 37 3P Learning

41 BC Apprenticeship Workplace 10 Str Outcome Outcome Description Activities ebooks Measurement BC.10.AW.M.2c Applying strategies to convert imperial units to SI units. Centimetres Metres Converting cm mm Kilometre Conversions Metres Kilometres Converting Units of Length Nautical Mile, Kilometre, Knot Measuring Length Converting Units of Area Operations with Length Perimeter: Composite Shapes Perimeter Circles Perimeter: Triangles Perimeter Perimeter of Shapes Perimeter: Squares Rectangles Area: Squares Rectangles Area: Triangles Area: Right Triangles Area: Circles 1 Area: Circles 2 Area: Quadrilaterals Volume: Prisms Volume: Pyramids Volume: Rectangular Prisms 1 Volume: Cylinders Grams Kilograms Kilogram Conversions Grams Milligrams Converting Units of Mass Millilitres Litres Temperature 3P Learning 38

42 BC Apprenticeship Workplace 10 Str Outcome Outcome Description Activities ebooks Measurement BC.10.AW.M.3 Solve verify problems that involve SI imperial linear measurements, including decimal fractional measurements. Centimetres Metres Converting cm mm Kilometre Conversions Metres Kilometres Converting Units of Length Nautical Mile, Kilometre, Knot Measuring Length Converting Units of Area Operations with Length Perimeter: Composite Shapes Perimeter Circles Perimeter: Triangles Perimeter Perimeter of Shapes Perimeter: Squares Rectangles Area: Squares Rectangles Area: Triangles Area: Right Triangles Area: Circles 1 Area: Circles 2 Area: Quadrilaterals Volume: Prisms Volume: Pyramids Volume: Rectangular Prisms 1 Volume: Cylinders Grams Kilograms Kilogram Conversions Grams Milligrams Converting Units of Mass Millilitres Litres Temperature 39 3P Learning

43 BC Apprenticeship Workplace 10 Str Outcome Outcome Description Activities ebooks Measurement Geometry Geometry Geometry Geometry Geometry Geometry Number BC.10.AW.M.4 BC.10.AW.G.1 BC.10.AW.G.2 BC.10.AW.G.3 BC.10.AW.G.4 BC.10.AW.G.5 BC.10.AW.G.6 BC.10.AW.N.1 Solve problems that involve SI imperial area measurements of regular, composite irregular 2-D shapes 3-D objects, including decimal fractional measurements, verify the solutions. Analyze puzzles games that involve spatial reasoning, using problem-solving strategies. Demonstrate an understing of the Pythagorean theorem. Demonstrate an understing of similarity of convex polygons, including regular irregular polygons. Demonstrate an understing of primary trigonometric ratios (sine, cosine, tangent). Solve problems that involve parallel, perpendicular transversal lines, pairs of angles formed between them. Demonstrate an understing of angles, including acute, right, obtuse, straight reflex. Solve problems that involve unit pricing currency exchange, using proportional reasoning. Area: Squares Rectangles Area: Triangles Area: Right Angled Triangles Area: Circles 1 Area: Circles 2 Area: Quadrilaterals Volume: Composite Figures Volume: Prisms Volume: Pyramids Volume: Rectangular Prisms 1 Volume: Cylinders Nets Surface Area: Square Pyramids Surface Area: Cones Surface Area: Rectangular Pyramids Surface Area: Rectangular Prisms Pythagorean Theorem Pythagorean Triads Similar Figures Using Similar Triangles Similarity Proofs Similar Areas Volumes Sin A Cos A Tan A Elevation Depression Find Unknown Angles Find Unknown Sides Sides, Angles Diagonals Exterior Angles of a Triangle Equal, Complement or Supplement? Angles Parallel Lines Interior Exterior Angles Parallel Lines Measuring Angles Classifying Angles Best Buy Grade 7 Converting Units Grade 7 Area Perimeter Measuring Solids Grade 8 Pythagoras Theorem Similarity Congruence Trigonometry Grade 7 Angles Grade 7 Angles Decimals 3P Learning 40

44 BC Apprenticeship Workplace 10 Str Outcome Outcome Description Activities ebooks Number BC.10.AW.N.2 Demonstrate an understing of income, including wages, salary, contracts, commissions piecework. Wages Salaries Commission Piecework Royalties Budgeting Earning Money Algebra BC.10.AW.A.1 Solve problems that require the manipulation application of formulas related to perimeter, area, the Pythagorean theorem, primary trigonometric ratios income. Constructing Formulae Volume: Rearrange Formula Surface Area: Rearrange Formula Substitution in Formulae Real Formulae More Substitution in Formulae Measuring Solids 41 3P Learning

45 BC Foundations Pre-calculus 10 Str Outcome Outcome Description Activities ebooks Measurement Measurement BC.10.FP.M.1 BC.10.FP.M.2 Solve problems that involve linear measurement, using SI imperial units of measure, estimation strategies measurement strategies. Apply proportional reasoning to problems that involve conversions between SI imperial units of measure. Centimetres Metres Converting cm mm Kilometre Conversions Metres Kilometres Converting Units of Length Nautical Mile, Kilometre, Knot Measuring Length Operations with Length Perimeter: Composite Shapes Perimeter Circles Perimeter: Triangles Perimeter: Triangles 2 Perimeter Perimeter of Shapes Perimeter: Squares Rectangles 1 Grams Kilograms Kilogram Conversions Grams Milligrams Converting Units of Mass Millilitres Litres Temperature Centimetres Metres Converting cm mm Kilometre Conversions Metres Kilometres Converting Units of Length Nautical Mile, Kilometre, Knot Measuring Length Operations with Length Perimeter: Composite Shapes Perimeter Circles Perimeter: Triangles Perimeter: Triangles 2 Perimeter Perimeter of Shapes Perimeter: Squares Rectangles 1 Grams Kilograms Kilogram Conversions Grams Milligrams Converting Units of Mass Millilitres Litres Temperature Grade 7 Converting Units Grade 7 Area Perimeter Measuring Solids Grade 7 Converting Units Grade 7 Area Perimeter Measuring Solids Similarity Congruence 3P Learning 42

46 BC Foundations Pre-calculus 10 Str Outcome Outcome Description Activities ebooks Measurement Measurement Algebra Number Algebra Number BC.10.FP.M.3 BC.10.FP.M.4 BC.10.FP.AN.1 BC.10.FP.AN.2 Solve problems, using SI imperial units, that involve the surface area volume of 3-D objects, including right cones, right cylinders, right prisms, right pyramids spheres. Develop apply the primary trigonometric ratios (sine, cosine, tangent) to solve problems that involve right triangles. Demonstrate an understing of factors of whole numbers by determining the prime factors, greatest common factor, least common multiple, square root cube root. Demonstrate an understing of irrational numbers by representing, identifying simplifying irrational numbers, ordering irrational numbers. Surface Area: Rectangular Prisms Surface Area: Cuboids Surface Area: Cylinders Surface Area: Triangular Prisms Surface Area: Square Pyramids Surface Area: Spheres Surface Area: Cones Surface Area: Rearrange Formula Surface Area: Rectangular Pyramids Volume: Rectangular Prisms 1 Volume: Cuboid 1 Converting Volume Volume: Rectangular Prisms 2 Volume: Cuboid 2 Volume: Cylinders Volume: Triangular Prisms Volume: Triangular Prisms 1 Volume: Composite Figures Volume: Prisms Volume: Pyramids Volume: Cones Volume: Spheres Sin A Cos A Tan A Find Unknown Angles Find Unknown Sides Elevation Depression Pythagoras Theorem Hypotenuse of a Right Triangle Using Similar Triangles Using SImilar Triangles 1 Greatest Common Factor Factors Multiples Least Common Multiple Irrational Numbers Simplifying Irrational Numbers Adding Subtracting Irrational Numbers Multiplying Irrational Numbers Exping Irrational Number Expressions Dividing Irrational Numbers Exping Binomial Irrational Numbers Grade 7 Converting Units Grade 7 Area Perimeter Measuring Solids Similarity Congruence Trigonometry Grade 7 Whole Numbers Grade 10 Irrational Numbers Exponents 43 3P Learning

47 BC Foundations Pre-calculus 10 Str Outcome Outcome Description Activities ebooks Algebra Number Algebra Number Algebra Number BC.10.FP.AN.3 BC.10.FP.AN.4 BC.10.FP.AN.5 BC.10.FP.RF.1 BC.10.FP.RF.2 Demonstrate an understing of powers with integral rational exponents. Demonstrate an understing of the multiplication of polynomial expressions (limited to monomials, binomials trinomials), concretely, pictorially symbolically. Demonstrate an understing of common factors trinomial factoring, concretely, pictorially symbolically. Interpret explain the relationships among data, graphs situations. Demonstrate an understing of relations functions. Exponents Properties of Exponents Exponent Notation Negative Exponents Multiplication Division with Exponents Multiplication with Exponents Integer Exponents Exping Binomial Products Special Binomial Products Exping with Negatives Exping Brackets Factoring Expressions Factoring with Exponents Factoring with Negatives Factoring Factoring Quadratics 1 Factoring Quadratics 2 Factoring Fractions 1 Factoring Fractions 2 Highest Common Algebraic Factor Pattern Rules Tables Function Rules Tables Graphing from a Table of Values Graphing from a Table of Values 2 Ordered Pairs Pattern Rules Tables Function Rules Tables Graphing from a Table of Values Graphing from a Table of Values 2 Ordered Pairs Exponents Grade 10 Irrational Numbers Exponents Grade 8 Exping Factorising Grade 8 Simplifying Algebra Simplifying Algebra Grade 10 Factorising Grade 10 Quadratic Equations Grade 8 Linear hips Grade 8 Straight Lines Linear hips Grade 10 Straight Lines Grade 10 Parabolas Grade 10 Simple Non Linear Graphs Grade 8 Linear hips Grade 8 Straight Lines Linear hips Grade 10 Straight Lines Grade 10 Parabolas Grade 10 Simple Non Linear Graphs 3P Learning 44

48 BC Foundations Pre-calculus 10 Str Outcome Outcome Description Activities ebooks BC.10.FP.RF.3 Demonstrate an understing of slope with respect to rise run, line segments lines, rate of change, parallel lines perpendicular lines. Slope of a Line y=ax Gradients for Real Gradient Are they Parallel? Are they Perpendicular? Grade 8 Linear hips Grade 8 Straight Lines Linear hips Grade 10 Straight Lines BC.10.FP.RF.4 Describe represent linear relations, using words, ordered pairs, tables of values, graphs equations. Equation from Point Gradient Equation from Two Points Equation of a Line 1 Equation of a Line 2 Equation of a Line 3 Grade 8 Linear hips Grade 8 Straight Lines Linear hips Grade 10 Straight Lines BC.10.FP.RF.5 Determine the characteristics of the graphs of linear relations, including the intercepts, slope, domain range. Intercepts Gradient Slope of a Line Domain Range Grade 8 Linear hips Grade 8 Straight Lines Linear hips Grade 10 Straight Lines BC.10.FP.RF.6 Relate linear relations expressed in slope intercept form, general form, slope point form to their graphs. General Form of a Line Equation from Point Gradient Equation from Two Points Which Straight Line? Grade 8 Linear hips Grade 8 Straight Lines Linear hips Grade 10 Straight Lines BC.10.FP.RF.7 Determine the equation of a linear relation, given a graph, a point the slope, two points, a point the equation of a parallel or perpendicular line to solve problems. General Form of a Line Equation from Point Gradient Equation from Two Points Are they Parallel? Are they Perpendicular? Which Straight Line? Grade 8 Linear hips Grade 8 Straight Lines Linear hips Grade 10 Straight Lines BC.10.FP.RF.8 Represent a linear function, using function notation. Function Notation 1 Grade 10 BC.10.FP.RF.9 Solve problems that involve systems of linear equations in two variables, graphically algebraically. Simultaneous Equations 1 Simultaneous Equations 2 Simultaneous Linear Equations Equations Inequalities 45 3P Learning

49 BC Foundations of Mathematics 11 Str Outcome Outcome Description Activities ebooks Measurement BC.F11.A1 Measurement BC.F11.A2 Measurement BC.F11.A3 Geometry BC.F11.B1 Geometry BC.F11.B2 Geometry BC.F11.B3 Solve problems that involve the application of rates. Solve problems that involve scale diagrams, using proportional reasoning. Demonstrate an understing of the relationships among scale factors, areas, surface areas volumes of similar 2-D shapes 3-D objects. Derive proofs that involve the properties of angles triangles. Solve problems that involve the properties of angles triangles. Solve problems that involve the cosine law the sine law, including the ambiguous case. Travel Graphs Rates Word Problems Rates Average Speed Distance Travelled Converting Rates Rates Calculations Similarity Proofs Using Similar Triangles Similar Figures Scale Measurement Scale Factor Floor Plans Elevations Similar Areas Volumes Equal, Complement, or Supplement? Parallel Lines Angles in a Revolution Angles Parallel Lines Angle Sum of a Quadrilateral Angle Sum of a Triangle Exterior Angles of a Triangle Interior Exterior Angles Parallel Lines Ratio of Intercepts Equal, Complement, or Supplement? Angle Sum of a Triangle Exterior Angles of a Triangle Sin A Cos A Sine Rule 1 Sine Rule 2 Cosine Rule 1 Cosine Rule 2 Area Rule 1 Area Rule 2 Area Problems Find Unknown Angles Find Unknown Sides Bearings Decimals Similarity Congruence Measuring Solids Grade 7 Angles Polygons Angles Grade 7 Angles Polygons Angles Grade 10 Non Right Angled Triangles 3P Learning 46

50 BC Foundations of Mathematics 11 Str Outcome Outcome Description Activities ebooks Logical Reasoning Logical Reasoning Statistics Statistics BC.F11.C1 BC.F11.C2 BC.F11.D1 BC.F11.D2 BC.F11.E1 BC.F11.E2 Analyze prove conjectures, using inductive deductive reasoning, to solve problems. Analyze puzzles games that involve spatial reasoning, using problemsolving strategies. Demonstrate an understing of normal distribution, including: stard deviation z-scores. Interpret statistical data, using confidence intervals, confidence levels margin of error. Model solve problems that involve systems of linear inequalities in two variables. Demonstrate an understing of the characteristics of quadratic functions, including vertex, intercepts, domain range axis of symmetry. Calculating Stard Deviation Interpreting Stard Deviation Equivalent z-scores Calculating z-scores Comparing z-scores Normal Distribution Calculating Stard Deviation Interpreting Stard Deviation Equivalent z-scores Calculating z-scores Comparing z-scores Intersecting Linear Regions Linear Regions Simultaneous Equations 1 Simultaneous Equations 2 Simultaneous Equations 3 Quadratic Equations 1 Quadratic Equations 2 Quadratic Formula Grouping in Pairs Factoring Quadratics 1 Factoring Quadratics 2 Completing the Square Vertex of a Parabola Domain Domain Range Parabolas Marbles Parabolas Rectangles Quadratic Inequalities The Discriminant Graphing Parabolas Roots of the Quadratic Equation Reducible to Quadratics Grade 10 Quadratic Equations Grade 10 Parabolas 47 3P Learning

51 BC Pre-calculus 11 Str Outcome Outcome Description Activities ebooks Algebra Number Algebra Number Algebra Number Algebra Number Algebra Number Algebra Number BC.P11.A1 BC.P11.A2 BC.P11.A3 BC.P11.A4 BC.P11.A5 BC.P11.A6 Trigonometry BC.P11.B1 Trigonometry BC.P11.B2 Demonstrate an understing of the absolute value of real numbers. Solve problems that involve operations on Irrational Numbers Irrational Number expressions with numerical variable radics. Solve problems that involve Irrational Number equations (limited to square roots). Determine equivalent forms of rational expressions (limited to numerators denominators that are monomials, binomials or trinomials). Perform operations on rational expressions (limited to numerators denominators that are monomials, binomials or trinomials). Solve problems that involve rational equations (limited to numerators denominators that are monomials, binomials or trinomials). Demonstrate an understing of angles in stard position [0 to 360 ]. Solve problems, using the three primary trigonometric ratios for angles from 0 to 360 in stard position. Absolute Value Inequalities Absolute Value Expressions Absolute Value Absolute Value Equations Simplifying Irrational Numbers Multiplying Irrational Numbers Dividing Irrational Numbers Exping Irrational Number Expressions Exping Binomial Irrational Numbers Rationalising the Denominator Special Binomial Products Domain Equations with Square Roots Equations with Cube Roots Domain Algebraic Fractions 2 Exp then Simplify Simplifying Expressions Simplifying Binomial Expressions Special Binomial Products Factoring Fractions 1 Domain Algebraic Fractions 1 Algebraic Fractions 2 Algebraic Fractions 3 Factoring Fractions 2 Simplifying Binomial Expressions Domain Equations with Fractions Equations with Fractions 2 Measuring Angles Equal, Complement, or Supplement? Which Quadrant? Transformations: Coordinate Plane Pythagoras Theorem Distance Between Two Points Sign of the Angle Sin A Cos A Tan A Find Unknown Angles Find Unknown Sides Trigonometry Problems 1 Trigonometry Problems 2 Exact Trigonometric Ratios Sine Cosine Curves Elevation Depression Grade 10 Irrational Numbers Exponents Grade 10 Grade 10 Grade 10 Factorising Equations Inequalities Angles Polygons Trigonometry Grade 10 Non Right Angled Triangles Grade 10 Trigonometryic hips 3P Learning 48

52 BC Pre-calculus 11 Str Outcome Outcome Description Activities ebooks Trigonometry BC.P11.B3 BC.P11.C1 BC.P11.C2 BC.P11.C3 BC.P11.C4 Solve problems, using the cosine law sine law, including the ambiguous case. Factor polynomial expressions of the form: ax² + bx + c, a 0 a²x² - b²y², a 0, b 0. a(f(x))² + b(f(x)) + c, a 0 a²(f(x))² - b²(g(y))², a 0, b 0. where a, b c are rational numbers. Graph analyze absolute value functions (limited to linear quadratic functions) to solve problems. Analyze quadratic functions of the form y=a(x - p)² + q determine the: vertex domain range direction of opening axis of symmetry x- y-intercepts. Analyze quadratic functions of the form y=ax² + bx + c to identify characteristics of the corresponding graph, including: vertex domain range direction of opening axis of symmetry x- y-intercepts to solve problems. Sine Rule 1 Sine Rule 2 Cosine Rule 1 Cosine Rule 2 Area Rule 1 Area Rule 2 Highest Common Algebraic Factor Factoring Quadratics 1 Factoring Quadratics 2 Grouping in Pairs Completing the Square Completing the Square 2 Polynomial Long Division Polynomial Factor Theorem Equations Reducible to Quadratics Piecemeal Domain Absolute Value Graphs Absolute Value Expressions Absolute Value Equations Graphing Parabolas Vertex of a Parabola The Discriminant Roots of the Quadratic Sum Product of Roots Equations Reducible to Quadratics Parabolas Marbles Parabolas Rectangles Graphing Parabolas The Discriminant Roots of the Quadratic Sum Product of Roots Completing the Square Completing the Square 2 Grade 10 Non Right Angled Triangles Grade 10 Quadratic Equations Grade 10 Parabolas Grade 10 Polynomials Grade 11 Continuity Grade 10 Quadratic Equations Grade 10 Parabolas Grade 10 Quadratic Equations Grade 10 Parabolas 49 3P Learning

53 BC Pre-calculus 11 Str Outcome Outcome Description Activities ebooks BC.P11.C5 BC.P11.C6 BC.P11.C7 BC.P11.C8 BC.P11.C9 BC.P11.C10 BC.P11.C11 Solve problems that involve quadratic equations. Solve, algebraically graphically, problems that involve systems of linearquadratic quadratic-quadratic equations in two variables. Solve problems that involve linear quadratic inequalities in two variables. Solve problems that involve quadratic inequalities in one variable. Analyze arithmetic sequences series to solve problems. Analyze geometric sequences series to solve problems. Graph analyze reciprocal functions (limited to the reciprocal of linear quadratic functions). Factoring Quadratics 1 Factoring Quadratics 2 Grouping in Pairs Quadratic Equations 1 Quadratic Equations 2 Completing the Square Completing the Square 2 Quadratic Formula Graphing Parabolas Sum Product of Roots Roots of the Quadratic The Discriminant Breakeven Point Linear Modelling Solve Systems by Graphing Simultaneous Linear Equations Simultaneous Equations 1 Simultaneous Equations 2 Simultaneous Equations 3 Intersecting Linear Regions Intersecting Non Linear Regions Graphing Inequalities 1 Graphing Inequalities 2 Linear Regions Non Linear Regions Quadratic Inequalities Find the Pattern Rule Sigma Notation 1 Sigma Notation 2 Terms: Arithmetic Progressions Pattern Rules Tables Sum: Arithmetic Progressions Sum: Geometric Progressions Limiting Sum Sigma Notation 1 Sigma Notation 2 Terms: Geometric Progressions 1 Terms: Geometric Progressions 2 Graphing Hyperbolas Grade 10 Quadratic Equations Grade 10 Parabolas Equations Inequalities Grade 11 Sequence Series - Arithmetic Grade 11 Sequence Series - Geometric Grade 10 Simple Non Linear Graphs 3P Learning 50

54 BC Apprenticeship Workplace 11 Str Outcome Outcome Description Activities ebooks Measurement Measurement Geometry BC.AW.11.A1 BC.AW.11.A2 BC.AW.11.B1 Solve problems that involve SI imperial units in surface area measurements verify the solutions. Solve problems that involve SI imperial units in volume capacity measurements. Solve problems that involve two three right triangles. Geometry BC.AW.11.B2 Solve problems that involve scale. Geometry BC.AW.11.B3 Geometry BC.AW.11.B4 Model draw 3-D objects their views. Draw describe exploded views, component parts scale diagrams of simple 3-D objects. Surface Area: Cuboids Surface Area: Triangular Prisms Surface Area: Rectangular Prisms Surface Area: Cylinders Surface Area: Cones Surface Area: Square Pyramids Surface Area: Rectangular Pyramids Surface Area: Spheres Surface Area: Rearrange Formula Error in Measurement Millilitres Litres Litre Conversions Capacity Word Problems Capacity Addition Converting Volume Volume: Rectangular Prisms 1 Volume: Rectangular Prisms 2 Volume: Cylinders Volume: Triangular Prisms Volume: Pyramids Volume: Cones Volume: Prism Volume: Spheres Volume: Composite Figures Volume: Rearrange Formula Similar Areas Volume Similar Figures Similarity Proofs Using Similar Triangles Elevation Depression Trigonometry Problems 1 Trigonometry Problems 2 Scale Factor Scale Measurement Similar Figures Similarity Proofs Nets Elevations Floor Plans Nets Elevations Floor Plans Relate Shapes Solids Measuring Solids Measuring Solids Trigonometry Similarity Congruence 51 3P Learning

55 BC Apprenticeship Workplace 11 Str Outcome Outcome Description Activities ebooks Number BC.AW.11.C1 Number BC.AW.11.C2 Number BC.AW.11.C3 Number BC.AW.11.C4 Number BC.AW.11.C5 Algebra BC.AW.11.D1 Analyze puzzles games that involve numerical reasoning, using problem-solving strategies. Solve problems that involve personal budgets. Demonstrate an understing of compound interest. Demonstrate an understing of financial institution services used to access manage finances. Demonstrate an understing of credit options, including: credit cards loans. Solve problems that require the manipulation application of formulas related to: volume capacity surface area slope rate of change simple interest finance charges. Profit Loss Special Allowances Piecework Royalties Budgeting Wages Salaries Commission Working Overtime Reading from a Bill Calculating Income Tax Purchase Options Deductions Tax Instalments Calculating Dividends Credit Card Repayments Shares Simple Interest Compound Interest Compound Interest by Formula Depreciation Declining Balance Depreciation Present Future Value Tables Future Value of Investments 1 Future Value of Investments 2 Simple Interest Compound Interest Compound Interest by Formula Depreciation Straight Line Depreciation Declining Balance Depreciation Simple Interest Compound Interest Compound Interest by Formula Depreciation Declining Balance Depreciation Comparing Loans Comparing Home Loans Credit Card Repayments Simple Substitution Real Formulae Find the Mistake Checking Solutions Substitution in Formulae Earning Money Grade 10 Interest Grade 10 Depreciation Grade 10 Interest Grade 10 Depreciation Grade 10 Interest Grade 10 Depreciation Equations Inequalities Measuring Solids 3P Learning 52

56 BC Apprenticeship Workplace 11 Str Outcome Outcome Description Activities ebooks Algebra Algebra Statistics BC.AW.11.D2 BC.AW.11.D3 BC.AW.11.E1 Demonstrate an understing of slope: as rise over run as rate of change by solving problems. Solve problems by applying proportional reasoning unit analysis. Solve problems that involve creating interpreting graphs, including: bar graphs histograms line graphs circle graphs. Which Straight Line? Gradients for Real Horizontal Vertical Lines Slope of a Line Gradient Tan y=ax Equation of a Line 1 Rates Calculations Rate Word Problems Similar Areas Volumes Using Similar Triangles Tally Charts Histogram or Polygon? Travel Graphs Bar Graphs 1 Line Graphs: Interpretation Divided Bar Graphs Creating a Sector Graph Frequency Histograms Cumulative Frequency Histogram Dot Plots Step Graphs Reading from a Column Graph Box--Whisker Plots1 Box--Whisker Plots 2 Stem Leaf Introduction Double Stem Leaf Plots Sector Graph Calculations Creating a Sector Graph Sector Graph Angles Correlation Grade 8 Linear hips Grade 8 Straight Lines Linear hips Grade 10 Straight Lines Under Review Data Grade 10 Interpreting Data 53 3P Learning

57 BC Foundations of Mathematics 12 Str Outcome Outcome Description Activities ebooks Financial Mathematics BC.12.F.A1.1 Financial Mathematics BC.12.F.A1.2 Financial Mathematics BC.12.F.A1.3 Financial Mathematics BC.12.F.A1.4 Financial Mathematics BC.12.F.A1.5 Financial Mathematics BC.12.F.A1.6 Financial Mathematics BC.12.F.A1.7 Financial Mathematics BC.12.F.A1.8 Financial Mathematics BC.12.F.A2.1 Explain the advantages disadvantages of compound interest simple interest. Identify situations that involve compound interest. Graph compare, in a given situation, the total interest paid or earned for different compounding periods. Determine, given the principal, interest rate number of compounding periods, the total interest of a loan. Graph describe the effects of changing the value of one of the variables in a situation that involves compound interest. Determine, using technology, the total cost of a loan under a variety of conditions; e.g., different amortization periods, interest rates, compounding periods terms. Compare explain, using technology, different credit options that involve compound interest, including bank store credit cards special promotions. Solve a contextual problem that involves compound interest. Identify describe examples of assets that appreciate or depreciate. Simple Interest Compound Interest Compound Interest by Formula Depreciation Comparing Home Loans Declining Balance Depreciation Future Value of Investments 1 Future Value of Investments 2 Inflation Depreciation Comparing Home Loans Declining Balance Depreciation Future Value of Investments 1 Future Value of Investments 2 Inflation Depreciation Comparing Home Loans Declining Balance Depreciation Future Value of Investments 1 Future Value of Investments 2 Inflation Depreciation Comparing Home Loans Declining Balance Depreciation Future Value of Investments 1 Future Value of Investments 2 Inflation Depreciation Comparing Home Loans Declining Balance Depreciation Future Value of Investments 1 Future Value of Investments 2 Inflation Depreciation Comparing Home Loans Declining Balance Depreciation Future Value of Investments 1 Future Value of Investments 2 Inflation Grade 10 Interest Grade 10 Depreciation Grade 10 Interest Grade 10 Depreciation Grade 10 Interest Grade 10 Depreciation Grade 10 Interest Grade 10 Depreciation Grade 10 Interest Grade 10 Depreciation Grade 10 Interest Grade 10 Depreciation Grade 10 Interest Grade 10 Depreciation 3P Learning 54

58 BC Foundations of Mathematics 12 Str Outcome Outcome Description Activities ebooks Financial Mathematics BC.12.F.A2.2 Financial Mathematics BC.12.F.A2.3 Financial Mathematics BC.12.F.A2.4 Financial Mathematics BC.12.F.A2.5 Financial Mathematics BC.12.F.A3.1 Financial Mathematics BC.12.F.A3.2 Financial Mathematics BC.12.F.A3.3 Financial Mathematics BC.12.F.A3.4 Financial Mathematics BC.12.F.A3.5 Financial Mathematics BC.12.F.A3.6 Financial Mathematics BC.12.F.A P Learning Compare, using examples, renting, leasing buying. Justify, for a specific set of circumstances, if renting, buying or leasing would be advantageous. Solve a problem involving renting, leasing or buying that requires the manipulation of a formula. Solve, using technology, a contextual problem that involves cost-benefit analysis. Determine compare the strengths weaknesses of two or more portfolios. Determine, using technology, the total value of an investment when there are regular contributions to the principal. Graph compare the total value of an investment with without regular contributions. Apply the Rule of 72 to solve investment problems, explain the limitations of the rule. Determine, using technology, possible investment strategies to achieve a financial goal. Explain the advantages disadvantages of long-term short-term investment options. Explain, using examples, why smaller investments over a longer term may be better than larger investments over a shorter term. Best Buy Successive Discounts Future Value of an Annuity Future Value of an Annuity Compound Interest Compound Interest by Formula Depreciation Comparing Home Loans Declining Balance Depreciation Future Value of Investments 1 Future Value of Investments 2 Inflation Future Value of an Annuity Depreciation Comparing Home Loans Declining Balance Depreciation Future Value of Investments 1 Future Value of Investments 2 Inflation Future Value of an Annuity Depreciation Comparing Home Loans Declining Balance Depreciation Future Value of Investments 1 Future Value of Investments 2 Future Value of an Annuity Earning Money

59 BC Foundations of Mathematics 12 Str Outcome Outcome Description Activities ebooks Financial Mathematics BC.12.F.A3.8 Logical Reasoning Logical Reasoning Logical Reasoning Logical Reasoning Logical Reasoning BC.12.F.B1.1 BC.12.F.B1.2 BC.12.F.B1.3 BC.12.F.B2.1 BC.12.F.B2.2 Solve an investment problem. Determine, explain verify a strategy to solve a puzzle or to win a game; e.g., - guess check - look for a pattern - make a systematic list - draw or model - eliminate possibilities - simplify the original problem - work backward - develop alternative approaches. Identify correct errors in a solution to a puzzle or in a strategy for winning a game. Create a variation on a puzzle or a game, describe a strategy for solving the puzzle or winning the game. Provide examples of the empty set, disjoint sets, subsets universal sets in context, explain the reasoning. Organize information such as collected data number properties, using graphic organizers, explain the reasoning. Depreciation Comparing Home Loans Declining Balance Depreciation Future Value of Investments 1 Future Value of Investments 2 Inflation Future Value of an Annuity Sector Graph Calculations Creating a Sector Graph Frequency Histograms Histograms Cumulative Frequency Histogram Cumulative Frequency Table Dot Plots Caroll Diagram Stem Leaf Introduction Double Stem Leaf Plots Correlation Circle Graphs Divided Bar Graphs Data Grade 10 Interpreting Data 3P Learning 56

60 BC Foundations of Mathematics 12 Str Outcome Outcome Description Activities ebooks Logical Reasoning Logical Reasoning Logical Reasoning Logical Reasoning Logical Reasoning Logical Reasoning Logical Reasoning Logical Reasoning Logical Reasoning Logical Reasoning Logical Reasoning Logical Reasoning 57 3P Learning BC.12.F.B2.3 BC.12.F.B2.4 BC.12.F.B2.5 BC.12.F.B2.6 BC.12.F.B2.7 BC.12.F.B3.1 BC.12.F.B3.2 BC.12.F.B3.3 BC.12.F.B3.4 BC.12.F.B3.5 BC.12.F.B3.6 BC.12.F.B3.7 BC.12.F.C1.1 BC.12.F.C1.2 Explain what a specified region in a Venn diagram represents, using connecting words (, or, not) or set notation. Determine the elements in the complement, the intersection or the union of two sets. Explain how set theory is used in applications such as Internet searches, database queries, data analysis, games puzzles. Identify correct errors in a given solution to a problem that involves sets. Solve a contextual problem that involves sets, record the solution, using set notation. Analyze an if-then statement, make a conclusion, explain the reasoning. Make justify a decision, using what if? questions, in contexts such as probability, finance, sports, games or puzzles, with or without technology. Determine the converse, inverse contrapositive of an if-then statement; determine its veracity;, if it is false, provide a counterexample. Demonstrate, using examples, that the veracity of any statement does not imply the veracity of its converse or inverse. Demonstrate, using examples, that the veracity of any statement does imply the veracity of its contrapositive. Identify describe contexts in which a biconditional statement can be justified. Analyze summarize, using a graphic organizer such as a truth table or Venn diagram, the possible results of given logical arguments that involve biconditional, converse, inverse or contrapositive statements. Provide examples of statements of probability odds found in fields such as media, biology, sports, medicine, sociology psychology. Explain, using examples, the relationship between odds (part-part) probability (part-whole). Venn Diagrams - 'And' 'Or' Venn Diagrams Scale Simple Data Grade 10 Interpreting Data

61 BC Foundations of Mathematics 12 Str Outcome Outcome Description Activities ebooks BC.12.F.C1.3 BC.12.F.C1.4 BC.12.F.C1.5 BC.12.F.C1.6 BC.12.F.C2.1 BC.12.F.C2.2 BC.12.F.C2.3 BC.12.F.C2.4 BC.12.F.C2.5 BC.12.F.C2.6 BC.12.F.C3.1 BC.12.F.C3.2 BC.12.F.C3.3 BC.12.F.C3.4 BC.12.F.C4.1 Express odds as a probability vice versa. Determine the probability of, or the odds for against, an outcome in a situation. Explain, using examples, how decisions may be based on probability or odds on subjective judgments. Find the Complementary Events With Replacement Without Replacement Dice Coins Solve a contextual problem that involves odds or probability. Classify events as mutually exclusive or non mutually exclusive, explain the Complementary Events reasoning. Determine if two events are complementary, explain the reasoning. Represent, using set notation or graphic organizers, mutually exclusive (including - 'And' 'Or' complementary) non mutually exclusive events. Solve a contextual problem that involves the probability of mutually exclusive or non mutually exclusive events. Solve a contextual problem that involves the probability of Complementary Events, complementary events. Create solve a problem that involves mutually exclusive or non - 'And' 'Or' mutually exclusive events. Compare, using examples, dependent independent events. Complementary Events Determine the probability of an event, With Replacement given the occurrence of a previous Without Replacement event. Dice Coins - 'And' 'Or' Determine the probability of two dependent or two independent events. Create solve a contextual problem that involves determining the probability of dependent or independent events. Represent solve counting problems, Tree Diagrams using a graphic organizer. 3P Learning 58

62 BC Foundations of Mathematics 12 Str Outcome Outcome Description Activities ebooks BC.12.F.C4.2 BC.12.F.C P Learning BC.12.F.C4.4 BC.12.F.C5.1 BC.12.F.C5.2 BC.12.F.C5.3 Generalize the fundamental counting principle, using inductive reasoning. Identify explain assumptions made in solving a counting problem. Solve a contextual counting problem, using the fundamental counting principle, explain the reasoning. Represent the number of arrangements of n elements taken n at a time, using factorial notation. Determine, with or without technology, the value of a factorial. Simplify a numeric or algebraic fraction containing factorials in both the numerator denominator. BC.12.F.C5.4 Solve an equation that involves factorials. BC.12.F.C5.5 BC.12.F.C5.6 BC.12.F.C5.7 BC.12.F.C5.8 BC.12.F.C5.9 BC.12.F.D1.3 BC.12.F.D1.5 BC.12.F.D1.6 Determine the number of permutations of n elements taken r at a time. Determine the number of permutations of n elements taken n at a time where some elements are not distinct. Explain, using examples, the effect on the total number of permutations of n elements when two or more elements are identical. Generalize strategies for determining the number of permutations of n elements taken r at a time. Solve a contextual problem that involves probability permutations. Match equations in a given set to their corresponding graphs. Interpret the graph of a polynomial function that models a situation, explain the reasoning. Solve, using technology, a contextual problem that involves data that is best represented by graphs of polynomial functions, explain the reasoning. Counting Techniques 1 Counting Techniques 2 Counting Principle Counting Techniques 1 Counting Techniques 2 Counting Principle Combinations Permutations Combinations Permutations Combinations Permutations Permutations Permutations Permutations Permutations Permutations Identifying Graphs Graphing Parabolas Graphing Exponentials Graphing from a Table of Values Exponential or Log Graph? Graphing Cubics Parabolas Rectangles Parabolas Marbles Parabolas Rectangles Parabolas Marbles Grade 10 Simple Nonlinear Graphs

63 BC Foundations of Mathematics 12 Str Outcome Outcome Description Activities ebooks BC.12.F.D2.1 BC.12.F.D2.2 BC.12.F.D2.3 BC.12.F.D2.4 BC.12.F.D2.5 BC.12.F.D2.6 BC.12.F.D3.1 BC.12.F.D3.2 BC.12.F.D3.3 BC.12.F.D3.4 BC.12.F.D3.5 Describe, orally in written form, the characteristics of exponential or logarithmic functions by analyzing their graphs. Describe, orally in written form, the characteristics of exponential or logarithmic functions by analyzing their equations. Match equations in a given set to their corresponding graphs. Graph data determine the exponential or logarithmic function that best approximates the data. Interpret the graph of an exponential or logarithmic function that models a situation, explain the reasoning. Solve, using technology, a contextual problem that involves data that is best represented by graphs of exponential or logarithmic functions, explain the reasoning. Describe, orally in written form, the characteristics of sinusoidal functions by analyzing their graphs. Describe, orally in written form, the characteristics of sinusoidal functions by analyzing their equations. Match equations in a given set to their corresponding graphs. Graph data determine the sinusoidal function that best approximates the data. Interpret the graph of a sinusoidal function that models a situation, explain the reasoning. Exponential or Log Graph? Exponential Equations Equations with Logs Exponential Growth Decay Graphing Exponentials Exponential Equations Equations with Logs Exponential Growth Decay Graphing Exponentials Exponential or Log Graph? Non Linear Graphs Identifying Graphs Graphing Parabolas Graphing Cubics Function Notation 1 Function Notation 2 Function Notation 3 Odd Even Horizontal Vertical Change Grade 10 Logarithms Grade 10 Exponential Power Graphs Grade 10 Logarithms Grade 10 Exponential Power Graphs Grade 10 Simple Nonlinear Graphs Grade 10 Logarithms Grade 10 Exponential Power Graphs Exponential Growth Decay Exponential Growth Decay Sine Cosine Curves Period Amplitude Sine Cosine Curves Period Amplitude Sine Cosine Curves 3P Learning 60

64 BC Foundations of Mathematics 12 Str Outcome Outcome Description Activities Mathematics Research Project Mathematics Research Project Mathematics Research Project Mathematics Research Project Mathematics Research Project BC.12.F.D3.6 BC.12.F.E1.1 BC.12.F.E1.2 BC.12.F.E1.3 BC.12.F.E1.4 BC.12.F.E1.5 Solve, using technology, a contextual problem that involves data that is best represented by graphs of sinusoidal functions, explain the reasoning. Collect primary or secondary data (statistical or informational) related to the topic. Assess the accuracy, reliability relevance of the primary or secondary data collected by: - identifying examples of bias points of view - identifying describing the data collection methods - determining if the data is relevant - determining if the data is consistent with information obtained from other sources on the same topic. Interpret data, using statistical methods if applicable. Identify controversial issues, if any, present multiple sides of the issues with supporting data. Organize present the research project, with or without technology. Line Graphs: Interpretation Divided Bar Graphs Sector Graph Calculations Circle Graphs Frequency Histograms Cumulative Frequency Histogram Cumulative Frequency Table Box--Whisker Plots 1 Box--Whisker Plots 2 Dot Plots Caroll Diagram Stem Leaf Introduction Calculating Interquartile Range Mean Median Mode Data Extremes Range Mean from Frequency Table Mode from Frequency Table Median from Frequency Table Median Cumulative Frequency Correlation ebooks Under review Under review Under review Grade 10 Interpreting Data Under review Under review 61 3P Learning

65 BC Apprenticeship Workplace 12 Str Outcome Outcome Description Activities ebooks Measurement BC.12.AW.A1.1 Measurement BC.12.AW.A1.2 Measurement BC.12.AW.A1.3 Measurement BC.12.AW.A1.4 Measurement BC.12.AW.A1.5 Measurement BC.12.AW.A1.6 Measurement BC.12.AW.A1.7 Measurement BC.12.AW.A1.8 Measurement BC.12.AW.A1.9 Geometry BC.12.AW.B1.1 Geometry BC.12.AW.B1.2 Geometry BC.12.AW.B2.1 Explain why, in a given context, a certain degree of precision is required. Explain why, in a given context, a certain degree of accuracy is required. Explain, using examples, the difference between precision accuracy. Compare the degree of accuracy of two given instruments used to measure the same attribute. Relate the degree of accuracy to the uncertainty of a given measure. Analyze precision accuracy in a contextual problem. Calculate maximum minimum values, using a given degree of tolerance in context. Describe, using examples, the limitations of measuring instruments used in a specific trade or industry; e.g., tape measure versus Vernier caliper. Solve a problem that involves precision, accuracy or tolerance. Identify describe the use of the sine law cosine law in construction, industrial, commercial artistic applications. Solve a problem, using the sine law or cosine law, when a diagram is given. Describe illustrate properties of triangles, including isosceles equilateral. Error in Measurement Percentage Error Error in Measurement Percentage Error Sine Rule 1 Sine Rule 2 Cosine Rule 1 Cosine Rule 2 Triangles: Acute, Right, Obtuse Plane Figure Theorems Nets Hypotenuse of a Right Triangle Pythagoras Theorem Pythagorean Triads Angle Sum of a Triangle Exterior Angles of a Triangle Grade 10 Non Right Angled Triangles Polygons Angles 3P Learning 62

66 BC Apprenticeship Workplace 12 Str Outcome Outcome Description Activities ebooks Geometry BC.12.AW.B2.2 Geometry BC.12.AW.B2.3 Geometry BC.12.AW.B2.4 Geometry BC.12.AW.B2.5 Geometry BC.12.AW.B2.6 Geometry BC.12.AW.B3.1 Geometry BC.12.AW.B3.2 Geometry BC.12.AW.B3.3 Geometry BC.12.AW.B3.4 Geometry BC.12.AW.B3.5 Geometry BC.12.AW.B3.6 Geometry BC.12.AW.B3.7 Geometry BC.12.AW.B P Learning Describe illustrate properties of quadrilaterals in terms of angle measures, side lengths, diagonal lengths angles of intersection. Describe illustrate properties of regular polygons. Explain, using examples, why a given property does or does not apply to certain polygons. Identify explain an application of the properties of polygons in construction, industrial, commercial, domestic artistic contexts. Solve a contextual problem that involves the application of the properties of polygons. Identify a single transformation that was performed, given the original 2-D shape or 3-D object its image. Draw the image of a 2-D shape that results from a given single transformation. Draw the image of a 2-D shape that results from a given combination of successive transformations. Create, analyze describe designs, using translations, rotations reflections in all four quadrants of a coordinate grid. Identify describe applications of transformations in construction, industrial, commercial, domestic artistic contexts. Explain the relationship between reflections lines or planes of symmetry. Determine explain whether a given image is a dilation of another given shape, using the concept of similarity. Draw, with or without technology, a dilation image for a given 2-D shape or 3-D object, explain how the original 2-D shape or 3-D object its image are proportional. Plane Figure Theorems Angle Sum of a Quadrilateral Area: Quadrilaterals Interior Exterior Angles Plane Figure Theorems Plane Figure Theorems Transformations Transformations: Coordinate Plane Rotations: Coordinate Plane Transformations Transformations: Coordinate Plane Rotations: Coordinate Plane Rotations: Coordinate Plane Transformations: Coordinate Plane Rotational Symmetry Symmetry or Not? Congruent Triangles Using Similar Triangles Similar Figures Scale Factor Similarity Proofs Polygons Angles Polygons Angles Polygons Angles Polygons Angles Similarity Congruence

67 BC Apprenticeship Workplace 12 Str Outcome Outcome Description Activities ebooks Geometry BC.12.AW.B3.9 Number BC.12.AW.C1.1 Number BC.12.AW.C1.2 Number BC.12.AW.C1.3 Number BC.12.AW.C2.1 Number Number Number BC.12.AW.C2.2 BC.12.AW.C2.3 BC.12.AW.C3.1 Number BC.12.AW.C3.2 Number BC.12.AW.C3.3 Number BC.12.AW.C3.4 Number BC.12.AW.C3.5 Solve a contextual problem that involves transformations. Determine, explain verify a strategy to solve a puzzle or to win a game; e.g., - guess check - look for a pattern - make a systematic list - draw or model - eliminate possibilities - simplify the original problem - work backward - develop alternative approaches. Identify correct errors in a solution to a puzzle or in a strategy for winning a game. Create a variation on a puzzle or a game, describe a strategy for solving the puzzle or winning the game. Describe explain various options for buying, leasing leasing to buy a Purchase Options vehicle. Solve, with or without technology, problems that involve the purchase, lease or lease to purchase of a vehicle. Justify a decision related to buying, leasing or leasing to buy a vehicle, based on factors such as personal finances, intended use, maintenance, warranties, mileage insurance. Calculating Income Tax Budgeting Graphs from Bills Identify expenses in operating a small Deductions Tax business, such as a hot dog st. Installments Reading from a Bill GST (also called VAT) Special Allowances Identify feasible small business options for a given community. Generate options that might improve the profitability of a small business. Determine the break-even point for a small business. Explain factors, such as seasonal variations hours of operation, that might impact the profitability of a small business. Breakeven Point 3P Learning 64

68 BC Apprenticeship Workplace 12 Str Outcome Outcome Description Activities ebooks Algebra Algebra Algebra Algebra Algebra Algebra Algebra Algebra BC.12.AW.D1.1 BC.12.AW.D1.2 BC.12.AW.D1.3 BC.12.AW.D1.4 BC.12.AW.D1.5 BC.12.AW.D1.6 BC.12.AW.D1.7 BC.12.AW.D1.8 Identify describe the characteristics of a linear relation represented in a graph, table of values, number pattern or equation. Sort a set of graphs, tables of values, number patterns /or equations into linear nonlinear relations. Write an equation for a given context, including direct or partial variation. Create a table of values for a given equation of a linear relation. Sketch the graph for a given table of values. Explain why the points should or should not be connected on the graph for a context. Create, with or without technology, a graph to represent a data set, including scatterplots. Describe the trends in the graph of a data set, including scatterplots. Table of Values Find the Pattern Rule Pattern Rules Tables Function Rules Tables Graphing from a Table of Values Reading Values from a Line Determining a Rule for a Line Which Straight Line? Modelling Linear hips y=ax Direct Variation Determining a Rule for a Line Pattern Rules Tables Function Rules Tables Graphing from a Table of Values Graphing from a Table of Values 2 Graphing from a Table of Values Graphing from a Table of Values 2 Non Linear Graphs Correlation Line Graphs: Interpretation Grade 8 Linear Grade 8 Straight Lines Linear Coordinate Geometry Grade 10 Straight Lines Grade 8 Linear Grade 8 Straight Lines Linear Coordinate Geometry Grade 10 Straight Lines Grade 8 Linear Grade 8 Straight Lines Linear Coordinate Geometry Grade 10 Straight Lines Grade 8 Linear Grade 8 Straight Lines Linear Coordinate Geometry Grade 10 Straight Lines Grade 8 Linear Grade 8 Straight Lines Linear Coordinate Geometry Grade 10 Straight Lines 65 3P Learning

69 BC Apprenticeship Workplace 12 Str Outcome Outcome Description Activities ebooks Algebra BC.12.AW.D1.9 Algebra Algebra Algebra Algebra Statistics BC.12.AW.D1.10 BC.12.AW.D1.11 BC.12.AW.D1.12 BC.12.AW.D1.13 BC.12.AW.E1.1 Statistics BC.12.AW.E1.2 Statistics BC.12.AW.E1.3 Statistics BC.12.AW.E1.4 Statistics BC.12.AW.E1.5 Sort a set of scatterplots according to the trends represented (linear, nonlinear or no trend). Solve a contextual problem that requires interpolation or extrapolation of information. Relate slope rate of change to linear relations. Match given contexts with their corresponding graphs, explain the reasoning. Solve a contextual problem that involves the application of a formula for a linear relation. Explain, using examples, the advantages disadvantages of each measure of central tendency. Determine the mean, median mode for a set of data. Identify correct errors in a calculation of a measure of central tendency. Identify the outlier(s) in a set of data. Explain the effect of outliers on mean, median mode. Correlation Modelling Linear hips y=ax Direct Variation Determining a Rule for a Line Gradient Gradients for Real Which Straight Line? Horizontal Vertical Lines Which Straight Line? Modelling Linear hips Gradients for Real Mean Median Mode Mean from Frequency Table Median from Frequency Table Median Cumulative Frequency Grade 8 Linear Grade 8 Straight Lines Linear Coordinate Geometry Grade 10 Straight Lines Grade 8 Linear Grade 8 Straight Lines Linear Coordinate Geometry Grade 10 Straight Lines Grade 8 Linear Grade 8 Straight Lines Linear Coordinate Geometry Grade 10 Straight Lines Data Data Data 3P Learning 66

70 BC Apprenticeship Workplace 12 Str Outcome Outcome Description Activities ebooks Statistics BC.12.AW.E1.6 Statistics BC.12.AW.E1.7 Statistics BC.12.AW.E1.8 Statistics BC.12.AW.E1.9 Statistics BC.12.AW.E1.10 Statistics BC.12.AW.E2.1 Statistics BC.12.AW.E2.2 Statistics BC.12.AW.E2.3 Statistics BC.12.AW.E2.4 Statistics BC.12.AW.E2.5 BC.12.AW.F1.1 Calculate the trimmed mean for a set of data, justify the removal of the outliers. Explain, using examples such as course marks, why some data in a set would be given a greater weighting in determining the mean. Calculate the mean of a set of numbers after allowing the data to have different weightings (weighted mean). Explain, using examples from print other media, how measures of central tendency outliers are used to provide different interpretations of data. Solve a contextual problem that involves measures of central tendency. Explain, using examples, percentile ranks in a context. Explain decisions based on a given percentile rank. Explain, using examples, the difference between percent percentile rank. Explain the relationship between median percentile. Solve a contextual problem that involves percentiles. Describe explain the applications of probability; e.g., medication, warranties, insurance, lotteries, weather prediction, 100- year flood, failure of a design, failure of a product, vehicle recalls, approximation of area. Calculating Interquartile Range Box--Whisker Plots 1 Box--Whisker Plots 2 Box--Whisker Plots 1 Box--Whisker Plots 2 Grade 10 Interpreting Data Grade 10 Interpreting Data 67 3P Learning

71 BC Apprenticeship Workplace 12 Str Outcome Outcome Description Activities ebooks BC.12.AW.F1.2 BC.12.AW.F1.3 BC.12.AW.F1.4 BC.12.AW.F1.5 BC.12.AW.F1.6 BC.12.AW.F1.7 Calculate the probability of an event based on a data set; e.g., determine the probability of a romly chosen light bulb being defective. Express a given probability as a fraction, decimal percent in a statement. Explain the difference between odds probability. Determine the probability of an event, given the odds for or against. Explain, using examples, how decisions may be based on a combination of theoretical probability calculations, experimental results subjective judgements. Solve a contextual problem that involves a given probability. Fair Games Possible Outcomes Simple Complementary Events With Replacement Without Replacement Dice Coins Tables Two-way Table Relative Frequency Venn Diagrams Possible Outcomes Simple Complementary Events With Replacement Without Replacement Dice Coins Tables Two-way Table Relative Frequency Venn Diagrams Possible Outcomes Simple Complementary Events With Replacement Without Replacement Dice Coins Tables Two-way Table Relative Frequency Venn Diagrams 3P Learning 68

72 BC Pre-calculus 12 Str Outcome Outcome Description Activities ebooks Trigonometry BC.12.P.A1.1 Trigonometry BC.12.P.A1.2 Trigonometry BC.12.P.A1.3 Trigonometry BC.12.P.A1.4 Trigonometry BC.12.P.A1.5 Trigonometry BC.12.P.A1.6 Trigonometry BC.12.P.A1.7 Trigonometry BC.12.P.A1.8 Trigonometry BC.12.P.A1.9 Trigonometry BC.12.P.A2.1 Trigonometry BC.12.P.A2.2 Sketch, in stard position, an angle (positive or negative) when the measure is given in degrees. Describe the relationship among different systems of angle measurement, with emphasis on radians degrees. Sketch, in stard position, an angle with a measure of 1 radian. Sketch, in stard position, an angle with a measure expressed in the form kπ radians, where k-q. Express the measure of an angle in radians (exact value or decimal approximation), given its measure in degrees. Express the measure of an angle in degrees, given its measure in radians (exact value or decimal approximation). Determine the measures, in degrees or radians, of all angles in a given domain that are coterminal with a given angle in stard position. Determine the general form of the measures, in degrees or radians, of all angles that are coterminal with a given angle in stard position. Explain the relationship between the radian measure of an angle in stard position the length of the arc cut on a circle of radius r, solve problems based upon that relationship. Derive the equation of the unit circle from the Pythagorean theorem. Describe the six trigonometric ratios, using a point P (x, y) that is the intersection of the terminal arm of an angle the unit circle. Converting Radians Degrees Converting Radians Degrees Converting Radians Degrees Unit Circle Reductions Trig Equations 1 Trig Equations 2 Trig Equations 3 Trigonometric Intercepts Unit Circle Reductions Trig Equations 1 Trig Equations 2 Trig Equations 3 Trig Equations 4 Length of an Arc Sin A Cos A Tan A Trigonometry Grade 12 Trigonometry Polar Coordinates Trigonometry Grade 12 Trigonometry Polar Coordinates Trigonometry Grade 12 Trigonometry Polar Coordinates Trigonometry Grade 12 Trigonometry Polar Coordinates Trigonometry Grade 12 Trigonometry Polar Coordinates Trigonometry Grade 12 Trigonometry Polar Coordinates Trigonometry Grade 10 Trigonometric hips Grade 12 Trigonometry Polar Coordinates Trigonometry Grade 10 Trigonometric hips Grade 12 Trigonometry Polar Coordinates Grade 12 Trigonometry Polar Coordinates Grade 10 Circle Graphs Trigonometry Grade 10 Trigonometric hips Grade 12 Trigonometry Polar Coordinates 69 3P Learning

73 BC Pre-calculus 12 Str Outcome Outcome Description Activities ebooks Trigonometry BC.12.P.A2.3 Trigonometry BC.12.P.A3.1 Trigonometry BC.12.P.A3.2 Trigonometry BC.12.P.A3.3 Trigonometry BC.12.P.A3.4 Trigonometry BC.12.P.A3.5 Trigonometry BC.12.P.A3.6 Trigonometry BC.12.P.A3.7 Trigonometry BC.12.P.A3.8 Generalize the equation of a circle with centre (0, 0) radius r. Determine, with technology, the approximate value of a trigonometric ratio for any angle with a measure expressed in either degrees or radians. Determine, using a unit circle or reference triangle, the exact value of a trigonometric ratio for angles expressed in degrees that are multiples of 0, 30, 45, 60 or 90, or for angles expressed in radians that are multiples of 0, π/6, π/4, π/3 or π/2, explain the strategy. Determine, with or without technology, the measures, in degrees or radians, of the angles in a specified domain, given the value of a trigonometric ratio. Explain how to determine the exact values of the six trigonometric ratios, given the coordinates of a point on the terminal arm of an angle in stard position. Determine the measures of the angles in a specified domain in degrees or radians, given a point on the terminal arm of an angle in stard position. Determine the exact values of the other trigonometric ratios, given the value of one trigonometric ratio in a specified domain. Sketch a diagram to represent a problem that involves trigonometric ratios. Solve a problem, using trigonometric ratios. Graphing Circles Centre Radius 1 Centre Radius 2 Exact Trigonometric Ratios Sign of the Angle Exact Trigonometric Ratios Exact Trigonometric Ratios Sign of the Angle Which Quadrant? Grade 10 Circle Graphs Trigonometry Grade 10 Trigonometric hips Trigonometry Grade 10 Trigonometric hips Trigonometry Grade 10 Trigonometric hips Trigonometry Grade 10 Trigonometric hips Trigonometry Grade 10 Trigonometric hips Trigonometry Grade 10 Trigonometric hips Trigonometry Grade 10 Trigonometric hips Trigonometry Grade 10 Trigonometric hips 3P Learning 70

74 BC Pre-calculus 12 Str Outcome Outcome Description Activities ebooks Trigonometry BC.12.P.A4.1 Trigonometry BC.12.P.A4.2 Trigonometry BC.12.P.A4.3 Trigonometry BC.12.P.A4.4 Trigonometry BC.12.P.A4.5 Trigonometry BC.12.P.A4.6 Trigonometry BC.12.P.A4.7 Trigonometry BC.12.P.A4.8 Trigonometry BC.12.P.A4.9 Trigonometry BC.12.P.A4.10 Trigonometry BC.12.P.A4.11 Sketch, with or without technology, the graph of y=sin x, y=cos x or y=tan x. Determine the characteristics (amplitude, asymptotes, domain, period, range zeros) of the graph of y=sin x, y=cos x or y=tan x. Determine how varying the value of a affects the graphs of y=a sin x y=a cos x. Determine how varying the value of d affects the graphs of y=sin x + d y=cos x + d. Determine how varying the value of c affects the graphs of y=sin (x + c) y=cos (x + c). Determine how varying the value of b affects the graphs of y=sin (bx) y=cos (bx) Sketch, without technology, graphs of the form y=a sin b(x c) + d or y=a cos b(x c) + d, using transformations, explain the strategies. Determine the characteristics (amplitude, asymptotes, domain, period, phase shift, range zeros) of the graph of a trigonometric function of the form y=a sin b(x c) + d or y=a cos b(x c) + d. Determine the values of a, b, c d for functions of the form y=a sin b(x c) + d or y=a cos b(x c) + d that correspond to a given graph, write the equation of the function. Determine a trigonometric function that models a situation to solve a problem. Explain how the characteristics of the graph of a trigonometric function relate to the conditions in a problem situation. Sine Cosine Curves Period Amplitude Trig Graphs in Radians Period Amplitude Sine Cosine Curves Sine Cosine Curves Period Amplitude Sine Cosine Curves Period Amplitude Trig Graphs in Radians Period Amplitude Trig Graphs in Radians Period Amplitude Trigonometry Grade 10 Trigonometric hips 71 3P Learning

75 BC Pre-calculus 12 Str Outcome Outcome Description Activities ebooks Trigonometry BC.12.P.A4.12 Trigonometry BC.12.P.A5.1 Trigonometry BC.12.P.A5.2 Trigonometry BC.12.P.A5.3 Trigonometry BC.12.P.A5.4 Trigonometry BC.12.P.A5.5 Trigonometry BC.12.P.A5.6 Trigonometry BC.12.P.A6.1 Trigonometry BC.12.P.A6.2 Trigonometry BC.12.P.A6.3 Trigonometry BC.12.P.A6.4 Solve a problem by analyzing the graph of a trigonometric function. Verify, with or without technology, that a given value is a solution to a trigonometric equation. Determine, algebraically, the solution of a trigonometric equation, stating the solution in exact form when possible. Determine, using technology, the approximate solution of a trigonometric equation in a restricted domain. Relate the general solution of a trigonometric equation to the zeros of the corresponding trigonometric function (restricted to sine cosine functions). Determine, using technology, the general solution of a given trigonometric equation. Identify correct errors in a solution for a trigonometric equation. Explain the difference between a trigonometric identity a trigonometric equation. Verify a trigonometric identity numerically for a given value in either degrees or radians. Explain why verifying that the two sides of a trigonometric identity are equal for given values is insufficient to conclude that the identity is valid. Determine, graphically, the potential validity of a trigonometric identity, using technology. Trigonometric Intercepts Trig Graphs in Radians Period Amplitude Sine Cosine Curves Trig Equations 1 Trig Equations 2 Trig Equations 3 Trig Equations 4 Trigonometry Problems 1 Trigonometry Problems 2 Trig Equations 1 Trig Equations 2 Trig Equations 3 Trig Equations 4 Trig Equations 1 Trig Equations 2 Trig Equations 3 Trig Equations 4 Trigonometric Intercepts Trigonometry Grade 10 Trigonometric hips Trigonometry Grade 10 Trigonometric hips 3P Learning 72

76 BC Pre-calculus 12 Str Outcome Outcome Description Activities ebooks Trigonometry Trigonometry Trigonometry BC.12.P.A6.5 BC.12.P.A6.6 BC.12.P.A6.7 BC.12.P.B1.1 BC.12.P.B1.2 BC.12.P.B1.3 BC.12.P.B1.4 BC.12.P.B1.5 BC.12.P.B1.6 BC.12.P.B1.7 BC.12.P.B1.8 BC.12.P.B1.9 BC.12.P.B2.1 BC.12.P.B2.2 Determine the non-permissible values of a trigonometric identity. Prove, algebraically, that a trigonometric identity is valid. Determine, using the sum, difference double-angle identities, the exact value of Double Angles a trigonometric ratio. Sketch the graph of a function that is the sum, difference, product or quotient of two functions, given their graphs. Write the equation of a function that is the sum, difference, product or quotient of two or more functions, given their equations. Determine the domain range of Domain a function that is the sum, difference, product or quotient of two functions. Domain Range Write a function h(x) as the sum, difference, product or quotient of two or more functions. Determine the value of the composition Composition of of functions when evaluated at a point, 1 including: f(f(a)), f(g(a)), g(f(a)). Determine, given the equations of two functions f(x) g(x), the equation of the Composition of composite function: f(f(x)), f(g(x)), g(f(x)) 1 explain any restrictions. Sketch, given the equations of two functions f(x) g(x), the graph of the composite function: f(f(x)), f(g(x)), g(f(x)). Write a function h(x) as the composition of Composition of two or more functions. 1 Write a function h(x) by combining two or more functions through operations on, compositions of, functions. Compare the graphs of a set of functions of the form y k=f(x) to the graph of y=f(x), generalize, using inductive reasoning, a rule about the effect of k. Compare the graphs of a set of functions of the form y=f(x - h) to the graph of y=f(x), generalize, using inductive reasoning, a rule about the effect of h. Grade 10 Grade 10 Grade 10 Grade 10 Grade 10 Grade 10 Grade 10 Grade P Learning

77 BC Pre-calculus 12 Str Outcome Outcome Description Activities ebooks BC.12.P.B2.3 BC.12.P.B2.4 BC.12.P.B2.5 BC.12.P.B3.1 BC.12.P.B3.2 BC.12.P.B3.3 BC.12.P.B3.4 BC.12.P.B3.5 BC.12.P.B4.1 Compare the graphs of a set of functions of the form y - k=f(x - h) to the graph of y=f(x), generalize, using inductive reasoning, a rule about the effects of h k. Sketch the graph of y - k=f(x), y=f(x - h) or y - k=f(x - h) for given values of h k, given a sketch of the function y=f(x), where the equation of y=f(x) is not given. Write the equation of a function whose graph is a vertical /or horizontal translation of the graph of the function y=f(x). Compare the graphs of a set of functions of the form y=af(x) to the graph of y=f(x), generalize, using inductive reasoning, a rule about the effect of a. Compare the graphs of a set of functions of the form y=f(bx) to the graph of y=f(x), generalize, using inductive reasoning, a rule about the effect of b. Compare the graphs of a set of functions of the form y=af(bx) to the graph of y=f(x), generalize, using inductive reasoning, a rule about the effects of a b. Sketch the graph of y=af(x), y=f(bx) or y=af(bx) for given values of a b, given a sketch of the function y=f(x), where the equation of y=f(x) is not given. Write the equation of a function, given its graph which is a vertical /or horizontal stretch of the graph of the function y=f(x). Sketch the graph of the function y - k=af(b(x - h)) for given values of a, b, h k, given the graph of the function y=f(x), where the equation of y=f(x) is not given. Grade 10 Grade 10 Grade 10 Grade 10 Grade 10 Grade 10 Grade 10 Parabolas 3P Learning 74

78 BC Pre-calculus 12 Str Outcome Outcome Description Activities ebooks BC.12.P.B4.2 BC.12.P.B5.1 BC.12.P.B5.2 BC.12.P.B5.3 BC.12.P.B5.4 BC.12.P.B5.5 BC.12.P.B6.1 BC.12.P.B6.2 BC.12.P.B6.3 BC.12.P.B6.4 Write the equation of a function, given its graph which is a translation / or stretch of the graph of the function y=f(x). Generalize the relationship between the coordinates of an ordered pair the coordinates of the corresponding ordered pair that results from a reflection through the x-axis, the y-axis or the line y=x. Sketch the reflection of the graph of a function y=f(x) through the x-axis, the y-axis or the line y=x, given the graph of the function y=f(x), where the equation of y=f(x) is not given. Generalize, using inductive reasoning, explain rules for the reflection of the graph of the function y=f(x) through the x-axis, the y-axis or the line y=x. Sketch the graphs of the functions y= f(x), y=f( x) x= f(y), given the graph of the function y=f(x), where the equation of y=f(x) is not given. Write the equation of a function, given its graph which is a reflection of the graph of the function y=f(x) through the x-axis, the y-axis or the line y=x. Explain how the graph of the line y=x, can be used to sketch the inverse of a relation. Explain how the transformation (x, y)=> (y, x) can be used to sketch the inverse of a relation. Sketch the graph of the inverse relation, given the graph of a relation. Determine if a relation its inverse are functions. Transformations: Coordinate Plane Inverse functions Graphing Inverse Inverse Trigonometric Graph Inverse Trig Inverse functions Graphing Inverse Inverse Trigonometric Graph Inverse Trig Inverse functions Graphing Inverse Inverse Trigonometric Graph Inverse Trig Inverse functions Graphing Inverse Inverse Trigonometric Graph Inverse Trig Inverse functions Graphing Inverse Inverse Trigonometric Graph Inverse Trig Inverse functions Graphing Inverse Inverse Trigonometric Graph Inverse Trig Grade 10 Grade 10 Grade 10 Grade 10 Grade 10 Grade 10 Grade 10 Grade P Learning

79 BC Pre-calculus 12 Str Outcome Outcome Description Activities ebooks BC.12.P.B6.5 BC.12.P.B6.6 BC.12.P.B6.7 BC.12.P.B6.8 BC.12.P.B7.1 BC.12.P.B7.2 BC.12.P.B7.3 BC.12.P.B7.4 BC.12.P.B8.1 Determine restrictions on the domain of a function in order for its inverse to be a function. Determine the equation sketch the graph of the inverse relation, given the equation of a linear or quadratic relation. Explain the relationship between the domains ranges of a relation its inverse. Determine, algebraically or graphically, if two functions are inverses of each other. Explain the relationship between logarithms exponents. Express a logarithmic expression as an exponential expression vice versa. Determine, without technology, the exact value of a logarithm, such as log 2 (8). Estimate the value of a logarithm, using benchmarks, explain the reasoning; e.g. since log 2 (8)= 3 log 2 (16)= 4, log 2 9 is approximately equal to 3.1. Develop generalize the laws for logarithms, using numeric examples exponent laws. Inverse functions Graphing Inverse Inverse Trigonometric Graph Inverse Trig Inverse functions Graphing Inverse Inverse Trigonometric Graph Inverse Trig Log Base e Graphing Exponentials Exponential or Log Graph? Log Laws Change of Base Equations with Logs Log Laws Grade 10 Grade 10 Grade 10 Logarithms Grade 10 Logarithms Grade 10 Logarithms Grade 10 Logarithms Exponents Grade 10 Logarithms BC.12.P.B8.2 Derive each law of logarithms. Grade 10 Logarithms BC.12.P.B8.3 BC.12.P.B8.4 Determine, using the laws of logarithms, an equivalent expression for a logarithmic expression. Determine, with technology, the approximate value of a logarithmic expression, such as log 2 (9). Log Laws Grade 10 Logarithms Grade 10 Logarithms 3P Learning 76

80 BC Pre-calculus 12 Str Outcome Outcome Description Activities ebooks BC.12.P.B9.1 BC.12.P.B9.2 BC.12.P.B9.3 BC.12.P.B9.4 BC.12.P.B9.5 BC.12.P.B9.6 BC.12.P.B9.7 BC.12.P.B10.1 BC.12.P.B10.2 Sketch, with or without technology, a graph of an exponential function of the form y=a^x, a > 0. Identify the characteristics of the graph of an exponential function of the form y=a^x, a > 0, including the domain, range, horizontal asymptote intercepts, explain the significance of the horizontal asymptote. Sketch the graph of an exponential function by applying a set of transformations to the graph of y=a^x, a > 0, state the characteristics of the graph. Sketch, with or without technology, the graph of a logarithmic function of the form y=log 2 (x), a > 1. Identify the characteristics of the graph of a logarithmic function of the form y=log 2 (x), a > 1, including the domain, range, vertical asymptote intercepts, explain the significance of the vertical asymptote. Sketch the graph of a logarithmic function by applying a set of transformations to the graph of y=log 2 (x), a > 1, state the characteristics of the graph. Demonstrate, graphically, that a logarithmic function an exponential function with the same base are inverses of each other. Determine the solution of an exponential equation in which the bases are powers of one another. Determine the solution of an exponential equation in which the bases are not powers of one another, using a variety of strategies. Graphing Exponentials Exponential or Log Graph? Graphing Exponentials Exponential or Log Graph? Exponential or Log Graph? Grade 10 Logarithms Grade 10 Exponential Power Graphs Grade 10 Simple Nonlinear Graphs Grade 10 Logarithms Grade 10 Exponential Power Graphs Grade 10 Simple Nonlinear Graphs Grade 10 Logarithms Grade 10 Exponential Power Graphs Grade 10 Simple Nonlinear Graphs Grade 10 Logarithms Grade 10 Exponential Power Graphs Grade 10 Simple Nonlinear Graphs Grade 10 Logarithms Grade 10 Exponential Power Graphs Grade 10 Simple Nonlinear Graphs Grade 10 Logarithms Grade 10 Exponential Power Graphs Grade 10 Simple Nonlinear Graphs Grade 10 Logarithms Grade 10 Exponential Power Graphs Grade 10 Simple Nonlinear Graphs Grade 10 Logarithms Grade 10 Logarithms 77 3P Learning

81 BC Pre-calculus 12 Str Outcome Outcome Description Activities ebooks BC.12.P.B10.3 BC.12.P.B10.4 BC.12.P.B10.5 BC.12.P.B10.6 BC.12.P.B10.7 BC.12.P.B10.8 BC.12.P.B11.1 BC.12.P.B11.2 BC.12.P.B11.3 BC.12.P.B11.4 Determine the solution of a logarithmic equation, verify the solution. Explain why a value obtained in solving a logarithmic equation may be extraneous. Solve a problem that involves exponential growth or decay. Solve a problem that involves the application of exponential equations to loans, mortgages investments. Solve a problem that involves logarithmic scales, such as the Richter scale the ph scale. Solve a problem by modelling a situation with an exponential or a logarithmic equation. Explain how long division of a polynomial expression by a binomial expression of the form x a, x Є I, is related to synthetic division. Divide a polynomial expression by a binomial expression of the form x a, x Є I, using long division or synthetic division. Explain the relationship between the linear factors of a polynomial expression the zeros of the corresponding polynomial function. Explain the relationship between the remainder when a polynomial expression is divided by x a, x Є I, the value of the polynomial expression at x=a (remainder theorem). Log Laws Change of Base Equations with Logs Exponential Growth Decay Exponential Growth Decay Compound Interest Compound Interest by Formula Future Value of Investments 1 Future Value of Investments 2 Exponential Growth Decay Compound Interest Compound Interest by Formula Future Value of Investments 1 Future Value of Investments 2 Polynomial Long Division Polynomial Factor Theorem Grade 10 Logarithms Grade 10 Polynomials Grade 10 Polynomials Grade 10 Polynomials 3P Learning 78

82 BC Pre-calculus 12 Str Outcome Outcome Description Activities ebooks BC.12.P.B11.5 BC.12.P.B12.1 BC.12.P.B12.2 BC.12.P.B12.3 BC.12.P.B12.4 BC.12.P.B12.5 BC.12.P.B12.6 BC.12.P.B12.7 BC.12.P.B13.1 BC.12.P.B13.2 BC.12.P.B13.3 BC.12.P.B13.4 Explain apply the factor theorem to express a polynomial expression as a product of factors. Identify the polynomial functions in a set of functions, explain the reasoning. Explain the role of the constant term leading coefficient in the equation of a polynomial function with respect to the graph of the function. Generalize rules for graphing polynomial functions of odd or even degree. Explain the relationship between: y the zeros of a polynomial function, y the roots of the corresponding polynomial equation, y the x-intercepts of the graph of the polynomial function. Explain how the multiplicity of a zero of a polynomial function affects the graph. Sketch, with or without technology, the graph of a polynomial function. Solve a problem by modelling a given situation with a polynomial function analyzing the graph of the function. Sketch the graph of the function y= x, using a table of values, state the domain range. Sketch the graph of the function y k=a* (b(x - h)) by applying transformations to the graph of the function y= x, state the domain range. Sketch the graph of the function y= (f(x)), given the graph of the function y=f(x), explain the strategies used. Compare the domain range of the function y= (f(x)), to the domain range of the function y=f(x), explain why the domains ranges may differ. Polynomial Factor Theorem Odd Even Polynomial Factor Theorem Grade Graphing Parabolas Graphing Cubics Parabolas Marbles Parabolas Rectangles Domain Domain Range Domain Domain Range Grade 10 Polynomials Grade 10 Polynomials Grade 10 Polynomials Grade 10 Sketching Polynomials Grade 10 Polynomials Grade 10 Sketching Polynomials 10 Polynomials Grade 10 Sketching Polynomials Grade 10 Polynomials Grade 10 Sketching Polynomials Grade 10 Polynomials Grade 10 Sketching Polynomials 79 3P Learning

83 BC Pre-calculus 12 Str Outcome Outcome Description Activities ebooks Permutations, Combinations Binomial Theorem Permutations, Combinations Binomial Theorem Permutations, Combinations Binomial Theorem Permutations, Combinations Binomial Theorem Permutations, Combinations Binomial Theorem BC.12.P.B13.5 BC.12.P.B13.6 BC.12.P.B14.1 BC.12.P.B14.2 BC.12.P.B14.3 BC.12.P.B14.4 BC.12.P.B14.5 BC.12.P.B14.6 BC.12.P.B14.7 BC.12.P.C1.1 BC.12.P.C1.2 BC.12.P.C1.3 BC.12.P.C2.1 BC.12.P.C2.2 Describe the relationship between the roots of a radical equation the x-intercepts of the graph of the corresponding radical function. Determine, graphically, an approximate solution of a radical equation. Graph, with or without technology, a rational function. Analyze the graphs of a set of rational functions to identify common characteristics. Explain the behaviour of the graph of a rational function for values of the variable near a non-permissible value. Determine if the graph of a rational function will have an asymptote or a hole for a non-permissible value. Match a set of rational functions to their graphs, explain the reasoning. Describe the relationship between the roots of a rational equation the x-intercepts of the graph of the corresponding rational function. Determine, graphically, an approximate solution of a rational equation. Count the total number of possible choices that can be made, using graphic organizers such as lists tree diagrams. Explain, using examples, why the total number of possible choices is found by multiplying rather than adding the number of ways the individual choices can be made. Solve a simple counting problem by applying the fundamental counting principle. Count, using graphic organizers such as lists tree diagrams, the number of ways of arranging the elements of a set in a row. Determine, in factorial notation, the number of permutations of n different elements taken n at a time to solve a problem. Domain Domain Range How many Combinations? Counting Techniques 1 Counting Techniques 2 How many Combinations? Counting Techniques 1 Counting Techniques 2 How many Combinations? Permutations 3P Learning 80

84 BC Pre-calculus 12 Str Outcome Outcome Description Activities ebooks Permutations, Combinations Binomial Theorem Permutations, Combinations Binomial Theorem Permutations, Combinations Binomial Theorem Permutations, Combinations Binomial Theorem Permutations, Combinations Binomial Theorem Permutations, Combinations Binomial Theorem Permutations, Combinations Binomial Theorem Permutations, Combinations Binomial Theorem Permutations, Combinations Binomial Theorem Permutations, Combinations Binomial Theorem Permutations, Combinations Binomial Theorem Permutations, Combinations Binomial Theorem BC.12.P.C2.3 BC.12.P.C2.4 BC.12.P.C2.5 BC.12.P.C2.6 BC.12.P.C3.1 BC.12.P.C3.2 BC.12.P.C3.3 BC.12.P.C3.4 BC.12.P.C3.5 BC.12.P.C3.6 BC.12.P.C4.1 BC.12.P.C4.2 Determine, using a variety of strategies, the number of permutations of n different elements taken r at a time to solve a problem. Explain why n must be greater than or equal to r in the notation n Pr. Solve an equation that involves n Pr notation, such as n P2=30. Explain, using examples, the effect on the total number of permutations when two or more elements are identical. Explain, using examples, the difference between a permutation a combination. Determine the number of ways that a subset of k elements can be selected from a set of n different elements. Determine the number of combinations of n different elements taken r at a time to solve a problem. Explain why n must be greater than or equal to r in the notation n Cr. Explain, using examples, why there exists symmetry about r n - r in n Cr. (both notations). Solve an equation that involves n Cr notation, such as n C2=15 (both notations). Explain the patterns found in the exped form of (x + y) n, n 4 n Є N, by multiplying n factors of (x + y). Explain how to determine the subsequent row in Pascal s triangle, given any row. Permutations Permutations Permutations Permutations Combinations Permutations Combinations Permutations Combinations Combinations Combinations Combinations Pascal s Triangle, Expansion Pascal s Triangle, Expansion Grade 12 Binomials Pascal's Triangle 81 3P Learning

85 BC Pre-calculus 12 Str Outcome Outcome Description Activities ebooks Permutations, Combinations Binomial Theorem Permutations, Combinations Binomial Theorem Permutations, Combinations Binomial Theorem Permutations, Combinations Binomial Theorem BC.12.P.C4.3 BC.12.P.C4.4 BC.12.P.C4.5 BC.12.P.C4.6 Relate the coefficients of the terms in the expansion of (x + y) n to the (n + 1) row in Pascal s triangle. Explain, using examples, how the coefficients of the terms in the expansion of (x + y) n are determined by combinations. Exp, using the binomial theorem, (x + y) n. Determine a specific term in the expansion of (x + y) n. Pascal s Triangle, Expansion Pascal s Triangle, Expansion Pascal s Triangle, Expansion Pascal s Triangle, Expansion 3P Learning 82

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