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CURRICULUM OBJECTIVES PROBLEM SOLVING WITH WHOLE NUMBERS Types of Problems 1 2 3 Strategies FRACTIONS Terms Fractions 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 1 2 3 4 5 6 7 8 9 10 11 12 13 any combination of mathematical operations with whole numbers any combination of mathematical operations with averages, medians, modes, factors, prime numbers any combination of mathematical operations with exponents, squares of numbers, square roots develop good work habits read all parts of question carefully determine what is asked for or required separate information given from question being asked record information given and solution required separately decide what arithmetic process will solve the problem work neatly and arrange work in rows where possible label the answer in terms of values given in question estimate an answer check every step and compare with estimated answer compare estimated answer with answer found translate English statements into mathematical expressions draw pictures of problem supply missing information if necessary write full statements to answer questions develop calculator skills use clue words to solve word problems; e.g. total, sum, how much, how many, increased, altogether, less, fewer, more, difference, left, remains, times, at, divide, and each define fraction, numerator, denominator define mixed number, proper fraction define improper fractions define common denominator the proper way to write fractions compare and reduce fractions write equivalent fractions add fractions: like and unlike denominators add fractions: find common denominators subtract fractions: like and unlike denominators subtract fractions: find common denominators reduce fractions to lowest terms cancelling fractions 14 15 16 17 18 19 DECIMALS Terms Decimals PERCENT Terms Percent INTRODUCTION 1 2 3 4 5 6 7 8 9 10 11 12 13 multiply fractions divide fractions use division rule: cancel, invert 2nd fraction, then multiply change mixed numbers to improper fractions, as appropriate change improper fractions to mixed numbers, as appropriate report answer in lowest terms or mixed numbers, as appropriate 14 15 16 17 18 19 20 21 22 define: decimal, decimal system define mixed decimal define terminating decimals define repeating decimals define lowest common multiple (LCM) use of the decimal point convert mixed numbers to decimals multiply and divide by powers of 10 zero as a place holder add and subtract decimals place decimal points under each other borrowing and carrying decimals multiply decimals and placement of decimal in final answer divide decimals and placement of decimal in final answer expressing remainders as decimals round off decimals estimate when working with decimals work with money compare decimals and fractions convert decimals to fractions convert fractions to decimals convert repeating decimals to fractions 1 2 3 4 5 6 7 8 9 define percent use of the “%” sign add and subtract with percents multiply and divide with percents convert fraction to percent convert percent to fraction convert decimals to percents convert percents to decimals convert fractions to decimals to percents TO RATIO, PROPORTION, AND PERCENT Percent 1 2 3 4 5 6 7 Ratio Proportion LINES AND ANGLES Terms 8 9 10 11 12 13 14 15 16 17 18 19 20 21 1 2 3 4 5 6 7 8 9 10 Construction Angles 11 12 13 14 definition and calculation of percent use formula “r/100 = P/W” to find percent of a number use formula “r/100 = P/W” to find what percent one number is of another use formula “r/100 = P/W” to find a number when a percent is given discuss other terms: “r” represents Percent rate discuss other terms: “P” represents part of the number discuss other terms: “W“ represents the whole (entire) number define ratio how to write ratios reduce ratios distinguish between equivalent and non-equivalent ratios compare and write equivalent ratios define proportion explain relation between ratio and proportion how to write proportions discuss proportional discuss mean discuss extreme discuss product discuss true proportion discuss direct proportion define lines: point, line, line segment, ray define lines: vertex, angle, perpendicular, parallel lines define angles: acute, right, obtuse, straight, complete, reflex define transversal lines define alternate angles define corresponding angles define interior angles define angle relations: complementary, supplementary define angle relations: adjacent, vertical, opposite, exterior investigate angle relations when transversal intersects two parallel lines draw perpendic ular lines and 90 degree angles construct parallel lines label angles: 3 capital letters, middle one is vertex find relation of angles when transversal cuts parallel lines Protractor 15 16 17 18 19 INTRODUCTION TO GEOMETRIC FIGURES Definition 1 Circles 2 3 4 5 6 Polygons Three-dimensional Working with Geometric Figures 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 CHARACTERISTICS discuss angles, using circle as a base for measuring angles discuss degree as unit of measure for angles use protractor to measure angles classify angles and angle relation use three step approach to measuring an angle: center point of protractor on vertex of angle, one arm of angle on base line of protractor, and decide on measurement units/scale define geometry define and/or diagram: circle, radius , diameter define and/or diagram: circumference, chord, arc, segment, sector define and/or diagram: tangent, semi- circle measure radius, diameter, and circumference investigate relation between radius, diameter, circumference explain and use use compass to construct circle, given radius and diameter define polygon types of polygons: triangle, quadrilateral, pentagon types of polygons: hexagon, octagons recognize that polygons are named by number of sides distinguish between polygons and non-polygons distinguish between regular and irregular polygons identify concave, convex, and regular polygons types of triangles: scalene, isosceles, equilateral types of triangles: acute, obtuse, right triangles; hypotenuse explain Pythagorean Theorem types of quadrilaterals and characteristics: trapezoid parallelograms (rectangle, square, rhombus) define polyhedron explain relation between polyhedrons and polygons types: cube, prism, pyramid, cones, spheres, cylinders circle: find radius/diameter, given circumference circle: find circumference, given radius/diameter triangle: use Pythagorean Theorem to find length of one side of a triangle triangle: use Pythagorean Theorem to confirm that triangle is right triangle OF GEOMETRIC FIGURES Terms Symmetry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 Congruence 20 21 22 23 24 25 26 27 28 29 Similarity CONSTRUCTION 30 31 32 33 define symmetry define line symmetry define line of symmetry define plane of symmetry define axis of symmetry define congruence identify point segment identify ray identify plane identify vertex (vertices) identify hypotenuse identify side define similarity as it applies to geometric figures find more than one line of symmetry in certain shapes draw lines of symmetry, using compass and straight edge complete symmetrical figure, given area and line of symmetry in paper, construct shapes with more than 1 line of symmetry draw diagrams to illustrate planes of symmetry for cylinder, prism, cone, and sphere Determine number of planes of symmetry for cylinder, prism, cone, and sphere identify congruent figures (same size and shape) match vertices, segments and sides check congruence by comparing figures in various positions use slides, flips, and turns test for congruence: superimpose tracing of one figure over another figure use a compass to mark congruent segments congruent angles importance of congruence: i.e. congruent stairs are safer congruent three-dimensional objects triangle: axioms of congruence: SSS, SAS, ASA: all triangles right triangle: axioms of congruence: RSA and RSS similar figures have equal corresponding angles similar figures have proportional corresponding sides use similarity relations to calculate unknown values OF GEOMETRIC FIGURES Terms Drawing Figures 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 PROBLEM SOLVING WITH GEOMETRIC FIGURES Types of Problems Strategies 1 2 3 4 5 6 7 8 9 define: vertex, ray, arms of an angle, degree, and rotation define: right angle, acute and obtuse angles, and straight angle define complementary and supplementary angles drawing instruments: ruler, compass, divider, pencil, protractor, set square of triangle 30 degrees/60 degrees or 45 degrees construct line segments, using ruler and compass construct an angle equal to another angle, using ruler and compass right bisect a line segment, using ruler and compass construct and measure angles, using ruler, compass, and protractor designate angles: 3 capital letters – middle letter at vertex review triangles: acute, obtuse, right review triangles: equilateral (equiangular), isosceles, scalene construct and measure parallel lines construct and measure triangles construct and measure equivalent angle s construct and measure squares construct and measure rectangles construct and measure parallelograms bisect angles, using ruler and compass construct altitudes and perpendiculars, using ruler and compass construct a triangle congruent to a given triangle, using ruler, compass, and protractor practical constructions and applications requiring any combination of mathematical operations involving whole geometric figures develop good work habits read all parts of question carefully determine what is asked for or required separate information given from question being asked record information given and solution required separately decide what arithmetic process will solve the problem work neatly and arrange work in rows where possible label the answer in terms of values given in question THE METRIC SYSTEM Metric System AREA, PERIMETER, AND VOLUME Perimeter 10 11 12 13 14 15 16 17 18 estimate an answer check every step and compare with estimated answer compare estimated answer with answer found translate English statements into mathematical expressions draw pictures of problem supply missing information if necessary write full statements to answer questions develop calculator skills use clue words to solve word problems; e.g. total, sum, how much, how many, increased, altogether, less, fewer, more, difference, left, remains, times, at, divide and each 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 explain metric system and its base of ten explain International System (SI Units) fundamental units: length – metre (m) fundamental units: mass – gram (g) fundamental units: capacity – litre (L) fundamental units: time – second (s) fundamental units: temperature (degrees C) metric prefixes and abbreviations milli, ( m ) e.g. mm, mg mL centi, ( c ) e.g. cm, cg, cL deci, ( d ) e.g. dm, dg, dL unit (metre, gram, litre) m, g, L deka, ( da ) e.g. dam, dag, daL hecto, ( h ) e.g. hm, hg, hL kilo, ( k ) e.g. km, kg, kL derived units such as area (square m.) derived units such as volume (cubic cm.) derived units such as capacity (cubic dm) concept of place value convert one metric unit of measure into another 1 2 3 define perimeter explain that circumference is the perimeter of a circle formula for finding perimeter of polygons: Perimeter (P) = sum of length of all sides formula for finding perimeter of regular polygons: Perimeter (P) = number of sides (n) x length of sides (s) practice finding perimeter of a variety of figures: square, rectangle, pentagon, decagon, equilateral, irregular shapes define area measure area in square units 4 5 Area 6 7 8 9 10 11 12 13 14 15 16 17 Volume 18 19 20 21 22 formula: formula: formula: formula: 2 area of square: A = side x side = s area of a rectangle: A = length x width = l x w area of triangle: A = ½ base x height = ½ x b x h area of parallelogram: A = base x height = b x h 2 formula: area of circle: A = pi x radius squared = r area of irregular shapes surface area of 3-dimensional figures application of area: e.g. flooring coverings, paint, etc. practice finding area of rectangle, square, triangle practice finding area of cube, parallelogram, circle, irregular shapes define volume measure volume in cubic units 3 formula: volume of a cube: V = side x side x side = s formula: volume of a rectangular prism: V = length x width x height = l x w x h formula: volume of a cylinder: V = pi x radius squared x 2 23 INTRODUCTION TO INTEGERS Integers 1 2 3 4 5 6 7 8 9 10 INTRODUCTION TO EQUATIONS: EQUALITIES AND INEQUALITIES Terms 1 2 3 4 5 6 height = x r x h applications of volume: e.g. amount of gravel to buy, capacity of fuel tank, etc. review of thermometer temperature reading definition of integers using a number line standard form of integers: signs of operation standard form of integers: signs of quantity use of negative and positive integers: + shows gain use of negative and positive integers: - shows loss order integers from least to greatest and vice versa add, subtract, multiply, divide with integers practical applications of integers (golf, banking, etc.) define equation use and understand: variable, constant use and understand: algebraic expressions, term, factors, coefficient use and understand: replacement and solution order of operations (BEDMAS) symbols: +, -, x, ÷, =, and √ Equations Equalities and Inequalities PROBLEM SOLVING WITH EQUATIONS AND EQUALITIES Types of Problems Strategies 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 symbols: ( ), [ ], { } symbols: , >, <, , equality and inequality use of “• • ” in place of “x” for multiplying use letters to represent numbers order of operations solve equations use opposite operations to isolate the variable Principle of Equations: doing same thing on both sides use distributive property build equations solve equations with integers combine like terms to solve equations translate English statements into mathematical statements use mathematical symbols appropriate to grade level define equality and inequality 23 24 25 using terms equality and inequality correctly solving inequalities combine like terms to solve inequalities 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 requiring any combination of mathematical operations involving equations (equalities) and inequalities develop good work habits read all parts of question carefully determine what is asked for or required separate information given from question being asked record information given and solution required separately decide what arithmetic process will solve the problem work neatly and arrange work in rows where possible label the answer in terms of values given in question estimate an answer check every step and compare with estimated answer compare estimated answer with answer found translate English statements into mathematical expressions draw pictures of problem supply missing information if necessary write full statements to answer questions develop calculator skills 18 use clue words to solve word problems; e.g. total, sum, how much, how many, increased, altogether, less, fewer, more, difference, left, remains, times, at, divide, and each INCOME Compute Income 1 2 3 4 5 6 7 8 9 10 Deductions Income Tax MONEY MANAGEMENT Money Management Credit 11 12 13 14 15 16 17 18 19 20 21 22 1 2 3 4 5 6 7 8 9 10 11 12 13 hourly wages: compute hours worked per week find weekly wage based on hourly rate find monthly wage based on hourly rate weekly wages: find hourly rate from weekly wage and hours worked find monthly wages and annual wage monthly/bi-weekly wages: find hourly rate from monthly wage and hours worked find weekly and monthly wages calculations involving overtime pay piece work and calculations commission: define and calculate: given rate and amount of sales define and discuss: fees, tips, pensions, and bonuses define: net income, take-home pay, gross income explain and fill in Tax Exemption Return (TD1) deduction: income tax, Canada Pension, Employment Insurance other deductions: union dues, health and life insurance define terms and become familiar with current forms read information from T4 slips read information from General Tax Guide calculate: Total Income, Net Income, Taxable Income calculate tax payable: balance due or refund complete a tax return for a given case discuss disadva ntages of selling refund to tax preparers recognizing needs as opposed to wants setting immediate goals (health, clothing, housing) setting short-range goals (improving earning) setting intermediate and long-range goals (financial independence, travel, luxury items) putting goals set in order of priority achieving goals through budget and money management practice money management with sample net incomes control spending: use ledgers and journals define credit types of credit: installment plans, equalized payments types of credit: credit cards, bank loans compare interest rates on overdue payments contrast credit cards with debit cards BANKING Financial Institutions 14 15 16 17 18 19 20 investigate bank interest charges on loans how to manage credit cards advantages of credit: taking advantage of sales advantages of credit: collecting rewards/air miles disadvantages of credit: overspending disadvantages of credit: bankruptcy disadvantages of credit: items cost much more 1 chartered banks, trust companies, mortgage loan, credit union contrast bank, trust company, credit union services: savings, loans, money orders, safekeeping services: business deposits, travel services, mail service services: investment services, line of credit types of accounts: true savings – high interest on small amounts types of accounts: checking/savings types of accounts: personal checking: no interest, monthly charge types of accounts: term deposits, GICs: money locked in at a higher rate of interest discuss advantages of each type of account using a banking machine advantages and disadvantages of using a banking machine advantages and disadvantages of using telephone or internet banking fill out deposit and withdrawal slips fill out checks, money orders, and traveller’s check balance a sample account, given a balance, series of withdrawals, deposits, checks, and bank charges discuss bank charges/include in calculating bank balance reading a passbook and bank statement regular (at least monthly) bank reconciliation importance of keeping accurate up-to-date records effect of and charges for overdrafts and NSF checks 2 3 4 5 6 7 8 9 10 11 12 13 Bank Forms Balance Account 14 15 16 17 18 19 20 21 CALCULATING INTEREST Terms Simple Interest 1 2 3 4 5 6 define simple and compound interest, rate of interest, and principal define mortgage and amortization concept of making money work for you define and calculate I = Prt calculate simple interest for various amounts, times, and rates calculate value of investment at maturity Compound Interest Mortgages PROBLEM SOLVING IN PERSONAL FINANCE Types of Problems 7 8 9 10 11 12 13 14 15 16 17 18 19 20 define compound interest find compound interest using Compound Interest Tables calculate value of investment at maturity discuss advantages/disadvantages of compound interest define mortgage read an amortization table find monthly payments find total interest paid over the term of a mortgage find total amount paid at end of term discuss flexible and fixed mortgages discuss benefits of weekly or bi-weekly payments discuss anniversary dates for pay downs discuss penalties for early repayment benefits of shopping for the best rate for your purpose 1 Requiring any combination of mathematical operations involving income, money management, bank ing, or interest develop good work habits read all parts of question carefully determine what is asked for or required separate information given from question being asked record information given and solution required separately decide what arithmetic process will solve the problem work neatly and arrange work in rows where possible label the answer in terms of values given in question estimate an answer check every step and compare with estimated answer compare estimated answer with answer found translate English statements into mathematical expressions draw pictures of problem supply missing information if necessary write full statements to answer questions develop calculator skills use clue words to solve word problems; e.g. total, sum, how much, how many, increased, altogether, less, fewer, more, difference, left, remains, times, at, divide, and each 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18