New Brunswick Program Of Studies
MathleticsNew Brunswick Program ofStudiesUnderstanding Practice and Fluency (UPF)Grades 7 – 8November, 2021
MathleticsNew Brunswick Program of StudiesUnderstanding, Practice and Fluency (UPF)November 20211
Grade 7 . 31 Number .31.1 Develop number sense . 32 Patterns & Relations .62.1 Use patterns to describe the world and solve problems . 62.2 Represent algebraic expressions in multiple ways. 63 Shape & Space .83.1 Use direct and indirect measurement to solve problems . 83.2 Describe 3-D objects and 2-D shapes, and analyze the relationships . 83.3 Describe and analyze position and motion of objects and shapes . 84 Statistics and Probability . 104.1 Collect, display and analyze data to solve problems . 104.2 Use experimental or theoretical probabilities to solve problems. 10Grade 8 .111 Number . 111.1 Develop number sense . 112 Patterns & Relations . 132.1 Use patterns to describe the world and solve problems . 132.2 Represent algebraic expressions in multiple ways. 133 Shape & Space . 143.1 Use direct and indirect measurement to solve problems . 143.2 Describe 3-D objects and 2-D shapes, and analyze the relationships . 143.3 Describe and analyze position and motion of objects and shapes . 153.4 Collect, display and analyze data to solve problems . 153.5 Use experimental or theoretical probabilities to solve problems. 152
Grade 71 Number1.1 Develop number senseOutcomeQuests1. Determine and apply thedivisibility rules for 2, 3, 4, 5, 6, 8, 9or 10, and explain why a numbercannot be divided by 0.Divisibility rules2. Demonstrate an understandingof the addition, subtraction,multiplication and division ofdecimals (for more than1-digit divisors or 2-digitmultipliers, the use of technology isexpected) to solve problems.Operations withdecimals3. Solve problems involvingpercents from 1% to 100%.Percents, fractions &decimals4. Demonstrate an understandingof the relationship between positiverepeating decimals and positivefractions, and positive terminatingdecimals and positive fractions.Decimals & fractions3ContentIntroducing divisibility rules fordividing by 2Introducing divisibility rules fordividing by 3Introducing divisibility rules fordividing by 4Introducing divisibility rules fordividing by 5Introducing divisibility rules fordividing by 6Introducing divisibility rules fordividing by 8Introducing divisibility rules fordividing by 9Introducing divisibility rules fordividing by 10Divisibility rules: dividing by 2,3, 4, 5, 6, 10Solving decimal wordproblems, 4 operationsAdding decimalsSubtracting decimalsMultiplying decimalsMultiplying decimals usingplace valueDividing decimalsApplying order of operations,decimalsSolving word problemsinvolving percentagesConverting percents intofractions & decimalsInvestigating terminating &repeating decimalsConverting terminatingdecimals to fractionsConverting repeating decimalsto fractions
5. Demonstrate an understandingof adding and subtracting positivefractions and mixed numbers, withlike and unlike denominators,concretely, pictorially andsymbolically (limited to positivesums and differences).Add fractions & mixednumbersSubtract fractions &mixed numbers6. Demonstrate an understandingof addition and subtraction ofintegers, concretely, pictorially andsymbolically.Add & subtractfractions, wordproblemsUnderstand integersAdd & subtract integers4Converting fractions toterminating decimalsConverting fractions torepeating decimalsAdding fractions, likedenominatorAdding a whole number & afractionAdding improper fractions, likedenominatorAdding mixed numbers, likedenominatorAdding fractions, unlikedenominatorAdding improper fractions,unlike denominatorAdding mixed numbers, unlikedenominatorSubtracting fractions, likedenominatorSubtracting a fraction from awhole numberSubtracting improperfractions, like denominatorSubtracting with mixednumbers, like denominatorSubtracting fractions, unlikedenominatorSubtracting improperfractions, unlike denominatorSubtracting with mixednumbers, unlike denominatorAdding & subtractingfractions, word problemsInvestigating integersComparing & ordering integersUnderstanding opposites incontextAdding & subtracting negativeintegersAdding & subtracting integers,word problemsAdding integers with twocoloured countersAdding & subtracting integerson a number lineAdding integersSubtracting integers
7. Compare and order positivefractions, positive decimals (tothousandths) and whole numbersby using: benchmarks, place value,equivalent fractions and/ordecimals.Compare & orderfractions & decimals5Adding & subtracting integers,order of operationsOrdering fractions & decimalson a number lineIdentifying a number between2 given numbersComparing & ordering properfractionsOrdering terminating &repeating decimals
2 Patterns & Relations2.1 Use patterns to describe the world and solve problemsOutcome1. Demonstrate an understandingof oral and written patterns andtheir equivalent linear relations.2. Create a table of values from alinear relation, graph the table ofvalues, and analyze the graph todraw conclusions and solveproblems.QuestsContentPatterns & linearrelationsRepresenting written patternsas linear relationsDiscrete linear relationsGraphing discrete linearrelations using a tableMatching graphs & linearrelationsCreating tables of values forlinear relations2.2 Represent algebraic expressions in multiple waysOutcomeQuestsContent3. Demonstrate an understandingof preservation of equality by:modelling preservation of equality,concretely, pictorially andsymbolically, applying preservationof equality to solve equations.4. Explain the difference betweenan expression and an equation.Preservation of equalityUnderstanding thepreservation of equalityEquivalent forms of equationsSolving 1-step equations usinga balanceExpressions &equations5. Evaluate an expression given thevalue of the variable(s).6. Model and solve problems thatcan be represented by one-steplinear equations of the form x a b, concretely, pictorially andsymbolically, where a and b areintegers.7. Model and solve problems thatcan be represented by linearequations of the form: ax b c; ax b; x/a b, a 0 concretely,pictorially and symbolically, wherea, b and c are whole numbers.Evaluate an expressionDistinguishing betweenexpressions & equationsIdentifying parts ofexpressions & equationsEvaluating expressions usingsubstitutionSolving linear equations withintegersModelling & solving 1-stepequations, algebra tilesLinear equations,integersLinear equations,whole numbers6Solving 2-step equationsModelling & solving 2-stepequations, algebra tilesModelling real-life scenariosusing equationsSolving 1-step equationsSolving 1-step equations usingalgebra tiles
Checking solutions of twostep equations7
3 Shape & Space3.1 Use direct and indirect measurement to solve problemsOutcome1. Demonstrate an understandingof circles by: describing therelationships among radius,diameter and circumference ofcircles, relating circumference to pi,determining the sum of the centralangles, constructing circles with agiven radius or diameter, solvingproblems involving the radii,diameters and circumferences ofcircles.2. Develop and apply a formula fordetermining the area of: triangles,parallelograms, circles.QuestsContentCirclesFinding the circumference ofcirclesIntroducing the parts of acircleIntroducing circumferenceDetermining sum of the centralangles of a circleDetermine the areaDetermining the area of atriangleDetermining the area of aparallelogramDetermining the area of acircle3.2 Describe 3-D objects and 2-D shapes, and analyze the relationshipsOutcome3. Perform geometric constructions,including: perpendicular linesegments, parallel line segments,perpendicular bisectors, anglebisectors.QuestsIdentify lines & anglesContentIdentifying parallel &perpendicular lines3.3 Describe and analyze position and motion of objects and shapesOutcomeQuests4. Identify and plot points in thefour quadrants of a Cartesian planeusing integral ordered pairs.The Cartesian plane5. Perform and describetransformations (translations,Transformations on theCartesian plane8ContentIntroducing CartesiancoordinatesDrawing shapes on thecoordinate planeSuccessive translations on thecoordinate plane
rotations or reflections) of a 2-Dshape in all four quadrants of aCartesian plane (limited to integralnumber vertices).Plotting rotations on thecoordinate planePlotting reflections on thecoordinate planePlotting combinations oftransformations9
4 Statistics and Probability4.1 Collect, display and analyze data to solve problemsOutcome1. Demonstrate an understandingof central tendency and range by:determining the measures ofcentral tendency (mean, median,mode) and range, determining themost appropriate measures ofcentral tendency to report findings.2. Determine the effect on themean, median and mode when anoutlier is included in a data set.3. Construct, label and interpretcircle graphs to solve problems.QuestsContentMeasures of centraltendency & rangeMeanMedianModeRangeChoosing statistical measuresfor dataInvestigate outliersInvestigating the effect ofoutliersCircle graphsInterpreting & constructingcircle graphs4.2 Use experimental or theoretical probabilities to solve problemsOutcome4. Express probabilities as ratios,fractions and percents.5. Identify the sample space (wherethe combined sample space has 36or fewer elements) for a probabilityexperiment involving twoindependent events.6. Conduct a probability experimentto compare the theoreticalprobability (determined using a treediagram, table or another graphicorganizer) and experimentalprobability of two independentevents.QuestsContentProbability: decimal,fraction, percentSample spaceProbability: decimals, fractions& percentsIdentifying the sample spaceTheoretical &experimentalprobabilityUnderstanding independenteventsDetermining theoreticalprobability, tree diagramsExploring fair games10
Grade 81 Number1.1 Develop number senseOutcomeQuests1. Demonstrate an understandingof perfect squares and squareroots, concretely, pictorially andsymbolically (limited to wholenumbers).2. Determine the approximatesquare root of numbers that are notperfect squares (limited to wholenumbers).3. Demonstrate an understandingof percents greater than or equal to0%.Squares & square rootsPerfect squaresFinding square rootsEstimate square rootsEstimating square rootsPercents greater thanor equal to 0%4. Demonstrate an understandingof ratio and rate.5. Solve problems that involverates, ratios and proportionalreasoning.Understand ratio & rate6. Demonstrate an understandingof multiplying and dividing positivefractions and mixed numbers,concretely, pictorially andsymbolically.Multiply fractions &mixed numbersPercents greater than 100%Converting percents tofractions & mixed numbersConverting percents todecimalsSolving problems involvingconsecutive percentsIncreasing & decreasingamounts by percentsSolving problems involvingcombined percentsUnit rateIntroduction to ratiosSimplifying & comparing ratesSolving rate problemsDividing a quantity in a givenratioSolving ratio problemsSolving proportions problemsMultiplying unit fractions bywhole numbersMultiplying proper fractions bywhole numbersMultiplying mixed numbers bywhole numbersMultiplying fractionsMultiplying mixed numbersDividing fractions & wholenumbersRates, ratios &proportional reasoningDivide fractions &mixed numbers11Content
7. Demonstrate an understandingof multiplication and division ofintegers, concretely, pictorially andsymbolically.Multiply & divideintegers12Dividing fractionsDividing whole numbers &mixed numbersDividing mixed numbers &fractionsDividing mixed numbersDividing fractions, wordproblemsMultiplying integersDividing integersMultiplying & dividing integersMultiplying integers usingmodelsDividing integers using models
2 Patterns & Relations2.1 Use patterns to describe the world and solve problemsOutcome1. Graph and analyze two-variablelinear relations.QuestsLinear relationsContentGraphing discrete linearrelationshipsIdentifying equation from adiscrete linear graph2.2 Represent algebraic expressions in multiple waysOutcome2. Model and solve problems usinglinear equations of the form: ax b;x/a b, a 0; ax b c; x/a b c,a 0; a(x b) c concretely,pictorially and symbolically, wherea, b and c are integers.QuestsLinear equations,integers13ContentModelling & solving 2-steplinear equationsSolving linear equation wordproblemsSolving 2-step linearequations, mixed operationsSolving 1-step linearequations, add & subtractSolving 1-step linearequations, multiply & divideSolving 1-step linearequations, mixed operationsSolving linear equations,distributive propertyChecking solutions usingsubstitution
3 Shape & Space3.1 Use direct and indirect measurement to solve problemsOutcomeQuests1. Develop and apply thePythagorean Theorem to solveproblems.Pythagorean Theorem2. Draw and construct nets for 3-Dobjects.Nets of 3-D objects3. Determine the surface area of:right rectangular prisms, righttriangular prisms, right cylinders tosolve problems.Surface area4. Develop and apply formulas fordetermining the volume of rightprisms and right cylinders.VolumeContentIdentifying the sides of a righttriangleConverse of the PythagoreanTheoremFinding the length of themissing side, short sideFinding the length of themissing side, hypotenuseFinding the length of themissing sideMatching right triangles toword problemsIdentifying Pythagorean triplesConnecting prisms with theirnetsConnecting 3-D objects withtheir netsFinding the surface area ofrectangular prismsFinding the surface area oftriangular prismsFinding the surface area ofcylindersFinding the volume of cubes &rectangular prismsFinding the volume oftriangular prismsFinding the volume ofcylindersSolving volume problems, rightprisms & cylinders3.2 Describe 3-D objects and 2-D shapes, and analyze the relationshipsOutcomeQuests5. Draw and interpret top, front andside views of 3-D objects composedof right rectangular prisms.Top, front & side viewsof 3-D objects14ContentDrawing top, front & sideviews of 3-D objects
3.3 Describe and analyze position and motion of objects and shapesOutcome6. Demonstrate an understandingof tessellation by: explaining theproperties of shapes that maketessellating possible, creatingtessellations, identifyingtessellations in the environment.QuestsTessellationContentInvestigating tessellationsusing transformationsRecognizing tessellations3.4 Collect, display and analyze data to solve problemsOutcome1. Critique ways in which data ispresented.QuestsCritique data displaysContentCritiquing data displays3.5 Use experimental or theoretical probabilities to solve problemsOutcome2. Solve problems involving theprobability of independent events.QuestsProbability ofindependent events15ContentFinding the probability of 2independent events
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of perfect squares and square roots, concretely, pictorially and symbolically (limited to whole numbers). Squares & square roots Perfect squares Finding square roots 2. Determine the approximate square root of numbers that are not perfect squares (limited to whole numbers). Estimate square roo
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