Duplin County Schools
7th Grade - Unit 1 – Accentuate The Negative (22 days)Things to Emphasize:IntegersNumber lineChip modelStandards:7.NS.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical line.7.NS.2 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.7.NS.3 Solve real-world and mathematical problems involving the four operations with rational numbers.7.EE.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. 7.EE.4 Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Materials/Technology:Chips (two different colors)Large number line on wall is helpfulAdditional Resources:DPI - Lessons for Learning – James BondDPI - Lessons for Learning – Sign Your NameQuick Glance:Inv 1 (all): Extending the Number SystemInv 2 (all): Adding and Subtracting Rational NumbersInv 3 (all): Multiplying and Dividing Rational NumbersInv 4 (all): Properties of OperationsVocabulary:Absolute valueAdditive inverse and identifyAlgorithmCommutative PropertyDistributive propertyExpanded formFactored formIntegersMultiplicative inverse and identityNegativeOrder of OperationsPositiveRational numbersEvidence of Learning:Unit Readiness Assessment2 Check Ups1 Partner Quiz1 Unit Test1 Unit Project1 Self Assessment1 School Net Assessment - Named: 7th Grade – Accentuate the NegativeImportant Notes:A large number line (vertical or horizontal) on the wall is an awesome tool to reference throughout the whole year7th Grade - Unit 2 – Moving Straight Ahead (20 days)Things to Emphasize:Expressions – writing, simplifying, and evaluatingEquations – writing and solvingInequalities – writing and solvingStandards:7.RP.2 – Recognize and represent proportional relationships between quantities.7.EE.1 – Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.7.EE.2 – Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related.7.EE.3 – Solve multi-step real-life and mathematical problems posed with positive and negative ration numbers in any form.7.EE.4 – Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.Materials/Technology:Additional Resources:DPI - Lessons for Learning – Number TricksDPI - Lessons for Learning - Sweet AlgebraQuick Glance:Supplemental: Review of ExpressionsInv 3 (all but 3.5): Solving EquationsSupplemental: Solving InequalitiesSupplemental: Writing Equations and InequalitiesVocabulary:CoefficientConstant termDependent variableEquationEquivalentEvaluateExpressionIndependent variableInequalityLike termsLinear relationshipProportional relationshipVariableEvidence of Learning:Unit Readiness Assessment2 Check Ups1 Partner Quiz1 Unit Project1 Unit Test1 Unit Project1 School Net Assessment - Named: 7th Grade – Moving Straight AheadImportant Notes:Make sure students get ample practice solving equations, they will have opportunites to practice throughout the school year, but this lays the foudnations7th Grade - Unit 3 – Stretching and Shrinking (20 days)Things to Emphasize:SimilarityScale factorProportional relationshipsStandards:7.RP.2 – Recognize and represent proportional relationships between quantities.7.RP.3 – Use proportional relationships to solve multistep ratio and percent problems.7.NS.3 – Solve real-world mathematical problems involving the four operations with rational numbers. (Extend to complex fractions)7.EE.4 – Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.7.G.1 – Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.7.G.2 – Draw geometric shapes with given conditions, focus on constructing triangles.Materials/Technology:Similar real life objectsRulersShapes setAdditional Resources:DPI - Lessons for Learning – Murphy to ManteoQuick Glance:Inv 1 (all): Enlarging and Reducing ShapesInv 2 (all): Similar FiguresInv 3 (all): Scaling Perimeter and AreaInv 4 (all): Similarity and RatiosVocabulary:Adjacent sidesCorresponding sides and anglesEquivalent ratiosMidpointNested trianglesOrdered pairProportionRatioScale factorSimilarEvidence of Learning:Unit Readiness Assessment2 Check Ups1 Partner Quiz1 Unit Project1 Unit Test1 Unit Project1 School Net Assessment - Named: 7th Grade – Stretching and ShrinkingImportant Notes:7th Grade - Unit 4 – Comparing and Scaling (18 days)Things to Emphasize:Proportionality in graph, table, and equationScalingEquivalent ratiosUnit rateStandards:7.RP.1 – Compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or different units.7.RP.2 – Recognize and represent proportional relationships between quantities.7.RP.3 – Use proportional relationships to solve multistep ratio and percent problems.7.NS.3 – Solve real-world mathematical problems involving the four operations with rational numbers. (Extend to complex fractions)Materials/Technology:Grid PaperCalculatorsAdditional Resources:Quick Glance:Inv 1 (all): Ways of Comparing: Ratios and ProportionsInv 2 (all): Comparing and Scaling RatesInv 3 (3.1, 3.2): Using Ratios, Percents, and Proportions Vocabulary:CommissionComplex fractionsConstant of proportionalityDiscountGratuity/taxPart-to-part ratioPart-to-whole ratioPercent of changeProportionRateRatioSimple interestUnit rateEvidence of Learning:Unit Readiness Assessment1 Check Up1 Partner Quiz1 Unit Project1 Unit Test1 Unit Project1 School Net Assessment - Named: 7th Grade – Comparing and ScalingImportant Notes:Tax, commissions, etc. are one of the most applicable areas of math that students will see on a regular basis7th Grade - Unit 5 – Shapes and Design (20 days)Things to Emphasize:Supplementary, complementary, vertical and adjacent anglesInterior and exterior angles of polygonsStandards:7.G.2 Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions.7.G.5 Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.7.EE.2 Understand that rewriting an expression in different forms in a problem context can shed light on the problem an dhow the quantities in it are related.7.EE.4 Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.Materials/Technology:PolystripsProtractors and rulesShapes setAdditional Resources:Quick Glance:Inv 1 (all): The Family of PolygonsInv 2 (all): Designing Polygons: The Angle ConnectionInv 3 (3.1, 3.2, 3.4): Designing Triangles and QuadrilateralsVocabulary:Adjacent anglesComplementary anglesDegreeExterior anglesInterior anglesParallelPerpendicularQuadrilateralsSupplementary anglesSymmetryTriangles (types)Vertical anglesEvidence of Learning:Unit Readiness Assessment1 Check Up1 Partner Quiz1 Unit Test1 Unit Project1 School Net Assessment - Named: 7th Grade – Shapes and DesignImportant Notes:7th Grade - Unit 6 – Filling and Wrapping (25 days)Things to Emphasize:VolumeSurface AreaCircle – Circumference and AreaStandards:7.NS.3 – Solve real-world and mathematical problems involving the four operations with rational numbers.7.G.3 – Describe the two-dimensional figures that result from slicing three-dimensional figures.7.G.4 - Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.7.G.6 – Solve real-world and mathematical problems involving area, volume and surface area of two-and three-dimensional objects composed of triangles, quadrilateral, polygons, cubes, and right prismsMaterials/Technology:Additional Resources:DPI Lessons for Learning – Changing Surface AreasDPI - Lessons for Learning – Packing to PerfectionDPI - Lessons for Learning – Slicing PiQuick Glance:Inv 2 (2.2, 2.3) and Supplement: Polygonal Prisms: Volume and Surface AreaInv 3 (all): Area and Circumference of CirclesVocabulary:AreaCircumferenceCross sectionCubeDiameterDimensionsEdgeFaceHorizontal Parallel cutPerpendicular cutPrismPyramidRadiusSurface areaVerticalVolumeEvidence of Learning:Unit Readiness Assessment2 Check Ups1 Partner Quiz1 Unit Project1 Unit Test1 Unit Project1 School Net Assessment - Named: 7th Grade – Filling and WrappingImportant Notes:Students need to discover pi themselves (circumference/diameter)!Only work with volume and surface area of prisms and pyramids (no cylinders, cones, or spheres in 7th grade)7th Grade - Unit 7 – What Do you Expect? (20 days)Things to Emphasize:Probability modelsSample spaceCompound eventsStandards:7.SP.5 – Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of an even occurring.7.SP.6 – Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability.7.SP.7 – Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies.7.SP.8 – Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.Materials/Technology:Additional Resources:Quick Glance:Inv 1 (all): A First Look at ChanceInv 2 (all): Experimental and Theoretical ProbabilityInv 3 (3.1, 3.2): Making Decisions With ProbabilityInv 4 (all but 4.4): Analyzing Compound Events Using an Area ModelVocabulary:Area modelCompound eventEqually likelyExpected valueExperimental probabilityFair gameFavorable outcomePredictionProbabilityRelative frequencySample spaceSimulationTheoretical probabilityTree diagramTrialEvidence of Learning:Unit Readiness Assessment1 Check Up1 Partner Quiz1 Unit Project1 Unit Test1 Unit Project1 School Net Assessment - Named: 6th Grade – What Do You Expect?Important Notes:There are so many real life examples with probability, think outside the box and do plenty of experiments Area models will be used throughout middle and high school math class, so make sure you expose students to them7th Grade - Unit 8 – Statistics (14 days)Things to Emphasize:Analyzing data more than creating data displaysComparing data and making predictionsMeasures of centerStandards:7.SP.1 – Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population.7.SP.2 – Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples of the same size to gauge the variation of estimates or predictions.7.SP.3 – Informally assess the degree of visual overlap of two numerical data distributions with similar variability, measuring the difference between the centers by expression it as a multiple of the measure of variability.7.SP.4 – Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations.Materials/Technology:Additional Resources:DPI - Lessons for Learning – X Marks the SpotSamples and Populations – CM Unit 8Georgia - Statistics Quick Glance:Samples and Populations (validity and making predictions)Box and Whisker Plots – comparing IQRS and centersMeasures of Center – median and meanComparing Data SetsVocabulary:Box plotDistributionFrequencyHistogramInferenceMADMeanMeasures of centerMedianMode RangeOutliersRandom sampleSampleSkewedVariationEvidence of Learning:Unit Readiness Assessment from Samples and PopulationsQuizzes and unit test from Samples and Populations1 School Net Assessment - Named: 7th Grade - StatisticsImportant Notes:Try and allow students to gather as much real life data, make it applicable to their life (comparing twitter users, avg shoe sale)Can pick and choose which resources you would like to use, many options for this unitGrades is always a good topic to bring in here – can compare grades throughout year and each 9 weeks ................
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