Duplin County Schools
Review at the beginning – fractions, complex fractions, and proportions, will need these concepts for Unit 1, can have review day, build into warm-ups each day, etc.Accentuate the Negative – Unit 1 (22 days)7.NS.1.; 7.NS.2; 7.NS.3; 7.EE.1; 7.EE.4bInvestigationsACE ?’sNotes1. Extending the Number SystemProblem 1.1 – Playing Math FeverUsing positive and negative numbersI can find the total value of a combination of positive and negative integers1-8, 56-58, 78DPI - Lessons for Learning – James Bond Game – fun game for students to begin to understand negative numbers Problem 1.2 – Extending the Number LineI can use a number line to compare two numbers.9-35, 59-75, 79-87Problem 1.3 – From Sauna to SnowbankUsing a number lineI can use a number line to represent a number sentence and vice versa.34-48, 76-77Problem 1.4 – In the ChipsUsing a chip modelI can use a chip model to represent addition and subtraction.49-55, 88-90Important to have multiple representations, the chips can be thought of as money and IOU’sThese chips are the concrete piece of learning about negatives, then moving to number line as representational, and then to the abstract rules – essential for students to understand the concepts behind negative numbers 2. Adding and Subtracting Rational NumbersProblem 2.1 – Extending Addition to Rational NumbersI can predict whether the result of addition of two numbers will be positive, negative, or zero.1-17, 60, 64Has a lots of fractions and decimals, so quick review (can be built in warm-ups)Problem 2.2 – Extending Subtraction to Rational NumbersI can use a chip model or number line to determine an algorithm for subtraction.18-37, 61-62, 65-66Problem 2.3 – The + / - ConnectionI can relate algorithms for addition and subtraction.38-49, 63, 67-68Problem 2.4 – Fact FamiliesI can rewrite sentences to make it easier to solve for a variable.50-59, 69Do not have to do D and E3. Multiplying and Dividing Rational NumbersProblem 3.1 – Multiplication Patterns With IntegersI can represent multiplication of inters on a number line and chipboard.1-9, 37, 49-53As a group do A, make on wall with runners, can reference the number line on the wall the whole year!Problem 3.2 – Multiplication of Rational NumbersI can use an algorithm for multiplying integers.10-13, 38-41, 54Problem 3.3 – Division of Rational NumbersI can use an algorithm for dividing integers and relate it to multiplication.14-35, 42-45, 55-59Fractions and decimalsThere are plenty of ACE questions students can use to practice simplifying expressionsConversation as class around HProblem 3.4 – Playing the Integer Product GameApplying multiplication and division integersI can observe a pattern in the game to help me win.36, 46-48, 60DPI - Lessons for Learning – “Sign” Your Name4. Properties of OperationsProblem 4.1 – Order of OperationsI can apply the order of operations for integers.1-7, 20-45, 53-63Review Order of Operations before, can be built in warm-up, students should already know this, they are just adding in working with negative numbersProblem 4.2 – The Distributive PropertyI can use the Distributive Property to expand and factor expressions involving integers.8-18, 46-52, 64-73Problem 4.3 – What Operations Are Needed?I can analyze a problem to decide what operation I will use to solve.19Brining in profit, income, and expense problems are also good herePractice with operations with negative numbersTraditional practice with operations with negative numbersVariety of practice worksheetsOnline practiceNotes: Always utilizing the chips and number line. There are Lessons for Learning activities that can support this unit as well.Do not assign all of the ACE questions. These are to pull for homework and good differentiation questions with the extensions, but they are not meant to all be assigned.Moving Straight Ahead – Unit 2 (20 days)7.EE.1; 7.EE.2; 7.EE.3; 7.EE.4; 7.RP.2InvestigationsACE ?’sNotes1. Supplement - ReviewReview of Combining Like TermsI can simplify expressions by combining like bining Like Terms – a great activity to get students to sort cards in whatever way they feel as a group, then come back together as a class to discuss sorting methodsRace to the Top Combining Like Terms – the final answer is 655xReview of Distributive Property and FactoringI can apply the Distributive Property and factor expressions.Factoring and Distributing Using Area Model – area models are used throughout middle and high schoolReview of Order of OperationsI can evaluate expressions by utilizing the Order of Operations.Order of Operations Practice – this contains different levels of worksheets, could use for differentiation3. Solving EquationsProblem 3.1 – Solving Equations Using Tables and GraphsI can relate the coordinates of a point on a table to the equation of the line.1-4, 35, 37-38, 49Problem 3.2 – Mystery Pouches in the Kingdom of MontarekExploring equalityI can discover the meaning of equality.5-8, 36, 39, 40The equal sign is the heart of all mathematics! Important to emphasize equality and what it means.Problem 3.3 – From Pouches to VariablesWriting equationsI can use the properties of equality to solve linear equations9-16, 42-43, 51Problem 3.4 - Solving Linear EquationsI can discover strategies to solve linear equations.17-29, 41, 44-47, 50, 52-53, 55-58Practice - Solving EquationsI can solve two-step equations.Bring out whiteboards, relay race, games, worksheets, etc. where students get lots of practice solvingMaking sure to include problems with variables other than x and when the variable is on the other side of the equation as wellTwo-Step Equation Practice4. InequalitiesReview – Inequalities with shading on number lineI can represent solutions to inequalities.Practice - Solving inequalitiesI can solve inequalities.Two-Step Inequalities Practice – includes number line for students to shade5. Writing equations and inequalities Practice – Writing Equations and InequalitiesI can write equations and inequalities that represent scenarios.Can reference back to the geometry unit, when finding angle measurements and students have to set up equations for vertical, adjacent, compl, and supp, anglesOnline practice Practice – Writing and Solving Equations and InequalitiesI can write and solve equations and inequalities.DPI - Lessons for Learning – Number Tricks – the “Four Column Solving” piece at the end is great! DPI - Lessons for Learning – Sweet AlgebraNotes:Do not assign all of the ACE questions. These are to pull for homework and good differentiation questions with the extensions, but they are not meant to all be assigned.Stretching and Shrinking – Unit 3 (20 days)7.G.1; 7.G.2; 7.RP.2; 7.RP.3; 7.EE.4; 7.NS.3InvestigationsNotes1. Enlarging and Reducing ShapesThis is a quick introduction, do not spend more than 2 days on these two problemsProblem 1.1 – Solving a MysteryIntroduction to similarityI can know when two figures are similar.1-4, 8-17, 20-24Can supplement on your own quickly, by bringing similar objects (same shape, different size) and having a quick class conversation about the side lengths, area, corresponding sides, angles, etc. of the similar objectsProblem 1.2 – Scaling Up and DownCorresponding sides and anglesI can determine the relationship between scale factor and the measurements of the new figure.5-7, 18-192. Similar FiguresThese wumps will be referenced throughout, could be helpful to make large ones and laminate so you can hang up and reference throughout yearProblem 2.1 – Drawing WumpsMaking similar figuresI can determine if two shapes are similar by looking at a coordinate rule.1-2, 14-15, 29Have conversation predicting what will happen to the Wumps by looking at the rule before diving in to the problemsCan separate columns into different groups to help save time and then have them present to the classProblem 2.2 – Hats Off to the WumpsChanging a figure’s size and locationI can determine what types of coordinate rules produce similar figures.3-4, 16-18, 30-31Can save time by having each group plot a different hat and show to the class, all students can fill in the table, but they would only plot 1 columnProblem 2.3 – Mouthing Off and Nosing AroundScale factorsI can decide when two shapes are similar or not.5-13, 19-28, 32-363. Scaling Perimeter and AreaProblem 3.2 – Rep-Tile TrianglesForming rep-tiles with similar trianglesI can determine which types of triangles are rep-tiles.4-6, 33-38, 45-47Problem 3.3 – Designing Under ConstraintsScale factors and similar shapesI can use scale factors to draw similar figures or find missing side lengths.7-21, 39, 48-52Problem 3.4 – Out of ReachFinding lengths with similar trianglesI can use similar triangles to find a distance.22-28, 40-42, 53 Practice – Scale drawingsI can compute actual lengths from a scale drawing.DPI - Lessons for Learning – Murphy to ManteoCould also have them draw scale drawing of classroom, school, bedroom, etc.4. Similarity and RatiosProblem 4.1 – Ratios Within Similar ParallelogramsI can find information from the ratio of adjacent side lengths within a rectangle.1-2, 41-43Problem 4.2 – Ratios Within Similar TrianglesI can use ratios of side lengths to determine if triangles are similar.3-14, 49-50Problem 4.3 – Finding Missing PartsUsing Similarity to find measurementsI can find unknown side lengths, perimeters, and area.15-18, 19-31, 44-48Problem 4.4 – Using Shadows to Find HeightsI can estimate heights of tall objects.32-39, 40, 51Students can go outside and find heights of trees, flag poles, etc. by measure shadow of object and compare to themselves with how tall they are and their own shadowNotes:The unit project is a good one for this unit dealing with scaling up and downDo not assign all of the ACE questions. These are to pull for homework and good differentiation questions with the extensions, but they are not meant to all be paring and Scaling – Unit 4 (18 days)7.RP.1; 7.RP.2; 7.RP.3, 7.NS.3InvestigationsACE ?’sNotes1. Ways of Comparing: Ratios and Proportions Problem 1.1 – Surveying OpinionsAnalyzing comparison statementsI can compare the relationship between two different quantities.1-9, 33-38, 66-74Problem 1.2 – Mixing JuiceComparing ratiosI can discover strategies to help determine which mix is more concentrated.10-12, 39-43Problem 1.3 – Time to ConcentrateScaling ratiosI can scale up or down to change units.13-18, 44-56Problem 1.4 – Keeping Things in ProportionScaling to solve proportionsI can find missing values in a proportion.19-32, 57-65, 75-78Practice – More practice solvingI can solve for missing side lengths.Can pull questions from unpacking documentsPractice Worksheets2. Comparing and Scaling RatesProblem 2.1 – Sharing PizzaComparison strategiesI can determine whether two ratios are equivalent.1-3, 14-17, 28Problem 2.2 – Comparing Pizza PricesScaling ratesI can use rate tables to find missing values.4-8, 18-23, 29Problem 2.3 – Finding CostsUnit rate and constant of proportionalityI can find a unit rate in a description, an equation, a table, and a graph.9-13, 24-26, 27Unit rate both waysPractice - More graphs, constant of proportionality, solving for tax and commissionsPull questions from unpacking documentsVariety of optionsComparing price reductions3. Using Ratios, Percents, and ProportionsProblem 3.1 – Commissions, Markups, and DiscountsProportions with percentsI can use proportions and percent tables to find various percentages.1-14, 35-38, 54Problem 3.2 – Measuring to the UnitMeasurement conversionsI can use unit rates, proportions, equations, and rate tables to scale a variety of units.15-25, 39-50, 55Incorporate practice with complex fractionsNotes:Do not assign all of the ACE questions. These are to pull for homework and good differentiation questions with the extensions, but they are not meant to all be assigned.Shapes and Design – Unit 5 (10 days)7.G.2, 7.G.5, 7.EE.2, 7.EE.4InvestigationsACE ?’sNotes1. The Family of PolygonsProblem 1.1 – Sorting and Sketching PolygonsI can analyze and sort polygons by their properties1-4, 37-44, 46, 64-65Shapes setProblem 1.2 – In a SpinAngles and rotationsI can understand angle measures and their rotations.5-9, 45, 47-48, 66-67PolystripsProblem 1.4 – Measuring AnglesI can measure an angle with a protractor and/or angle ruler.19-28, 30-32, 55-57, 68-69Ruler, angle rulers, protractorsProblem 1.5 – Design Challenge IDrawing with tools—ruler and protractorI can determine how to draw a unique triangle by using the minimum number of sides and angles.33-36, 58-63Rules, angle rulers, protractors3. Designing Triangles and Quadrilaterals Problem 3.1 – Building TrianglesI can discover ways to make triangles with side lengths and how many unique triangles can be made.1-5, 28Breaking spaghetti is a good/easy/cheap thing for students to break into 3 pieces and make triangles. Go to some students and break it for them so it won’t make a triangle.Problem 3.2 – Design Challenge IIDrawing TrianglesI can determine the smallest number of side and angle measurements to draw an exact copy of a triangle.6-9, 40Problem 3.4 – Parallel Lines and TransversalsI can discover what is true about angle measures of parallel lines cut by transversals. 17, 39Can do A-C as a whole classYou could also have students discover the relationships themselves by giving them a parallel lines cut by a transversal and a protractor and have them measure the angles to see what they observe pretty easyPractice with vertical, adjacent, supplementary, and complementary anglesNot as much with solving equations, again will come back laterOnline practiceOnline questionsNotes:Do not assign all of the ACE questions. These are to pull for homework and good differentiation questions with the extensions, but they are not meant to all be assigned.Filling and Wrapping – Unit 6 (25 days)7.G.3; 7.G.4; 7.G.6; 7.NS.3InvestigationsACE ?’sNotes2. Polygonal Prisms - Launch - Conversation around volume I can explain and understand what volume is.Stacks of paper is easy to startProblem 2.2 – Packing a PrismCalculating volume of prismsI can discover a general strategy to find the volume of any prism.3-12, 20-24, 30Problem 2.3 – Slicing Prisms and PyramidsI can determine what shapes are made when slicing 3D figures.13-14, 25-29, 31Think about Fruit Ninja or slicing a loaf of breadStick to right rectangular prisms and right rectangular pyramidsInteractive Cross Section CutterPractice - VolumeI can calculate the volume of objects.Easy to pick items in the classroom and have students find surface area and volumeDPI - Lessons for Learning – Packing to PerfectionPractice – Surface AreaI can calculate the surface area of objects.Surface area formulas are NOT expect at this level, thinking about making nets and solving by decomposing figures, building on what students’ learned from 6th gradeDPI - Lessons for Learning – Changing Surface AreasSupplement – Finding ProportionsFinding Missing LengthsPractice Worksheets3. Area and Circumference of Circles - Problem 3.1 – Going Around in CirclesCircumferenceI can determine the relationship between diameter/radius of a circle and its circumference1-9, 35, 48It’s key for students to discover pi for themselves, and students can just use the estimation of 3 for many problems involving piHave objects already in mind for students to measure and a string is usually easier for students to use to measureCircle Worksheet Aligned with Investigation – can be used to pull Problems 3.1-3.4 togetherProblem 3.2 – Pricing PizzaConnecting area, diameter, and radiusI can determine how the area of a circle increases as the circle’s radius/diameter increases.10-22, 36, 49Problem 3.4 – Connecting Circumference and AreaI can discover the relationship between the circumference and area of a circle.30-34, 44-47The connection between the circle and the parallelogram is great, can have students cut out the circle and challenge them to make another shape out of it so they can see how it forms a parallelogramCan replace this investigation with this DPI - Lessons for Learning – Slicing PiPractice – Finding circumference and areaI can find the circumference and area of a circle.Pull questions from unpacking documentsVariety of WorksheetsOnline PracticeNotes:Do not assign all of the ACE questions. These are to pull for homework and good differentiation questions with the extensions, but they are not meant to all be assigned.What Do You Expect? – Unit 7 (20 days)7.SP.5; 7.SP.6; 7.SP.7.; 7.SP.8InvestigationsACE ?’sNotes1. A First Look at Chance - Problem 1.1 – Choosing CerealTossing coins to find probabilitiesI can determine how collecting more data can help predict outcomes.1-5, 19-20, 30Coins or chips with two different colorsAlso good to keep data, get groups to compile data onto one paper and can reference throughout unit and gives more data to compareProblem 1.2 – Tossing Paper CupsFinding more probabilitiesI can model with an experiment to help determine possible outcomes and the likelihood of each outcome.6-8, 21-23, 31Paper cups, smaller ones work a little easierProblem 1.3 – One More TryFinding experimental probabilitiesI can determine the relative frequency of an outcome.9-10, 24-25Problem 1.4 – Analyzing EventsUnderstanding equally likelyI can determine whether the outcomes of an even are equally likely.11-18, 26-292. Experimental and Theoretical Probability - Problem 2.1 – Predicting to WinFinding theoretical probabilitiesI can compare experimental probability to theoretical probability.1-3, 14-17, 35Bucket containing 9 red blocks, 6 yellow blocks, and 3 blue blocksProblem 2.2 – Choosing MarblesDeveloping probability modelsI can discover properties of theoretical probabilities.4-7, 18-25Problem 2.3 – Designing a Fair GamePondering possible and probableI can decide whether a game is fair or not.8-10, 26-27, 36Coins or chips with two different colorsProblem 2.4 – Winning the Bonus PrizeUsing strategies to find theoretical probabilitiesI can determine all of the probabilities for a compound event.11-13, 28-34, 37-383. Making Decisions With Probability - Problem 3.1 – Designing a Spinner to Find ProbabilitiesI can determine probability using a spinner1-4, 15-25, 41-42Can also use the spinner on Smart Notebook ACE #15 is a good question to review fractions, decimals, and percentsProblem 3.2 – Making DecisionsAnalyzing fairnessI can determine what things we must consider when using a tool to simulate a fair game.5-8, 26-30A and B only4. Analyzing Compound Events Using an Area Model - Problem 4.1 – Drawing Area Models to Find the Sample SpaceI can use an area model to represent a situation to help analyze probabilities.1-6, 23-28, 46-49Area models are something students will use through middle school and in high school – they will need area models when they get to high school probabilityProblem 4.2 – Making PurpleArea models and probabilityI can use an area model to analyze probabilities with two-stage outcomes.7-14, 29-33, 50Problem 4.3 – One-and-One Free ThrowsSimulating a probability situationI can compare area models for different situations.15-17, 34-40, 51-52Making sure to have conversation around expected valueNotes:Do not assign all of the ACE questions. These are to pull for homework and good differentiation questions with the extensions, but they are not meant to all be assigned.Samples and Populations – Unit 8Supplement Unit (14 days)7.SP.1; 7.SP.2; 7.SP.3; 7.SP.4Resources I Can StatementsGeorgia Statistics Unit – can use this entire unit. This unit has several real life aspects of students collecting, organizing, and analyzing data.Samples and Populations Unit from Connected Math, can do whole unit with class or supplement throughout with investigations and ACE questions.Variety of Resources – you will find a variety of resources here that you can pull from.Options by Standard – this website lets you click on the specific standard and will then come up with a variety of activities, videos, etc. for each standard.NC DPI - Lessons for Learning – X Marks the Spot – 7.SP.3Fruit Loops Vs. CheeriosI can make inferences and predictions about populations.I can collect and use multiple samples of data to make generalizations.I can compare two data sets.I can collect, organize, and analyze data.I can determine and compare measures of center.I can generate multiple representations of data.I can utilize measures of center and variability to draw inferences about multiple populations. Notes:Helpful to review box and whisker plots and other representations of data at the beginning, can build into warm-ups or have a review day before diving into this unitFor 7th Grade, the emphasize is more on analyze data, rather than creating data displaysGrades is always a good topic to tie in here ................
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