Proportional Relationships CC Math 7 Time Frame: Sub-Topics

Unit Name:Sub-TopicsBig IdeaProportional RelationshipsCourse: CC Math 7Time Frame: 6 weeks Unit rates (including with complex fractions) Understanding the constant of proportionality in tables, graphs, equation, diagrams and verbal descriptions Connecting constant of proportionality, unit rate, and slope in representations Understanding what proportional means Application problems involving proportions Scale drawings with figuresRatio is a multiplicative comparison of two quantities. Proportions allow us to scale up or scale down data whilekeeping the ratio intact.Story Board/ Unit FlowHook Lesson:MakingLemonadeConcept #1:What does itmean to beproportional?Practice:Practice:Concept #2:DeterminingProportionalityRate & UnitRateSolve byComparingRatesPractice:Concept #4:(Embedded)Constant ofProportionality/EquationsPractice: WritingEquations toRepresent aProportionalRelationshipPre-Unit:Concept #3:ConnectConstant ofProp., Unit ross ProductsCommon Core Math 7 Unit Plan: Proportional ReasoningMultipleMethods forSolvingProportions1

Concept #5:RepresentingRelationshipswith EquationsProblem Solving:Concept #5:Rates andProportionsScale DrawingFiguresProblem Solving:Scale Drawings &Missing SIdeLengthsSummativeAssessmentRationale:In grade seven students extend their reasoning about ratios and proportional relationships in several ways. They identify unit rates inrepresentations of proportional relationships. They work with equations in two variables to represent and analyze proportionalrelationships. In grade seven students extend their understanding of multiplicative reasoning to proportions. Students determine iftwo quantities are in a proportional relationship and they represent proportional relationships. Students use various methods tomodel, explain and solve ratio problems with fractions. Grade seven students identify unit rates in tables, graphs, equations,diagrams, and verbal descriptions of proportional relationships. As students work with proportional relationships, they writeequations of the form y cx, where c is a constant of proportionality (i.e., a unit rate.). They recognize the unit rate as the verticalincrease in a “unit rate triangle” or “slope triangle”. Students compute lengths and reproduce a scale drawing at a different scaleEssential Questions What is a unit rate? Are these data proportional? Which method is most helpful to solve in eachsituation? What is the constant of proportionality? What has a better unit rate? When do I use proportional comparisons?Key VocabularyAbsoluteEquivalent FractionsCross-productsMultiplicativeUnit tant of ProportionalityCommon Core Math 7 Unit Plan: Proportional ReasoningPrior Knowledge Equivalent Fractions (Pre-Unit) Multiply and Divide Fractions (Prior toSolving) Solving One-Step Equations (Prior toEquations) Ratios in Tables (Pre-Unit) Use Ratio Concepts (Reviewed in HookLesson) Unit Conversions (Not necessary for thisunit, but related)2

Common Core Math Standards Taught and Assessed (M indicates Major standard, A/S indicates Additional or Supporting standard)7 Ratio and Proportional RelationshipsAnalyze proportional relationships and use them to solve real-world and mathematical problems.1. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or differentunits. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour,equivalently 2 miles per hour. (M)2. Recognize and represent proportional relationships between quantities. (M)a. Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on acoordinate plane and observing whether the graph is a straight line through the origin. (M)b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportionalrelationships. (M)c. Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchasedat a constant price p, the relationship between the total cost and the number of items can be expressed as t pn. (M)d. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to thepoints (0, 0) and (1, r) where r is the unit rate. (M)3. Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns,gratuities and commissions, fees, percent increase and decrease, percent error. (M)7 GeometryDraw, construct, and describe geometrical figures and describe the relationships between them.1. Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing andreproducing a scale drawing at a different scale. (A/S)Common Core Math 7 Unit Plan: Proportional Reasoning3

Time1-2Periods1-2PeriodsLesson TitleHook Lesson:MakingLemonadeProportional LabKnowledge Type,Claims, & MathPracticesKT: C, RKClaim: 2, 3MP: 5, 7KT: CClaim: 1, 2, 3MP: 1, 3, 8Materials Lemonade powderWater BottlesSame-Size SpoonsStrawsPaper TowelsCupsTaster Cups Stop WatchesPretzel SticksCars (Matchbox orHot Wheels)Rulers/measuringtapeTapeStudents participate in a series of activities where onetask is proportional and one is not. For each activity, theywill record the data in a t-chart and graph it.Proportional LabStudent PagesBy comparing and contrasting the two tasks inProportional Lab, students will see that Task 1 has a ratioand forms a straight line through (0,0). Then given twonew scenarios, the students will have to determine if thedata is proportional. Posters (optional)Markers (optional)Students will compare and contrast data that areproportional and data that are not proportional to comeup with four big ideas about what it means to beproportional. Then given scenarios, tables, graphs orfractions, the student will determine if the information isproportional or not. Chalk/tape formarking intervals onconcrete/blacktopMeasuring tapeStudents will sprint for different set intervals of time andcompare their results to gain a conceptual understandingof rate. They will then complete a ratio table and graphresulting pairs to discuss and analyze rate and where rateis seen in a table and a graph. 1 Period1 Period1-2PeriodsWhat Does ItMean to BeProportional?KT: CClaim: 1, 2, 3MP: 1, 3, 8UnderstandingProportionsKT: CClaim: 1, 2, 3MP: 1, 3, 8Speed RacersKT: CClaim: 1MP: 7Lesson Overview Common Core Math 7 Unit Plan: Proportional ReasoningStudents will use different ratios of powdered lemonadeand water to make and test lemonade. Students will drawtape diagrams to represent the mixtures and tounderstand the idea of ratios.4

1 PeriodSpeed RacersRevisitedKT: CClaim: 1, 2, 3,4MP: 81 PeriodUnderstandingUnit RateKT: CClaim: 1, 2, 4MP: 72Periods(Optional)Which is theBetter DealOrTeachers Find orCreate Practicewith Unit RateKT: PClaim: 1MP: 3, 6Speed RacersActivity pages Calculators(optional) Calculators(optional)Students will use ratio tables to calculate the value of “1”of something. Then they study the original and unit ratesto describe a pattern and method to calculate unit rate.Students will practice calculating unit price using theirmethod of choice. Students will use unit rate in contextto determine better deals, and analyze when a smaller orlarger unit rate is most desirable.One period should deal with unit rate of complexfractions.Rate of Changeon a Graph Slope TrianglesKT: CClaim: 1, 3MP: 5, 61 PeriodProportional LabRevisitedKT: RKClaim: 1, 2, 3,4MP: 71 PeriodTeachers Find orCreate Practice7.2dKT: PClaim: 1MP: 3, 61 Period Students will revisit the Speed Racers activity. Given anew racer and his data presented in a table, students willhave to find his speed which is also the slope of the datawhen graphed. Then they will find the slope of all theprevious characters, compare slope to speed/unit rateand constant of proportionality, and write speedequations. RulersStudents will learn to draw triangles on graphs on lines tounderstand slope as a constant ratio and as a means tocalculate slope.Proportional Labactivity sheetsStudents go back to Proportional Lab to find the slopes ofthe data using slope triangles. Then they will find unitrates and compare them to slopes to discover thatproportional relationships have a constant slope which isequal to the unit rate (constant of proportionality).NoneStudents should practice analyzing graphs that correspondto real world scenarios. Students should identify the slopeas well as the contextual meaning of a given point(emphasizing connection to unit rate). See Robot Racesfor sample.Common Core Math 7 Unit Plan: Proportional Reasoning5

1-2PeriodsPre-Unit:SolvingProportionsKT: CClaim: 1MP: 3, 81-2PeriodsPre Unit:Cross ProductsKT: CClaim: 1MP:1 PeriodPre Unit:Practice SolvingProportionsPre Unit:Rates on aDouble-SidedNumber Line1-2Periods1-2Periods1 Period2-3PeriodsProportion MatchUpFour Methods toSolve ProportionsChoose One ormore for RK:Art ClassRobot RacesLeaky FaucetsAmusement Parks NoneStudents will discover that proportions are comprised ofequivalent fractions. Students use equivalent fractions tosolve problems involving proportions. Calculators(optional)Students will discover that the cross-products ofproportions are equal. They will use that information topractice solving for the missing number in a proportion.KT: PClaim: 1MP: 3, 6 CalculatorsStudents will practice solving proportions by using eitherequivalent fractions or cross products.KT: CClaim: 1MP: 7 Two HandballsMeter SticksUsing a few scenarios such as measuring the rebound of abouncing ball from a given drop height, counting clapsover time or walking rates, students will solve proportionsby creating double-number lines.KT: PClaim: 2MP: 1, 6 CalculatorsStudents will practice building double-sided number linesfrom scenarios and set up a proportion to solve for themissing quantity.RulersCalculator(optional)Students will work out three problems in groups of 4.They are each responsible for one of four methods—double-sided number line, using unit rate, graphing, orwriting an equation. Then they will share how they solvedit in their groups and then compare and contrast themethods. They will brainstorm the benefits to using eachmethod.KT: RKClaim: 1, 2, 3,MP: 2, 3, 7, 8KT: RKClaim: 2, 3, 4MP: 7 Varies (see lessonyou select fordetails)Common Core Math 7 Unit Plan: Proportional ReasoningStudents will make predictions, explain connections, andproblem solve while using multiple representations ofproportional relationships. Each relational knowledgetasks has a unique distinction and focus.6