Grade 6 Mathematics Instructional Toolkit
Grade 6 Mathematics Instructional ToolkitThe Grade 6 Mathematics Instructional Toolkit is intended to assist teachers with planning instruction aligned tothe Florida Standards. This toolkit is not intended to replace your district’s curriculum, but rather it serves tosupport the teaching and learning of the grade 6 Mathematics Florida Standards. This toolkit includes abreakdown of information related to the Grade 6 Mathematics Florida Standards Assessment (FSA), CPALMS andFlorida Students, the Grade 6 Mathematics Florida Standards, and standards aligned resources.Grade 6 Mathematics Florida Standards AssessmentThis section highlights some key information related to the Grade 6 Mathematics FSA that can be found on theFSA Portal. These items include the Test Design Summary and Blueprint, Test Item Specifications and FSAPractice Tests.Test Design Summary and BlueprintThe grade 6 mathematics standards can be broken down into five major reporting categories as assessed on theGrade 6 Mathematics FSA with a corresponding weight. This information can also be found on page 4 of the TestDesign Summary and Blueprint. Ratio and Proportional Relationships (15%)The Number System (21%)Expressions and Equations (30%)Geometry (15%)Statistics and Probability (19%)Test Item SpecificationsThe grade 6 Test Item Specification document indicates the alignment of items with the Florida Standards.Assessment limits are included in the specifications, which define the range of content knowledge in theassessment items for the standard. Sample items for each standard are also included in the specificationsdocument. Each standard in this toolkit lists the corresponding page number in the specifications documentalong with any assessment limits.Practice TestsPractice Tests are available for students to become familiar with the various item types that may be used on theGrade 6 Mathematics FSA. Within the Test Item Specification document, page 40, is a chart aligning standards toeach item type and item number on the Paper-Based Practice Test. Each Paper-Based Practice Test is providedwith an answer key. It is important to note that students are not permitted to use a calculator of any kind on theGrade 6 Mathematics FSA.1 Page
CPALMS: Official Source of Florida StandardsThis section features information and tools that are found on CPALMS.Grade 6 Mathematics Course DescriptionThe Grade 6 Mathematics Course Description provides an overview for the course with standards alignedresources for educators, students, and parents.Mathematics Formative Assessment System (MFAS)One resource available on CPALMS that has been designed specifically for mathematics instruction is theMathematics Formative Assessment System (MFAS). The system includes a task or problem that teachers canimplement with their students. It also includes various levels of rubrics that help the teacher interpret students’responses. In addition to using the MFAS tasks as formative assessments for students, these tasks can be used byteachers to plan lessons that are closely aligned to the standards.Model Eliciting Activity (MEAs)Model Eliciting Activities (MEAs) are open-ended, interdisciplinary problem-solving activities that are meant toreveal students’ thinking about the concepts embedded in these realistic activities. Students will work in teams toapply their knowledge of mathematics and science while considering constraints and tradeoffs. Each MEA isaligned to at least two subject areas, including mathematics, English language arts and/or literacy in the contentareas, and science.Mathematical PracticesThe Mathematical Practices are habits of mind that describe varieties of expertise that mathematics educators atall levels should seek to develop in their students. The Mathematical Practices should be infused during thecourse and will be assessed throughout the Grade 6 Mathematics FSA. More information about eachMathematical Practice can be found by clicking on the links below.MAFS.K12.MP.1.1 Make sense of problems and persevere in solving them.MAFS.K12.MP.2.1 Reason abstractly and quantitatively.MAFS.K12.MP.3.1 Construct viable arguments and critique the reasoning of others.MAFS.K12.MP.4.1 Model with mathematics.MAFS.K12.MP.5.1 Use appropriate tools strategically.MAFS.K12.MP.6.1 Attend to precision.MAFS.K12.MP.7.1 Look for and make use of structure.MAFS.K12.MP.8.1 Look for and express regularity in repeated reasoning.Depth of KnowledgeFlorida has adopted Webb’s four-level Depth of Knowledge (DOK) model of content complexity as a means ofclassifying the cognitive demand presented by the Florida standards. It is important to distinguish between theDOK rating for a given standard and the possible DOK ratings for assessment items designed to address thestandard. This is particularly important for assessment purposes, since 50% or more of assessment itemsassociated with a given standard should meet or exceed the DOK level of the standard. The DOK Levels areidentified for each standard throughout this document. Please visit the CPALMS Content Complexity page for moreinformation about the DOK complexity for standards. For more information about the DOK complexity formathematics assessments, please visit page 9 of the mathematics Test Design Summary and Blueprint on the FSAPortal.2 Page
Florida StudentsResources specifically designed with students in mind are available on Florida Students. Florida Students is aninteractive site that provides educational resources and student tutorials aligned to the Florida Standards. This siteshould not be used as a lesson guide, but rather a tool to help students obtain mastery in various mathematicalconcepts.Grade 6 Mathematics Florida StandardsThis section includes a breakdown of each standard by domain and cluster. Standards should not be taught in theorder below. To do so would strip the coherence of the mathematical ideas and miss opportunity to enhance themajor work of the grade with the supporting clusters and/or standards. In addition to the breakdown, eachstandard has the corresponding DOK Level, example resources, and assessment limits with page number in theGrade 6 Mathematics Item Specification.Domain: Ratio and ProportionCluster 1 (Major): Understand ratio concepts and use ratio reasoning to solve problems.Standard CodeMAFS.6.RP.1.1MAFS.6.RP.1.2StandardUnderstand the concept of a ratio and useratio language to describe a ratio relationshipbetween two quantities. For example, “Theratio of wings to beaks in the bird house at thezoo was 2:1, because for every 2 wings therewas 1 beak.” “For every vote candidate !received, candidate C received nearly threevotes.”Content Complexity: DOK Level 2: BasicApplication of Skills & ConceptsUnderstand the concept of a unit rate a/bassociated with a ratio a:b with b 0, and userate language in the context of a ratiorelationship. For example, “This recipe has aratio of 3 cups of flour to 4 cups of sugar, sothere is 3/4 cup of flour for each cup of sugar.”“We paid 75 for 15 hamburgers, which is arate of 5 per hamburger.”Content Complexity: DOK Level 2: BasicApplication of Skills & ConceptsMAFS.6.RP.1.33 PageUse ratio and rate reasoning to solve realworld and mathematical problems, e.g., byreasoning about tables of equivalent ratios,tape diagrams, double number line diagrams,or equations.Assessment Limit(s)Page 9; Whole numbersshould be used for thequantities. Ratios can beexpressed as fractions, with“:” or with words; Items mayinvolve mixed units withineach system (e.g. converthours/min to seconds).ResourcesMFAS:InterpretingRatiosPage 10; Items using thecomparison of a ratio willuse whole numbers. Ratescan be expressed asfractions, with “:” or withwords. Items may involvemixed units within eachsystem (e.g. converthours/min to seconds).Name the amount of eitherquantity in terms of theother as long as one of thevalues is one unit.Pages 11; Rates can beexpressed as fractions, with“:” or with words; Items mayinvolve mixed units withineach system (e.g. convertMFAS: BookRatesLesson: “MyFavoriteRecipe”VirtualManipulative:Planet SizeComparison:RatioMFAS: TheMeaning of PiLesson: Don’tChase a Car!
a) Make tables of equivalent ratios relatingquantities with whole-numbermeasurements, find missing values in thetables, and plot the pairs of values on thecoordinate plane. Use tables to compareratios.b) Solve unit rate problems including thoseinvolving unit pricing and constant speed.For example, if it took 7 hours to mow 4lawns, then at that rate, how many lawnscould be mowed in 35 hours? At what ratewere lawns being mowed?c) Find a percent of a quantity as a rate per100 (e.g., 30% of a quantity means 30/100times the quantity); solve problemsinvolving finding the whole, given a partand the percent.d) Use ratio reasoning to convertmeasurement units; manipulate andtransform units appropriately whenmultiplying or dividing quantities.e) Understand the concept of Pi as the ratioof the circumference of a circle to itsdiameter.hours/min to seconds).Percent found as a rate per100. Quadrant I only forMAFS.6.RP.1.3a.There is abetter way Content Complexity: DOK Level 2: BasicApplication of Skills & ConceptsDomain: The Number SystemCluster 1 (Major): Apply and extend previous understandings of multiplication and division to divide fractions byfractions.Standard CodeMAFS.6.NS.1.14 PageStandardInterpret and compute quotients of fractions,and solve word problems involving division offractions by fractions, e.g., by using visualfraction models and equations to representthe problem. For example, create a storycontext for (2/3) (3/4) and use a visualfraction model to show the quotient; use therelationship between multiplication anddivision to explain that (2/3) (3/4) 8/9because 3/4 of 8/9 is 2/3. (In general, (a/b) (c/d) ad/bc.) How much chocolate will eachperson get if 3 people share 1/2 lb of chocolateequally? How many 3/4-cup servings are in 2/3of a cup of yogurt? How wide is a rectangularstrip of land with length 3/4 mi and area 1/2Assessment Limit(s)Page 12; At least the divisoror dividend needs to be anon-unit fraction. Dividing aunit fraction by a wholenumber or vice versa (e.g.,11 𝑞 or 𝑞 𝑎, where a is a𝑎whole number) is belowgrade level.ResourcesMFAS: JuicingFractionsLesson:Dividing byFractionsDiscovery
square mi?Content Complexity: DOK Level 2: BasicApplication of Skills & ConceptsCluster 2 (Additional): Compute fluently with multi-digit numbers and find common factors and multiples.Standard CodeMAFS.6.NS.2.2StandardFluently divide multi-digit numbers using thestandard algorithm.Content Complexity: DOK Level 1: RecallMAFS.6.NS.2.3Fluently add, subtract, multiply, and dividemulti-digit decimals using the standardalgorithm for each operation.Assessment Limit(s)Page 13; Items may onlyhave 5-digit dividendsdivided by 2-digit divisors or4-digit dividends divided by2- or 3-digit divisors.Numbers in items arelimited to non-decimalrational numbers.Page 14; Items may includevalues to the thousandthsplace. Items may be set upin standard algorithm form.ResourcesMFAS: LongDivision-2Lesson:Cracking theCode: alsContent Complexity: DOK Level 1: RecallMAFS.6.NS.2.4Find the greatest common factor of two wholenumbers less than or equal to 100 and theleast common multiple of two whole numbersless than or equal to 12. Use the distributiveproperty to express a sum of two wholenumbers 1–100 with a common factor as amultiple of a sum of two whole numbers withno common factor. For example, express 36 8 as 4 (9 2).Page 15; Whole numbersless than or equal to 100.Least common multiple oftwo whole numbers lessthan or equal to 12.Lesson:Where WillWe Stay?MFAS: UsingtheDistributivePropertyLesson:Factoring outthe GreatestContent Complexity: DOK Level 2: BasicApplication of Skills & ConceptsCluster 3 (Major): Apply and extend previous understandings of numbers to the system of rational numbers.Standard CodeMAFS.6.NS.3.55 PageStandardUnderstand that positive and negativenumbers are used together to describequantities having opposite directions or values(e.g., temperature above/below zero,elevation above/below sea level,credits/debits, positive/negative electriccharge); use positive and negative numbers torepresent quantities in real-world contexts,explaining the meaning of 0 in each situation.Assessment Limit(s)Page 16; Items should notrequire the student toperform an itive orNegative, It’sAll About
Shopping!MAFS.6.NS.3.6MAFS.6.NS.3.76 PageContent Complexity: DOK Level 2: BasicApplication of Skills & ConceptsUnderstand a rational number as a point onthe number line. Extend number line diagramsand coordinate axes familiar from previousgrades to represent points on the line and inthe plane with negative number coordinates.a) Recognize opposite signs of numbers asindicating locations on opposite sides of 0on the number line; recognize that theopposite of the opposite of a number isthe number itself, e.g., –(–3) 3, and that0 is its own opposite.b) Understand signs of numbers in orderedpairs as indicating locations in quadrantsof the coordinate plane; recognize thatwhen two ordered pairs differ only bysigns, the locations of the points arerelated by reflections across one or bothaxes.c) Find and position integers and otherrational numbers on a horizontal orvertical number line diagram; find andposition pairs of integers and otherrational numbers on a coordinate plane.Content Complexity: DOK Level 2: BasicApplication of Skills & ConceptsUnderstand ordering and absolute value ofrational numbers.a) Interpret statements of inequality asstatements about the relative position oftwo numbers on a number line diagram.For example, interpret -3 -7 as astatement that -3 is located to the right of-7 on a number line oriented from left toright.b) Write, interpret, and explain statementsof order for rational numbers in real-worldcontexts. For example, write -3 oC -7 oCto express the fact that -3 oC is warmerthan -7 oC.c) Understand the absolute value of arational number as its distance from 0 onthe number line; interpret absolute valueas magnitude for a positive or negativequantity in a real-world situation. Forexample, for an account balance of -30dollars, write -30 30 to describe thePages 17; Plotting of pointsin the coordinate planeshould include somenegative values (not justfirst quadrant). Do notexceed a 10 10 coordinategrid, though scales can vary.MFAS: PointLocationsPage 18; N/AMFAS:AbsoluteAltitudesLesson:Modern MathWarfareProblemSolving Task:Above andBelow SeaLevel
size of the debt in dollars.d) Distinguish comparisons of absolute valuefrom statements about order. Forexample, recognize that an accountbalance less than -30 dollars represents adebt greater than 30 dollars.MAFS.6.NS.3.8Content Complexity: DOK Level 2: BasicApplication of Skills & ConceptsSolve real-world and mathematical problemsby graphing points in all four quadrants of thecoordinate plane. Include use of coordinatesand absolute value to find distances betweenpoints with the same first coordinate or thesame second coordinate.Content Complexity: DOK Level 2: BasicApplication of Skills & ConceptsPage 17; Plotting of points inthe coordinate plane shouldinclude some negativevalues (not just firstquadrant).Numbers in MAFS.6.NS.3.8must be positive or negativerational numbers. Do notuse polygons/vertices forMAFS.6.NS.3.8. Do notexceed a 10 10 coordinategrid, though scales can vary.MFAS: GardenCoordinatesMEA: Dig It!Domain: Expressions and EquationsCluster 1 (Major): Apply and extend previous understandings of arithmetic to algebraic expressions.Standard CodeMAFS.6.EE.1.1StandardWrite and evaluate numerical expressionsinvolving whole-number exponents.Assessment Limit(s)Page 19; Whole numberbases. Whole numberexponents.Content Complexity: DOK Level 1: RecallMAFS.6.EE.1.27 PageWrite, read, and evaluate expressions in which Page 20; N/Aletters stand for numbers.a) Write expressions that record operationswith numbers and with letters standing fornumbers. For example, express thecalculation “Subtract y from 5” as 5 – y.b) Identify parts of an expression usingmathematical terms (sum, term, product,factor, quotient, coefficient); view one ormore parts of an expression as a singleentity. For example, describe theexpression 2 (8 7) as a product of twofactors; view (8 7) as both a single entityand a sum of two terms.c) Evaluate expressions at specific values oftheir variables. Include expressions thatarise from formulas used in real-worldResourcesMFAS: Paul’sPenniesLesson: It’sHip 2b 2eXponent sMFAS: WritingExpressionsLesson: Feelthe Heat!
problems. Perform arithmetic operations,including those involving whole-numberexponents, in the conventional orderwhen there are no parentheses to specifya particular order (Order of Operations).For example, use the formulas V s³ and A 6 s² to find the volume and surface areaof a cube with sides of length s 1/2.Content Complexity: DOK Level 2: BasicApplication of Skills & ConceptsApply the properties of operations to generateequivalent expressions. For example, apply thedistributive property to the expression 3 (2 x)to produce the equivalent expression 6 3x;apply the distributive property to theexpression 24x 18y to produce the equivalentexpression 6 (4x 3y); apply properties ofoperations to y y y to produce theequivalent expression 3y.MAFS.6.EE.1.3Content Complexity: Level 1: RecallIdentify when two expressions are equivalent(i.e., when the two expressions name thesame number regardless of which value issubstituted into them). For example, theexpressions y y y and 3y are equivalentbecause they name the same numberregardless of which number y stands for.MAFS.6.EE.1.4Page 21; Positive rationalnumbers, values mayinclude exponents. Variablesmust be included in theexpression. For items usingdistribution, coefficientsmay be fractions beforedistribution but must beinteger values aftersimplification.MFAS: EqualSides,EquivalentExpressionsPage 22; Numbers in itemsmust be nonnegativerational numbers. Variablesmust be included in sLesson:CollectivelyCollectingLesson: HaveYou Met YourMatch?Content Complexity: Level 2: Basic Applicationof Skills & ConceptsCluster 2 (Major): Reason about and solve one-variable equations and inequalities.Standard CodeMAFS.6.EE.2.5StandardUnderstand solving an equation or inequalityas a process of answering a question: whichvalues from a specified set, if any, make theequation or inequality true? Use substitutionto determine whether a given number in aspecified set makes an equation or inequalitytrue.Content Complexity: Level 2: Basic Applicationof Skills & ConceptsMAFS.6.EE.2.68 PageUse variables to represent numbers and writeexpressions when solving a real-world orAssessment Limit(s)Pages 23 & 24; Numbers initems must be nonnegativerational numbers. Onevariable linear equationsand inequalities. Anequation or inequalityshould be given if a contextis included. Inequalities arerestricted to or . Lists ofnumbers should not use setnotationPage 25; Numbers in itemsshould not require studentsResourcesMFAS: FindingSolutions ofEquationsLesson: HowMuch wasLunch?MFAS: WritingReal-World
mathematical problem; understand that avariable can represent an unknown number,or, depending on the purpose at hand, anynumber in a specified set.Content Complexity: Level 3: StrategicThinking & Complex ReasoningMAFS.6.EE.2.7Solve real-world and mathematical problemsby writing and solving equations of the form x p q and px q for cases in which p, q and xare all non-negative rational numbers.Content Complexity: Level 2: Basic Applicationof Skills & ConceptsMAFS.6.EE.2.8Write an inequality of the form x c or x c torepresent a constraint or condition in a realworld or mathematical problem. Recognizethat inequalities of the form x c or x c haveinfi
Grade 6 Mathematics Instructional Toolkit The Grade 6 Mathematics Instructional Toolkit is intended to assist teachers with planning instruction aligned to the Florida Standards. This toolkit is not intended to replace your district’s curriculum, but rather it serves to support the teaching and learnin
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