Georgia Standards Of Excellence Curriculum Map Mathematics
GeorgiaStandards of ExcellenceCurriculum MapMathematicsGSE Grade 6These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement.
Georgia Department of EducationCamden Middle School GSE Grade 61st SemesterUnit 1September 21Unit 2October 18Number SystemFluencyRate, Ratio andProportionalReasoning UsingEquivalent bMGSE6.RP.3cMGSE6.RP.3d2nd SemesterUnit 3December 6Unit 4January 17ExpressionsOne-StepEquations 3dUnit 5February 14Unit 6March 21Area and ons)Unit 7May 9RationalExplorations:Numbers and GSE6.NS.7cMGSE6.NS.7dMGSE6.NS.8MGSE6.G.3Unit 8Show WhatWe KnowALLThese units were written to build upon concepts from prior units, so later units contain tasks that depend upon the concepts addressed in earlier units.All units will include the Mathematical Practices and indicate skills to maintain.NOTE: Mathematical standards are interwoven and should be addressed throughout the year in as many different units and tasks as possible in order to stress the natural connections that exist among mathematical topics.Grades 6-8 Key:NS The Number SystemRP Ratios and Proportional RelationshipsEE Expressions and EquationsG GeometrySP Statistics and Probability.Richard Woods, State School SuperintendentJuly 2016 Page 2 of 7All Rights Reserved
Georgia Department of EducationGeorgia Standards of Excellence Grade 6 MathematicsCurriculum Map RationaleUnit 1: Extending students’ experience with whole number computation in elementary grades, division of fractions by fractions and all four operations ondecimals are a focus in the first unit. Tasks utilize hands-on activities as a means to building understanding, rather than rote memorization of algorithms.Students also find common factors and multiples and deepen and extend their understanding of the distributive property to work with fractions.Unit 2: Students work extensively with ratios and rational thinking through tasks and activities that generate deep understanding. The unit explores unit rateand comparative “size”, while focusing on real-world problems.Unit 3: Students begin a more formal study of algebra as they move from arithmetic experiences to algebraic representations. Students learn to translate verbalphrases and numeric situations into algebraic expressions, understand like-terms, and work with exponential notation.Unit 4: Extending the study of algebra, students reason about and solve one-step equations and inequalities. Often two quantities are not balanced or equal,and this unit introduces them to inequalities and how numbers compare, including work with number lines.Unit 5: Students extend their work with area and volume from simple figures in elementary school to more complex figures, including those with sides offractional lengths. Complex figures will be composed and decomposed into familiar triangles and rectangles in order to compute their areas. Nets of solidfigures allow students to calculate the surface area of three-dimensional figures.Unit 6: Students are introduced to the study of statistics, first by learning what constitutes a statistical question, then by collecting data through such questionsand data sorting and analyzing. Statistical measures allow for the description of data through single-number summaries of center and distribution, and studentsexplore and become familiar with what data “looks like” and find meaning in their samples.Unit 7: Up to this point, students have only encountered numbers with values greater than or equal to zero (Natural Numbers, Counting Numbers, and WholeNumbers). Unit 7 introduces students conceptually to circumstances best described with negative numbers, numbers with a value less than zero- the set ofIntegers. Integer operations are taught in seventh grade, but by introducing students to integers in sixth grade, they have the opportunity to explore situationsappropriately represented by negative numbers, and graph points in all four quadrants of the coordinate plane. Using a number line, students learn aboutnumbers and their “opposites” (additive inverses), and absolute value (distance from zero). This unit is intentionally placed at the end of sixth grade, as it is notan expectation of the standards for sixth grade students to do any operations with integers. Instead, this unit is intended as an introduction. It leads directly intothe first seventh grade unit, Operations with Rational Numbers.Richard Woods, State School SuperintendentJuly 2016 Page 3 of 7All Rights Reserved
Georgia Department of EducationGSE Grade 6 Expanded Curriculum Map – 1st Semester1 Make sense of problems and persevere in solving them.2 Reason abstractly and quantitatively.3 Construct viable arguments and critique the reasoning of others.4 Model with mathematics.Standards for Mathematical Practice5 Use appropriate tools strategically.6 Attend to precision.7 Look for and make use of structure.8 Look for and express regularity in repeated reasoning.1st SemesterUnit 1Unit 2Unit 3Unit 4Number System FluencyRate, Ratio and ProportionalReasoning Using EquivalentExpressionsOne-Step Equations and InequalitiesApply and extend previousunderstandings of arithmetic to algebraicexpressions. MGSE6.EE.1 Write andevaluate numerical expressions involvingwhole-number exponents.MGSE6.EE.2 Write, read, andevaluate expressions in which lettersstand for numbers.MGSE6.EE.2a Write expressions thatrecord operations with numbers and withletters standing for numbers.MGSE6.EE.2b Identify parts of an expressionusing mathematical terms (sum, term, product,factor, quotient, coefficient); view one or moreparts of an expression as a single entity.MGSE6.EE.2c Evaluate expressions atspecific values for their variables. Includeexpressions that arise from formulas in realworld problems. Perform arithmeticoperations, including those involving wholenumber exponents, in the conventional orderwhen there are no parentheses to specify aparticular order (Order of Operations).MGSE6.EE.3 Apply the properties ofoperations to generate equivalent expressions.MGSE6.EE.4 Identify when two expressionsare equivalent (i.e., when the two expressionsname the same number regardless of whichvalue is substituted into them).MGSE6.NS.4 Find the common multiples oftwo whole numbers less than or equal to 12and the common factors of two whole numbersless than or equal to 100.a. Find the greatest common factor of 2whole numbers and use the distributiveproperty to express a sum of two wholenumbers 1-100 with a common factorReason about and solve onevariable equations and inequalities.MGSE6.EE.5 Understand solving an equationor inequality as a process of answering aquestion: which values from a specified set, ifany, make the equation or inequality true? Usesubstitution to determine whether a givennumber in a specified set makes an equation orinequality true.MGSE6.EE.6 Use variables to representnumbers and write expressions when solving areal-world or mathematical problem;understand that a variable can represent anunknown number, or, depending on thepurpose at hand, any number in a specified set.MGSE6.EE.7 Solve real-world andmathematical problems by writing and solvingequations of the form 𝑥𝑥 𝑝𝑝 𝑞𝑞 and 𝑝𝑝𝑝𝑝 𝑞𝑞 forcases in which p, q and x are all nonnegativerational numbers.MGSE6.EE.8 Write an inequality of the form𝑥𝑥 𝑐𝑐 or 𝑥𝑥 𝑐𝑐 to represent a constraint orcondition in a real-world or mathematicalproblem. Recognize that inequalities of theform 𝑥𝑥 𝑐𝑐 or 𝑥𝑥 𝑐𝑐 have infinitely manysolutions; represent solutions of suchinequalities on number line diagrams.Represent and analyzequantitative relationships betweendependent and independent variables.MGSE6.EE.9 Use variables to represent twoquantities in a real-world problem that changein relationship to one another.a. Write an equation to express one quantity,the dependent variable, in terms of theother quantity, the independent variable.Apply and extend previousUnderstand ratio concepts and useunderstandings of multiplication andratio reasoning to solve problems.division to divide fractions by fractions.MGSE6.RP.1 Understand the concept of aMGSE6.NS.1 Interpret and computeratio and use ratio language to describe aratio relationship between two quantities.quotients of fractions, and solve wordFor example, “The ratio of wings to beaksproblems involving division of fractions byin the bird house at the zoo was 2:1,fractions, including reasoning strategies such asbecause for every 2 wings there was 1using visual fraction models and equations tobeak.” “For every vote candidate Arepresent the problem.received, candidate C received nearlyFor example: How much chocolate will each person get if three votes.”MGSE6.RP.2 Understand the concept of a3 people share 1/2 lb of chocolate equally?rate a / b associated with a ratio a: b How many 3/4-cup servings are in 2/3 of a unitwith b 0 (b not equal to zero), and usecup of yogurt?rate language in the context of a ratio How wide is a rectangular strip of landrelationship. For example, "This recipewith length 3/4 mi and area 1/2 square mi?has a ratio of 3 cups of flour to 4 cups of Create a story context for (2/3) (3/4)andsugar, so there is 3/4 cup of flour for eachuse a visual fraction model to show thecup of sugar." "We paid 75 for 15quotient;hamburgers, which is a rate of 5 per Three pizzas are cut so each person at the hamburger."table receives ¼ pizza. How many people are MGSE6.RP.3 Use ratio and rate reasoningat the table?to solve real-world and mathematical Use the relationship between multiplication problems utilizing strategies such as tablesof equivalent ratios, tape diagrams (barand division to explain that (2/3) (3/4) models), double number line diagrams,8/9 becaus3 3/4 of 8/9 is2/3. (In general,and/or equations.(a/b) (c/d) ad/bc.)MGSE6.RP.3a Make tables of equivalentCompute fluently with multi-digitratios relating quantities with whole-numbernumbers and find common factors andmeasurements, find missing values in themultiples. MGSE6.NS.2 Fluently dividetables, and plot the pairs of values on themulti-digit numbers using the standardcoordinate plane. Use tables to comparealgorithm.ratios.MGSE6.NS.3 Fluently add, subtract, multiply,MGSE6.RP.3b Solve unit rate problemsand divide multi‐digit decimals using theincluding those involving unit pricing andstandard algorithm for each operation.constant speed. For example, If it took 7 hoursMGSE6.NS.4 Find the common multiples oftwo whole numbers less than or equal to 12 and to mow 4 lawns, then at that rate, how manyRichard Woods, State School SuperintendentJuly 2016 Page 4 of 7All Rights Reserved
Georgia Department of Educationthan or equal to 100.a. Find the greatest common factor of 2whole numbers and use the distributiveproperty to express a sum of two wholenumbers 1-100 with a common factor as amultiple of a sum of two whole numberswith no common factors. (GCF)Example: 36 8 4(9 2)b. Apply the least common multiple of twowhole numbers less than or equal to 12 tosolve real-world problems.lawns could be mowed in 35 hours? At whatrate were lawns being mowed?MGSE6.RP.3c Find a percent of a quantity asa rate per 100 (e.g. 30% of a quantity means30/100 times the quantity); given a percent,solve problems involving finding the wholegiven a part and the part given the whole.MGSE6.RP.3d Given a conversion factor, useratio reasoning to convert measurement unitswithin one system of measurement andbetween two systems of measurements(customary and metric); manipulate andtransform units appropriately whenmultiplying or dividing quantities. Forexample, given 1 in. 2.54 cm, how manycentimeters are in 6 inches?b.as a multiple of a sum of two wholenumbers with no common factors. (GCF)Example: 36 8 4(9 2)Apply the least common multiple of twowhole numbers less than or equal to 12 tosolve real-world problems.Richard Woods, State School SuperintendentJuly 2016 Page 5 of 7All Rights Reservedb.Analyze the relationship between thedependent and independent variablesusing graphs and tables, and relate theseto the equation. For example, in aproblem involving motion at constantspeed, list and graph ordered pairs ofdistances and times, and write theequation d 65t to represent therelationship between distance and time.Understand ratio concepts and useratio reasoning to solve problems.MGSE6.RP.3 Use ratio and rate reasoning tosolve real-world and mathematical problems,e.g., by reasoning about tables of equivalentratios, tape diagrams, double number linediagrams, or equations.MGSE6.RP.3a Make tables of equivalentratios relating quantities with whole-numbermeasurements, find missing values in thetables, and plot the pairs of values on thecoordinate plane. Use tables to compare ratios.MGSE6.RP.3b Solve unit rate problemsincluding those involving unit pricing andconstant speed.MGSE6.RP.3c Find a percent of a quantity asa rate per 100 (e.g. 30% of a quantity means30/100 times the quantity); given a percent,solve problems involving finding the wholegiven a part and the part given the whole.MGSE6.RP.3d Given a conversion factor, useratio reasoning to convert measurement unitswithin one system of measurement andbetween two systems of measurements(customary and metric); manipulate andtransform units appropriately whenmultiplying or dividing quantities. Forexample, given 1 in. 2.54 cm, how manycentimeters are in 6 inches?
Georgia Department of EducationGSE Grade 6 Expanded Curriculum Map – 2nd SemesterStandards for Mathematical Practice1 Make sense of problems and persevere in solving them.2 Reason abstractly and quantitatively.3 Construct viable arguments and critique the reasoning of others.4 Model with mathematics.5 Use appropriate tools strategically.6 Attend to precision.7 Look for and make use of structure.8 Look for and express regularity in repeated reasoning.2nd SemesterUnit 5Area and VolumeUnit 6StatisticsUnit 7Rational Explorations: Numbers andtheir OppositesUnit 8Show What We KnowSolve real-world andmathematical problems involving area,surface area, and volume.MGSE6.G.1 Find area of right triangles,other triangles, quadrilaterals, and polygonsby composing into rectangles or decomposinginto triangles and other shapes; apply thesetechniques in the context of solving real-worldand mathematical problems.MGSE6.G.2 Find the volume of a rightrectangular prism with fractional edge lengthsby packing it with unit cubes of theappropriate unit fraction edge lengths (1/2 u),and show that the volume is the same aswould be found by multiplying the edgelengths of the prism. Apply the formulas V (length) x (width) x (height) and V (area ofbase) x (height) to find volumes of rightrectangular prisms with fractional edgelengths in the context of solving real-worldand mathematical problems.MGSE6.G.4 Represent three-dimensionalfigures using nets made up of rectangles andtriangles, and use the nets to find the surfacearea of these figures. Apply these techniques inthe context of solving real-world andmathematical problems.Develop understanding ofstatistical variability.MGSE6.SP.1 Recognize a statistical questionas one that anticipates variability in the datarelated to the question and accounts for it inthe answers.MGSE6.SP.2 Understand that a set of datacollected to answer a statistical question has adistribution which can be described by itscenter, spread, and overall shape.MGSE6.SP.3 Recognize that a measure ofcenter for a numerical data set summarizes allof its values with a single number, while ameasure of variation describes how its valuesvary with a single number.Summarize and describe distributions.MGSE6.SP.4 Display numerical data in plotson a number line, including dot plots,histograms, and box plots.MGSE6.SP.5 Summarize numerical data setsin relation to their context, such as by:a. Reporting the number of observations.b. Describing the nature of the attributeunder investigation, including how it wasmeasured and its units of measurement.c. Giving quantitative measures of center(median and/or mean) and variability(interquartile range).d. Relating the choice of measures of centerand variability to the shape of the datadistribution and the context in which thedata was gathered.Apply and extend previousunderstandings of numbers to the system ofrational numbers.MGSE6.NS.5 Understand that positive andnegative numbers are used together to describequantities having opposite directions or values(e.g., temperature above/below zero, elevationabove/below sea level, debits/credits,positive/negative electric charge); use positiveand negative numbers to represent quantities inreal-world contexts, explaining the meaning of0 in each situation.MGSE6.NS.6 Understand a rational numberas a point on the number line. Extend numberline diagrams and coordinate axes familiarfrom previous grades to represent points on theline and in the plane with negative numbercoordinates.MGSE6.NS.6a Recognize opposite signs ofnumbers as indicating locations on oppositesides of 0 on the number line; recognize thatthe opposite of the opposite of a number is thenumber itself, e.g., –(–3) 3, and that 0 is itsown opposite.MGSE6.NS.6b Understand signs of numbersin ordered pairs as indicating locations inquadrants of the coordinate plane; recognizethat when two ordered pairs differ only bysigns, the locations of the points are related byreflections across one or both axes.MGSE6.NS.6c Find and position integers andother rational numbers on a horizontal orvertical number line diagram; find and positionpairs of integers and other rational numbers ona coordinate plane.ALLRichard Woods, State School SuperintendentJuly 2016 Page 6 of 7All Rights Reserved
Georgia Department of EducationMGSE6.NS.7 Understand ordering andabsolute value of rational numbers.MGSE6.NS.7a Interpret statements ofinequality as statements about the relativeposition of two numbers on a number linediagram.MGSE6.NS.7b Write, interpret, and explainstatements of order for rational numbers inreal-world contexts.MGSE6.NS.7c Understand the absolute valueof a rational number as its distance from 0 onthe number line; interpret absolute value asmagnitude for a positive or negative quantityin a real-world situation.MGSE6.NS.7d Distinguish comparisons ofabsolute value from statements about order.MGSE6.NS.8 Solve real-world andmathematical problems by graphing points inall four quadrants of the coordinate plane.Include use of coordinates and absolute valueto find distances between points with the samefirst coordinate or the same second coordinate.Solve real-world andmathematical problems involving area,surface area, and volume.MGSE6.G.3 Draw polygons in the coordinateplane given coordinates for the vertices; usecoordinates to find the length of a side joiningpoints with the same first coordinate or thesame second coordinate. Apply thesetechniques in the context of solving real-worldand mathematical problems.Richard Woods, State School SuperintendentJuly 2016 Page 7 of 7All Rights Reserved
Georgia Standards of Excellence Grade 6 Mathematics Curriculum Map Rationale . Unit 1: Extending students’ experience with whole number computation in elementary grades, division of fractions by fractions and all four operations on decimals are a focus in the first unit. Tasks utilize hands-on activities as a means to building understanding,
Curriculum for Excellence Management Board’s foreword The Curriculum for Excellence Management Board is committed to a staged approach to ensuring assessment meets the needs of all learners, as an integral part of Curriculum for Excellence. The first stage was the announcement by the Cabinet Secretary's predecessor on 23 September 2009 of key
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Georgia Studies Teacher Notes for the Georgia Standards of Excellence in Social Studies Georgia Department of Education 7.13.2020 Page 1 of 159 The Teacher Notes were developed to help teachers understand the depth and breadth of the standards. In some cases, information provided in this document goes beyond the scope of the standards and can be used for background and enrichment information .
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Georgia Department of Education July 2019 Page 3 of 7 Georgia Standards of Excellence Grade 7 Mathematics Curriculum Map Rationale Unit 1: Building upon the understanding of rational numbers developed in 6th grade, this unit moves to exploring and ultimately formalizing rules for operations (addition, subtraction, multiplication and division) with integers.
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Artificial intelligence (AI) – a broad concept used in policy discussions to refer to many different types of technology – greatly influences and impacts the way people seek, receive, impart and access information and how they exercise their right to freedom of expression in the digital ecosystem. If implemented responsibly, AI can benefit societies, but there is a genuine risk that its .
