Course Number: 1205010 
Course Path: Section: Grades PreK to 12 Education Courses > Grade Group: Grades 6 to 8 Education Courses > Subject: Mathematics > SubSubject: General Mathematics > 
Abbreviated Title: M/J GRADE 6 MATH  
Course Attributes:


Course Type: Core Academic Course  Course Level: 2 
Course Status: Course Approved  
GENERAL NOTES
MAFS.6
In Grade 6, instructional time should focus on four critical areas: (1) connecting ratio and rate to whole number multiplication and division and using concepts of ratio and rate to solve problems; (2) completing understanding of division of fractions and extending the notion of number to the system of rational numbers, which includes negative numbers; (3) writing, interpreting, and using expressions and equations; and (4) developing understanding of statistical thinking.
 Students use reasoning about multiplication and division to solve ratio and rate problems about quantities. By viewing equivalent ratios and rates as deriving from, and extending, pairs of rows (or columns) in the multiplication table, and by analyzing simple drawings that indicate the relative size of quantities, students connect their understanding of multiplication and division with ratios and rates. Thus students expand the scope of problems for which they can use multiplication and division to solve problems, and they connect ratios and fractions. Students solve a wide variety of problems involving ratios and rates.
 Students use the meaning of fractions, the meanings of multiplication and division, and the relationship between multiplication and division to understand and explain why the procedures for dividing fractions make sense. Students use these operations to solve problems. Students extend their previous understandings of number and the ordering of numbers to the full system of rational numbers, which includes negative rational numbers, and in particular negative integers. They reason about the order and absolute value of rational numbers and about the location of points in all four quadrants of the coordinate plane.
 Students understand the use of variables in mathematical expressions. They write expressions and equations that correspond to given situations, evaluate expressions, and use expressions and formulas to solve problems. Students understand that expressions in different forms can be equivalent, and they use the properties of operations to rewrite expressions in equivalent forms. Students know that the solutions of an equation are the values of the variables that make the equation true. Students use properties of operations and the idea of maintaining the equality of both sides of an equation to solve simple onestep equations. Students construct and analyze tables, such as tables of quantities that are equivalent ratios, and they use equations (such as 3x = y) to describe relationships between quantities.
 Building on and reinforcing their understanding of number, students begin to develop their ability to think statistically. Students recognize that a data distribution may not have a definite center and that different ways to measure center yield different values. The median measures center in the sense that it is roughly the middle value. The mean measures center in the sense that it is the value that each data point would take on if the total of the data values were redistributed equally, and also in the sense that it is a balance point. Students recognize that a measure of variability (interquartile range or mean absolute deviation) can also be useful for summarizing data because two very different set of data can have the same mean and median yet be distinguished by their variability. Students learn to describe and summarize numerical data sets, identifying clusters, peaks, gaps, and symmetry, considering the context in which the data were collected.
Students in Grade 6 also build on their work with area in elementary school by reasoning about relationships among shapes to determine area, surface area, and volume. They find areas of right triangles, other triangles, and special quadrilaterals by decomposing these shapes, rearranging or removing pieces, and relating the shapes to rectangles. Using these methods, students discuss, develop, and justify formulas for areas of triangles and parallelograms. Students find areas of polygons and surface areas of prisms and pyramids by decomposing them into pieces whose area they can determine. They reason about right rectangular prisms with fractional side lengths to extend formulas for the volume of a right rectangular prism to fractional side lengths. They prepare for work on scale drawings and constructions in Grade 7 by drawing polygons in the coordinate plane.
English Language Development ELD Standards Special Notes Section:
Teachers are required to provide listening, speaking, reading and writing instruction that allows English language learners (ELL) to communicate information, ideas and concepts for academic success in the content area of Mathematics. For the given level of English language proficiency and with visual, graphic, or interactive support, students will interact with grade level words, expressions, sentences and discourse to process or produce language necessary for academic success. The ELD standard should specify a relevant content area concept or topic of study chosen by curriculum developers and teachers which maximizes an ELL's need for communication and social skills. To access an ELL supporting document which delineates performance definitions and descriptors, please click on the following link:
http://www.cpalms.org/uploads/docs/standards/eld/MA.pdf
For additional information on the development and implementation of the ELD standards, please contact the Bureau of Student Achievement through Language Acquisition at sala@fldoe.org.
Additional Instructional Resources:
A.V.E. for Success Collection is provided by the Florida Association of School Administrators: http://www.fasa.net/4DCGI/cms/review.html?Action=CMS_Document&DocID=139. Please be aware that these resources have not been reviewed by CPALMS and there may be a charge for the use of some of them in this collection.
Florida Standards Implementation Guide Focus Section:
The Mathematics Florida Standards Implementation Guide was created to support the teaching and learning of the Mathematics Florida Standards. The guide is compartmentalized into three components: focus, coherence, and rigor.Focus means narrowing the scope of content in each grade or course, so students achieve higher levels of understanding and experience math concepts more deeply. The Mathematics standards allow for the teaching and learning of mathematical concepts focused around major clusters at each grade level, enhanced by supporting and additional clusters. The major, supporting and additional clusters are identified, in relation to each grade or course. The cluster designations for this course are below.
Major Clusters
MAFS.6.RP.1 Understand ratio concepts and use ratio reasoning to solve problems.
MAFS.6.NS.1 Apply and extend previous understandings of multiplication and division to divide fractions.
MAFS.6.NS.3 Apply and extend previous understandings of numbers to the system of rational numbers.
MAFS.6.EE.1 Apply and extend previous understanding of arithmetic to algebraic expressions.
MAFS.6.EE.2 Reason about and solve onestep equations and inequalities.
MAFS.6.EE.3 Represent and analyze quantitative relationships between dependent and independent variables.
Supporting Clusters
MAFS.6.G.1 Solve realworld and mathematical problems involving area, surface area, and volume.
Additional Clusters
MAFS.6.NS.2 Compute fluently with multidigit numbers and find common factors and multiples.
MAFS.6.SP.1 Develop understanding of statistical variability.
MAFS.6.SP.2 Summarize and describe distributions.
Note: Clusters should not be sorted from major to supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting and additional clusters.
Course Standards
Name  Description 
MAFS.6.EE.1.1:  Write and evaluate numerical expressions involving wholenumber exponents. 
MAFS.6.EE.1.2:  Write, read, and evaluate expressions in which letters stand for numbers. Write expressions that record operations with numbers... 
MAFS.6.EE.1.3:  Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the... Remarks/Examples: Examples of Opportunities for InDepth Focus By applying properties of operations to generate equivalent expressions, students use properties of operations that they are familiar with from previous grades’ work with numbers — generalizing arithmetic in the process. 
MAFS.6.EE.1.4:  Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is... 
MAFS.6.EE.2.5:  Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any,... 
MAFS.6.EE.2.6:  Use variables to represent numbers and write expressions when solving a realworld or mathematical problem; understand that a... 
MAFS.6.EE.2.7:  Solve realworld and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which... Remarks/Examples: Examples of Opportunities for InDepth Focus When students write equations of the form x + p = q and px = q to solve realworld and mathematical problems, they draw on meanings of operations that they are familiar with from previous grades’ work. They also begin to learn algebraic approaches to solving problems.^{16} ^{16} For example, suppose Daniel went to visit his grandmother, who gave him $5.50. Then he bought a book costing $9.20 and had $2.30 left. To find how much money he had before visiting his grandmother, an algebraic approach leads to the equation x + 5.50 – 9.20 = 2.30. An arithmetic approach without using variables at all would be to begin with 2.30, then add 9.20, then subtract 5.50. This yields the desired answer, but students will eventually encounter problems in which arithmetic approaches are unrealistically difficult and algebraic approaches must be used. 
MAFS.6.EE.2.8:  Write an inequality of the form x c or x c to represent a constraint or condition in a realworld or mathematical problem.... 
MAFS.6.EE.3.9:  Use variables to represent two quantities in a realworld problem that change in relationship to one another; write an equation... 
MAFS.6.G.1.1:  Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or... 
MAFS.6.G.1.2:  Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit... 
MAFS.6.G.1.3:  Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining... 
MAFS.6.G.1.4:  Represent threedimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of... 
MAFS.6.NS.1.1:  Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by... Remarks/Examples: Examples of Opportunities for InDepth Focus This is a culminating standard for extending multiplication and division to fractions. Fluency Expectations or Examples of Culminating Standards Students interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions. This completes the extension of operations to fractions. 
MAFS.6.NS.2.2:  Fluently divide multidigit numbers using the standard algorithm. Remarks/Examples: Fluency Expectations or Examples of Culminating Standards Students fluently divide multidigit numbers using the standard algorithm. This is the culminating standard for several years’ worth of work with division of whole numbers. 
MAFS.6.NS.2.3:  Fluently add, subtract, multiply, and divide multidigit decimals using the standard algorithm for each operation. Remarks/Examples: Fluency Expectations or Examples of Culminating Standards Students fluently add, subtract, multiply, and divide multidigit decimals using the standard algorithm for each operation. This is the culminating standard for several years’ worth of work relating to the domains of Number and Operations in Base Ten, Operations and Algebraic Thinking, and Number and Operations — Fractions. 
MAFS.6.NS.2.4:  Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers... 
MAFS.6.NS.3.5:  Understand that positive and negative numbers are used together to describe quantities having opposite directions or values... 
MAFS.6.NS.3.6:  Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from... 
MAFS.6.NS.3.7:  Understand ordering and absolute value of rational numbers.Interpret statements of inequality as statements about the relative... 
MAFS.6.NS.3.8:  Solve realworld and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of... Remarks/Examples: Examples of Opportunities for InDepth Focus When students work with rational numbers in the coordinate plane to solve problems, they combine and consolidate elements from the other standards in this cluster. 
MAFS.6.RP.1.1:  Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example,... 
MAFS.6.RP.1.2:  Understand the concept of a unit rate a/b associated with a ratio a:b with b 0, and use rate language in the context of a ratio... 
MAFS.6.RP.1.3:  Use ratio and rate reasoning to solve realworld and mathematical problems, e.g., by reasoning about tables of equivalent ratios,... Remarks/Examples: Examples of Opportunities for InDepth Focus When students work toward meeting this standard, they use a range of reasoning and representations to analyze proportional relationships. 
MAFS.6.SP.1.1:  Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in... 
MAFS.6.SP.1.2:  Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center,... 
MAFS.6.SP.1.3:  Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of... 
MAFS.6.SP.2.4:  Display numerical data in plots on a number line, including dot plots, histograms, and box plots. 
MAFS.6.SP.2.5:  Summarize numerical data sets in relation to their context, such as by: Reporting the number of observations.Describing the... 
MAFS.K12.MP.1.1:  Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the... 
MAFS.K12.MP.2.1:  Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in... 
MAFS.K12.MP.3.1:  Construct viable arguments and critique the reasoning of others. Mathematically proficient students understand and use stated... 
MAFS.K12.MP.4.1:  Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in... 
MAFS.K12.MP.5.1:  Use appropriate tools strategically. Mathematically proficient students consider the available tools when solving a mathematical... 
MAFS.K12.MP.6.1:  Attend to precision. Mathematically proficient students try to communicate precisely to others. They try to use clear definitions... 
MAFS.K12.MP.7.1:  Look for and make use of structure. Mathematically proficient students look closely to discern a pattern or structure. Young... 
MAFS.K12.MP.8.1:  Look for and express regularity in repeated reasoning. Mathematically proficient students notice if calculations are repeated,... 
LAFS.6.SL.1.1:  Engage effectively in a range of collaborative discussions (oneonone, in groups, and teacherled) with diverse partners on... 
LAFS.6.SL.1.2:  Interpret information presented in diverse media and formats (e.g., visually, quantitatively, orally) and explain how it... 
LAFS.6.SL.1.3:  Delineate a speakers argument and specific claims, distinguishing claims that are supported by reasons and evidence from claims... 
LAFS.6.SL.2.4:  Present claims and findings, sequencing ideas logically and using pertinent descriptions, facts, and details to accentuate main... 
LAFS.68.RST.1.3:  Follow precisely a multistep procedure when carrying out experiments, taking measurements, or performing technical tasks. 
LAFS.68.RST.2.4:  Determine the meaning of symbols, key terms, and other domainspecific words and phrases as they are used in a specific... 
LAFS.68.RST.3.7:  Integrate quantitative or technical information expressed in words in a text with a version of that information expressed... 
LAFS.68.WHST.1.1:  Write arguments focused on disciplinespecific content. Introduce claim(s) about a topic or issue, acknowledge and distinguish... 
LAFS.68.WHST.2.4:  Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and... 
ELD.K12.ELL.MA.1:  English language learners communicate information, ideas and concepts necessary for academic success in the content area of... 
ELD.K12.ELL.SI.1:  English language learners communicate for social and instructional purposes within the school setting. 