6th Grade Math

Number and Operations

The student will develop number and operation sense needed to represent numbers and number relationships verbally, symbolically, and graphically and to compute fluently and make reasonable estimates in problem solving.

Understanding numbers/Representing Numbers/Relationships Among Numbers/Number Systems

⎯identify the place value of a given digit (6-M[HM/1,2,4,8]A/IT)

⎯represent numbers using a variety of models and equivalent forms (i.e., whole numbers, mixed numbers, fractions, decimals, and percents) (6-M[HM/1,2,4,8]A/IT)

⎯develop understanding of equivalent number representations (i.e., fractions, decimals, and percents) (6-M[HM/1,2,4,8]D/IT)

⎯compare and order whole numbers, fractions, decimals, and percents using the appropriate symbol (<, >, and =) (6-M[HM/1,2,4,8]A/IT)

⎯connect whole numbers, mixed numbers, fractions, and decimals to locations on the number line (6-M[HM/1,2,4,8]A/IT)

⎯demonstrate understanding of percents greater than 100 and less than one (6-M[HM/1,2,4,8]D/M)

⎯identify a ratio using three forms: 3 to 5; 3/5; 3:5 (6-M[HM/1,2,4,8]D/M)

⎯determine if two ratios form a proportion, and find the missing number in a proportion (6-M[HM/1,2,4,8]D/IT)

⎯identify prime and composite numbers up to 50 (6-M[HM/1,2,4,8]A/IT)

⎯develop meaning for integers using real-world examples (6-M[HM/1,2,4,8]I/E)

⎯represent integers with concrete objects, pictures, and symbols (6-M[HM/1,2,4,8]I/E)

⎯develop meaning for number theory concepts (i.e., divisibility, factors, and multiples) (6-M[HM/1,2,4,8]D/IT)

Understand operations and how they relate to one another

⎯explain how arithmetic operations on fractions and decimals affect the results (6-M[HM/1,2,4,8]D/M)

⎯use the associative and commutative properties of addition and multiplication to simplify computations with (6-M[HM/1,2,4,8]D/IT)

⎯use the distributive property to simplify computations with integers, fractions, and decimals (6-M[HM/1,2,4,8]D/IT)

⎯apply order of operations when computing with whole numbers (6-M[HM/1,2,4,8]A/IT)

⎯use the inverse relationships of addition and subtraction and multiplication and division to simplify computations and solve problems (6-M[HM/1,2,4,8]D/IT)

Solve problems, compute fluently, and make reasonable estimates

⎯compute with whole numbers, fractions, decimals, and percents in problem-solving situations (e.g., mental computation, estimation, calculators, computers, and paper and pencil) (6-M[HM/1,2,4,8]D/IT)

⎯analyze procedures for computing with fractions, decimals, and integers (6-M[HM/1,2,4,8]D/M)

⎯solve one-step real-world problems involving fractions (6-M[HM/1,2,4,8]D/M)

⎯estimate the answers to computations involving whole numbers, fractions, and decimals in real-world problems (6-M[HM/1,2,4,8]D/IT)

⎯use estimation to select a reasonable answer to a computation involving whole numbers, fractions, and/or decimals (6-M[HM/1,2,4,8]A/IT)

⎯recognize when an estimate is more appropriate than an exact answer in a variety of problem situations (6-M[HM/1,2,4,8]I/M)

⎯connect ratios to a variety of models, real-world situations, and symbolic representations (6-M[HM/6]A/M)

⎯compute efficiently and accurately with whole numbers, fractions, and decimals (6-M[HM/1,2,4,8]A/IT)

⎯select a reasonable solution to a real-world division problem in which the remainder must be considered (6-M[HM/1,2,4,8]A/IT)

⎯read, write, and represent whole numbers and decimals in expanded notation (6-M[HM/1,2,4,8]D/B)

⎯integers, fractions, and decimals (6-M[HM/1,2,4,8]D/M)

⎯apply order of operations when computing with decimals (6-M[HM/1,2,4,8]D/M)

⎯use math journals as a means of demonstrating understanding of math concepts and terms (6-M[HM/1,2,4,8]I/B)

Algebra

The student will understand and generalize patterns as they represent and analyze quantitative relationships and change in a variety of contexts and problems using graphs, tables, and equations.

Understand patterns, relations, and functions

⎯represent, analyze, and extend geometric and numerical patterns (6-M[HM/ALL]D/IT)

⎯generalize patterns in data represented in graphs (6-M[HM/ALL]D/IT)

⎯apply function rules (6-M[HM/ALL]A/IT)

Represent and analyze mathematical situations and structures using algebraic symbols

⎯develop an initial conceptual understanding of different uses of variables (6-M[HM/ALL]D/IT)

⎯represent mathematical statements and real-world situations using symbols (6-M[HM/ALL]D/IT)

⎯evaluate algebraic expressions for a given value of the variable (6-M[HM/ALL]A/IT)

⎯find missing addends or factors represented as variables in simple equations (6-M[HM/ALL]A/IT)

⎯model algebraic expressions using manipulatives, technology, and paper and pencil (6-M[HM/ALL]I/IT)

Use mathematical models to represent and understand quantitative relationships

⎯make a graph to represent a simple real-world problem or situation (6-M[HM/ALL]A/IT)

Analyze change in various contexts

⎯describe how changes in one quantity or variable result in changes in another (6-M[HM/ALL]D/IT)

⎯extend geometric and numerical patterns (6-M[HM/ALL]A/E)

⎯generalize patterns in data represented in tables (6-M[HM/ALL]A/E)

⎯select an equation that represents a given mathematical relationship

(6-M[HM/ALL]A/E)

⎯use ordered pairs to describe given points in Quadrant 1 of a coordinate system (6-M[HM/ALL]A/E)

Geometry

The student will develop an understanding of geometric concepts and relationships as the basis for geometric modeling and reasoning to solve problems involving one-, two-, and three-dimensional figures.

Analyze characteristics and properties of two- and three-dimensional shapes

⎯describe, classify, and understand relationships among types of two-dimensional figures (6-M[HM/5,7]D/M)

⎯compare and classify angles as acute, obtuse, right, and straight

⎯identify and use appropriate mathematical language to describe characteristics of lines (e.g., parallel, perpendicular,

⎯classify quadrilaterals using their defining properties (6-M[HM/5,7]A/M)

⎯describe similarity and congruence

Specify locations and describe spatial relationships using coordinate geometry and other representational systems

⎯plot a given set of points in Quadrant I of a coordinate system, use ordered pairs to describe or specify points, and find the distance between 2 points on the x- or y-axis (6-M[HM/5,7]D/E)

Apply transformations and use symmetry to analyze mathematical situations

⎯predict, and describe the results of transformations of two-dimensional figures (e.g., slides/translations, flips/ reflections, and turns/rotations) (6-M[HM/5,7]D/M)

⎯describe line and rotational symmetry in two-dimensional figures (6-M[HM/5,7]D/M)

⎯describe a motion or a series of motions that will show that two shapes are congruent. (6-M[HM/

Use visualization, spatial reasoning, and geometric modeling to solve problems

⎯draw two-and three-dimensional geometric figures with specified properties, (e.g., side lengths, angle measure) (6-M[HM/5,7]D/M)

⎯use spatial reasoning to identify the three-dimensional figure created from a two-dimensional representation (net) of that figure (i.e., cube, rectangular prism, pyramid, cone, or cylinder) (6-M[HM/5,7]A/M)

⎯use visualization and spatial reasoning (e.g., geometric models) to solve real-world problems (6-M[HM/ALL]A/M)

⎯classify two-dimensional geometric figures using properties (6-M[HM/5,7]A/M)

⎯identify parallel, perpendicular, and intersecting lines (6-M[HM/5,7]A/M)

⎯identify the results of transformations of two-dimensional figures (e.g., slides/translations, flips/reflections, and turns/rotations) (6-M[HM/5,7]A/M)

⎯identify and build a three-dimensional object from a two-dimensional representation (net) of that object and vice versa (e.g., cube, rectangular prism, pyramid, cone, or cylinder) (6-M[HM/5,7]D/M)

Measurement

The student will become familiar with the units and processes of measurement in order to use a variety of tools, techniques, and formulas to determine and to estimate measurements in mathematical and real-world problems.

Understand measurable attributes of objects and the units, systems, and processes of measurement

⎯demonstrate understanding of both metric and customary systems of measurement (6-M[HM/3,7]D/E)

⎯convert from one unit to another within the same system (metric and customary) (6-M[HM/3,7]A/M)

⎯select units of appropriate size and type to measure angles, perimeter, area, capacity, volume, and weight (6-M[HM/3,7]A/E)

Apply appropriate techniques, tools, and formulas to determine measurements

⎯estimate measurements involving length, perimeter, circumference, area, and volume (6-M[HM/3,7]D/M)

⎯use a variety of manipulatives to develop formulas to determine the area of trapezoids and circles (6-M[HM/3,7]D/E)

⎯determine the area of triangles and parallelograms using a formula (6-M[HM/3,7]D/E)

⎯explore surface area and volume of selected prisms and cylinders using models and manipulatives (6-M[HM/3,7]D/E)

⎯solve problems involving measurement using ratio and proportion (6-M[HM/3,7]D/E)

⎯use scales to read maps (6-M[HM/3,7]D/IT)

⎯recognize the need for measurement precision (6-M[HM/3,7]D/IT)

⎯use strategies to estimate perimeter and area of rectangles (6-M[HM/3,7]A/E)

⎯apply formulas to determine the area of rectangles and triangles (6-M[HM/3,7]A/E)

⎯solve problems involving ratio and proportion (6-M[HM/3,7]A/E)

⎯determine the distance between two points on the x- or the y- axis in Quadrant I A/E

⎯identify relationships among units within the same system (metric and customary) (6-M[HM/3,7]D)

⎯identify and use units of appropriate size and type to measure angles, perimeter, area, surface area, and volume (6-M[HM/3,7]D)

⎯complete investigations to develop formulas to determine the circumference of circles (6-M[HM/3,7]D/E)

Data Analysis and Probability

The student will understand and apply basic statistical and probability concepts in order to organize and analyze data and to make predictions and conjectures

Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer questions

⎯formulate questions, design studies, and collect real-world data (6-M[HM/3,6]D/IT)

⎯understand how data-collection methods affect the nature of the data set (6-M[HM/3,6]D/IT)

⎯examine various representations of data to evaluate how accurately the data is depicted (6-M[HM/3,6]D/IT)

⎯interpret bar and line graphs to answer questions and solve real-world problems (6-M[HM/ALL]A/)

Select and use appropriate statistical methods to analyze data

⎯determine, use, and interpret measures of center and spread (e.g., mean, median, mode, and interquartile range) (6-M[HM/3,6]M)

⎯connect data sets and their graphical representations (i.e., bar graphs, circle graphs, and stem-and leaf-plots) (6-M[HM/3,7])

Develop and evaluate inferences and predictions that are based on data

⎯make predictions and conjectures based on data (6-M[HM/3,7]I/D/IT)

⎯Explain the importance of sample size in investigations (6-M[HM/3,6]D/M)

⎯determine if a sample is biased ) (6-M[HM/3,6]A/M)

⎯make conjectures to formulate new questions for future studies (6-M[HM/3,6]I/M)

⎯conduct a survey using random sampling (6-M[HM/3,6]D/M)

Understand and apply basic concepts of probability

⎯make and test conjectures about the results of experiments and simulations (6-M[HM/3,6]D/M)

⎯model situations by devising and carrying out experiments and simulations (6-M[HM/3,6]D/M)

⎯determine all possible outcomes of a simple event (6-M[HM ]D/M

⎯determine the mean of a data set (6-M[HM/3,6]A/M)

⎯determine the mode of a data set (6-M[HM/3,6]A/M)

⎯determine the median from a stem-and-leaf-plot (6-M[HM/3,6]A/M)

⎯connect data sets and their graphical representations (i.e., bar graphs, circle graphs, and stem-and-leaf-plots) (6-M[HM/3,6]A/IT)

⎯use a tree diagram or organized list to determine all possible outcomes of a simple compound event (6-M[HM/3,6]A/M)

⎯represent the likelihood of an event using a number from 0-1 (6-M[HM/3,6]A/M)

Computation

The student will learn to compute using concrete objects.

Counting/Identifying/Matching/Ordering Numbers