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6.NO
Number and Operations
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6.NO.1
Students shall understand numbers, ways of representing numbers, relationships among numbers and number systems.
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6
Rational Numbers
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6.NO.1.6.1
Demonstrate conceptual understanding to find a specific percent of a number, using models, real-life examples, or explanations
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6.NO.1.6.2
Find decimal and percent equivalents for proper fractions and explain why they represent the same value
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6.NO.1.6.3
Round and compare decimals to a given place value including thousandths
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6.NO.1.6.4
Convert, compare and order fractions (mixed numbers and improper fractions) decimals and percents and find their approximate locations on a number line
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Decimal numbers: Convert decimals to mixed numbers (Sixth grade - B.4)
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Decimal numbers: Decimal number lines (Sixth grade - B.9)
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Rational numbers: Compare rational numbers (Sixth grade - D.1)
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Rational numbers: Put rational numbers in order (Sixth grade - D.2)
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Fractions and mixed numbers: Compare fractions with like and unlike denominators (Sixth grade - T.6)
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Fractions and mixed numbers: Compare fractions: word problems (Sixth grade - T.7)
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Fractions and mixed numbers: Convert between improper fractions and mixed numbers (Sixth grade - T.8)
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Fractions and mixed numbers: Convert between decimals and fractions or mixed numbers (Sixth grade - T.9)
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Fractions and mixed numbers: Put a mix of decimals, fractions, and mixed numbers in order (Sixth grade - T.10)
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Ratios, proportions, and percents: Convert between percents, fractions, and decimals (Sixth grade - Z.6)
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Ratios, proportions, and percents: Compare percents to each other and to fractions (Sixth grade - Z.7)
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Ratios, proportions, and percents: Compare percents and fractions: word problems (Sixth grade - Z.8)
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6.NO.1.6.5
Recognize and identify perfect squares and their square roots
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6.NO.2
Students shall understand meanings of operations and how they relate to one another.
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6
Number Theory
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6.NO.2.6.1
Use divisibility rules to determine if a number is a factor of another number (4, 6, 9)
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6.NO.2.6.2
Apply the distributive property of multiplication over addition to simplify computations with whole numbers
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6.NO.2.6.3
Apply the addition, subtraction, multiplication and division properties of equality to onestep equations with whole numbers
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6.NO.2.6.4
Apply rules (conventions) for order of operations to whole numbers with and without parentheses
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6
Understand Operations
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6.NO.2.6.5
Model multiplication and division of fractions (including mixed numbers) and decimals using pictures and physical objects
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6.NO.3
Students shall compute fluently and make reasonable estimates.
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6
Computational Fluency
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6.NO.3.6.1
Apply, with and without appropriate technology, algorithms with computational fluency to perform whole number operations (+, -, x, /)
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6.NO.3.6.2
Develop and analyze algorithms for computing with fractions (including mixed numbers) and decimals and demonstrate, with and without technology, computational fluency in their use and justify the solution
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6.NO.3.6.3
Solve, with and without appropriate technology, multistep problems using a variety of methods and tools (i.e., objects, mental computation, paper and pencil)
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6
Estimation
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6.NO.3.6.4
Estimate reasonable solutions to problem situations involving fractions and decimals
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6
Application of Computation
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6.NO.3.6.5
Find and use factorization (tree diagram) including prime factorization of composite numbers (expanded and exponential notation) to determine the greatest common factor (GCF) and least common multiple (LCM)
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6.NO.3.6.6
Use proportional reasoning and ratios to represent problem situations and determine the reasonableness of solutions with and without appropriate technology (Ex. unit rates)
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Consumer math: Unit prices: which is the better buy? (Sixth grade - G.2)
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Consumer math: Unit prices with fractions and decimals (Sixth grade - G.3)
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Ratios, proportions, and percents: Write a ratio to describe objects in a picture (Sixth grade - Z.1)
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Ratios, proportions, and percents: Equivalent ratios (Sixth grade - Z.2)
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Ratios, proportions, and percents: Proportions (Sixth grade - Z.3)
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Ratios, proportions, and percents: Unit rates and equivalent rates (Sixth grade - Z.4)
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Ratios, proportions, and percents: Scale drawings (Sixth grade - Z.5)
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6.NO.3.6.7
Determine the percent of a number and solve related problems in real world situations
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6.A
Algebra
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6.A.4
Students shall recognize, describe and develop patterns, relations and functions.
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6
Patterns, Relations and Functions
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6.A.4.6.1
Solve problems by finding the next term or missing term in a pattern or function table using real world situations
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6.A.4.6.2
Interpret and write an algebraic rule for a one-operation function table
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6.A.5
Students shall represent and analyze mathematical situations and structures using algebraic symbols.
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6
Expressions, Equations and Inequalities
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6.A.5.6.1
Model, write and solve onestep equations by informal methods using manipulatives and appropriate technology
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6.A.5.6.2
Write simple algebraic expressions using appropriate operations (+, -, x, /) with one variable
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6.A.5.6.3
Evaluate algebraic expressions with one variable using appropriate properties and operations (+, -, x, /)
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6.A.6
Students shall develop and apply mathematical models to represent and understand quantitative relationships.
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6
Algebraic Models and Relationships
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6.A.6.6.1
Complete, with and without appropriate technology, and interpret tables and line graphs that represent the relationship between two variables in quadrant I
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6.A.7
Students shall analyze change in various contexts.
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6
Analyze Change
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6.A.7.6.1
Identify and compare situations with constant or varying rates of change
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6.G
Geometry
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6.G.8
Students shall analyze characteristics and properties of 2 and 3 dimensional geometric shapes and develop mathematical arguments about geometric relationships.
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6
Characteristics of Geometric Shapes
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6.G.8.6.1
Identify three-dimensional geometric figures using models(rectangular prisms, cylinders, cones, pyramids and spheres)
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6.G.8.6.2
Investigate with manipulatives or grid paper what happens to the perimeter and area of a 2- dimensional shape when the dimensions are changed
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6.G.8.6.3
Identify, describe, draw, and classify triangles as equilateral, isosceles, scalene, right, acute, obtuse, and equiangular
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6.G.8.6.4
Draw, label and determine relationships among the radius, diameter, center and circumference (e.g. radius is half the diameter) of a circle
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6.G.8.6.5
Identify similar figures and explore their properties
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6.G.9
Students shall apply transformations and the use of symmetry to analyze mathematical situations.
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6
Symmetry and Transformations
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6.G.9.6.1
Identify and describe line and rotational symmetry in twodimensional shapes, patterns and designs
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6.G.9.6.2
Describe positions and orientations of shapes under transformation (translation, reflection and rotation) recognizing the size and shape do not change
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6.G.10
Students shall specify locations and describe spatial relationships using coordinate geometry and other representational systems.
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6
Coordinate Geometry
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6.G.10.6.1
Use ordered pairs to plot points in Quadrant I
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6.G.10.6.2
Plot points that form the vertices of a geometric figure and draw, identify and classify the figure.
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6.G.11
Students shall use visualization, spatial reasoning and geometric modeling.
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6
Spatial Visualization and Models
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6.G.11.6.1
Identify two-dimensional patterns (nets) for threedimensional solids, such as prisms, pyramids, cylinders, and cones
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6.M
Measurement
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6.M.12
Students shall use attributes of measurement to describe and compare mathematical and real-world objects.
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6
Attributes and Tools
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6.M.12.6.1
Identify and select appropriate units and tools from both systems to measure
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6.M.12.6.2
Make conversions within the same measurement system in real world problems
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6.M.12.6.3
Compare and contrast the differences among linear units, square units, and cubic units
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6.M.12.6.4
Determine which unit of measure or measurement tool matches the context for a problem situation
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6.M.13
Students shall identify and use units, systems and processes of measurement.
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6
Attributes and Tools
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6.M.13.6.1
Solve real world problems involving one elapsed time, counting forward and backward (calendar and clock)
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6.M.13.6.2
Determine which unit of measure or measurement tool matches the context for a problem situation
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6.M.13.6.3
Draw and measure distance to the nearest mm and 1/8 inch accurately
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6.M.13.6.4
Establish and apply formulas to find area and perimeter of triangles, rectangles, and parallelograms
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6.M.13.6.5
Find the distance between two points on a number line
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6.M.13.6.6
Use estimation to check the reasonableness of measurements obtained from use of various instruments (including angle measures)
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6.DAP
Data Analysis and Probability
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6.DAP.14
Students shall formulate questions that can be addressed with data and collect, organize and display relevant data to answer them.
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6
Collect, organize and display data
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6.DAP.14.6.1
Formulate questions, design studies, and collect data about a characteristic shared by two populations or different characteristics within one population
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6.DAP.14.6.2
Collect data and select appropriate graphical representations to display the data including Venn diagrams
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6.DAP.14.6.3
Construct and interpret graphs, using correct scale, including line graphs and double-bar graphs
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6.DAP.15
Students shall select and use appropriate statistical methods to analyze data.
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6
Data Analysis
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6.DAP.15.6.1
Interpret graphs such as double line graphs and circle graphs
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6.DAP.15.6.2
Compare and interpret information provided by measures of central tendencies (mean, median and mode) and measures of spread (range)
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6.DAP.16
Students shall develop and evaluate inferences and predictions that are based on data.
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6
Data Analysis
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6.DAP.16.6.1
Use observations about differences in data to make justifiable inferences
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6.DAP.17
Students shall understand and apply basic concepts of probability.
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6
Data Analysis
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6.DAP.17.6.1
Distinguish between theoretical and experimental probability
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