MA.6.NSO: Number Sense and Operations

MA.6.NSO.1: Extend knowledge of numbers to negative numbers and develop an understanding of absolute value.

MA.6.NSO.1.1: Extend previous understanding of numbers to define rational numbers. Plot, order and compare rational numbers.

Comparing and Ordering Decimals
Ordering Percents, Fractions, and Decimals Greater Than 1
Rational Numbers, Opposites, and Absolute Values

MA.6.NSO.1.2: Given a mathematical or real-world context, represent quantities that have opposite direction using rational numbers. Compare them on a number line and explain the meaning of zero within its context.

Integers, Opposites, and Absolute Values
Rational Numbers, Opposites, and Absolute Values

MA.6.NSO.1.3: Given a mathematical or real-world context, interpret the absolute value of a number as the distance from zero on a number line. Find the absolute value of rational numbers.

Integers, Opposites, and Absolute Values
Rational Numbers, Opposites, and Absolute Values

MA.6.NSO.1.4: Solve mathematical and real-world problems involving absolute value, including the comparison of absolute value.

Integers, Opposites, and Absolute Values
Rational Numbers, Opposites, and Absolute Values

MA.6.NSO.2: Add, subtract, multiply and divide positive rational numbers.

MA.6.NSO.2.1: Multiply and divide positive multi-digit numbers with decimals to the thousandths, including using a standard algorithm with procedural fluency.

Multiplying Decimals (Area Model)
Multiplying with Decimals

MA.6.NSO.2.2: Extend previous understanding of multiplication and division to compute products and quotients of positive fractions by positive fractions, including mixed numbers, with procedural fluency.

Dividing Fractions
Dividing Mixed Numbers
Multiplying Fractions
Multiplying Mixed Numbers

MA.6.NSO.2.3: Solve multi-step real-world problems involving any of the four operations with positive multi-digit decimals or positive fractions, including mixed numbers.

Adding Fractions (Fraction Tiles)
Adding Whole Numbers and Decimals (Base-10 Blocks)
Dividing Fractions
Dividing Mixed Numbers
Fractions with Unlike Denominators
Multiplying Decimals (Area Model)
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals
Subtracting Whole Numbers and Decimals (Base-10 Blocks)

MA.6.NSO.3: Apply properties of operations to rewrite numbers in equivalent forms.

MA.6.NSO.3.1: Given a mathematical or real-world context, find the greatest common factor and least common multiple of two whole numbers.

Equivalent Fractions (Fraction Tiles)
Fractions Greater than One (Fraction Tiles)
Modeling Fractions (Area Models)
Pattern Flip (Patterns)

MA.6.NSO.3.2: Rewrite the sum of two composite whole numbers having a common factor, as a common factor multiplied by the sum of two whole numbers.

Equivalent Algebraic Expressions II

MA.6.NSO.3.3: Evaluate positive rational numbers and integers with natural number exponents.

Order of Operations

MA.6.NSO.3.4: Express composite whole numbers as a product of prime factors with natural number exponents.

Factor Trees (Factoring Numbers)
Finding Factors with Area Models

MA.6.NSO.3.5: Rewrite positive rational numbers in different but equivalent forms including fractions, terminating decimals and percentages.

Ordering Percents, Fractions, and Decimals Greater Than 1
Percents, Fractions, and Decimals

MA.6.NSO.4: Extend understanding of operations with integers.

MA.6.NSO.4.1: Apply and extend previous understandings of operations with whole numbers to add and subtract integers with procedural fluency.

Adding and Subtracting Integers
Adding and Subtracting Integers with Chips
Adding on the Number Line

MA.6.AR: Algebraic Reasoning

MA.6.AR.1: Apply previous understanding of arithmetic expressions to algebraic expressions.

MA.6.AR.1.1: Given a mathematical or real-world context, translate written descriptions into algebraic expressions and translate algebraic expressions into written descriptions.

Using Algebraic Expressions

MA.6.AR.1.2: Translate a real-world written description into an algebraic inequality in the form of x > a, x < a, x >= a or x <= a. Represent the inequality on a number line.

Exploring Linear Inequalities in One Variable
Solving Linear Inequalities in One Variable

MA.6.AR.1.3: Evaluate algebraic expressions using substitution and order of operations.

Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II

MA.6.AR.1.4: Apply the properties of operations to generate equivalent algebraic expressions with integer coefficients.

Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II

MA.6.AR.2: Develop an understanding for solving equations and inequalities. Write and solve one-step equations in one variable.

MA.6.AR.2.1: Given an equation or inequality and a specified set of integer values, determine which values make the equation or inequality true or false.

Exploring Linear Inequalities in One Variable
Solving Linear Inequalities in One Variable

MA.6.AR.2.2: Write and solve one-step equations in one variable within a mathematical or real-world context using addition and subtraction, where all terms and solutions are integers.

Modeling One-Step Equations
Solving Algebraic Equations II
Solving Equations on the Number Line

MA.6.AR.2.3: Write and solve one-step equations in one variable within a mathematical or real-world context using multiplication and division, where all terms and solutions are integers.

Solving Algebraic Equations II

MA.6.AR.2.4: Determine the unknown decimal or fraction in an equation involving any of the four operations, relating three numbers, with the unknown in any position.

Solving Algebraic Equations II
Solving Equations on the Number Line

MA.6.AR.3: Understand ratio and unit rate concepts and use them to solve problems.

MA.6.AR.3.1: Given a real-world context, write and interpret ratios to show the relative sizes of two quantities using appropriate notation: a/b, a to b, or a : b where b is not equal to 0.

Beam to Moon (Ratios and Proportions)
Part-to-part and Part-to-whole Ratios

MA.6.AR.3.2: Given a real-world context, determine a rate for a ratio of quantities with different units. Calculate and interpret the corresponding unit rate.

Beam to Moon (Ratios and Proportions)
Road Trip (Problem Solving)

MA.6.AR.3.3: Extend previous understanding of fractions and numerical patterns to generate or complete a two- or three-column table to display equivalent part-to-part ratios and part-to-part-to-whole ratios.

Part-to-part and Part-to-whole Ratios

MA.6.AR.3.4: Apply ratio relationships to solve mathematical and real-world problems involving percentages using the relationship between two quantities.

Part-to-part and Part-to-whole Ratios
Percent of Change
Percents and Proportions

MA.6.AR.3.5: Solve mathematical and real-world problems involving ratios, rates and unit rates, including comparisons, mixtures, ratios of lengths and conversions within the same measurement system.

Beam to Moon (Ratios and Proportions)
Part-to-part and Part-to-whole Ratios
Percents and Proportions
Road Trip (Problem Solving)
Unit Conversions

MA.6.GR: Geometric Reasoning

MA.6.GR.1: Apply previous understanding of the coordinate plane to solve problems.

MA.6.GR.1.1: Extend previous understanding of the coordinate plane to plot rational number ordered pairs in all four quadrants and on both axes. Identify the x- or y-axis as the line of reflection when two ordered pairs have an opposite x- or y-coordinate.

Points in the Coordinate Plane

MA.6.GR.1.2: Find distances between ordered pairs, limited to the same x-coordinate or the same y-coordinate, represented on the coordinate plane.

Points in the Coordinate Plane

MA.6.GR.1.3: Solve mathematical and real-world problems by plotting points on a coordinate plane, including finding the perimeter or area of a rectangle.

City Tour (Coordinates)
Points in the Coordinate Plane

MA.6.GR.2: Model and solve problems involving two-dimensional figures and three-dimensional figures.

MA.6.GR.2.1: Derive a formula for the area of a right triangle using a rectangle. Apply a formula to find the area of a triangle.

Area of Triangles

MA.6.GR.2.2: Solve mathematical and real-world problems involving the area of quadrilaterals and composite figures by decomposing them into triangles or rectangles.

Area of Parallelograms
Area of Triangles

MA.6.GR.2.3: Solve mathematical and real-world problems involving the volume of right rectangular prisms with positive rational number edge lengths using a visual model and a formula.

Balancing Blocks (Volume)
Prisms and Cylinders

MA.6.GR.2.4: Given a mathematical or real-world context, find the surface area of right rectangular prisms and right rectangular pyramids using the figure’s net.

Surface and Lateral Areas of Prisms and Cylinders
Surface and Lateral Areas of Pyramids and Cones

MA.6.DP: Data Analysis and Probability

MA.6.DP.1: Develop an understanding of statistics and determine measures of center and measures of variability. Summarize statistical distributions graphically and numerically.

MA.6.DP.1.1: Recognize and formulate a statistical question that would generate numerical data.

Box-and-Whisker Plots
Describing Data Using Statistics
Histograms
Movie Reviewer (Mean and Median)
Polling: Neighborhood
Populations and Samples
Reaction Time 2 (Graphs and Statistics)
Stem-and-Leaf Plots

MA.6.DP.1.2: Given a numerical data set within a real-world context, find and interpret mean, median, mode and range.

Box-and-Whisker Plots
Describing Data Using Statistics
Mean, Median, and Mode
Movie Reviewer (Mean and Median)
Populations and Samples
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)
Real-Time Histogram
Stem-and-Leaf Plots

MA.6.DP.1.3: Given a box plot within a real-world context, determine the minimum, the lower quartile, the median, the upper quartile and the maximum. Use this summary of the data to describe the spread and distribution of the data.

Box-and-Whisker Plots

MA.6.DP.1.4: Given a histogram or line plot within a real-world context, qualitatively describe and interpret the spread and distribution of the data, including any symmetry, skewness, gaps, clusters, outliers and the range.

Describing Data Using Statistics
Histograms
Polling: City
Populations and Samples
Real-Time Histogram
Sight vs. Sound Reactions

MA.6.DP.1.5: Create box plots and histograms to represent sets of numerical data within real-world contexts.

Box-and-Whisker Plots
Histograms
Polling: City
Populations and Samples
Real-Time Histogram
Sight vs. Sound Reactions

MA.6.DP.1.6: Given a real-world scenario, determine and describe how changes in data values impact measures of center and variation.

Box-and-Whisker Plots
Describing Data Using Statistics
Mean, Median, and Mode