6.MP: Mathematical practice

(Framing Text): Students become mathematically proficient in engaging with mathematical content and concepts as they learn, experience, and apply these skills and attitudes.

6.MP.1: Make sense of problems and persevere in solving them.

Biconditional Statements
Conditional Statements
Estimating Population Size
Pattern Flip (Patterns)

6.MP.1.a: Explain the meaning of a problem and look for entry points to its solution. Analyze givens, constraints, relationships, and goals. Make conjectures about the form and meaning of the solution, plan a solution pathway, and continually monitor progress asking, “Does this make sense?” Consider analogous problems, make connections between multiple representations, identify the correspondence between different approaches, look for trends, and transform algebraic expressions to highlight meaningful mathematics. Check answers to problems using a different method.

Biconditional Statements
Fraction, Decimal, Percent (Area and Grid Models)
Improper Fractions and Mixed Numbers
Linear Inequalities in Two Variables
Modeling One-Step Equations
Multiplying with Decimals
Pattern Flip (Patterns)
Polling: City
Solving Equations on the Number Line
Using Algebraic Expressions

6.MP.2: Reason abstractly and quantitatively.

Conditional Statements
Estimating Population Size

6.MP.3: Construct viable arguments and critique the reasoning of others.

Biconditional Statements

6.MP.3.a: Understand and use stated assumptions, definitions, and previously established results in constructing arguments. Make conjectures and build a logical progression of statements to explore the truth of their conjectures. Justify conclusions and communicate them to others. Respond to the arguments of others by listening, asking clarifying questions, and critiquing the reasoning of others.

Biconditional Statements
Conditional Statements

6.MP.4: Model with mathematics.

Estimating Sums and Differences

6.MP.5: Use appropriate tools strategically.

Elapsed Time

6.MP.5.a: Consider the available tools and be sufficiently familiar with them to make sound decisions about when each tool might be helpful, recognizing both the insight to be gained as well as the limitations. Identify relevant external mathematical resources and use them to pose or solve problems. Use tools to explore and deepen their understanding of concepts.

Segment and Angle Bisectors

6.MP.6: Attend to precision.

Biconditional Statements
Fraction, Decimal, Percent (Area and Grid Models)
Using Algebraic Expressions

6.MP.6.a: Communicate precisely to others. Use explicit definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose. Specify units of measure and label axes to clarify the correspondence with quantities in a problem. Calculate accurately and efficiently, and express numerical answers with a degree of precision appropriate for the problem context.

Arithmetic Sequences
Finding Patterns
Fraction, Decimal, Percent (Area and Grid Models)
Function Machines 2 (Functions, Tables, and Graphs)
Geometric Sequences
Pattern Flip (Patterns)

6.MP.7: Look for and make use of structure.

Pattern Flip (Patterns)

6.MP.7.a: Look closely at mathematical relationships to identify the underlying structure by recognizing a simple structure within a more complicated structure. See complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, see 5 – 3(x – y)2 as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y.

Arithmetic Sequences
Finding Patterns
Function Machines 2 (Functions, Tables, and Graphs)
Geometric Sequences
Pattern Flip (Patterns)

6.MP.8: Look for and express regularity in repeated reasoning.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Finding Patterns
Geometric Sequences
Pattern Finder
Pattern Flip (Patterns)

6.MP.8.a: Notice if reasoning is repeated, and look for both generalizations and shortcuts. Evaluate the reasonableness of intermediate results by maintaining oversight of the process while attending to the details.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

6.RP: Ratios and Proportional Relationships

(Framing Text): Understand ratio concepts and use ratio reasoning to solve problems.

6.RP.1: Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. The following are examples of ratio language: “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every two wings there was one beak.” “For every vote candidate A received, candidate C received nearly three votes.”

Beam to Moon (Ratios and Proportions)
Part-to-part and Part-to-whole Ratios
Proportions and Common Multipliers
Road Trip (Problem Solving)

6.RP.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 relationship. The following are examples of rate language: 'This recipe has a ratio of four cups of flour to two cups of sugar, so the rate is two cups of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”' (In sixth grade, unit rates are limited to non-complex fractions.)

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

6.RP.3: Use ratio and rate reasoning to solve real-world (with a context) and mathematical (void of context) problems, using strategies such as reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations involving unit rate problems.

6.RP.3.b: Solve unit rate problems including those involving unit pricing and constant speed.

Road Trip (Problem Solving)

6.RP.3.c: Find a percent of a quantity as a rate per 100. Solve problems involving finding the whole, given a part and the percent. (For example, 30% of a quantity means 30/100 times the quantity.)

Percent of Change
Percents and Proportions
Percents, Fractions, and Decimals
Polling: Neighborhood
Real-Time Histogram
Time Estimation

6.RP.3.d: Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

Unit Conversions

6.NS: The Number System

(Framing Text): Apply and extend previous understandings of multiplication and division of whole numbers to divide fractions by fractions.

6.NS.1: Interpret and compute quotients of fractions.

6.NS.1.a: Compute quotients of fractions by fractions, for example, by applying strategies such as visual fraction models, equations, and the relationship between multiplication and division, to represent problems.

Dividing Fractions
Dividing Mixed Numbers

6.NS.1.b: Solve real-world problems involving division of fractions by fractions. For example, how much chocolate will each person get if three people share 1/2 pound of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mile and area 1/2 square mile?

Dividing Fractions
Dividing Mixed Numbers

(Framing Text): Compute (add, subtract, multiply and divide) fluently with multi-digit numbers and decimals and find common factors and multiples.

6.NS.3: Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

Adding Whole Numbers and Decimals (Base-10 Blocks)
Multiplying Decimals (Area Model)
Multiplying with Decimals
Subtracting Whole Numbers and Decimals (Base-10 Blocks)
Sums and Differences with Decimals

6.NS.3.a: Fluently divide multi-digit decimals using the standard algorithm, limited to a whole number dividend with a decimal divisor or a decimal dividend with a whole number divisor.

No Alien Left Behind (Division with Remainders)

6.NS.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 less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor.

Pattern Flip (Patterns)

(Framing Text): Apply and extend previous understandings of numbers to the system of rational numbers.

6.NS.5: Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (for example, temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of zero in each situation.

Adding and Subtracting Integers
Adding on the Number Line
Addition of Polynomials
Integers, Opposites, and Absolute Values

6.NS.6: Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.

6.NS.6.a: Recognize opposite signs of numbers as indicating locations on opposite sides of zero on the number line; recognize that the opposite of the opposite of a number is the number itself.

Adding and Subtracting Integers
Adding on the Number Line
Integers, Opposites, and Absolute Values
Rational Numbers, Opposites, and Absolute Values
Solving Algebraic Equations I

6.NS.6.b: Understand that the signs of numbers in ordered pairs indicate their location in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.

Points in the Coordinate Plane

6.NS.6.c: Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.

Integers, Opposites, and Absolute Values
Modeling Fractions (Area Models)
Points in the Coordinate Plane

6.NS.7: Understand ordering and absolute value of rational numbers.

6.NS.7.a: Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram.

Integers, Opposites, and Absolute Values

6.NS.7.c: Understand the absolute value of a rational number as its distance from zero on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world context.

Absolute Value with Linear Functions
Integers, Opposites, and Absolute Values
Rational Numbers, Opposites, and Absolute Values

6.NS.7.d: Distinguish comparisons of absolute value from statements about order.

Integers, Opposites, and Absolute Values

6.NS.8: Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same x-coordinate or the same y-coordinate.

City Tour (Coordinates)
Elevator Operator (Line Graphs)
Points in the Coordinate Plane
Points, Lines, and Equations
Slope

6.EE: Expressions and Equations

(Framing Text): Apply and extend previous understandings of arithmetic to algebraic expressions involving exponents and variables.

6.EE.1: Write and evaluate numerical expressions involving whole-number exponents.

Order of Operations

6.EE.2: Write, read, and evaluate expressions in which letters represent numbers.

6.EE.2.a: Write expressions that record operations with numbers and with letters representing numbers.

Solving Equations on the Number Line
Using Algebraic Equations
Using Algebraic Expressions

6.EE.2.b: Identify parts of an expression using mathematical terms (for example, sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity and a sum of two terms.

Compound Interest
Equivalent Algebraic Expressions II
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Using Algebraic Equations
Using Algebraic Expressions

6.EE.2.c: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, applying the Order of Operations when there are no parentheses to specify a particular order.

Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Order of Operations
Solving Equations on the Number Line

6.EE.3: Apply the properties of operations to generate equivalent expressions.

Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Solving Algebraic Equations II

6.EE.4: Identify when two expressions are equivalent.

Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Modeling the Factorization of x²+bx+c
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II

(Framing Text): They reason about and solve one-variable equations and inequalities.

6.EE.5: Understand solving an equation or inequality as a process of answering the question: Which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.

Compound Inequalities
Exploring Linear Inequalities in One Variable
Linear Inequalities in Two Variables
Solving Algebraic Equations II
Solving Equations on the Number Line
Solving Linear Inequalities in One Variable

6.EE.6: Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.

Equivalent Algebraic Expressions I
Solving Algebraic Equations II

6.EE.7: Solve real-world and mathematical problems by writing and solving equations of the form x + a = b and ax = b for cases in which a, b and x are all non-negative rational numbers.

Absolute Value Equations and Inequalities
Modeling One-Step Equations
Solving Algebraic Equations I
Solving Algebraic Equations II
Solving Equations on the Number Line

6.EE.8: Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.

Absolute Value Equations and Inequalities
Comparing and Ordering Decimals
Compound Inequalities
Exploring Linear Inequalities in One Variable
Linear Inequalities in Two Variables
Rational Numbers, Opposites, and Absolute Values
Solving Linear Inequalities in One Variable

6.G: Geometry

(Framing Text): Solve real-world and mathematical problems involving area, surface area, and volume.

6.G.1: Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing and decomposing into rectangles, triangles and/or other shapes; apply these techniques in the context of solving real-world and mathematical problems.

Area of Parallelograms
Area of Triangles
Chocomatic (Multiplication, Arrays, and Area)
Fido's Flower Bed (Perimeter and Area)
Perimeter and Area of Rectangles

6.G.2: Find the volume of a right rectangular prism with appropriate unit fraction edge lengths by packing it with cubes of the appropriate unit fraction edge lengths (for example, 3½ x 2 x 6), and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = lwh and V = bh to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. (Note: Model the packing using drawings and diagrams.)

Prisms and Cylinders

6.G.3: Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same x coordinate or the same y coordinate. Apply these techniques in the context of solving real-world and mathematical problems.

Points in the Coordinate Plane

6.G.4: Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.

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

6.SP: Statistics and Probability

(Framing Text): Develop understanding of statistical variability of data.

6.SP.1: Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers.

Polling: City
Polling: Neighborhood
Reaction Time 2 (Graphs and Statistics)

6.SP.2: Understand that a set of data collected to answer a statistical question has a distribution that can be described by its center, spread/range and overall shape.

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

6.SP.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 variation describes how its values vary with a single number.

Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)

(Framing Text): Summarize and describe distributions.

6.SP.4: Display numerical data in plots on a number line, including dot plots, histograms and box plots. Choose the most appropriate graph/plot for the data collected.

Box-and-Whisker Plots
Histograms
Mascot Election (Pictographs and Bar Graphs)
Mean, Median, and Mode
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)
Real-Time Histogram
Stem-and-Leaf Plots

6.SP.5: Summarize numerical data sets in relation to their context, such as by:

6.SP.5.b: Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.

Reaction Time 2 (Graphs and Statistics)
Time Estimation

6.SP.5.c: Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations (for example, outliers) from the overall pattern with reference to the context in which the data were gathered.

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
Sight vs. Sound Reactions
Stem-and-Leaf Plots