MAFS.6.EE: Expressions and Equations

MAFS.6.EE.1: Apply and extend previous understandings of arithmetic to algebraic expressions.

MAFS.6.EE.1.1: Write and evaluate numerical expressions involving whole-number exponents.

Order of Operations

MAFS.6.EE.1.2: Write, read, and evaluate expressions in which letters stand for numbers.

MAFS.6.EE.1.2.a: Write expressions that record operations with numbers and with letters standing for numbers.

Using Algebraic Equations

MAFS.6.EE.1.2.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, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).

Order of Operations

MAFS.6.EE.2: Reason about and solve one-variable equations and inequalities.

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, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.

Modeling and Solving Two-Step Equations
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division
Solving Two-Step Equations

MAFS.6.EE.2.6: 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.

Using Algebraic Equations

MAFS.6.EE.2.7: Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.

Modeling and Solving Two-Step Equations
Road Trip (Problem Solving)
Solving Two-Step Equations

MAFS.6.EE.2.8: 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.

Compound Inequalities
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division
System of Two Quadratic Inequalities

MAFS.6.G: Geometry

MAFS.6.G.1: Solve real-world and mathematical problems involving area, surface area, and volume.

MAFS.6.G.1.1: Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.

Area of Parallelograms
Area of Triangles
Fido's Flower Bed (Perimeter and Area)
Segment and Angle Bisectors

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 fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.

Balancing Blocks (Volume)
Fraction Artist 1 (Area Models of Fractions)
Fraction Artist 2 (Area Models of Fractions)
Prisms and Cylinders - Activity A

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 points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems.

City Tour (Coordinates)
Points in the Coordinate Plane - Activity A
Pythagorean Theorem with a Geoboard

MAFS.6.G.1.4: 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.

Classifying Triangles
Segment and Angle Bisectors
Surface and Lateral Area of Prisms and Cylinders
Surface and Lateral Area of Pyramids and Cones

MAFS.6.RP: Ratios and Proportional Relationships

MAFS.6.RP.1: Understand ratio concepts and use ratio reasoning to solve problems.

MAFS.6.RP.1.1: Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.

Part-to-part and Part-to-whole Ratios
Polling: Neighborhood

MAFS.6.RP.1.2: Understand the concept of a unit rate a/b associated with a ratio a:b with b is not equal to 0, and use rate language in the context of a ratio relationship.

Part-to-part and Part-to-whole Ratios
Polling: Neighborhood
Road Trip (Problem Solving)

MAFS.6.RP.1.3: Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

MAFS.6.RP.1.3.a: Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.

Elevator Operator (Line Graphs)
Part-to-part and Part-to-whole Ratios
Points in the Coordinate Plane - Activity A
Polling: Neighborhood

MAFS.6.RP.1.3.b: Solve unit rate problems including those involving unit pricing and constant speed.

Road Trip (Problem Solving)

MAFS.6.RP.1.3.c: Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.

Percent of Change
Percents and Proportions
Polling: Neighborhood

MAFS.6.SP: Statistics and Probability

MAFS.6.SP.1: Develop understanding of statistical variability.

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, spread, and overall shape.

Describing Data Using Statistics
Mean, Median and Mode
Movie Reviewer (Mean and Median)
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)

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 variation describes how its values vary with a single number.

Describing Data Using Statistics
Mean, Median and Mode
Movie Reviewer (Mean and Median)
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)

MAFS.6.SP.2: Summarize and describe distributions.

MAFS.6.SP.2.4: Display numerical data in plots on a number line, including dot plots, histograms, and box plots.

Box-and-Whisker Plots
Describing Data Using Statistics
Histograms
Mascot Election (Pictographs and Bar Graphs)
Populations and Samples
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)
Real Number Line - Activity A

MAFS.6.SP.2.5: Summarize numerical data sets in relation to their context, such as by:

MAFS.6.SP.2.5.b: Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.

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

MAFS.6.SP.2.5.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 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)

MAFS.6.SP.2.5.d: Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.

Mean, Median and Mode
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)

MAFS.6.NS: The Number System

MAFS.6.NS.1: Apply and extend previous understandings of multiplication and division to divide fractions by fractions.

MAFS.6.NS.1.1: Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem.

Dividing Fractions
Dividing Mixed Numbers
Fraction Artist 1 (Area Models of Fractions)
Fraction Artist 2 (Area Models of Fractions)

MAFS.6.NS.2: Compute fluently with multi-digit numbers and find common factors and multiples.

MAFS.6.NS.2.2: Fluently divide multi-digit numbers using the standard algorithm.

No Alien Left Behind (Division with Remainders)

MAFS.6.NS.2.3: Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

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

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

Chocomatic (Multiplication, Arrays, and Area)

MAFS.6.NS.3: Apply and extend previous understandings of numbers to the system of rational numbers.

MAFS.6.NS.3.5: Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., 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 0 in each situation.

Real Number Line - Activity A
Real Number Line - Activity B

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 previous grades to represent points on the line and in the plane with negative number coordinates.

MAFS.6.NS.3.6.a: Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., -(-3) = 3, and that 0 is its own opposite.

Comparing and Ordering Integers
Real Number Line - Activity A
Real Number Line - Activity B

MAFS.6.NS.3.6.b: Understand signs of numbers in ordered pairs as indicating locations 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.

City Tour (Coordinates)
Points in the Coordinate Plane - Activity A
Real Number Line - Activity A
Real Number Line - Activity B

MAFS.6.NS.3.6.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.

City Tour (Coordinates)
Comparing and Ordering Integers
Points in the Coordinate Plane - Activity A
Real Number Line - Activity A

MAFS.6.NS.3.7: Understand ordering and absolute value of rational numbers.

MAFS.6.NS.3.7.a: Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram.

Ordering Percents, Fractions and Decimals

MAFS.6.NS.3.7.b: Write, interpret, and explain statements of order for rational numbers in real-world contexts.

Comparing and Ordering Decimals
Comparing and Ordering Fractions
Comparing and Ordering Integers
Fraction Garden (Comparing Fractions)
Modeling Fractions (Area Models)
Ordering Percents, Fractions and Decimals
Ordering Percents, Fractions, and Decimals Greater Than 1

MAFS.6.NS.3.7.c: Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation.

Comparing and Ordering Integers
Real Number Line - Activity A
Real Number Line - Activity B

MAFS.6.NS.3.7.d: Distinguish comparisons of absolute value from statements about order.

Comparing and Ordering Integers
Real Number Line - Activity A
Real Number Line - Activity B

MAFS.6.NS.3.8: 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 first coordinate or the same second coordinate.

City Tour (Coordinates)
Elevator Operator (Line Graphs)
Points in the Coordinate Plane - Activity A
Pythagorean Theorem with a Geoboard
Real Number Line - Activity A
Real Number Line - Activity B