RP: Ratios and Proportional Relationships

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

RP.M.6.1: Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. (e.g., “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 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)

RP.M.6.2: 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. (e.g., “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”)

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

RP.M.6.3: 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.

RP.M.6.3.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.

 Function Machines 2 (Functions, Tables, and Graphs)
 Points, Lines, and Equations
 Slope

RP.M.6.3.b: Solve unit rate problems including those involving unit pricing and constant speed. (e.g., If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?)

 Household Energy Usage
 Road Trip (Problem Solving)

RP.M.6.3.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.

 Percents and Proportions

RP.M.6.3.d: Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

 Unit Conversions

NS: The Number System

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

NS.M.6.4: Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem. (e.g., Create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb 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 mi and area ½ square mi?)

 Dividing Fractions
 Dividing Mixed Numbers

(Framing Text): Compute fluently with multi-digit numbers and find common factors and multiples.

NS.M.6.6: 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
 Square Roots
 Subtracting Whole Numbers and Decimals (Base-10 Blocks)
 Sums and Differences with Decimals

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

NS.M.6.8: 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.

 Integers, Opposites, and Absolute Values

NS.M.6.9: 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.

NS.M.6.9.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.

 Adding and Subtracting Integers
 Adding on the Number Line
 Integers, Opposites, and Absolute Values
 Rational Numbers, Opposites, and Absolute Values

NS.M.6.9.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.

 Points in the Coordinate Plane

NS.M.6.9.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

NS.M.6.10: Understand ordering and absolute value of rational numbers.

NS.M.6.10.a: Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. (e.g., interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right.)

 Comparing and Ordering Decimals
 Integers, Opposites, and Absolute Values
 Rational Numbers, Opposites, and Absolute Values
 Treasure Hunter (Decimals on the Number Line)

NS.M.6.10.b: Write, interpret, and explain statements of order for rational numbers in real-world contexts (e.g., write –3° C > –7° C to express the fact that –3° C is warmer than –7° C).

 Estimating Population Size
 Integers, Opposites, and Absolute Values
 Modeling Decimals (Area and Grid Models)

NS.M.6.10.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. (e.g., for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars).

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

NS.M.6.10.d: Distinguish comparisons of absolute value from statements about order. (e.g., recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars.)

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

NS.M.6.11: 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.

 Points in the Coordinate Plane

EE: Expressions and Equations

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

EE.M.6.12: Write and evaluate numerical expressions involving whole-number exponents.

 Order of Operations

EE.M.6.13: Write, read and evaluate expressions in which letters stand for numbers.

EE.M.6.13.a: Write expressions that record operations with numbers and with letters standing for numbers. (e.g., Express the calculation, “Subtract y from 5” as 5 – y.)

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

EE.M.6.13.b: Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. (e.g., Describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms.)

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

EE.M.6.13.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 (e.g., use the formulas V = s³ and A = 6 s² to find the volume and surface area of a cube with sides of length s = 1/2).

 Order of Operations
 Solving Equations on the Number Line

EE.M.6.14: Apply the properties of operations to generate equivalent expressions (e.g., apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y).

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

EE.M.6.15: Identify when two expressions are equivalent; i.e., when the two expressions name the same number regardless of which value is substituted into them. (e.g., The expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.)

 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): Reason about and solve one-variable equations and inequalities.

EE.M.6.16: 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.

 Solving Algebraic Equations II

EE.M.6.17: 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.

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

EE.M.6.18: 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.

 Absolute Value Equations and Inequalities
 Solving Equations on the Number Line

EE.M.6.19: 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
 Compound Inequalities
 Exploring Linear Inequalities in One Variable
 Linear Inequalities in Two Variables
 Solving Linear Inequalities in One Variable

G: Geometry

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

G.M.6.21: 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)

G.M.6.24: 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

SP: Statistics and Probability

(Framing Text): Develop understanding of statistical variability.

SP.M.6.25: Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. (e.g., “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages.)

 Polling: Neighborhood
 Reaction Time 2 (Graphs and Statistics)

SP.M.6.26: Through informal observation, understand that a set of data collected to answer a statistical question has a distribution which can be described by its center (mean/median), 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
 Sight vs. Sound Reactions
 Stem-and-Leaf Plots

SP.M.6.27: Recognize that a measure of center for a numerical data set summarizes all of its values with a single number.

 Box-and-Whisker Plots
 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)
 Stem-and-Leaf Plots

(Framing Text): Summarize and describe distributions.

SP.M.6.28: Display numerical data in plots on a number line, including dot plots, histograms and box plots.

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

SP.M.6.29: Summarize numerical data sets in relation to their context, such as by:

SP.M.6.29.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

SP.M.6.29.c: Giving quantitative measures of center (median and/or mean), 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)
 Sight vs. Sound Reactions
 Stem-and-Leaf Plots

SP.M.6.29.d: Relating the choice of measures of center to the shape of the data distribution and 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)
 Reaction Time 1 (Graphs and Statistics)
 Reaction Time 2 (Graphs and Statistics)

Correlation last revised: 4/4/2018

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.