NY-6.RP: Ratios and Proportional Relationships

1.1: Understand ratio concepts and use ratio reasoning to solve problems.

NY-6.RP.1: Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.

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

NY-6.RP.2: Understand the concept of a unit rate a/b associated with a ratio a:b with b not equal to zero, and use rate language in the context of a ratio relationship.

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

NY-6.RP.3: Use ratio and rate reasoning to solve real-world and mathematical problems.

NY-6.RP.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

NY-6.RP.3.b: Solve unit rate problems.

 Household Energy Usage
 Road Trip (Problem Solving)

NY-6.RP.3.c: Find a percent of a quantity as a rate per 100. Solve problems that involve finding the whole given a part and the percent, and finding a part of a whole given the percent.

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

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

 Unit Conversions

NY-6.NS: The Number System

2.1: Apply and extend previous understandings of multiplication and division to divide fractions by fractions.

NY-6.NS.1: Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions.

 Dividing Fractions
 Dividing Mixed Numbers

2.2: Compute fluently with multi-digit numbers and find common factors and multiples.

NY-6.NS.3: Fluently add, subtract, multiply, and divide multi-digit decimals using a 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

2.3: Apply and extend previous understandings of numbers to the system of rational numbers.

NY-6.NS.5: Understand that positive and negative numbers are used together to describe quantities having opposite directions or values. Use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.

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

NY-6.NS.6: Understand a rational number as a point on the number line. Use number lines and coordinate axes to represent points on a number line and in the coordinate plane with negative number coordinates.

NY-6.NS.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, 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

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

 Adding on the Number Line
 City Tour (Coordinates)
 Elevator Operator (Line Graphs)
 Fraction Garden (Comparing Fractions)
 Integers, Opposites, and Absolute Values
 Modeling Decimals (Area and Grid Models)
 Modeling Fractions (Area Models)
 Points in the Coordinate Plane
 Points, Lines, and Equations
 Rational Numbers, Opposites, and Absolute Values

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

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

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

NY-6.NS.7.b: Write, interpret, and explain statements of order for rational numbers in real-world contexts.

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

NY-6.NS.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.

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

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

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

NY-6.NS.8: Solve real-world and mathematical problems by graphing points on a 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
 Points, Lines, and Equations
 Slope

NY-6.EE: Expressions, Equations, and Inequalities

3.1: Apply and extend previous understandings of arithmetic to algebraic expressions.

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

 Order of Operations

NY-6.EE.2: Write, read, and evaluate expressions in which letters stand for numbers.

NY-6.EE.2.a: Write expressions that record operations with numbers and with letters standing for numbers.

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

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

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

NY-6.EE.2.c: Evaluate expressions given specific values for their variables. Include expressions that arise from formulas in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order (Order of Operations).

 Order of Operations
 Solving Equations on the Number Line

NY-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

NY-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

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

NY-6.EE.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.

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

NY-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.

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

NY-6.EE.7: Solve real-world and mathematical problems by writing and solving equations of the form x + p = q; x - p = q; px = q; and x/p = 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

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

 Absolute Value Equations and Inequalities
 Compound Inequalities
 Exploring Linear Inequalities in One Variable
 Linear Inequalities in Two Variables
 Solving Linear Inequalities in One Variable

NY-6.G: Geometry

4.1: Solve real-world and mathematical problems involving area, surface area, and volume.

NY-6.G.1: Find area of triangles, trapezoids, and other polygons by composing into rectangles or decomposing into triangles and quadrilaterals. 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)

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

 Points in the Coordinate Plane

NY-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

NY-6.SP: Statistics and Probability

5.1: Develop understanding of statistical variability.

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

 Polling: Neighborhood
 Reaction Time 2 (Graphs and Statistics)

NY-6.SP.1b: Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population.

 Polling: City
 Polling: Neighborhood

NY-6.SP.1c: Understand that the method and sample size used to collect data for a particular question is intended to reduce the difference between a population and a sample taken from the population so valid inferences can be drawn about the population. Generate multiple samples (or simulated samples) of the same size to recognize the variation in estimates or predictions.

 Polling: City
 Polling: Neighborhood
 Populations and Samples

NY-6.SP.2: Understand that a set of quantitative data collected to answer a statistical question has a distribution which can be described by its center, spread, 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

NY-6.SP.3: Recognize that a measure of center for a quantitative 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.

 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)
 Real-Time Histogram
 Stem-and-Leaf Plots

5.2: Summarize and describe distributions.

NY-6.SP.4: Display quantitative data in plots on a number line, including dot plots and histograms.

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

NY-6.SP.5: Summarize quantitative data sets in relation to their context.

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

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

NY-6.SP.5.c: Calculate range and measures of center, as well as describe any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.

 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

NY-6.SP.5.d: Relate the range and 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)

5.3: Investigate chance processes and develop, use, and evaluate probability models.

NY-6.SP.6: Understand that the probability of a chance event is a number between 0 and 1 inclusive, that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around ½ indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.

 Geometric Probability
 Probability Simulations
 Spin the Big Wheel! (Probability)
 Theoretical and Experimental Probability

NY-6.SP.8: Develop a probability model and use it to find probabilities of simple events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.

NY-6.SP.8.a: Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of simple events.

 Probability Simulations
 Spin the Big Wheel! (Probability)
 Theoretical and Experimental Probability

NY-6.SP.8.b: Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process.

 Spin the Big Wheel! (Probability)
 Theoretical and Experimental Probability

Correlation last revised: 4/4/2018

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