Next Generation Learning Standards

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.

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

NY-6.NS.2: Fluently divide multi-digit numbers using a standard algorithm.

No Alien Left Behind (Division with Remainders)

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

NY-6.NS.4: Find the greatest common factor of two whole numbers less than or equal to 100. 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 other than 1. Find the least common multiple of two whole numbers less than or equal to 12.

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

2.3.1.1: e.g., temperature above/below zero, elevation above/below sea level, debits/credits, positive/negative electric charge

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

Solving Algebraic Equations I

2.3.2.1.1: e.g., With the number 3, -(-3) = 3.

Adding and Subtracting Integers

Adding on the Number Line

Integers, Opposites, and Absolute Values

Rational Numbers, Opposites, and Absolute Values

Solving Algebraic Equations I

NY-6.NS.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.

Points in the Coordinate Plane

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 and Subtracting Integers

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

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).

Equivalent Algebraic Expressions I

Equivalent Algebraic Expressions II

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 *x*^{2}+*bx*+*c*

Simplifying Algebraic Expressions I

Simplifying Algebraic Expressions II

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

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

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

Modeling One-Step Equations

Solving Algebraic Equations I

Solving Algebraic Equations II

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

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

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

Chocomatic (Multiplication, Arrays, and Area)

Fido's Flower Bed (Perimeter and Area)

Perimeter and Area of Rectangles

NY-6.G.2: Find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.

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.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: City

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

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

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

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.

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

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)

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

Independent and Dependent Events

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: 9/15/2020