NY-7.RP: Ratios and Proportional Relationships

1.1: Analyze proportional relationships and use them to solve real-world and mathematical problems.

NY-7.RP.2: Recognize and represent proportional relationships between quantities.

NY-7.RP.2.a: Decide whether two quantities are in a proportional relationship.

Beam to Moon (Ratios and Proportions)
Direct and Inverse Variation
Estimating Population Size
Geometric Probability
Part-to-part and Part-to-whole Ratios
Percents and Proportions
Proportions and Common Multipliers

NY-7.RP.2.b: Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

Beam to Moon (Ratios and Proportions)
Dilations
Direct and Inverse Variation

NY-7.RP.2.c: Represent a proportional relationship using an equation.

Beam to Moon (Ratios and Proportions)
Direct and Inverse Variation
Geometric Probability
Part-to-part and Part-to-whole Ratios
Proportions and Common Multipliers

NY-7.RP.2.d: Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

Direct and Inverse Variation

NY-7.RP.3: Use proportional relationships to solve multistep ratio and percent problems.

Beam to Moon (Ratios and Proportions)
Part-to-part and Part-to-whole Ratios
Percent of Change
Percents and Proportions
Percents, Fractions, and Decimals
Proportions and Common Multipliers

NY-7.NS: The Number System

2.1: Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.

NY-7.NS.1: Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers. Represent addition and subtraction on a horizontal or vertical number line.

NY-7.NS.1.a: Describe situations in which opposite quantities combine to make 0.

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

NY-7.NS.1.b: Understand addition of rational numbers; p + q is the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.

Adding and Subtracting Integers
Adding on the Number Line
Improper Fractions and Mixed Numbers
Integers, Opposites, and Absolute Values
Rational Numbers, Opposites, and Absolute Values
Simplifying Algebraic Expressions I
Solving Algebraic Equations I
Sums and Differences with Decimals

NY-7.NS.1.c: Understand subtraction of rational numbers as adding the additive inverse, p - q = p + (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.

Adding and Subtracting Integers
Adding on the Number Line
Simplifying Algebraic Expressions I
Sums and Differences with Decimals

NY-7.NS.1.d: Apply properties of operations as strategies to add and subtract rational numbers.

Adding Fractions (Fraction Tiles)
Adding and Subtracting Integers
Adding on the Number Line
Estimating Sums and Differences
Fractions Greater than One (Fraction Tiles)
Improper Fractions and Mixed Numbers
Sums and Differences with Decimals

NY-7.NS.2: Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

NY-7.NS.2.a: Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.

Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals

NY-7.NS.2.b: Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real-world contexts.

Dividing Mixed Numbers

NY-7.NS.2.c: Apply properties of operations as strategies to multiply and divide rational numbers.

Adding and Subtracting Integers
Dividing Fractions
Dividing Mixed Numbers
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals

NY-7.NS.2.d: Convert a fraction to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.

Percents, Fractions, and Decimals

NY-7.NS.3: Solve real-world and mathematical problems involving the four operations with rational numbers.

Adding Fractions (Fraction Tiles)
Adding and Subtracting Integers
Adding on the Number Line
Dividing Fractions
Dividing Mixed Numbers
Estimating Population Size
Estimating Sums and Differences
Fractions Greater than One (Fraction Tiles)
Improper Fractions and Mixed Numbers
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals
Sums and Differences with Decimals

NY-7.EE: Expressions, Equations, and Inequalities

3.1: Use properties of operations to generate equivalent expressions.

NY-7.EE.1: Add, subtract, factor, and expand linear expressions with rational coefficients by applying the properties of operations.

Solving Algebraic Equations II

NY-7.EE.2: Understand that rewriting an expression in different forms in real-world and mathematical problems can reveal and explain how the quantities are related.

Exponents and Power Rules
Modeling the Factorization of ax2+bx+c
Modeling the Factorization of x2+bx+c

3.2: Solve real-life and mathematical problems using numerical and algebraic expressions, equations, and inequalities.

NY-7.EE.3: Solve multi-step real-world and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate. Assess the reasonableness of answers using mental computation and estimation strategies.

Adding Fractions (Fraction Tiles)
Adding and Subtracting Integers
Adding on the Number Line
Dividing Fractions
Dividing Mixed Numbers
Estimating Sums and Differences
Fractions Greater than One (Fraction Tiles)
Fractions with Unlike Denominators
Improper Fractions and Mixed Numbers
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals
Part-to-part and Part-to-whole Ratios
Percents, Fractions, and Decimals
Sums and Differences with Decimals

NY-7.EE.4: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.

NY-7.EE.4.a: Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach.

Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Solving Algebraic Equations II
Solving Equations on the Number Line
Solving Two-Step Equations

NY-7.EE.4.b: Solve word problems leading to inequalities of the form px + q > r, px + q >= r, px + q <= r, or px + q < r, where p, q, and r are rational numbers. Graph the solution set of the inequality on the number line and interpret it in the context of the problem.

Absolute Value Equations and Inequalities
Rational Numbers, Opposites, and Absolute Values
Solving Linear Inequalities in One Variable

NY-7.G: Geometry

4.1: Draw, construct, and describe geometrical figures and describe the relationships between them.

NY-7.G.1: Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

Dilations
Similar Figures

4.2: Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

NY-7.G.4: Apply the formulas for the area and circumference of a circle to solve problems.

Circumference and Area of Circles

NY-7.G.5: Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

Investigating Angle Theorems
Triangle Angle Sum

NY-7.G.6: Solve real-world and mathematical problems involving area of two-dimensional objects composed of triangles and trapezoids. Solve surface area problems involving right prisms and right pyramids composed of triangles and trapezoids. Find the volume of right triangular prisms, and solve volume problems involving three-dimensional objects composed of right rectangular prisms.

Prisms and Cylinders

NY-7.SP: Statistics and Probability

5.1: Draw informal comparative inferences about two populations.

NY-7.SP.1: Construct and interpret box-plots, find the interquartile range, and determine if a data point is an outlier.

Box-and-Whisker Plots
Describing Data Using Statistics
Reaction Time 2 (Graphs and Statistics)

NY-7.SP.3: Informally assess the degree of visual overlap of two quantitative data distributions.

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-7.SP.4: Use measures of center and measures of variability for quantitative data from random samples or populations to draw informal comparative inferences about the populations.

Box-and-Whisker Plots
Polling: City
Populations and Samples

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

NY-7.SP.8: Find probabilities of compound events using organized lists, sample space tables, tree diagrams, and simulation.

NY-7.SP.8.a: Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.

Independent and Dependent Events
Theoretical and Experimental Probability

NY-7.SP.8.b: Represent sample spaces for compound events using methods such as organized lists, sample space tables, and tree diagrams. For an event described in everyday language, identify the outcomes in the sample space which compose the event.

Permutations and Combinations

NY-7.SP.8.c: Design and use a simulation to generate frequencies for compound events.

Independent and Dependent Events

Correlation last revised: 7/15/2019

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