KY.7.RP: Ratios and Proportional Relationships

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

KY.7.RP.1: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.

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

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

KY.7.RP.2.a: Decide whether two quantities represent a proportional relationship.

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

KY.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
Perimeters and Areas of Similar Figures
Similar Figures

KY.7.RP.2.c: Represent proportional relationships by equations.

Beam to Moon (Ratios and Proportions)
Direct and Inverse Variation
Geometric Probability
Part-to-part and Part-to-whole Ratios
Perimeters and Areas of Similar Figures
Proportions and Common Multipliers

KY.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

KY.7.RP.3: Use percents to solve mathematical and real-world problems.

KY.7.RP.3.a: Find a percent of a quantity as a rate per 100; solve problems involving finding the whole, a part and a percent, given two of these.

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

KY.7.RP.3.b: 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

KY.7.NS: The Number System

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

KY.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 diagram.

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

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

KY.7.NS.1.b: Understand p + q as 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 and Subtracting Integers with Chips
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

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

KY.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

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

KY.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.

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

KY.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.

Adding and Subtracting Integers
Dividing Mixed Numbers

KY.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

KY.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)
Fractions with Unlike Denominators
Improper Fractions and Mixed Numbers
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals
Sums and Differences with Decimals

KY.7.EE: Expressions and Equations

3.1: Use properties of operations to generate equivalent expressions.

KY.7.EE.1: Apply properties of operations as strategies to add, subtract, factor and expand linear expressions with rational coefficients.

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

KY.7.EE.2: Understand that rewriting an expression in different forms in a problem context can clarify the problem and how the quantities in it are related.

Exponents and Power Rules
Modeling the Factorization of ax2+bx+c
Modeling the Factorization of x2+bx+c
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II

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

KY.7.EE.3: Solve real-life and mathematical problems posed with positive and negative rational numbers in any form, using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and 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

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

KY.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 specific rational numbers. Solve equations of these forms. Graph the solution set of the equality and interpret it in context of the problem.

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

KY.7.EE.4.b: Solve word problems leading to inequalities of the form px + q > r, px + q < r, px + q is greater than or equal to r, px + q is less than or equal to r; where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in context of the problem.

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

KY.7.G: Geometry

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

KY.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

KY.7.G.2: Draw (freehand, with ruler and protractor and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

Classifying Quadrilaterals
Classifying Triangles
Concurrent Lines, Medians, and Altitudes
Parallelogram Conditions
Special Parallelograms
Triangle Inequalities

KY.7.G.3: Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.

Pyramids and Cones

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

KY.7.G.4: Use formulas for area and circumference of circles and their relationships.

KY.7.G.4.a: Apply the formulas for the area and circumference of a circle to solve real-world and mathematical problems.

Circumference and Area of Circles

KY.7.G.4.b: Explore and understand the relationship between the radius, diameter, circumference and area of a circle.

Circumference and Area of Circles

KY.7.G.5: Apply properties of 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

KY.7.G.6: Solve problems involving area of two-dimensional objects and surface area and volume of three-dimensional objects.

KY.7.G.6.a: Solve real-world and mathematical problems involving area of two-dimensional objects composed of triangles, quadrilaterals and other polygons.

Area of Parallelograms
Area of Triangles
Chocomatic (Multiplication, Arrays, and Area)
Fido's Flower Bed (Perimeter and Area)
Perimeter and Area of Rectangles

KY.7.G.6.b: Solve real-world and mathematical problems involving volume and surface area, using nets as needed, of three-dimensional objects including cubes, pyramids and right prisms.

Prisms and Cylinders
Pyramids and Cones
Surface and Lateral Areas of Prisms and Cylinders
Surface and Lateral Areas of Pyramids and Cones

KY.7.SP: Statistics and Probability

5.1: Use random sampling to draw inferences about a population.

KY.7.SP.0: Create displays, including circle graphs (pie charts), scaled pictographs and bar graphs, to compare and analyze distributions of categorical data from both matching and different-sized samples.

Box-and-Whisker Plots
Correlation
Forest Ecosystem
Graphing Skills
Mascot Election (Pictographs and Bar Graphs)
Reaction Time 1 (Graphs and Statistics)
Real-Time Histogram
Stem-and-Leaf Plots

KY.7.SP.1: 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. Understand that random sampling tends to produce representative samples and support valid inferences.

Estimating Population Size
Polling: City
Polling: Neighborhood
Populations and Samples

KY.7.SP.2: Use data from a random sample to draw inferences about a population with an unknown characteristic of interest.

KY.7.SP.2.a: Generate multiple samples of categorical data of the same size to gauge the variation in estimates or predictions.

Polling: City
Polling: Neighborhood
Populations and Samples

KY.7.SP.2.b: Generate multiple samples (or simulated samples) of numerical data to gauge the variation in estimates or predictions.

Populations and Samples

KY.7.SP.2.c: Gauge how far off an estimate or prediction might be related to a population character of interest.

Polling: City
Polling: Neighborhood

5.2: Draw informal comparative inferences about two populations.

KY.7.SP.3: Describe the degree of visual overlap (and separation) from the graphical representations of two numerical data distributions (box plots, dot plots) with similar variabilities with similar contexts (same variable), measuring the difference between the centers (medians or means) by expressing this difference as a multiple of a measure of variability (interquartile range when comparing medians or the mean absolute deviation when comparing means).

Box-and-Whisker Plots
Describing Data Using Statistics
Mean, Median, and Mode
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)

KY.7.SP.4: Calculate and use measures of center (mean and median) and measures of variability (interquartile range when comparing medians and mean absolute deviation when comparing means) for numerical data from random samples to draw informal comparative inferences about two populations.

Box-and-Whisker Plots
Mean, Median, and Mode
Movie Reviewer (Mean and Median)
Populations and Samples
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)

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

KY.7.SP.5: Describe the probability of a chance event is a number between 0 and 1, which tells how likely the event is, from impossible (0) to certain (1). A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely and a probability near 1 indicates a likely event.

Geometric Probability
Lucky Duck (Expected Value)
Probability Simulations
Spin the Big Wheel! (Probability)
Theoretical and Experimental Probability

KY.7.SP.6: Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency and predict the approximate relative frequency given the probability.

Lucky Duck (Expected Value)
Probability Simulations
Spin the Big Wheel! (Probability)
Theoretical and Experimental Probability

KY.7.SP.7: Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.

KY.7.SP.7.a: Develop a uniform probability model by assigning equal probability to all outcomes and use the model to determine probabilities of events.

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

KY.7.SP.7.b: Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process.

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

KY.7.SP.8: Find probabilities of compound events using organized lists, tables, tree diagrams and simulation.

KY.7.SP.8.a: Explain 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

KY.7.SP.8.b: Represent sample spaces for compound events described in everyday language using methods such as organized lists, tables and tree diagrams.

Independent and Dependent Events
Permutations and Combinations

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

Independent and Dependent Events

Correlation last revised: 1/22/2020

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