Academic Standards

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.

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.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.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 *ax*^{2}+*bx*+*c*

Modeling the Factorization of *x*^{2}+*bx*+*c*

Simplifying Algebraic Expressions I

Simplifying Algebraic Expressions II

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.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.

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.

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.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.

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

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)

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