WV--College- and Career-Readiness Standards

RP.M.7.1: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. (e.g., If a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.)

Beam to Moon (Ratios and Proportions)

Household Energy Usage

Road Trip (Problem Solving)

Unit Conversions

RP.M.7.2: Recognize and represent proportional relationships between quantities.

RP.M.7.2.a: Decide whether two quantities are in a proportional relationship (e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin).

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

RP.M.7.2.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

RP.M.7.2.c: Represent proportional relationships by equations. (e.g., If total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.)

Beam to Moon (Ratios and Proportions)

Direct and Inverse Variation

Geometric Probability

Part-to-part and Part-to-whole Ratios

Proportions and Common Multipliers

RP.M.7.2.d: Explain what a point (x,y) on the graph of a proportional relationship means in terms of the situation. Focus special attention on the points (0,0) and (1,r) where r is the unit rate.

RP.M.7.3: Use proportional relationships to solve multistep ratio and percent problems (e.g., simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, and/or percent error).

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

NS.M.7.4: 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.

NS.M.7.4.a: Describe situations in which opposite quantities combine to make 0. (e.g., A hydrogen atom has 0 charge because its two constituents are oppositely charged.)

Adding and Subtracting Integers

Integers, Opposites, and Absolute Values

Rational Numbers, Opposites, and Absolute Values

NS.M.7.4.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. (i.e., To add “p + q” on the number line, start at “0” and move to “p” then move |q| 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

NS.M.7.4.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

NS.M.7.4.d: Apply properties of operations as strategies to add and subtract rational numbers.

Adding and Subtracting Integers with Chips

NS.M.7.5: Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

NS.M.7.5.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.

NS.M.7.6: Solve real-world and mathematical problems involving the four operations with rational numbers. Instructional Note: Computations with rational numbers extend the rules for manipulating fractions to complex fractions.

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

EE.M.7.7: Apply properties of operations as strategies to add, subtract, factor and expand linear expressions with rational coefficients.

Solving Algebraic Equations II

EE.M.7.8: Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. (e.g., a + 0.05a = 1.05a means that “increase by 5%” is the same as “multiply by 1.05.”)

Exponents and Power Rules

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

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

EE.M.7.9: Solve multi-step real-life 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; and assess the reasonableness of answers using mental computation and estimation strategies. (e.g., If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.)

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

EE.M.7.10: 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.

EE.M.7.10.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 fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. (e.g., The perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? An arithmetic solution similar to “54 – 6 – 6 divided by 2” may be compared with the reasoning involved in solving the equation 2w – 12 = 54. An arithmetic solution similar to “54/2 – 6” may be compared with the reasoning involved in solving the equation 2(w – 6) = 54.)

Modeling One-Step Equations

Modeling and Solving Two-Step Equations

Solving Algebraic Equations II

Solving Equations on the Number Line

Solving Two-Step Equations

EE.M.7.10.b: Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. (e.g., As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.)

Absolute Value Equations and Inequalities

Rational Numbers, Opposites, and Absolute Values

Solving Linear Inequalities in One Variable

G.M.7.11: 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

Perimeters and Areas of Similar Figures

Similar Figures

G.M.7.14: Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

Circumference and Area of Circles

G.M.7.15: 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.

G.M.7.16: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

Area of Parallelograms

Balancing Blocks (Volume)

Perimeter and Area of Rectangles

Prisms and Cylinders

Pyramids and Cones

Surface and Lateral Areas of Pyramids and Cones

SP.M.7.17: 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.

Polling: City

Polling: Neighborhood

SP.M.7.18: Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. (e.g., Estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be.)

Polling: City

Polling: Neighborhood

Populations and Samples

SP.M.7.19: Recognize that a measure of center for a numerical 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.

Reaction Time 1 (Graphs and Statistics)

Reaction Time 2 (Graphs and Statistics)

SP.M.7.20: Summarize numerical data sets in relation to their context, such as by:

SP.M.7.20.b: Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.

Reaction Time 2 (Graphs and Statistics)

Time Estimation

SP.M.7.20.c: Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing 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

SP.M.7.21: Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. (e.g., The mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable.)

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

SP.M.7.22: Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. (e.g., Decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.)

Box-and-Whisker Plots

Polling: City

Populations and Samples

SP.M.7.23: Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. 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

Probability Simulations

Spin the Big Wheel! (Probability)

Theoretical and Experimental Probability

SP.M.7.24: 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. (e.g., When rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.)

SP.M.7.25: 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.

SP.M.7.25.a: Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. (e.g., If a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected.)

Probability Simulations

Spin the Big Wheel! (Probability)

Theoretical and Experimental Probability

SP.M.7.25.b: Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. (e.g., Find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies?)

Spin the Big Wheel! (Probability)

Theoretical and Experimental Probability

SP.M.7.26: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

SP.M.7.26.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

SP.M.7.26.b: Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., “rolling double sixes”), identify the outcomes in the sample space which compose the event.

Independent and Dependent Events

Permutations and Combinations

SP.M.7.26.c: Design and use a simulation to generate frequencies for compound events. (e.g., Use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood?)

Independent and Dependent Events

Correlation last revised: 1/22/2020

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.