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CCRS StandardStandard IDEvidence of Student AttainmentTeacher
VocabularyKnowledgeSkillsUnderstandingResources1. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. Example: 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.Ratios & Proportional RelationshipsAnalyze proportional relationships and use them to solve real-world and mathematical problems.7.RP.1Students: Given ratios of fraction to fractions in contextual situations,
lCalculate the equivalent unit rate and justify the unit rate within the given context.l Unit rate
l RatioStudents know:
l Techniques for producing ratios equivalent to given ratios, including finding unit rates. Students are able to:
l Determine equivalent ratios (including unit rates) for ratios consisting of fractions. Students understand that:
l Unit rates are used to clearly communicate rates in contextual situations and allow for clearer comparisons. Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53903" \t "_blank" ALEX Resources2. Recognize and represent proportional relationships between quantities.
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.
b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
c. Represent proportional relationships by equations. Example: 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.
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.Ratios & Proportional RelationshipsAnalyze proportional relationships and use them to solve real-world and mathematical problems.7.RP.2Students:
l Justify relationships as proportional and identify the constant of proportionality using graphs, tables, equivalent ratios, and equations,
l Explain the relationships between representations of proportions and extend that relationship into a rule (equation).
Given the graph of a proportional relationship in a contextual situation, (i.e. buying CDs of equal price),
l Explain the association between the unit rate and any point on the line, (i.e. "If I paid $3/CD, then point (5, 15) means that I can buy 5 CDs for $15"). l Unit rate
l Proportional relationshipsStudents know:
l Characteristics of graphs, tables, and equations that define proportional situations,
l Relationships between graphs, tables, and equations in proportional situations,
l The role of unit rate in a graph of a proportional relationship. Students are able to:
l Produce graphs, tables, and the related equations,
l Communicate the relationships between graphs, tables, and equations in order to justify relationships as proportional. Students understand that:
l The constant of proportionality (unit rate) in a relationship communicates the rate of change for one variable with respect to the other, regardless of how the proportional relationship is represented.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53905" \t "_blank" ALEX Resources3. Use proportional relationships to solve multistep ratio and percent problems. Examples: Sample problems may involve simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.Ratios & Proportional RelationshipsAnalyze proportional relationships and use them to solve real-world and mathematical problems.7.RP.3Students:Given multi-step problems involving contexts with ratios and percents,
l Solve and justify solutions using a variety of representations and solution paths. Students know:
l Techniques for representing mathematical contexts that include percents and ratios,
l Techniques for producing ratios equivalent to given ratios, including finding unit rates. Students are able to:
l Strategically choose and apply representations that aid in solutions of percent and ratio problems,
l Solve and interpret the solutions.Students understand that:
l Patterns and relationships in mathematical contexts can be represented in a variety of ways in order to solve problems, including that a variety of representations of ratio and percent can be used to solve and interpret mathematical contexts.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53911" \t "_blank" ALEX Resources4. 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.
a. Describe situations in which opposite quantities combine to make 0. Example: A hydrogen atom has 0 charge because its two constituents are oppositely charged.
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.
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.
d. Apply properties of operations as strategies to add and subtract rational numbers.The Number SystemApply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.7.NS.1Students:
l Describe situations that illustrate the additive inverse property as adding opposites to equal zero.
Given contextual or mathematical problems involving both positive and negative rational numbers,
l Find and justify sums and differences of rational numbers through connections to a variety of representations (including distance on a number line) used for addition and subtraction of whole numbers and fractions. l Absolute value
lRational number
lAdditive inverse
lProperties of operations (Table 3) Students know:
l Strategies for modeling addition and subtraction of rational numbers (e.g. two-color chips and charge models for integers, distance on a number line),
l Characteristics of addition and subtraction problems (Table 1). Students are able to:
l Strategically choose and apply appropriate representations for operations and rational numbers in contexts in order to solve problems,
l Use logical reasoning to communicate and interpret solutions and solution paths for problems involving rational numbers.Students understand that:
l Finding sums and differences of rational numbers (negative and positive) involves determining direction and distance on the number line,
l Visual and concrete models help make sense of abstract mathematical representations of numbers and computations. Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53914" \t "_blank" ALEX Resources5. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.
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.
b. Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with nonzero 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.
c. Apply properties of operations as strategies to multiply and divide rational numbers.
d. Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.The Number SystemApply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.7.NS.2Students:
l Find and justify products and quotients of rational numbers (positive and negative) through connections to a variety of representations and properties of operations (including multiplicative identity and inverse) used for multiplication and division of whole numbers and fractions,
lUse long division to convert a rational number to a decimal and explain why it must end in a zero or repeat.l Rational number
l Properties of operations Students know:
l Techniques for accurately performing multiplication and division of whole numbers and fractions,
l The properties of operations (Table 3) and their appropriate application,
l Characteristics of multiplication and division problems. Students are able to:
l Accurately perform multiplication and division of whole numbers and fractions,
l Strategically choose and apply appropriate representations for operations with rational numbers in contexts in order to solve problems,
l Use logical reasoning to communicate and interpret solutions and solution paths,
l Use the division algorithm to convert fractions to decimals (terminating and repeating).Students understand that:
l Strategies for finding products and quotients of rational numbers (negative and positive) follow logically from patterns established with operations on whole numbers and fractions,
l The use of the standard algorithm for division helps makes sense of when the decimal form of a fraction repeats or terminates. Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53920" \t "_blank" ALEX Resources6. Solve real-world and mathematical problems involving the four operations with rational numbers. 1 (1computations with rational numbers extend the rules for manipulating fractions to complex fractions.)The Number SystemApply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.7.NS.3Students:Given a variety of word problems involving all four operations on rational numbers, involving a variety of complexities, (e.g.. mixed numbers, complex fractions, location of the unknown, etc.),
l Explain and justify solutions using a variety of representations including equations. l Complex fraction Students know:
l Characteristics of multiplication, division, addition, and subtraction contexts,
l Techniques for performing all four operations on rational numbers. Students are able to:
l Interpret mathematical contexts (involving addition, subtraction, multiplication, and division of rational numbers) and represent quantities and operations physically, pictorially, or symbolically,
l Strategically use a variety of representations to solve addition, subtraction, multiplication, and division word problems,
l Explain connections between physical/pictorial representations of mathematical contexts and related equations.Students understand that:
l Finding sums, differences, products, and quotients of rational numbers (negative and positive) follow logically from patterns established with operations on whole numbers and fractions.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53925" \t "_blank" ALEX Resources7. Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.Expressions & EquationsUse properties of operations to generate equivalent expressions.7.EE.1Students:Given contextual or mathematical problems which may be modeled by linear algebraic expressions with rational coefficients,
l Use properties of the operations (Table 3) to produce combined and re-written forms of the expressions that are useful in resolving the problem.l Properties of operations
l Rational coefficientsStudents know:
l The properties of operations (Table 3) and their appropriate application.Students are able to:
l Accurately add, subtract, factor, and expand linear algebraic expressions with rational coefficients. The students understand that:
l The distributive property, factoring, and combining like terms,are used to justify the equivalence of alternate forms of expressions for use in problem solving situations.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53927" \t "_blank" ALEX Resources8. 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. Example: a + 0.05a = 1.05a means that increase by 5% is the same as multiply by 1.05. Expressions & EquationsUse properties of operations to generate equivalent expressions.7.EE.2Students:
l Explain how combining or decomposing parts of algebraic expressions can reveal different aspects of the expression and be useful in interpreting a problem. (e.g., When determining the number of tiles needed for a border around a square pool of side n, the expression 4n + 4 shows counting 4 sides and then 4 corners. The expression 4(n+1) shows counting four sides which each include one corner. The expression 4(n+2) - 4 shows counting the outer border then subtracting the corners as they have been counted twice).Students know:
l The properties of operations (Table 3) and their appropriate application.Students are able to:
l Accurately add, subtract, factor, and expand linear algebraic expressions with rational coefficients. Students understand that:
l Rewriting expressions in multiple equivalent forms allows for thinking about problems in different ways,
l Different but equivalent forms of mathematical expressions reveal important features of the situation and aid in problem identification and solving.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53928" \t "_blank" ALEX Resources9. Solve multistep 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. Examples: 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.
Expressions & EquationsSolve real-life and mathematical problems using numerical and algebraic expressions and equations.7.EE.3Students:Given contextual problems involving any combination of numbers from the rational numbers,
l Model the problem with mathematical symbols, expressions, and equations that aid in solving the problem,
l Select strategies that are useful, choose the appropriate form of computation, reach a solution, and defend the solution in terms of the original context (including mental computation and estimation strategies).Students know:
l Techniques for estimation, mental computation, and their appropriate application,
l The properties of operations and equality (Tables 3 and 4), and their appropriate application.Students are able to:
l Translate verbal forms of a problem into mathematical symbols, expressions, and equations,
l Accurately use the properties of operations and equality to aid in solving the equation,
l Accurately compute with positive and negative rational numbers with and without technology,
l Use estimation and mental computation strategies to reach solutions and to judge reasonableness of answers found through paper/pencil or technology computation.
Students understand that:
l There are multiple ways to solve problems,
l Strategically using properties of operations and equality allows solutions to problems to be defended,
l Checking the reasonableness of answers leads to self correcting of errors,
l Problem solving takes effort, time, and perseverance.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53931" \t "_blank" ALEX Resources10. 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.
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. Example: The perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?
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. Example: 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.Expressions & EquationsSolve real-life and mathematical problems using numerical and algebraic expressions and equations.7.EE.4Students:Given a real world or mathematical situation,
l Define the variables and constants in the situation,
l Relate them to one another,
l Write equations describing the relationship,
l Solve the equation (linear situations) using properties of the operations and equality.
Given a contextual situation involving a linear inequality,
l Model the situation with an inequality,
l Solve the inequality,
l Graph the solution set of the inequality,
l Interpret and defend the solution in the context of the original problem.l VariableStudents know:
l The properties of operations, equality and inequality (Tables 3, 4 and 5), and their appropriate application,
l Techniques for solving linear equations and inequalities,
l Techniques for solving problems arithmetically (e.g., systematic guess, check, and revise) noting problem structure by examining smaller numbers or a simpler problem, or looking for a pattern and generalizing.Students are able to:
l Accurately use the properties of operations, equality, and inequality (Tables 3, 4 and 5) to produce equivalent forms of an algebraic expression, equation, or inequality to aid in solving the equations or inequality,
l Graph inequalities and identify the solution set on the graph. Students understand that:
lReal world problems can be interpreted, modeled, and solved using equations and inequalities,
l Solving an equation or inequality means finding all values of the variable that makes the statement true,
l In solving an equation the properties of operations and equality must be used to maintain the equality through successive manipulations until the solution is revealed,
l Problems may be frequently solved arithmetically, or modeled and solved algebraically, and that the structure of mathematics may be used to demonstrate that these strategies can and do lead to the same result.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53933" \t "_blank" ALEX Resources11. 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.GeometryDraw construct, and describe geometrical figures and describe the relationships between them.7.G.1Students:Given contextual or mathematical problems involving scale drawings of geometric figures,
l Solve, then communicate and justify solution paths for computing actual lengths and areas.
Given a scale drawing,
l Students will reproduce the drawing at a different scale.l Scale drawingStudents know:
l Strategies for computing actual lengths from scale drawings,
l Strategies for computing area,
l Units for measuring length and area,
l The interpretation of scale/ratio notation.Students are able to:
l Select and strategically apply methods to accurately compute actual lengths and areas from scale drawings,
l Choose and apply appropriate tools in order to reproduce a scale drawing at a different scale.Students understand that:
l A scale drawing represents a real object with accurate measurements where each of the measurements has been increased or decreased by the same factor,
l In scale drawings of geometric figures lengths change by the scale factor while areas change by the square of the scale factor. Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53939" \t "_blank" ALEX Resources12. 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.GeometryDraw construct, and describe geometrical figures and describe the relationships between them.7.G.2Students:Given sets of conditions for geometric shapes,
l Draw (freehand, with a ruler and protractor, and with technology) the corresponding shapes.
Given three measures (a combination of side lengths and angle measures) of a triangle,
l Use observations from the drawing, reasoning, and mathematical language, to justify whether the conditions determine a unique figure, more than one figure, or no figure.Students know:
l Techniques for using rulers, protractors, and technology to create geometric shapes,
l Descriptive language for attributes of triangles, (e.g. side opposite an angle, side adjacent to an angle, etc.). Students are able to:
l Compose and decompose geometric figures,
l Draw (freehand, with a ruler and protractor, or using technology) geometric shapes from given conditions,
l Use logical reasoning and mathematical language to justify whether given conditions will produce a unique figure, more than one figure, or no figure (with special emphasis on triangles).Students understand that:
l Shapes are categorized based on the characteristics of their attributes [angle size, side length, side relationships, (parallel or perpendicular)].Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53940" \t "_blank" ALEX Resources13. Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.GeometryDraw construct, and describe geometrical figures and describe the relationships between them.7.G.3Students: Given a 3-D figure, (e.g. right rectangular prism, right rectangular pyramid, cone, etc.),
l Describe the plane (2-D) section that results from slicing the 3-D figure.l Slicing
l Plane sectionStudents know:
l Strategies for visualizing and modeling geometric figures,
l Strategies for composing and decomposing geometric shapes,
l Descriptive language for attributes of 2-D and 3-D figures. Students are able to:
l Model and visualize 3-D figures,
l Describe the geometric attributes of the plane section resulting from the "slicing" of a 3-D shape, such as a right rectangular prism or right rectangular pyramid.Students understand that:
l Modeling, composing, and decomposing geometric figures aids in visualizing, investigating, and describing geometric problems.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53941" \t "_blank" ALEX Resources14. 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.GeometrySolve real-world and mathematical problems involving angle measure, area, surface area, and volume.7.G.4Students:
l Describe the relationship between the formulas for area and circumference of a circle and derive an equation relating the two formulas.
Given real world and mathematical problems involving area and circumference of circular regions,
Use a variety of representations including models, drawings, and equations based on area and circumference formulas to find and justify solutions and solution paths.l Area
l CircumferenceStudents know:
l Strategies for representing contexts involving area and circumference of circular regions,
l Strategies including standard formulas (A = r2, C = 2r or C = d) for computing the area and circumference of circular regions.Students are able to:
l Discriminate between contexts asking for circumference and those asking for area measurements,
l Strategically choose and apply appropriate methods for representing and calculating area and circumference of circular regions,
l Use properties of operation and equality to relate variables in formulas, (i.e., area and circumference of a circle). Students understand that:
l Circumference is measured in length units and is the distance around a circle,
l The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure, and when counting these squares is difficult such as in a circle, formulas allow for more accurate calculation of the area,
l The length of the radius of a circle is related to both the area and circumference of that region.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53943" \t "_blank" ALEX Resources15. Use facts about supplementary, complementary, vertical, and adjacent angles in a multistep problem to write and solve simple equations for an unknown angle in a figure.GeometrySolve real-world and mathematical problems involving angle measure, area, surface area, and volume.7.G.5Students:Given multi-step problems involving angle measures,
l Use knowledge of supplementary, complementary, vertical, and adjacent angles to create and solve equations for unkown angles, and justify solutions and solution paths. l Supplementary angles
l Complementary angles
l Vertical angles
l Adjacent anglesStudents know:
l Defining characteristics of, relationships among, and situations that produce, supplementary, complementary, vertical, and adjacent angles.
l Strategies for visually representing contexts involving angle measures. Students are able to:
l Visually represent verbal contexts involving angles,
l Strategically choose and apply appropriate methods for representing and calculating angle measures,
l Use logical reasoning to apply knowledge of supplementary, complementary, vertical, and adjacent angles to create equations and solve multi-step problems.Students understand that:
l Angle measure is additive,
l Angles created by two intersecting lines have relationships that can be used to solve problems.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53944" \t "_blank" ALEX Resources16. 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.GeometrySolve real-world and mathematical problems involving angle measure, area, surface area, and volume.7.G.6Students:Given real world and mathematical problems involving area, volume, and surface area (problems include figures composed of triangles, quadrilaterals, polygons, cubes, and right prisms),
l Use a variety of strategies to solve problems, and justify solutions and solution paths.l Area
l Volume
l Surface areaStudents know:
l Measureable attributes of objects, specifically area, volume, and surface area,
lStrategies for representing the surface area of a 3-D shape as a 2-D net,
l Strategies for determining area of polygons and volume of right prisms.Students are able to:
l Model the surface area of a 3-D shape as a 2-D net,
l Strategically choose and apply methods for determining area, volume, and surface area of geometric shapes composed of triangles, quadrilaterals, polygons, cubes and right prisms,
l Accurately compute area and surface area of polygons,
l Accurately compute volume of right prisms.Students understand that:
l Formulas represent generalizations of relationships among measurements of geometric objects that can be used to solve problems,
l Area and volume are additive,
l Surface area of a shape composed of right prisms is represented by the sum of the areas of the faces of the object,
l Models can represent measurable attributes of objects and help to solve problems. Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53945" \t "_blank" ALEX Resources17. 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.Statistics & ProbabilityUse random sampling to draw inferences about a population.7.SP.1Students:Given data collected on a sample from a population,
l Make, explain and justify inferences about the population, if any, that could be made from the sample data.
Given a statistical question about a population,
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&Fdd$If[$\$gdl2 $Ifgdl2 $IfgdMdd$If[$\$gdMscribe and justify a data collection process that would result in representative data from which inferences about the population can be drawn,
l Explain and justify their reasoning concerning data collection processes that do not allow generalizations, (i.e., non-representative samples) from the sample to the population. l Representative samples
l Population
l Sample
l Random sampling
l Inferences Students know:
l Methods of determining mean, median, interquartile range, and mean absolute deviation (from 6th grade),
l Characteristics of random sampling and representative samples,
l The relationship between a sample and the population that the sample was drawn from.Students are able to:
l Determine if a sampling procedure allows for inferences to be made about the population from which the sample was drawn,
l Use logical reasoning and statistical mathematical language to explain and justify examples of inferences, if any, that can be drawn about a population based on the analysis of the data and the data collection process,
l Draw valid conclusions from generated statistical models. Students understand that:
l Statistics can be used to gain information about a population by examining a sample of the population,
l Generalizations about a population from a sample are valid only if the sample is representative of that population,
l Random sampling tends to produce representative samples and support valid inferences.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53947" \t "_blank" ALEX Resources18. 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. Example: 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.Statistics & ProbabilityUse random sampling to draw inferences about a population.7.SP.2Students:Given data from a random sample,
l Analyze the data and explain inferences about the population that can be drawn from the sample data.
Given a population,
l Ask statistical questions and generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions.l Generate multiple samples
l Simulated samples
l Inferences
l PopulationStudents know:
l Strategies for generating random samples,
l Methods of determining mean, median, interquartile range, and mean absolute deviation (from 6th grade),
l Characteristics of random sampling and representative samples,
l The relationship between a sample and the population that the sample was drawn from.
Students are able to:
l Use statistical vocabulary to explain inferences about a population when analyzing data from random samples,
l Ask statistical questions about populations,
l Generate multiple random samples from populations in order to gauge the variation in estimates,
l Use variation in sample data to explain possible error in estimates and predictions.Students understand that:
l Statistics can be used to gain information about a population by examining a sample of the population,
l Generalizations about a population from a sample are valid only if the sample is representative of that population,
lRandom sampling tends to produce representative samples and support valid inferences. Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53948" \t "_blank" ALEX Resources19. 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. Example: 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.Statistics & ProbabilityDraw informal comparative inferences about two populations.7.SP.3Students:Given two sets of data with similar variabilities,
l Informally assess and describe the degree of visual overlap of the distributions by comparing visual representations of data sets, (e.g., line plots, coordinate plane graphs) and statistical measures of center and variability.l Numerical data distributions
l Variability
l Measures of center
l Measures of variability
l Mean absolute deviationStudents know:
l Methods of determining mean, median, interquartile range, and mean absolute deviation (from 6th grade),
l Methods for visually representing data, (e.g., line plots, coordinate graphs),
l Characteristics and definitions of mean, median, interquartile range, and mean absolute deviation.Students are able to:
l Calculate the mean, median, interquartile range, and mean absolute deviation,
l Organize data in ways that aid in identifying significant features of the data, (e.g. putting data in order to find the median, displaying in a graph to see overall shape),
l Describe the distribution of a set of data by referring to measures of center, spread, and shape,
l Effectively communicate a comparison of data sets using visual representations, (e.g., line plots, coordinate graphs) and statistical measures, (e.g., mean, variability).Students understand that:
l A set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape,
l Using different representations and descriptors of a data set can be useful in seeing important features of the situation being investigated,
l Statistical measures of center and variability that describe data sets can be used to compare data sets and answer questions.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53951" \t "_blank" ALEX Resources20. Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. Example: 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.Statistics & ProbabilityDraw informal comparative inferences about two populations.7.SP.4Students:
l Generate statistical questions that compare two populations,
lCollect and organize data from random samples to address the questions,
l Describe the sample distributions using measures of center and variability,
l Justify answers to the questions by drawing informal comparative inferences about the two populations from the data sets and their descriptive statistics. l Numerical data distributions
l Random samples
l Informal comparative inferencesStudents know:
l Methods of determining mean, median, interquartile range, and mean absolute deviation (from 6th grade),
l Methods for visually representing data, (e.g., line plots, coordinate graphs),
l Characteristics and definitions of mean, median, interquartile range, and mean absolute deviation.Students are able to:
l Calculate the mean, median, interquartile range, and mean absolute deviation,
l Organize data in ways that aid in identifying significant features of the data, (e.g. putting data in order to find the median, displaying in a graph to see overall shape),
l Describe the distribution of a set of data by referring to measures of center, spread, and shape,
l Draw inferences about populations from sample data,
l Justify answers to statistical questions involving comparison of two populations by using a variety of representations of sample data.Students understand that:
l A set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape,
l Using different representations and descriptors of a data set can be useful in seeing important features of the situation being investigated,
l Statistical measures of center and variability that describe data sets can be used to compare data sets and answer questions.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53953" \t "_blank" ALEX Resources21. 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.Statistics & ProbabilityInvestigate chance processes and develop, use, and evaluate probability models.7.SP.5Students:Given a variety of chance events,
l Associate numbers close to zero with unlikely events, and numbers close to one with likely events,
l Compare likelihoods of given events by associating larger numbers with the more likely events.l Probability
l Chance eventStudents know:
l Relationships between numerically represented probabilities and expressions of likelihood.Students will be able to:
l Describe the relationship of the likelihood of a chance event and its probability. Students understand that:
l The probability of a chance event is a number between 0 and 1 that expresses the likelihood that the event occurs.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53956" \t "_blank" ALEX Resources22. 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. Example: 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.Statistics & ProbabilityInvestigate chance processes and develop, use, and evaluate probability models.7.SP.6Students:Given the description of a chance event, (e.g., rolling a certain number on a number cube, getting heads when flipping a coin, drawing a red card from a deck of playing cards, etc.),
l Plan a data collection process, collect and organize the relevant data and use the long-run relative frequency to justify an approximation of the probability of the event.
Given the description of a chance event and its probability,
l Predict and justify the approximate relative frequency for a given number of occurrences, (e.g., if a number cube is rolled 600 times, predict that a 3 or a 6 would be rolled roughly 200 times, but probably not exactly 200 times).l Probability
l Chance event
l Long-run relative frequencyStudents will know:
l Methods for collecting and organizing data collected from observing chance events,
l Methods for calculating and/or expressing relative frequency.Students will be able to:
l Plan a data collection process for chance event occurrences,
l Collect and organize data from repeated occurrences of a chance event,
l Calculate relative frequency of a specific outcome of a chance event,
l Justify approximations of the probability of a chance event occurrence based on relative frequency of observed outcomes,
l Predict and justify approximate relative frequency of occurrence of a specific outcome based on the probability of a chance event.Students understand that:
l The observed relative frequency of a particular outcome of a chance event may be used to approximate the theoretical probability of that outcome in any random occurrence of the event,
l As the number of observations of a chance event gets large, the relative frequency of occurrence of any particular outcome tends to more closely match the theoretical probability of that outcome.
Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53957" \t "_blank" ALEX Resources23. 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.
a. Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. Example: 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.
b. Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. Example: 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?
Statistics & ProbabilityInvestigate chance processes and develop, use, and evaluate probability models.7.SP.7Students:Given the description of a chance event, (e.g., rolling a certain number on a number cube, getting heads when flipping a coin, drawing a red card from a deck of playing cards, etc.),
l Find and describe the probability of the event by developing probability models based on assigning equal probabilities to each of the possible outcomes (uniform probability model) and test whether or not this model may or may not fit the observed situation when the chance event occurs,
l Explain possible sources of discrepancy between developed probability models, (e.g., uniform probability model or other models) and observed frequencies.l Probability model
l Uniform probability model
l Observed frequenciesStudents know:
l Methods for collecting and organizing data collected from observing chance events,
l Methods for calculating and/or expressing relative frequency,
l Methods for modeling chance events by assigning equal probabilities to each outcome for the event.Students will be able to:
lDevelop models that assign equal probabilities to each possible outcome of a chance event,
l Develop models to observe and record relative frequencies of a particular outcome of a chance event in order to approximate the probability of a specific outcome,
l Use logical reasoning to explain sources of discrepancy between the probability of a specific outcome of a chance event, as determined by a uniform probability model and an experimental observation.Students will understand that:
lThe observed relative frequency of a particular outcome of a chance event may be used to approximate the theoretical probability of that outcome in any random occurrence of the event,
l As the number of observations of a chance event gets large, the relative frequency of occurrence of any particular outcome tends to more closely match the theoretical probability of that outcome.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53959" \t "_blank" ALEX Resources24. Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.
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.
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.
c. Design and use a simulation to generate frequencies for compound events. Example: 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?Statistics & ProbabilityInvestigate chance processes and develop, use, and evaluate probability models.7.SP.8Students:Given the description of a compound event, (e.g., rolling a sum of seven with two dice),
l Use models, (e.g., organized lists, tables, tree diagrams, and simulations) to find and explain the possible outcomes in the event and find the probability of each outcome.
Given a contextual or mathematical situation involving probability related to a compound event,
l Develop a simulation and data collection process, collect and organize the relevant data, and use the long-run relative frequency to justify an approximation of the probability of the event and an answer to the original question.l Probability
l Compound event
l Tree diagram
l Sample spaceStudents know:
l Methods for modeling compound events, (e.g., organized lists, tables, tree diagrams, simulation),
l Methods for calculating and/or expressing relative frequency,
l Methods for calculating probability from models of probability for compound events.Students will be able to:
l Calculate probability of a specific outcome of a compound event,
l Strategically use models of compound events to determine the possible outcomes and their probabilities,
l Use mathematical vocabulary to justify solutions and solution paths for solving problems involving the probability of specific events in a compound event,
l Set up and conduct simulations that model particular chance events and use the data from the simulation to approximate probabilities associated with the chance event.Students understand that:
l The observed relative frequency of a particular outcome of a chance event, including compound events, approximates the theoretical probability of that outcome in any random occurrence of the event,
l As the number of observations of a chance event gets large, the relative frequency of occurrence of any particular outcome tends to more closely match the theoretical probability of that outcome.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=53964" \t "_blank" ALEX Resources
HYPERLINK "http://alex.state.al.us/insight/lauderdaleco/standardprint/getstandards" \l "#" print
Grade 7 Mathematics CCRS Standards and Alabama COS
Franklin County Schools
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