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1 !! ' ' Scott%County%Public%Schools%! Seventh'Grade'Mathematics' Revised'2013' ' ' Pacing'Guide'and'Curriculum'Map'

2 Scott County Pacing Guide 7 th Grade Math Unit 0 Review of Prior Content Skills- 4 Weeks Rounding Place Value GCF LCM 2-6 Mixed s to Improper Fractions to Decimals 1-1 Order of Operations Unit 1 Number Systems A (Integers) -3 Weeks 2-1 Integers 2-2 Adding Integers EXT Additive Inverses and Absolute Value 2-3 Subtracting Integers 2-4 Multiplying and Dividing Integers Unit 2 Number Systems B (Decimals/Fractions) 4 Weeks 3-1 Adding and Subtracting Decimals 3-2 Multiplying Decimals 3-3 Dividing Decimals 3-5 Adding and Subtracting Fractions 3-6 Multiplying Fractions and Mixed Numbers 3-7 Dividing Fractions and Mixed Numbers Unit 3 Expressions and Equations 6 Weeks 1-2 Properties of Numbers 1-5 Simplifying Algebraic Expressions 1-3 Variables and Algebraic Expressions 2-5 Solving Equations Containing Integers 3-4 Solving Equations Containing Decimals 3-8 Solving Equations Containing Fractions 11-1 Solving Two-Step Equations 11-2 Solving Multi-Step Equations 11-3 Solving Equations with Variables on Both Sides 11-4 Inequalities 11-5 Solving Inequalities by Adding or Subtracting 11-6 Solving Inequalities by Multiplying or Dividing

3 11-7 Solving Multi-Step Inequalities Unit 4 Ratio & Proportional Relationships 4 Weeks 4-1 Rates 4-2 Identifying and Writing Proportions 4-3 Solving Proportions 4-4 Similar Figures and Proportions 4-5 Using Similar Figures 6-4 Percent of Change 6-5 Applications of Percents 6-6 Simple Interest Unit 5 Geometry 4 Weeks 4-6 Scale Drawings and Scale Models 8-1 Lab Find Missing Angles 8-5 Lab Draw Geometric Figures (Constructing Triangles) 9-1, 9-2 Area and Circumference of a Circle 9-4, 9-5, 9-6, Real-World using Area, Volume, and Surface Area 9 Ext. Slicing Three-Dimensional Figures (Cross Sections) Unit 6 Probability -3 Weeks 10-1, 10-5 Chance 10-2, 10-4 Estimation/Prediction, Probability Models 10-3, 10-9 Probability of Compound Events Unit 7- Statistics 3 Weeks 7-1 Measures of Central Tendency 7-2 Box and Whisker Plots 7-3, pg. 274B Random Sampling 6 th Grade Book 6-5 Dot Plots 6 th Grade Book 6-3 Mean Deviation End of Year 5-2 Interpreting Graphs 5-3 Slope and Rates of Change 5-4 Direct Variations!

4 Mini lessons 1-4 Translating Words into Math 2-7 Comparing and Ordering Rational Numbers 5-1 The Coordinate Plane 6-1 Fractions, Decimals and Percents 6-2 Estimating with Percents 6-3 Using Properties with Rational Numbers

5 1 st 2 nd 3 rd 4 th 7.EE.1 K R S P Expressions and Equations Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. Use properties of operations to generate equivalent expressions. 1 K Combine like terms with rational coefficients. 2 K Factor and expand linear expressions with rational coefficients using the distributive property. 3 R Apply properties of State Student Friendly operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. I can identify like terms. I can identify coefficients. I can combine like terms with rational coefficients. I can apply the distributive property. I can add, subtract, factor, and expand expressions using the properties. This means that I am able to apply the properties learned to given expressions.

6 1 st 2 nd 3 rd 4 th 7.EE.2 K R S P Expressions and Equations 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. For example, a a = 1.05a means that increase by 5% is the same as Use properties of operations to generate equivalent expressions. multiply by K Write equivalent expressions with fractions, decimals, percents, and integers. State Student Friendly I can rewrite problems with fractions, decimals, percents and integers to make equivalent expressions. This means I understand an expressions/equation can be written in different forms. 2 R Rewrite an expression in an equivalent form in order to provide insight about how quantities are related in a problem context. I can rewrite problems with fractions, decimals, percents and integers to make equivalent expressions/equations in order to solve problems. This means I understand an expressions/equation can be written in different forms to make it easier to solve the problem. %

7 1 st 2 nd 3 rd 4 th 7.EE.3 K R S P Expressions and Equations 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 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. For example: If a Solve real-life and mathematical problems using woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, numerical and algebraic expressions and or $2.50, for a new salary of $ If you want to place a towel bar 9 3/4 inches long in the center of equations. 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. 1 K Convert between numerical forms as appropriate. State Student Friendly I can convert fractions, decimals and percents. This means I understand the relationship between fractions, decimals, & percents. 2 R 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 3 R Apply properties of operations to calculate with numbers in any form. 4 R Assess the reasonableness of answers using mental computation and estimation strategies. I can use a calculator to check the solution of multi-step reallife and mathematical problems. I can apply properties of operations to solve mathematical problems with numbers in any form. For example: I know that 10% is 1/10 and.1 and I can use that knowledge to solve real-life problems. I can estimate using mental math. I can determine the reasonableness of answers using my estimate. Scott%County%Schools% %7 th %Grade% Mathematics!

8 1 st 2 nd 3 rd 4 th 7.EE.4ab K R S P Expressions and Equations 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 Solve real-life and mathematical problems using algebraic solution to an arithmetic solution, identifying the sequence of the operations used in numerical and algebraic expressions and each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is equations. 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. For 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. 1 K Fluently solve equations of the form px + q = r and p(x + q) = r with speed and accuracy. State Student Friendly I can solve two-step equations. 2 K Identify the sequence of operations used to solve an algebraic equation of the form px + q = r and p(x + q) = r. I can identify the sequence of operations used to solve 2 step equations. 3 K Graph the solution set of the inequality of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. I can graph the solution set of the inequality on a number line.

9 4 R Use variables and construct equations to represent quantities of the form px + q = r and p(x + q) = r from real-world and mathematical problems. I can write equations from real world mathematical problems. Example problems. Resource42022.pdf. 5 R Solve word problems leading to equations of the form px + q = r and p(x + q) = r. 6 R Compare an algebraic solution to an arithmetic solution by identifying the sequence of the operations used in each approach. (Ex: you know the area of a rectangle and the width, what is the length). 7 R 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. 8 R Interpret the solution set of an inequality in the context of the problem. I can write and solve 2 step equations from real world problems. I can check my solution to an algebraic equation. I can solve two-step inequalities. I can explain the meaning of the solution of an inequality. Scott%County%Schools% %7 th %Grade% Mathematics

10 1 st 2 nd 3 rd 4 th 7.G.1 K R S P Geometry Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from scale drawing and reproducing a scale drawing at a different scale. Draw, construct, and describe geometrical figures and describe the relationships between 1 K Use ratios and proportions to create scale drawing. 2 K Identify corresponding sides of scaled geometric figures. 3 K Compute lengths and areas State Student Friendly from scale drawings using strategies such as proportions. 4 R Solve problems involving scale drawings of geometric figures using scale factors. 5 P Reproduce a scale drawing that is proportional to a given geometric figure using a different scale. I can set up and solve ratios and proportions to make scale drawings. I can identify sides on two similar figures that correspond. I can set up and solve proportions to find the actual length and area of figures using scale models. I can find the scale factor of scale drawings and use it to solve real world problems. I can draw a scale drawing of a given figure.

11 1 st 2 nd 3 rd 4 th 7.G.2 K R S P Geometry 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. Draw, construct, and describe geometrical figures and describe the relationships between 1 K Know which conditions create unique triangles, more than one triangle, or no triangle. 2 R Analyze given conditions based State Student Friendly on the three measures of angles or sides of a triangle to determine when there is a unique triangle, more than one triangle, or no triangle. 3 S Construct triangles from three given angle measures to determine when there is a unique triangle, more than one triangle or no triangle using appropriate tools such as rulers, protractors, technology or others. I can determine which conditions create unique triangles, more than one triangles, or no triangle. I can analyze the conditions given to determine whether there is a unique triangle, more than one triangle, or no triangle. I can draw different types of triangles using a ruler, protractor, technology, or other tools.

12 1 st 2 nd 3 rd 4 th 7.G.3 K R S P Geometry Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. Draw, construct, and describe geometrical figures and describe the relationships between 1 K Define cross-section of a 3D figure as slicing 3D figure. State Student Friendly 2 K Describe the twodimensional figures that result from slicing a threedimensional figure such as a right rectangular prism or pyramid. 3 R Analyze three-dimensional shapes by examining two dimensional cross-sections. I can define a cross-section as a plane that divides a 3D figure. I can determine different 2D figures that result from slicing 3D figures at different angles. For example, you can slice a right rectangular prism with a plane parallel to one of the faces making the same figures as the face to which it is parallel. Additionally, if you slice it an an angle that is not parallel to one of the faces, you will get a different 2D figure (like a parallelogram or a triangle) I can analyze three-dimensional shapes by examining two-dimensional cross-sections. Scott%County%Schools% 7 th %Grade% Mathematics%

13 1 st 2 nd 3 rd 4 th 7.G.4 K R S P Geometry 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 circumference and area of a circle. Solve real-life and mathematical problems involving angle measure, area, surface area, and volume. 1 K Know the parts of a circle including radius, diameter, area, circumference, center, and chord. State Student Friendly 2 K Identify Pi. I can identify Pi. I can identify and define the parts of a circle (radius, diameter, area, circumference, center, chord, the irrational number). 3 K Know formulas for area and circumference of a circle. I can identify the formulas for area and circumference of a circle. C=d; C=2r; A=r2 4 K Given the area of a circle, find its circumference. I can find the area of a circle if given the circumference. 5 R Justify that Pi can be derived from the circumference and diameter of a circle. I can justify that pi can be derived from the circumference and diameter. 6 R Apply circumference or area formulas in order to solve mathematical and real-world problems. I can use the formulas for area and circumference of a circle in order to solve math and real-world problems.

14 7 R Justify the formulas for area and circumference of a circle and how they relate to π. 8 R Informally derive the relationship between circumference and area of a circle. I can justify the area and circumference formulas and how they relate to pi. I can informally derive the relationship between circumference and area.

15 1 st 2 nd 3 rd 4 th 7.G.5 K R S P Geometry Use facts about supplementary, complementary, vertical, adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. Solve real-life and mathematical problems involving angle measure, area, surface area, and volume. 1 K Identify and recognize angles: Supplementary, Complementary, Vertical, and Adjacent. 2 K Determine complements and State Student Friendly supplements of a given angle. I can define and identify angles (supplementary, complementary, vertical, and adjacent) I can determine an angle that will be complementary or supplementary to any given angle. 3 R Determine unknown angle measures by writing and solving algebraic equations based on relationships between angles and intersecting lines. I can write algebraic equations based on angle relationships. I can write algebraic equations based on intersecting lines. I can solve algebraic equations involving angle measurements.

16 1 st 2 nd 3 rd 4 th 7.G.6 K R S P Geometry 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. Solve real-life and mathematical problems involving angle measure, area, surface area, and volume. 1 K Know the formulas for area and volume and the procedure for finding surface area and when to use them in real-world and math problems for two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. 2 R Solve real-world and math problems involving area, surface area and volume of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. State Student Friendly I can memorize area, volume and surface area formulas for different figures. I can recognize when to use formulas to solve math and realworld problems involving area, volume, and surface area. V=Bh for all right prisms A = bh for all parallelograms A - ½ bh for all triangles LSA = Pbaseh; Lateral Surface area TSA = LSA + 2B I can apply formulas for area, volume, and surface area to solve mathematical and real-world problems.

17 1 st 2 nd 3 rd 4 th 7.NS.1a K R S P The Number System 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. Apply and extend previous understandings of operations with a. Describe situations in which opposite quantities combine to make 0. fractions to add, subtract, multiply, and divide rational numbers For example, a hydrogen atom has a 0 charge because its two subatomic particles are oppositely charged. 1 K Describe situations in which opposite quantities combine to make 0 State Student Friendly I can describe situations where opposite quantities combine to make zero.

18 1 st 2 nd 3 rd 4 th 7.NS.1b K R S P The Number System Understand p + q as the number located a distance IqI from p in the positive or negative direction depending on whether q is positive or negative. Show that a number and its positive have a sum of 0 (are additive inverse). Interpret sums Apply and extend previous understandings of operations with of rational numbers by describing real world contexts. fractions to add, subtract, multiply, and divide rational numbers 1 K Know that a number and its opposite have a sum of 0, and are additive inverses State Student Friendly I can identify additive inverses. 2 K I can add additive inverses to make 0. 3 K Know that when adding two numbers, p+q, if q is positive, the sum of p and q will be q spaces to the right of p on the number line 4 K Know that when adding two numbers, p+q, if q is negative, the sum of p and q will be q spaces to the left of p on the number line I can know that when adding a positive number I am moving to the right on the number line. I can know that when adding a negative number I am moving to the left on the number line. 5 R Apply and extend previous understanding to represent addition problems of rational numbers with a horizontal or vertical number line I can represent addition problems with a number line.

19 6 R Interpret sums of rational numbers by describing real world contexts 7 R Analyze and explain why the sum of p + q is located a distance of q in the positive or negative direction from p on a number line I can relate solutions of integer and fraction problems to real world situations. I can explain why you move left or right on a number line based on the type of addition problem.

20 1 st 2 nd 3 rd 4 th 7.NS.1c K R S P The Number System 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 Apply and extend previous understandings of operations with real-world contexts. fractions to add, subtract, multiply, and divide rational numbers 1 K Show that the distance between two rational numbers on the number line is the absolute value of their difference 2 R Apply and extend previous State Student Friendly understanding to represent subtraction problems of rational numbers with a horizontal or vertical number line 3 R Apply the additive inverse property to subtract rational numbers, p-q = p +(-q) 4 R Apply the principle of subtracting rational numbers in real-world contexts I can find the distance between two numbers on a number line by finding the absolute value of their difference. I can represent subtraction problems with a number line. I can change subtraction problems to addition problems using the additive inverse property. I can solve real world problems involving subtracting rational numbers.

21 1 st 2 nd 3 rd 4 th 7.NS.1d K R S P The Number System Apply properties of operations as strategies to add and subtract rational numbers. 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 1 R Apply properties of operations as strategies to add and subtract rational numbers State Student Friendly I can apply mathematical properties to add and subtract rational numbers. (additive inverse, commutative, associative)

22 1 st 2 nd 3 rd 4 th 7.NS.2a K R S P The Number System 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 Apply and extend previous understandings of multiplication and numbers by requiring that operations continue to satisfy the properties of division of fractions to multiply and divide rational numbers 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. 1 K Recognize that the process for multiplying fractions can be used to multiply rational numbers including integers State Student Friendly I can multiply fractions. 2 K I can multiply integers. 3 K Know and describe the rules when multiplying signed numbers I can multiply positive and negative fractions. 4 K I can multiply positive and negative integers. 5 R Apply the properties of operations, particularly distributive property, to multiply rational numbers 6 R Interpret the products of rational numbers by describing a real world context I can apply the distributive property to multiply rational numbers. I can write a real-world problem to fit with the product of rational numbers.

23 1 st 2 nd 3 rd 4 th 7.NS.2b K R S P The Number System 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 Apply and extend previous understandings of multiplication and numbers by describing real-world contexts. division of fractions to multiply and divide rational numbers 1 K Explain why integers can be divided except when the divisor is 0 State Student Friendly I can divide integers. 2 K I can explain why you cannot divide by zero. 3 K Describe why the quotient is I can describe why the answer to a division problem will always a rational number 4 K Know and describe the rules when dividing signed numbers, integers always be a rational number. I can divide negative and positive rational numbers. 5 K I can describe the rules for dividing integers. 6 K Recognize that: (p/q) = - I can recognize that (p/q) = -p/q = p/-q. p/q = p/-q 7 R Interpret the quotient of rational numbers by describing a real world context I can write a real-world problem to fit with the quotient of rational numbers.

24 1 st 2 nd 3 rd 4 th 7.NS.2c K R S P The Number System Apply properties of operations as strategies to multiply and divide rational numbers. Apply and extend previous understandings of multiplication and division of fractions to multiply and divide rational numbers 1 K Identify how properties of operations can be used to multiply and divide rational numbers (such as distributive property, multiplicative inverse property, multiplicative identity, commutative property for multiplication, associative property for multiplication, etc. ) 2 R Apply properties of State Student Friendly operations as strategies to multiply and divide rational numbers I can identify the properties of operations involving multiplication and division. I can apply the properties of operations involving multiplication and division. %

25 1 st 2 nd 3 rd 4 th 7.NS.2d K R S P The Number System Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in zeroes or eventually repeats. Apply and extend previous understandings of multiplication and division of fractions to multiply and divide rational numbers 1 K Convert a rational number to a decimal using long division 2 K Explain that the decimal State Student Friendly form of a rational number terminates (stops) in zeroes or repeats I can change fractions into decimals using long division. I can explain that rational numbers written as decimals have a decimal that terminates or repeats. %

26 1 st 2 nd 3 rd 4 th 7.NS.3 K R S P The Number System Solve real-world and mathematical problems involving the four operations with rational numbers.1 1 Computations with rational numbers extend the rules for manipulating Apply and extend previous understandings of multiplication and fractions to complex fractions division of fractions to multiply and divide rational numbers State Student Friendly 1 K Add rational numbers I can add rational numbers. 2 K Subtract rational numbers I can subtract rational numbers. 3 K Multiply rational numbers I can multiply rational numbers. 4 K Divide rational numbers I can divide rational numbers. 5 R Solve real-world mathematical problem by adding, subtracting, multiplying, and dividing rational numbers, including complex fractions I can solve real world problems by adding, subtracting, multiplying, and dividing rational numbers. Scott%County%Schools% %7 th %Grade% Mathematics!

27 1 st 2 nd 3 rd 4 th 7.RP.1 K R S P Ratio and Proportional Relationships Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as Analyze proportional relationships and use them to solve realworld the complex fraction (1/2)/(1/4) miles per hour, equivalently 2 miles per hour. and mathematics problems 1 K Compute unit rates associated with ratios of fractions in like or different units State Student Friendly I can find unit rates with ratios that have like and unlike units.

28 1 st 2 nd 3 rd 4 th 7.RP.2 K R S P Ratio and Proportional Relationships 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 Analyze proportional relationships and use them is a straight line through the origin. to solve real-world and mathematics problems 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. For 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. 1 K Know that a proportion is a statement of equality between two ratios State Student Friendly I can use cross product to determine if two ratios are proportional. 2 K Define constant of proportionality as a unit rate I can identify the unit rate as the constant of proportionality. 3 K Recognize what (0, 0) represents on the graph of a proportional relationship I can identify(0,0) as the starting point of proportional relationships. (0 candy bars = 0 money paid) 4 K Recognize what (1, r) on a graph represents, where r is the unit rate I can identify (1, r) on a graph as the unit rate. 5 R Analyze two ratios to determine if they are proportional to one another with a variety of strategies. (e.g. using tables, graphs, pictures, etc.) I can use tables, graphs, and pictures to determine whether two ratios are proportional.

29 6 R Analyze tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships to identify the constant of proportionality I can determine the constant of proportionality (unit rate) from a variety of data representations (tables, graphs, equations, diagrams, etc.) 7 R Represent proportional relationships by writing equations I can write equations to represent proportional relationships. 8 R Explain what the points on a graph of a proportional relationship means in terms of a specific situation. I can explain why (1, r) is the unit rate. 9 R I can explain that all points on the line graphed will be proportional to one another.

30 1 st 2 nd 3 rd 4 th 7.RP.3 K R S P Ratio and Proportional Relationships Use proportional relationships to solve multi-step ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. Analyze proportional relationships and use them to solve realworld and mathematics problems 1 K Recognize situations in which percentage proportional relationships apply 2 R Apply proportional reasoning State Student Friendly to solve multi-step ratio and percent problems, e.g., simple interest, tax, markups, markdowns, gratuities, commissions, fees, percent increase and decrease, percent error, etc. I can identify when to use percent proportions. I can analyze proportional relationships and use them to solve real-world and mathematical problems. Scott%County%Schools% %7 th %Grade% Mathematics!

31 1 st 2 nd 3 rd 4 th 7.SP.1 K R S P Statistics and Probability Understand that statistics can be used to gain information about a population by examining a sample of a population; generalizations about a population from a sample are valid only if the sample is a representation of that population. Use random sampling to draw interfaces about a population Understanding that random sampling tends to produce representative samples and support valid inferences. 1 K Know statistics terms such as population, sample, sample size, random sampling, generalizations, valid, biased and unbiased State Student Friendly I can define: Population Sample Sample Size Random Sampling Generalizations Valid Biased Unbiased 2 K Recognize sampling techniques such as convenience, random, systematic, and voluntary I can recognize the different types of sampling techniques. 3 K Know that generalizations about a population from a sample are valid only if the sample is representative of that population I understand that the sample group must be diverse enough to represent differences in the population. For example, if I am surveying 7th grade students at my school I want to ask both sexes and all ethnic groups represented at my school. I want to ask students from all parts of the school district not just one neighborhood.

32 4 R Apply statistics to gain information about a population from a sample of the population I can use statistics to learn things about a population by examining a smaller group of that population called a sample. 5 R Generalize that random sampling tends to produce representative samples and support valid inferences I can determine that random sampling shows a valid representation of the population.

33 1 st 2 nd 3 rd 4 th 7.SP.2 K R S P Statistics and Probability Use data from random sampling 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. Use random sampling to draw interfaces about a population For example, estimate the mean word length in a book by randomly sampling words from a book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be. State Student Friendly 1 K Define random sample I can define random sample. 2 K Identify an appropriate sample size I can identify an appropriate sample size based on the size of my population. 3 R Analyze & interpret data from a random sample to draw inferences about a population 4 R Generate multiple samples (or simulated samples) of the same size to determine the variation in estimates or predictions by comparing and contrasting the samples I can make an informed prediction or estimation about a population using data from a random sample of the population. I can use graphical or numerical data to compare random samples.

34 1 st 2 nd 3 rd 4 th 7.SP.3 K R S P Statistics and Probability 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. For example, Draw informal comparative inferences about two populations the mean height of players on the basketball team is 10 cm greater than the mean height of the 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. 1 K Identify measures of central tendency (mean, median, mode) in a data distribution State Student Friendly I can identify measures of central tendency. 2 K Identify measures of variation including upper quartile, lower quartile, upper extreme maximum, lower extreme maximum, range, interquartile range, and mean absolute deviation. (ie: box and whisker plot, dot plot, etc) I can identify measures of variability (lower extreme, lower quartile, upper quartile, upper extreme, range, interquartile range and mean absolute deviation*). 3 R Compare two numerical data distributions on a graph by visually comparing data displays, and assessing the degree of visual overlap I can represent the data graphically to show a difference in the two data sets; using a scatter plot, dot plot, or a box-and-whisker plot to show the spread the of data.

35 4 R Compare the differences in the measure of central tendency in two numerical data distributions by measuring the difference between the centers and expressing it as a multiple of a measure of variability I can find the variability of the data set and use the mean to say something about the differences of the two data sets.

36 1 st 2 nd 3 rd 4 th 7.SP.4 K R S P Statistics and Probability Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether words in a chapter of a seventhgrade Draw informal comparative inferences about two populations science book are generally longer than the words in a chapter of a fourthgrade science book. 1 K Find measures of central tendency (mean, median, and mode) and measures of variability (range, quartile, etc.) State Student Friendly I can find the measures of central tendency, measures of center. I can find the mean median and mode of the data sets and make a comparison. 2 K I can find the variability of the data set. (ex: range, quartile) 3 R Analyze and interpret data using measures of central tendency and variability 4 R Draw informal comparative inferences about two populations from random samples I can use the measures of center and variability to interpreter and analyze the data. I can draw informal comparative inferences about two populations from random samples.

37 1 st 2 nd 3 rd 4 th 7.SP.5 K R S P Statistics and Probability 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 unlike event, a probability Investigate chance processes and develop, use, and evaluate around ½ indicates an event that is neither unlikely nor likely, and a probability probability models near 1 indicates a likely event. 1 K Know that probability is expressed as a number between 0 and 1 2 K Know that a random event State Student Friendly with a probability of ½ either outcome is equally likely to happen 3 K Know that as probability moves closer to 1 it is increasingly likely to happen 4 K Know that as probability moves closer to 0 it is decreasingly likely to happen 5 R Draw conclusions to determine that a greater likelihood occurs as the number of favorable outcomes approaches the total number of outcomes I can express probability as a number between 0 and 1. I can explain that a random event with a probability of ½ is equally likely to happen or not happen. I can show that as probability moves closer to 1, it is most likely to occur. I can show that as probability moves closer to 0, the event is most likely to not occur. I can use the probability formula to determine if an event is likely or unlikely to occur.

38 1 st 2 nd 3 rd 4 th 7.SP.6 K R S P Statistics and Probability 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. For example, Investigate chance processes and develop, use, and evaluate when rolling a number cube 600 times, predict that a 3 or 6 would be rolled probability models roughly 200 times, but probably not exactly 200 times. 1 K Determine relative frequency (experimental probability) is the number of times an outcome occurs divided by the total number of times the experiment is completed 2 R Determine the relationship State Student Friendly between experimental and theoretical probabilities by using the law of large numbers 3 R Predict the relative frequency (experimental probability) of an event based on the (theoretical) probability I can determine experimental probability of an event. This means I can write the probability as the number of times a desired outcome occurs divided by the number of trials. I can determine from repeating an experiment many times, the experimental probability will approach the theoretical probability of the event. I can predict the experimental probability of an event based on the theoretical probability.

39 1 st 2 nd 3 rd 4 th 7.SP.4ab K R S P Statistics and Probability Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement Investigate chance processes and develop, use, and evaluate probability models 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. b. Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For 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? 1 K Recognize uniform (equally likely) probability State Student Friendly I can identify when the probability of getting various outcomes is equally likely. (Example: roll a die, spinner, coins) 2 K Use models to determine the probability of events I can use different models (tree diagrams and area models) to determine the probability of events from the sample space. 3 R Develop a uniform probability model and use it to determine the probability of each outcome/event I can create a probability model and use it to determine the probability for each outcome/event. 4 R Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process I can create a probability model by observing frequencies in data generated from chance process

40 5 R Analyze a probability model and justify why it is uniform or explain the discrepancy if it is not I can analyze a probability model and determine whether it is uniform or not and explain why it is so.

41 1 st 2 nd 3 rd 4 th 7.SP.8a K R S P Statistics and Probability Find probabilities of compound events using organized lists, tables, tree diagrams, and simulations. a. Understand that, just as with simple events, the probability of a compound Investigate chance processes and develop, use, and evaluate event is the fraction of outcomes in the sample space for which the compound probability models event occurs. 1 K Define and describe a compound event State Student Friendly Define and describe a compound event 2 K Know that the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs I know the probability of a compound event is the desired outcomes over the possible outcomes and that the compound event is a fraction of the sample space. 3 K I can determine the probability of a compound event using the sample space. This means the of desired outcome divided by of possible outcomes. 4 K Identify the outcomes in the sample space for an everyday event I can identify the outcomes in a sample space. 5 K Define simulation (The imitation of a real thing) I can define simulation. 6 R Design and use a simulation Find probabilities of compound events using I can find the probability of compound events using organized lists, tables, tree diagrams, etc.

42 organized lists, tables, tree diagrams, etc. and analyze the outcomes 7 R I can analyze the outcomes of compound events. 8 R Choose the appropriate method such as organized lists, tables and tree diagrams to represent sample spaces for compound events I can determine the most appropriate method to represent sample spaces for compound events. 9 R Design and use a simulation to generate frequencies for compound events I can design and use a simulation to generate frequencies for compound events.

43 1 st 2 nd 3 rd 4 th 7.SP.8b K R S P Statistics and Probability Find probabilities of compound events using organized lists, tables, tree diagrams, and simulations. b. Represent sample spaces for compound events using methods such as Investigate chance processes and develop, use, and evaluate organized lists, tables and tree diagrams. For an event described in everyday probability models language (e.g. rolling double sixes ), identify the outcomes in the sample space which compose the event. 1 K Represent a sample space for compound events in a variety of ways (tree diagram, list, table, etc) 2 K Identify the outcomes in the State Student Friendly sample space which compose the event using everyday language I can represent the sample space of compound events using tree diagrams, lists, tables, etc. I can identify the possible outcomes using everyday language.

44 1 st 2 nd 3 rd 4 th 7.SP.8c K R S P Statistics and Probability Find probabilities of compound events using organized lists, tables, tree diagrams, and simulations. c. Design and use a simulation to generate frequencies for compound events. Investigate chance processes and develop, use, and evaluate probability models 1 K Use frequencies from probability experiments to determine the likelihood of a compound event State Student Friendly I can use data from experiments to determine the likelihood of a compound event occurring. 2 P Design and use a probability simulation to generate I can design a probability experiment. 3 I can carry out the experiment I designed. 4 I can use the experimental data to determine the probability of a compound event. Scott%County%Schools% %7 th %Grade% Mathematics!