## 1. The kindergarten year starts developing the students numeracy skills which are imperative for future probability and statistics coursework. They begin to count, represent and recognize numbers, add and subtract, and classify objects as more or less than some other value and in categories.

## 2. Kindergarten

### 2.1. Know number names and the count sequence

2.1.1. K.CC.A.1 Count to 100 by 1's and tens

2.1.2. K.CC.A.2 Count forward beginning from a given number within the know sequence

2.1.3. K.CC.A.3 Write numbers from 0 to 20

### 2.2. Count to tell the number of objects

2.2.1. K.CC.B.4 Understand relationships between numbers and quantities; connection counting to cardinality

2.2.2. K.CC.B.5 Count to answer "how many?" questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects

### 2.3. Compare numbers

2.3.1. K.CC.C.6 Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group

2.3.2. K.CC.C.7 Compare tow numbers between 1 and 10 presented as written numerals

### 2.4. Understand addition and subtraction

2.4.1. K.OA.A.1 Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations

2.4.2. K.OA.A.2 Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem

2.4.3. K.OA.A.3 Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation

2.4.4. K.OA.A.4 For any number from 1 to 9, find the number that makes 10 when added to the given number

2.4.5. K.OA.A.5 Fluently add and subtract within 5

### 2.5. Work with numbers 11-19 to gain foundations for place value

2.5.1. K.NBT.A.1 Compose and decompose numbers from 11 to 19 into ten ones and some further ones; understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones

### 2.6. Describe and compare measurable attributes

2.6.1. K.MD.A.1 Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object

2.6.2. K.MD.A.2 Directly compare two objects with a measurable attribute in common, to see which object has "more of"/"less of" the attribute, and describe the difference

### 2.7. Classify objects and count the number of objects

2.7.1. K.MD.B.3 Classify objects into given categories; count the numbers of objects in each category and sort the categories by count

## 3. 1st Grade

### 3.1. Represent and solve involving addition and subtraction

3.1.1. 1.OA.A.1 Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions

3.1.2. 1.OA.A.2 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20

### 3.2. Understand and apply properties of operations and the relationship between addition and subtraction

3.2.1. 1.OA.B.3 Apply properties of operations as strategies to add and subtract

3.2.2. 1.OA.B.4 Understand subtraction as an unknown-addend problem

### 3.3. Add and subtract within 20

3.3.1. 1.OA.C.5 Relate counting addition and subtraction

3.3.2. 1.OA.C.6 Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making 10; decomposing a number lending to a 10; using the relationship between addition and subtraction; and creating equivalent but easier or known sums

### 3.4. Work with addition and subtraction equations

3.4.1. 1.OA.D.7 Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false

3.4.2. 1.OA.D.8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers

### 3.5. Extend the counting sequence

3.5.1. 1.NBT.A.1 Count to 20, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral

### 3.6. Understand place value

3.6.1. 1.NBT.B.2 Understand that the two digits of a two-digit number represent amounts of tens and ones

3.6.2. 1.NBT.B.3 Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <

### 3.7. Use place value understanding and properties of operations to add and subtract

3.7.1. 1.NBT.C.4 Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten

3.7.2. 1.NBT.C.5 Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used

3.7.3. 1.NBT.C.6 Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used

### 3.8. Represent and interpret data

3.8.1. 1.MD.C.4 Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another

### 3.9. In first grade, the students continue building their numeracy skills and start working with word problems (very commonly used in probstats). They can count higher and interpret data in up to 3 categories

## 4. 2nd Grade

### 4.1. Represent and solve addition and subtraction problems

4.1.1. 2.OA.A.1 Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions

### 4.2. Add and subtract within 20

4.2.1. 2.OA.B.2 Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers

### 4.3. Work with equal groups of objects to gain foundations for multiplication

4.3.1. 2.OA.C.3 Determine whether a group of objects has an odd or even number of members; write an equation to express an even number as a sum of two equal addends

4.3.2. 2.OA.C.4 Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends

### 4.4. Understand place value

4.4.1. 2.NBT.A.1 Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones

4.4.2. 2.NBT.A.2 Count within 1000; skip by 5s, 10s, and 100s

4.4.3. 2.NBT.A.3 Read and write numbers to 1000 using base-ten numerals, number names, and expanded form

4.4.4. 2.NBT.A.4 Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using <, =, and < symbols to record the results of comparisons

### 4.5. Use place value understanding and properties of operations to add and subtract

4.5.1. 2.NBT.B.5 Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction

4.5.2. 2.NBT.B.6 Add up to four two-digit numbers using strategies based on place value and properties of operations

4.5.3. 2.NBT.B.7 Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones, and sometimes it is necessary to compose or decompose tens or hundreds

4.5.4. 2.NBT.B.8 Mentally add 10 or 100 to a given number 100-900, and mentally subtract 10 or 100 from a given number 100-900

4.5.5. 2.NBT.B.9 Explain why addition and subtraction strategies work, using place value and the properties of operations

### 4.6. Represent and interpret data

4.6.1. 2.MD.D.9 Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units

4.6.2. 2.MD.D.10 Draw a picture graph and a bar graph to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph

### 4.7. Second Grade introduces three digit numbers and continues practice of addition and subtraction. Line plots and bar graphs are introduced.

## 5. 3rd Grade

### 5.1. Represent and solve involving multiplication and division

5.1.1. 3.OA.A.1 Interpret products of whole numbers

5.1.2. 3.OA.A.2 Interpret whole-number quotients of whole numbers

5.1.3. 3.OA.A.3 Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities

5.1.4. 3.OA.A.4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers

### 5.2. Understand properties of multiplication and the relationship between multiplication and division

5.2.1. 3.OA.B.5 Apply properties of operations as strategies to multiply and divide

5.2.2. 3.OA.B.6 Understand division as an unknown-factor problem

### 5.3. Multiply and divide within 100

5.3.1. 3.OA.C.7 Fluently multiply and divide within 1oo, using strategies such as the relationship between multiplication and division or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers

### 5.4. Solve problems involving the 4 operations, and identify and explain patterns in arithmetic

5.4.1. 3.OA.D.8 Solve two-step problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding

5.4.2. 3.OA.D.9 Identify arithmetic patterns, and explain them using properties of operations

### 5.5. Use place value understanding and properties of operations to perform multi-digit arithmetic

5.5.1. 3.NBT.A.1 Use place value understanding to round whole numbers to the nearest 10 or 100

5.5.2. 3.NBT.A.2 Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction

5.5.3. 3.NBT.A.3 Multiply one-digit whole numbers by multiples of 10 in the range 10-90 using strategies based on place value and properties of operations

### 5.6. Develop understanding of fractions as numbers

5.6.1. 3.NF.A.1 Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b

5.6.2. 3.NF.A.2 Understand a fraction as a number on the number line; represent fractions on a number line diagram

5.6.3. 3.NF.A.3 Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size

### 5.7. Represent and interpret data

5.7.1. 3.MD.B.3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step "how many more" and "how many less" problems using information presented in scaled bar graphs

5.7.2. 3.MD.B.4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units - whole numbers, halves, or quarters

### 5.8. Third grade introduces whole number products and quotient problems by building on the addition and subtraction skills the students learned in previous years. The students should be able to recognize arithmetic patterns, fractions, and round. The students also create line and bar graphs with several categories.

## 6. 4th Grade

### 6.1. Use the four operations with whole numbers to solve problems

6.1.1. 4.OA.A.1 Interpret a multiplication equation as a comparison

6.1.2. 4.OA.A.2 Multiply or divide to solve word problems involving multiplicative comparison

6.1.3. 4.OA.A.3 Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding

### 6.2. Gain familiarity with factors and multiples

6.2.1. 4.OA.B.4 Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite

### 6.3. Generate and analyze patterns

6.3.1. 4.OA.C.5 Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself

### 6.4. Generalize place value understanding for multi-digit whole numbers

6.4.1. 4.NBT.A.1 Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right

6.4.2. 4.NBT.A.2 Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each pace, using >, =, and < symbols to record the results of comparisons

6.4.3. 4.NBT.A.3 Use place value understanding to round multi-digit whole numbers to any place

### 6.5. Use place value understanding and properties of operations to perform multi-digit arithmetic

6.5.1. 4.NBT.B.4 Fluently add and subtract multi-digit whole numbers using the standard algorithm

6.5.2. 4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models

6.5.3. 4.NBT.B.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and. or are models

### 6.6. Extend understanding of fraction equivalence and ordering

6.6.1. 4.NF.A.1 Explain why a fraction a/b is equivalent to a fraction na/nb by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size> Use this principle to recognize and generate equivalent fractions

6.6.2. 4.NF.A.2 Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model

### 6.7. Build fractions from unit fractions

6.7.1. 4.NF.B.3 Understand fraction a/b with a>1 as a sum of fraction 1/b

6.7.2. 4.NF.B.4 Apply and extend previous understandings of multiplication to multiply a fraction by a whole number

### 6.8. Understand decimal notation for fractions, and compare decimal fractions

6.8.1. 4.NF.C.5 Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100

6.8.2. 4.NF.C.6 Use decimal notation for fractions with denominators 10 or 100

6.8.3. 4.NF.C.7 Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusion

### 6.9. Represent and interpret data

6.9.1. 4.MD.B.4 Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots

### 6.10. In the fourth grade, students continue practicing use of all four operations with whole numbers given in contexts and they are able to mentally assess the reasonableness of estimations. The students will be able to decipher between primes and composites. Comparisons with <,=, and < begin with fractions and whole numbers. The students learn how to multiply fraction by a whole number and change fractions to decimals.

## 7. 5th Grade

### 7.1. Write and interpret numerical expressions

7.1.1. 5.OA.A.1 Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols

7.1.2. 5.OA.A.2 Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them

### 7.2. Analyze patterns and relationships

7.2.1. 5.OA.B.3 Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane

### 7.3. Understand the place value system.

7.3.1. 5.NBT.A.1 Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left

7.3.2. 5.NBT.A.2 Explain patterns in the number of zeroes of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10

7.3.3. 5.NBT.A.3 Read, write, and compare decimals to thousandths

7.3.4. 5.NBT.A.4 Use place value understanding to round decimals to any place

### 7.4. Perform operations with multi-digit whole numbers and with decimals to hundredths.

7.4.1. 5.NBT.B.5 Fluently multiply multi-digit whole numbers using the standard algorithm

7.4.2. 5.NBT.B.6 Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models

7.4.3. 5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used

### 7.5. Use equivalent fractions as a strategy to add and subtract fractions.

7.5.1. 5.NF.A.1 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators

7.5.2. 5.NF.A.2 Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers

### 7.6. Convert like measurement units within a given measurement system.

7.6.1. 5.MD.A.1 Convert among different-sized standard measurement units within a given measurement system and use these conversions in solving multi-step, real world problems

### 7.7. Represent and interpret data.

7.7.1. 5.MD.B.2 Make a line plot to display a data set of measurements in fractions of a unit. Use operations on fractions for this grade to solve problems involving information presented in line plots

### 7.8. Apply and extend previous understandings of multiplication and division.

7.8.1. 5.NF.B.3 Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem

7.8.2. 5.NF.B.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction

7.8.3. 5.NF.B.5 Interpret multiplication as scaling (resizing),

7.8.4. 5.NF.B.6 Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem

7.8.5. 5.NF.B.7 Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions

### 7.9. Parentheses are introduced in numerical expressions and the students can compare the patterns between 2 expressions. The students get a formal introduction to the connection between the number of zeros of a product to the power of ten. The students learn how to add fractions without the same denominator. The students make a line plot.

## 8. 6th Grade

### 8.1. Develop understanding of statistical variability

8.1.1. 6.SP.A.1 Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers

8.1.2. 6.SP.A.2 Look at the center of a collection of data and look at the spread and shape

8.1.3. 6.SP.A.3 Recognize the center of a set of data as a summary of the values with a single number and note that the measure of variation is a description of how values vary

### 8.2. Summarize and describe distributions

8.2.1. 6.SP.B.4 Plot data on a number line, histogram, and box plot

8.2.2. 6.SP.B.5 Summarize data

### 8.3. The students recognize statistical questions have variability. With a set of data, they look at the center,spread, and shape then plot it.

## 9. 7th Grade

### 9.1. Use random sampling to draw inferences about a population

9.1.1. 7.SP.A.1 Realize that we can take a sample of the population and generalize about the general population based on the sample as long as the sample is representative of the population. Note that random samples tends to produce good representative samples

9.1.2. 7.SP.A.2 Use data from a random sample to make inferences about a population and gauge how far off the estimates and predictions might be

### 9.2. Draw informal comparative inferences about two populations

9.2.1. 7.SP.B.3 Informally determine the degree of overlap of 2 data sets with similar variability and measure the difference between the centers by expressing it as a multiple measure of variability

9.2.2. 7.SP.B.4 Compare 2 populations based on data from random samples

### 9.3. Investigate chance processes and develop, use, and evaluate probability models

9.3.1. 7.SP.C.5 Understand probabilities of an event are between 0 and 1 and larger numbers represent greater likelihood, numbers close to 1/2 are neither likely or unlikely, and numbers close to 1 are really likely

9.3.2. 7.SP.C.6 Approximate the probability of a chance event by collecting data on the chance process that produces it and looking at its long run relative frequency then predict the approximate relative frequency given the probability

9.3.3. 7.SP.C.7 Create a probability model and use it to find probability of events and then compare probabilities from a model to observed frequencies

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

### 9.4. The students investigate inferences involving random populations and estimate the accuracy of the predictions. They compare two data sets spread, shape, and center. Then they compare data between two populations. Probability is introduced and the students learn about the degree of likelihood of an event given it's probability. The students collect data and create representations for it.

## 10. 8th Grade

### 10.1. Investigate patterns of association in bivariate data

10.1.1. 8.SP..A.1 Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between 2 quantities. Describe patterns (clustering, outliers, positive/negative association, linear association, and nonlinear association)

10.1.2. 8.SP..A.2 Recognize that straight lines are frequently used to model relationships between 2 quantitative variables

10.1.3. 8.SP..A.3 Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept

10.1.4. 8.SP..A.4 Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies in a 2-way table. Construct and interpret a 2-way table summarizing data on 2 categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between 2 variables

### 10.2. Students are introduced to data sets with two variable quantities and are asked to describe the patterns of that data set.students learn that linear representations are common for bivariate data so slope and intercept are discussed. They represent their data with a two- way table.

## 11. Interpreting Categorical and Quantitative Data

### 11.1. Summarize, represent, and interpret data on a single count or measure variable

11.1.1. ID.A.1 Represent data with plots on the real number line (dot plots, histograms. and box plots)

11.1.2. ID.A.2 Use statistics appropriate to the shape of the data distribution to compare center and spread of two or more different data sets

11.1.3. ID.A.3 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points

11.1.4. ID.A.4 Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.

### 11.2. Summarize, represent, and interpret data on two categorical and quantitative variables

11.2.1. ID.B.6 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related

11.2.2. ID.B.5 Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data. Recognize possible associations and trends in the data.

### 11.3. Interpret linear models

11.3.1. ID.C.7 Interpret the slope and the intercept of a linear model in the context of data

11.3.2. ID.C.8 Compute and interpret the correlation coefficient of a linear fit

11.3.3. ID.C.9 Distinguish between correlation and causation

### 11.4. The students work with data sets by representing it on the real number line and analyzing the differences in data sets in terms of shape, center, and spread. They talk about mean and standard deviation. Two variable data is worked with then the difference between correlation and causation are discussed.

## 12. Making Inferences and Justifying Conclusions

### 12.1. Understand and evaluate random processes underlying statistical experiments

12.1.1. IC.A.1 Understand statistics as a process for making inferences about population parameters based on a random sample from that population

12.1.2. IC.A.2 Decide if a specified model is consistent with results from a given data-generating process e.g. using simulation

### 12.2. Make inferences and justify conclusions from sample surveys, experiments, and observational studies

12.2.1. IC.B.3 Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each

12.2.2. IC.B.4 Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling

12.2.3. IC.B.5 Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant

12.2.4. IC.B.6 Evaluate reports based on data

### 12.3. The students analyze statistics experiment data and usefulness in real world context.

## 13. Conditional Probability and the Rules of Probability

### 13.1. Understand independence and conditional probability and use them to interpret data

13.1.1. CP.A.1 Describe events as subsets of a sample space using characteristics of the outcomes, or as unions, intersections, or complements of other events

13.1.2. CP.A.2 Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent

13.1.3. CP.A.3 Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B

13.1.4. CP.A.5 Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations

### 13.2. Use the rules of probability to compute probabilities of compound events

13.2.1. CP.A.4 Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way as a sample space to decide if events are independent and to approximate conditional probabilities.

13.2.2. CP.B.6 Find the conditional probability of A given B as the fraction of B’s outcomes that also belong to A, and interpret the answer in terms of the model

13.2.3. CP.B.7 Apply the addition rule, P(A or B) = P(A) + P(B) - P(A and B), and interpret the answer in terms of the model

13.2.4. CP.B.9 Use permutations and combinations to compute probabilities of compound events and solve problems

### 13.3. The students work with intersection, unions, and complements of a subgroup of a sample space. Independence of events is discussed as well as conditional probability and probability addition. The students create two-way tables. Permutations and combinations are formally introduced.

## 14. Using Probability to Make Decisions

### 14.1. Calculate expected values and use them to solve problems

14.1.1. MD.A.1 Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions

14.1.2. MD.A.2 Calculate the expected value of a random variable’ interpret it as the mean of the probability distribution

14.1.3. MD.A.3 Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value

14.1.4. MD.A.4 Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value

### 14.2. Use probability to evaluate outcomes of decisions

14.2.1. MD.B.5 Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values

14.2.2. MD.B.6 Use probabilities to make fair decisions

14.2.3. MD.B.7 Analyze decision and strategies using probability concepts