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Oklahoma - Mathematics: Pre-Algebra
OK--Academic Standards | Adopted: 2016
PA.N: : Number & Operations
PA.N.1: : Read, write, compare, classify, and represent real numbers and use them to solve problems in various contexts.
PA.N.1.1: : Develop and apply the properties of integer exponents, including a⁰ = 1 (with a ≠ 0), to generate equivalent numerical and algebraic expressions.
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Dividing Exponential Expressions
Choose the correct steps to divide exponential expressions. Use the feedback to diagnose incorrect steps. 5 Minute Preview
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Exponents and Power Rules
Choose the correct steps to simplify expressions with exponents using the rules of exponents and powers. Use feedback to diagnose incorrect steps. 5 Minute Preview
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Multiplying Exponential Expressions
Choose the correct steps to multiply exponential expressions. Use the feedback to diagnose incorrect steps. 5 Minute Preview
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Simplifying Algebraic Expressions II
Will you adopt Spidro, Centeon, or Ping Bee? They're three very different critters with one thing in common: a hunger for simplified algebraic expressions! Learn how the distributive property can be used to combine variable terms, producing expressions that will help your pet grow up healthy and strong. You'll become a pro at identifying terms that can be combined – even terms with exponents and multiple variables. With enough practice, you and your pet will be ready for the competitive expression eating circuit. Good luck! 5 Minute Preview
PA.N.1.3: : Multiply and divide numbers expressed in scientific notation, express the answer in scientific notation.
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Unit Conversions
Use unit conversion tiles to convert from one unit to another. Tiles can be flipped to cancel units. Convert between metric units or between metric and U.S. customary units. Solve distance, time, speed, mass, volume, and density problems. 5 Minute Preview
PA.N.1.4: : Classify real numbers as rational or irrational. Explain why the rational number system is closed under addition and multiplication and why the irrational system is not. Explain why the sum of a rational number and an irrational number is irrational; and the product of a non-zero rational number and an irrational number is irrational.
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Rational Numbers, Opposites, and Absolute Values
Use a number line to compare rational numbers. Change values by dragging points on the number line. Compare the opposites and absolute values of the numbers. 5 Minute Preview
PA.N.1.5: : Compare real numbers; locate real numbers on a number line. Identify the square root of a perfect square to 400 or, if it is not a perfect square root, locate it as an irrational number between two consecutive positive integers.

Comparing and Ordering Decimals
Use grids to model decimal numbers and compare them graphically. Then compare the numbers on a number line. 5 Minute Preview

Integers, Opposites, and Absolute Values
Compare and order integers using draggable points on a number line. Also explore opposites and absolute values on the number line. 5 Minute Preview
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Operations with Radical Expressions
Identify the correct steps to complete operations with a radical expression. Use step-by-step feedback to diagnose incorrect steps. 5 Minute Preview

Rational Numbers, Opposites, and Absolute Values
Use a number line to compare rational numbers. Change values by dragging points on the number line. Compare the opposites and absolute values of the numbers. 5 Minute Preview

Simplifying Radical Expressions
Simplify a radical expression. Use step-by-step feedback to diagnose any incorrect steps. 5 Minute Preview
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Square Roots
Explore the meaning of square roots using an area model. Use the side length of a square to find the square root of a decimal number or a whole number. 5 Minute Preview
PA.A: : Algebraic Reasoning & Algebra
PA.A.1: : Understand the concept of function in real-world and mathematical situations, and distinguish between linear and nonlinear functions.
PA.A.1.2: : Use linear functions to represent and explain real-world and mathematical situations.
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Arithmetic Sequences
Find the value of individual terms in arithmetic sequences using graphs of the sequences and direct computation. Vary the common difference and examine how the sequences change in response. 5 Minute Preview

Compound Interest
Explore compound interest in-depth, from compounded annually to compounded continuously. In addition, compare the END POINTS graph, with dots that fit an exponential curve, to the ALL TIME graph, which has a more step-like appearance. 5 Minute Preview
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Function Machines 2 (Functions, Tables, and Graphs)
Drop a number into a function machine, and see what number comes out! You can use one of the six pre-set function machines, or program your own function rule into one of the blank machines. Stack up to three function machines together. Input and output can be recorded in a table and on a graph. 5 Minute Preview

Function Machines 3 (Functions and Problem Solving)
Drop a number into a function machine, and see what number comes out! You can use one of the six pre-set function machines, or program your own function rule into one of the blank machines. Stack up to three function machines together. Input and output can be recorded in a table and on a graph. 5 Minute Preview

Linear Functions
Determine if a relation is a function from the mapping diagram, ordered pairs, or graph. Use the graph to determine if it is linear. 5 Minute Preview

Slope-Intercept Form of a Line
Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
PA.A.1.3: : Identify a function as linear if it can be expressed in the form y = mx + b or if its graph is a straight line.

Function Machines 2 (Functions, Tables, and Graphs)
Drop a number into a function machine, and see what number comes out! You can use one of the six pre-set function machines, or program your own function rule into one of the blank machines. Stack up to three function machines together. Input and output can be recorded in a table and on a graph. 5 Minute Preview

Function Machines 3 (Functions and Problem Solving)
Drop a number into a function machine, and see what number comes out! You can use one of the six pre-set function machines, or program your own function rule into one of the blank machines. Stack up to three function machines together. Input and output can be recorded in a table and on a graph. 5 Minute Preview

Point-Slope Form of a Line
Compare the point-slope form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview

Points, Lines, and Equations
Compare the graph of a linear function to its rule and to a table of its values. Change the function by dragging two points on the line. Examine how the rule and table change. 5 Minute Preview

Slope-Intercept Form of a Line
Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
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Standard Form of a Line
Compare the standard form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
PA.A.2: : Recognize linear functions in real-world and mathematical situations; represent linear functions and other functions with tables, verbal descriptions, symbols, and graphs; solve problems involving linear functions and interpret results in the original context.
PA.A.2.1: : Represent linear functions with tables, verbal descriptions, symbols, and graphs; translate from one representation to another.

Arithmetic Sequences
Find the value of individual terms in arithmetic sequences using graphs of the sequences and direct computation. Vary the common difference and examine how the sequences change in response. 5 Minute Preview

Function Machines 1 (Functions and Tables)
Drop a number into a function machine, and see what number comes out! You can use one of the six pre-set function machines, or program your own function rule into one of the blank machines. Stack up to three function machines together. Input and output can be recorded in a table and on a graph. 5 Minute Preview

Function Machines 2 (Functions, Tables, and Graphs)
Drop a number into a function machine, and see what number comes out! You can use one of the six pre-set function machines, or program your own function rule into one of the blank machines. Stack up to three function machines together. Input and output can be recorded in a table and on a graph. 5 Minute Preview

Function Machines 3 (Functions and Problem Solving)
Drop a number into a function machine, and see what number comes out! You can use one of the six pre-set function machines, or program your own function rule into one of the blank machines. Stack up to three function machines together. Input and output can be recorded in a table and on a graph. 5 Minute Preview

Geometric Sequences
Explore geometric sequences by varying the initial term and the common ratio and examining the graph. Compute specific terms in the sequence using the explicit and recursive formulas. 5 Minute Preview

Linear Functions
Determine if a relation is a function from the mapping diagram, ordered pairs, or graph. Use the graph to determine if it is linear. 5 Minute Preview

Points, Lines, and Equations
Compare the graph of a linear function to its rule and to a table of its values. Change the function by dragging two points on the line. Examine how the rule and table change. 5 Minute Preview

Slope-Intercept Form of a Line
Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
PA.A.2.2: : Identify, describe, and analyze linear relationships between two variables.
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Slope-Intercept Form of a Line
Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
PA.A.2.3: : Identify graphical properties of linear functions including slope and intercepts. Know that the slope equals the rate of change, and that the y-intercept is zero when the function represents a proportional relationship.

Absolute Value with Linear Functions
Compare the graph of a linear function, the graph of an absolute-value function, and the graphs of their translations. Vary the coefficients and constants in the functions and investigate how the graphs change in response. 5 Minute Preview
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Cat and Mouse (Modeling with Linear Systems)
Experiment with a system of two lines representing a cat-and-mouse chase. Adjust the speeds of the cat and mouse and the head start of the mouse, and immediately see the effects on the graph and on the chase. Connect real-world meaning to slope, y-intercept, and the intersection of lines. 5 Minute Preview

Compound Interest
Explore compound interest in-depth, from compounded annually to compounded continuously. In addition, compare the END POINTS graph, with dots that fit an exponential curve, to the ALL TIME graph, which has a more step-like appearance. 5 Minute Preview

Exponential Functions
Explore the graph of an exponential function. Vary the coefficient and base of the function and investigate the changes to the graph of the function. 5 Minute Preview
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Function Machines 2 (Functions, Tables, and Graphs)
Drop a number into a function machine, and see what number comes out! You can use one of the six pre-set function machines, or program your own function rule into one of the blank machines. Stack up to three function machines together. Input and output can be recorded in a table and on a graph. 5 Minute Preview

Function Machines 3 (Functions and Problem Solving)
Drop a number into a function machine, and see what number comes out! You can use one of the six pre-set function machines, or program your own function rule into one of the blank machines. Stack up to three function machines together. Input and output can be recorded in a table and on a graph. 5 Minute Preview

Graphs of Polynomial Functions
Study the graphs of polynomials up to the fourth degree. Vary the coefficients of the equation and investigate how the graph changes in response. Explore things like intercepts, end behavior, and even near-zero behavior. 5 Minute Preview
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Linear Functions
Determine if a relation is a function from the mapping diagram, ordered pairs, or graph. Use the graph to determine if it is linear. 5 Minute Preview

Point-Slope Form of a Line
Compare the point-slope form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview

Points, Lines, and Equations
Compare the graph of a linear function to its rule and to a table of its values. Change the function by dragging two points on the line. Examine how the rule and table change. 5 Minute Preview

Slope-Intercept Form of a Line
Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview

Standard Form of a Line
Compare the standard form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
PA.A.2.5: : Solve problems involving linear functions and interpret results in the original context.

Absolute Value with Linear Functions
Compare the graph of a linear function, the graph of an absolute-value function, and the graphs of their translations. Vary the coefficients and constants in the functions and investigate how the graphs change in response. 5 Minute Preview

Arithmetic Sequences
Find the value of individual terms in arithmetic sequences using graphs of the sequences and direct computation. Vary the common difference and examine how the sequences change in response. 5 Minute Preview

Compound Interest
Explore compound interest in-depth, from compounded annually to compounded continuously. In addition, compare the END POINTS graph, with dots that fit an exponential curve, to the ALL TIME graph, which has a more step-like appearance. 5 Minute Preview

Function Machines 2 (Functions, Tables, and Graphs)
Drop a number into a function machine, and see what number comes out! You can use one of the six pre-set function machines, or program your own function rule into one of the blank machines. Stack up to three function machines together. Input and output can be recorded in a table and on a graph. 5 Minute Preview

Function Machines 3 (Functions and Problem Solving)
Drop a number into a function machine, and see what number comes out! You can use one of the six pre-set function machines, or program your own function rule into one of the blank machines. Stack up to three function machines together. Input and output can be recorded in a table and on a graph. 5 Minute Preview

Linear Functions
Determine if a relation is a function from the mapping diagram, ordered pairs, or graph. Use the graph to determine if it is linear. 5 Minute Preview

Slope-Intercept Form of a Line
Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
PA.A.3: : Generate equivalent numerical and algebraic expressions and use algebraic properties to evaluate expressions.
PA.A.3.1: : Use substitution to simplify and evaluate algebraic expressions.

Equivalent Algebraic Expressions I
Grumpy’s Restaurant is now hiring! As a new chef at this underwater bistro, you’ll learn the basics of manipulating algebraic expressions. Learn how to make equivalent expressions using the Commutative and Associative properties, how to handle pesky subtraction and division, and how to identify equivalent and non-equivalent expressions. 5 Minute Preview
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Equivalent Algebraic Expressions II
Continue your meteoric rise in the undersea culinary world in this follow-up to Equivalent Algebraic Expressions I. Make equivalent expressions by using the distributive property forwards and backwards, sort expressions by equivalence, and personally assist Chef Grumpy himself with a project that will bring him (and maybe you) fame and fortune. 5 Minute Preview
PA.A.3.2: : Justify steps in generating equivalent expressions by identifying the properties used, including the properties of operations (associative, commutative, and distributive laws) and the order of operations, including grouping symbols.

Equivalent Algebraic Expressions I
Grumpy’s Restaurant is now hiring! As a new chef at this underwater bistro, you’ll learn the basics of manipulating algebraic expressions. Learn how to make equivalent expressions using the Commutative and Associative properties, how to handle pesky subtraction and division, and how to identify equivalent and non-equivalent expressions. 5 Minute Preview

Equivalent Algebraic Expressions II
Continue your meteoric rise in the undersea culinary world in this follow-up to Equivalent Algebraic Expressions I. Make equivalent expressions by using the distributive property forwards and backwards, sort expressions by equivalence, and personally assist Chef Grumpy himself with a project that will bring him (and maybe you) fame and fortune. 5 Minute Preview
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Order of Operations
Select and evaluate the operations in an expression following the correct order of operations. 5 Minute Preview
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Simplifying Algebraic Expressions I
Meet Spidro, a quirky critter with an appetite for algebraic expressions! As Spidro's adopted owner, it's your responsibility to feed him so that he grows into… whatever it is that a Spidro grows into. But be careful - Spidro is a picky eater who prefers his food to be as simple as possible. Use the commutative property, distributive property, and the other properties of addition and multiplication to put expressions in simplest (and tastiest) form. 5 Minute Preview
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Simplifying Algebraic Expressions II
Will you adopt Spidro, Centeon, or Ping Bee? They're three very different critters with one thing in common: a hunger for simplified algebraic expressions! Learn how the distributive property can be used to combine variable terms, producing expressions that will help your pet grow up healthy and strong. You'll become a pro at identifying terms that can be combined – even terms with exponents and multiple variables. With enough practice, you and your pet will be ready for the competitive expression eating circuit. Good luck! 5 Minute Preview
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Solving Algebraic Equations II
Is solving equations tricky? If you know how to isolate a variable, you're halfway there. The other half? Don't do anything to upset the balance of an equation. Join our plucky variable friend as he encounters algebraic equations and a (sometimes grumpy) equal sign. With a little practice, you'll find that solving equations isn't tricky at all. 5 Minute Preview
PA.A.4: : Represent real-world and mathematical problems using equations and inequalities involving linear expressions. Solve and graph equations and inequalities symbolically and graphically. Interpret solutions in the original context.
PA.A.4.1: : Illustrate, write, and solve mathematical and real-world problems using linear equations with one variable with one solution, infinitely many solutions, or no solutions. Interpret solutions in the original context.
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Modeling One-Step Equations
Solve a linear equation using a tile model. Use feedback to diagnose incorrect steps. 5 Minute Preview
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Modeling and Solving Two-Step Equations
Solve a two-step equation using a cup-and-counter model. Use step-by-step feedback to diagnose and correct incorrect steps. 5 Minute Preview
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Solving Algebraic Equations II
Is solving equations tricky? If you know how to isolate a variable, you're halfway there. The other half? Don't do anything to upset the balance of an equation. Join our plucky variable friend as he encounters algebraic equations and a (sometimes grumpy) equal sign. With a little practice, you'll find that solving equations isn't tricky at all. 5 Minute Preview
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Solving Two-Step Equations
Choose the correct steps to solve a two-step equation. Use the feedback to diagnose incorrect steps. 5 Minute Preview
PA.A.4.3: : Represent real-world situations using equations and inequalities involving one variable.
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Arithmetic Sequences
Find the value of individual terms in arithmetic sequences using graphs of the sequences and direct computation. Vary the common difference and examine how the sequences change in response. 5 Minute Preview
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Geometric Sequences
Explore geometric sequences by varying the initial term and the common ratio and examining the graph. Compute specific terms in the sequence using the explicit and recursive formulas. 5 Minute Preview
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Solving Two-Step Equations
Choose the correct steps to solve a two-step equation. Use the feedback to diagnose incorrect steps. 5 Minute Preview
PA.GM: : Geometry & Measurement
PA.GM.1: : Solve problems involving right triangles using the Pythagorean Theorem.
PA.GM.1.2: : Use the Pythagorean Theorem to find the distance between any two points in a coordinate plane.
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Distance Formula
Explore the distance formula as an application of the Pythagorean theorem. Learn to see any two points as the endpoints of the hypotenuse of a right triangle. Drag those points and examine changes to the triangle and the distance calculation. 5 Minute Preview
PA.GM.2: : Calculate surface area and volume of three-dimensional figures.
PA.GM.2.1: : Calculate the surface area of a rectangular prism using decomposition or nets. Use appropriate measurements such as cm².
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Surface and Lateral Areas of Prisms and Cylinders
Vary the dimensions of a prism or cylinder and investigate how the surface area changes. Use the dynamic net of the solid to compute the lateral area and the surface area of the solid. 5 Minute Preview
PA.GM.2.2: : Calculate the surface area of a cylinder, in terms of π and using approximations for π, using decomposition or nets. Use appropriate measurements such as cm².
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Surface and Lateral Areas of Prisms and Cylinders
Vary the dimensions of a prism or cylinder and investigate how the surface area changes. Use the dynamic net of the solid to compute the lateral area and the surface area of the solid. 5 Minute Preview
PA.D: : Data & Probability
PA.D.1: : Display and interpret data in a variety of ways, including using scatterplots and approximate lines of best fit. Use line of best fit and average rate of change to make predictions and draw conclusions about data.
PA.D.1.1: : Describe the impact that inserting or deleting a data point has on the mean and the median of a data set. Know how to create data displays using a spreadsheet and use a calculator to examine this impact.
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Correlation
Explore the relationship between the correlation coefficient of a data set and its graph. Fit a line to the data and compare the least-squares fit line. 5 Minute Preview
PA.D.1.2: : Explain how outliers affect measures of central tendency.
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Describing Data Using Statistics
Investigate the mean, median, mode, and range of a data set through its graph. Manipulate the data and watch how the mean, median, mode, and range change (or, in some cases, how they don't change). 5 Minute Preview
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Mean, Median, and Mode
Build a data set and find the mean, median, and mode. Explore the mean, median, and mode illustrated as frogs on a seesaw, frogs on a scale, and as frogs stacked under a bar of variable height. 5 Minute Preview
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Movie Reviewer (Mean and Median)
Movie reviewers rate movies on a scale of 0 to 10. Each movie comes with a set of reviews that can be changed by the user. The mean of a data set can be explored using a see-saw balance model. Students can also find the median, mode, and range of the data set. 5 Minute Preview
PA.D.1.3: : Collect, display and interpret data using scatterplots. Use the shape of the scatterplot to informally estimate a line of best fit, make statements about average rate of change, and make predictions about values not in the original data set. Use appropriate titles, labels and units.
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Correlation
Explore the relationship between the correlation coefficient of a data set and its graph. Fit a line to the data and compare the least-squares fit line. 5 Minute Preview
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Least-Squares Best Fit Lines
Fit a line to the data in a scatter plot using your own judgment. Then compare the least squares line of best fit. 5 Minute Preview
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Solving Using Trend Lines
Examine the scatter plots for data related to weather at different latitudes. The Gizmo includes three different data sets, one with negative correlation, one positive, and one with no correlation. Compare the least squares best-fit line. 5 Minute Preview
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Trends in Scatter Plots
Examine the scatter plot for a random data set with negative or positive correlation. Vary the correlation and explore how correlation is reflected in the scatter plot and the trend line. 5 Minute Preview
PA.D.2: : Calculate experimental probabilities and reason about probabilities to solve real-world and mathematical problems.
PA.D.2.1: : Calculate experimental probabilities and represent them as percents, fractions and decimals between 0 and 1 inclusive. Use experimental probabilities to make predictions when actual probabilities are unknown.
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Geometric Probability
Randomly throw darts at a target and see what percent are "hits." Vary the size of the target and repeat the experiment. Study the relationship between the area of the target and the percent of darts that strike it 5 Minute Preview
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Independent and Dependent Events
Compare the theoretical and experimental probabilities of drawing colored marbles from a bag. Record results of successive draws to find the experimental probability. Perform the drawings with replacement of the marbles to study independent events, or without replacement to explore dependent events. 5 Minute Preview
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Probability Simulations
Experiment with spinners and compare the experimental probability of particular outcomes to the theoretical probability. Select the number of spinners, the number of sections on a spinner, and a favorable outcome of a spin. Then tally the number of favorable outcomes. 5 Minute Preview
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Theoretical and Experimental Probability
Experiment with spinners and compare the experimental probability of a particular outcome to the theoretical probability. Select the number of spinners, the number of sections on a spinner, and a favorable outcome of a spin. Then tally the number of favorable outcomes. 5 Minute Preview
PA.D.2.2: : Determine how samples are chosen (random, limited, biased) to draw and support conclusions about generalizing a sample to a population.
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Polling: City
Poll residents in a large city to determine their response to a yes-or-no question. Estimate the actual percentage of yes votes in the whole city. Examine the results of many polls to help assess how reliable the results from a single poll are. See how the normal curve approximates a binomial distribution for large enough polls. 5 Minute Preview
PA.D.2.3: : Compare and contrast dependent and independent events.
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Independent and Dependent Events
Compare the theoretical and experimental probabilities of drawing colored marbles from a bag. Record results of successive draws to find the experimental probability. Perform the drawings with replacement of the marbles to study independent events, or without replacement to explore dependent events. 5 Minute Preview
Correlation last revised: 9/16/2020
About STEM Cases
Students assume the role of a scientist trying to solve a real world problem. They use scientific practices to collect and analyze data, and form and test a hypothesis as they solve the problems.
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Each STEM Case uses realtime reporting to show live student results.
Introduction to the Heatmap
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STEM Cases take between 30-90 minutes for students to complete, depending on the case.
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Each STEM Case level has an associated Handbook. These are interactive guides that focus on the science concepts underlying the case.
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