9th Grade Mathematics

 

Measurement

Geometry and Spatial Sense

Patterns, Functions and Algebra

Data Analysis and Probability


 

Number, Number Sense
and Operations

(Based on State of Ohio
Curriculum Standards)

 

1. Identify and justify whether properties (closure, identity, inverse, commutative and associative) hold for a given set and operations; e.g., even integers and multiplication.

  1. Math Dictionary animation for kids  This is an outstanding website allowing you to explore a comprehensive view of math with many examples  4 Star

 2. Compare, order and determine equivalent forms for rational and irrational numbers.

  1. Ordering Percents, Fractions and Decimals -Compare and order numbers represented as percents, fractions, and decimals using area grids and a number line.

  2. Ordering Percents, Fractions and Decimals Greater Than 1-Compare and order numbers greater than 1 using area grids and a number line. Examine the numbers represented as percents, improper fractions, and decimals.

  3. Percents, Fractions and Decimals-Compare a quantity represented by an area with its percent, fraction, and decimal forms.

 3. Explain the effects of operations such as multiplication or division, and of computing powers and roots on the magnitude of quantities.

 

 4. Demonstrate fluency in computations using real numbers.

 

 5. Estimate the solutions for problem situations involving square and cube roots.

  1. 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.

Measurement

 1. Convert rates within the same measurement system; e.g., miles per hour to feet per second; kilometers per hour to meters per second.

 

 2. Use unit analysis to check computations involving measurement.

 

 3. Use the ratio of lengths in similar two-dimensional figures or three-dimensional objects to calculate the ratio of their areas or volumes respectively.

  1. Perimeters and Areas of Similar Figures-Manipulate two similar figures and vary the scale factor to see what changes are possible under similarity. Explore how the perimeters and areas of two similar figures compare.

  2. Similar Figures - Activity A-Vary the scale factor and rotation of an image and compare it to the pre-image.   Determine how the angle measures and side lengths of the two figures are related.

  3. Similar Polygons-Manipulate two similar figures and vary the scale factor to see what changes are possible under similarity.

 4. Use scale drawings and right triangle trigonometry to solve problems that include unknown distances and angle measures.

  1. Trig Triangle Basics -This is an excellent interactive tutorial that uses animations and audio explanations to clearly teach Sine, Cosine, and Tangent, and how to use them to solve triangle problems. Several sample problems are shown and there are exercises to try on your own. Be sure to click the "Play Audio" button to hear the commentary.

 5. Solve problems involving unit conversion for situations involving distances, areas, volumes and rates within the same measurement system.

 

Geometry and Spatial Sense

 

 1. Define the basic trigonometric ratios in right triangles: sine, cosine and tangent.

  1. Smart Board Lesson   Created by: Sonia Herman SB

  2. Trig Triangle Basics -This is an excellent interactive tutorial that uses animations and audio explanations to clearly teach Sine, Cosine, and Tangent, and how to use them to solve triangle problems. Several sample problems are shown and there are exercises to try on your own. Be sure to click the "Play Audio" button to hear the commentary.   

  3. Sine and Cosine Ratios - Activity A-Reshape and resize a right triangle and examine how the sine of angle A and the cosine of angle A change.

  4. Mathway This a step by step math solver for General Math, Geometry, Algebra, Pre Algebra, Trigonometry, Pre-calculus, Calculus.  A great program to show students step by step directions and also allow a teacher to create a presentation to be used on their LSD projector.  This is a great tool for facilitating and allowing at teacher to better present their instruction.   4 Star

 2. Apply proportions and right triangle trigonometric ratios to solve problems involving missing lengths and angle measures in similar figures.

  1. Smart Board Lesson   Created by: Sonia Herman SB

  2. Perimeters and Areas of Similar Figures-Manipulate two similar figures and vary the scale factor to see what changes are possible under similarity. Explore how the perimeters and areas of two similar figures compare.

  3. Similar Figures - Activity A-Vary the scale factor and rotation of an image and compare it to the pre-image. Determine how the angle measures and side lengths of the two figures are related.

  4. Similar Polygons-Manipulate two similar figures and vary the scale factor to see what changes are possible under similarity.
     

 3. Analyze two-dimensional figures in a coordinate plane; e.g., use slope and distance formulas to show that a quadrilateral is a parallelogram.

  1. Classifying Triangles-Place constraints on a triangle and determine what classifications must apply to the triangle.

  2. Distance Formula - Activity A-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.

  3. Geoboard: The Pythagorean Theorem-Build right triangles in an interactive geoboard and build squares on the sides of the triangles to discover the Pythagorean Theorem.

  4. Pythagorean Theorem - Activity A-Explore the Pythagorean Theorem using a dynamic right triangle. Examine a visual, geometric application of the Pythagorean Theorem, using the areas of squares on the sides of the triangle.

  5. Slope - Activity B-Explore the slope of a line, and learn how to calculate slope. Adjust the line by moving points that are on the line, and see how its slope changes.
     

Patterns, Functions and Algebra

 1. Define function with ordered pairs in which each domain element is assigned exactly one range element.

  1. Mathway This a step by step math solver for General Math, Geometry, Algebra, Pre Algebra, Trigonometry, Pre-calculus, Calculus.  A great program to show students step by step directions and also allow a teacher to create a presentation to be used on their LSD projector.  This is a great tool for facilitating and allowing at teacher to better present their instruction.   4 Star
  2. Algebraic Reasoning   Learn how to think algebraically with these clever weighing scales. Levels 1 and 2 contain two scales. Level 3 is more difficult and has three scales. Your goal is to determine the weight of one or more of the objects  4 Star
  3. Algebra Puzzle Find the value of each of the three objects presented in the puzzle. The numbers given represent the sum of the objects in each row or column. Sometimes, only one object will appear in a row or column. That makes the puzzle easier to solve. Other times, you will have to look for relationships among the objects.  4 Star
  4. Weigh the Wangdoodles  Your job is to find the weight of each Wangdoodle using the information provided by the scales. To be successful, you will have to make sure that the weight you assign to each Wangdoodle works on each scale. This activity is a fun but challenging introduction to multiple algebraic equations.  4 Star
  5. Simplifying Algebraic expressions
  6. Smart Board Algebra Lesson  This lesson has examples and videos.  Smart board manipulativeSB
  7. Algebra Tiles icon   Algebra Tiles Visualize multiplying and factoring algebraic expressions using tiles.   Algebra Tile manipulative
  8. Algebraic Skills: Signed Numbers -  This website will assist you in teaching this concept.
  9. Algebra Balance Scales icon Algebra Balance Scales Solve simple linear equations using a balance beam representation.
  10. Algebra Balance Scales - Negatives icon Algebra Balance Scales - Negatives Solve simple linear equations using a balance beam representation.
  11. Student Resources for Algebra Outstanding web site for teachers and students.
  12. Vertical Line Test
    Students learn about the vertical line test for functions by trying to connect points in the plane to build a function.

  13. Introduction to Functions-Determine if a relation is a function using the mapping diagram, ordered pairs, or the graph of the relation.  Drag arrows from the domain to the range, type in ordered pairs, or drag points to the graph to add inputs and outputs to the relation.

  14. 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.

     

 2. Generalize patterns using functions or relationships (linear, quadratic and exponential), and freely translate among tabular, graphical and symbolic representations.

  1. 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.

  2. Exponential Functions - Activity A-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.

    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.

    Quadratic and Absolute Value Functions-Compare the graph of a quadratic or absolute‑value function to its equations. Vary the coefficients of the equation and explore how the graph changes in response.
    Quadratics in Factored Form-
    Investigate the factors of a quadratic through its graph and through its equation. Vary the roots of the quadratic and examine how the graph and the equation change in response.
    Quadratics in Polynomial Form - Activity A-
    Compare the graph of a quadratic to its equation in polynomial form. Vary the coefficients of the equation and explore how the graph changes in response.
    Roots of a Quadratic-
    Find the root of a quadratic using its graph or the quadratic formula. Explore the graph of the roots and the point of symmetry in the complex plane. Compare the axis of symmetry and graph of the quadratic in the real plane.
     

 3. Describe problem situations (linear, quadratic and exponential) by using tabular, graphical and symbolic representations.

 

 4. Demonstrate the relationship among zeros of a function, roots of equations, and solutions of equations graphically and in words.

  1. Polynomials and Linear Factors-Create a polynomial as a product of linear factors. Vary the values in the linear factors to see how their connection to the roots of the function.

  2. Roots of a Quadratic-Find the root of a quadratic using its graph or the quadratic formula.Explore the graph of the roots and the point of symmetry in the complex plane. Compare the axis of symmetry and graph of the quadratic in the real plane.
     

5. Describe and compare characteristics of the following families of functions: linear, quadratic and exponential functions; e.g., general shape, number of roots, domain, range, rate of change, maximum or minimum.

  1. Quadratic Roots
    This website uses an animated slideshow to explain the three different options for the roots of a quadratic equation.

  2. Exponential Functions - Activity A-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.

  3. Linear Functions-Determine if a relation is a function from the mapping diagram, ordered pairs, or graph.

  4. Quadratic and Absolute Value Functions-Compare the graph of a quadratic or absolute‑value function to its equations. Vary the coefficients of the equation and explore how the graph changes in response.

  5. Quadratics in Factored Form-Investigate the factors of a quadratic through its graph and through its equation. Vary the roots of the quadratic and examine how the graph and the equation change in response

  6. Quadratics in Polynomial Form - Activity A-Compare the graph of a quadratic to its equation in polynomial form. Vary the coefficients of the equation and explore how the graph changes in response.

 

 6. Write and use equivalent forms of equations and inequalities in problem situations; e.g., changing a linear equation to the slope-intercept form.

  1. Slope-Intercept Form of a Line - Activity A-Compare the slope‑intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response

  2. Solving Linear Inequalities using Addition and Subtraction-Solve a linear inequality. Graph the solution on a dynamic number line.

  3. Solving Linear Inequalities using Multiplication and Division-Solve an inequality involving multiplication and division. Graph the solution on a number line.

  4. Using Tables, Rules and Graphs-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.

 7. Use formulas to solve problems involving exponential growth and decay.

  1. Exponential Functions - Activity A-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.

  2. Exponential Growth and Decay - Activity B-Explore the graph of the exponential growth or decay function. Vary the initial amount and the rate of growth or decay. Investigate the changes to the graph.

  3. Half-life-Investigate the decay of a radioactive substance. The half-life and the number of radioactive atoms can be adjusted, and theoretical or random decay can be observed. Data can be interpreted visually using a dynamic graph, a bar chart, and a table. Determine the half-lives of two sample isotopes as well as samples with randomly generated half-lives.

  4. Half-life Laboratory-Investigate the half life of a sample of radioactive particles as well as a dynamic graph of the number of particles vs. time. The half-life can be adjusted, along with the initial number of particles.
     

 

 8. Find linear equations that represent lines that pass through a given set of ordered pairs, and find linear equations that represent lines parallel or perpendicular to a given line through a specific point.

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

 9. Solve and interpret the meaning of 2 by 2 systems of linear equations graphically, by substitution and by elimination, with and without technology.

  1. Modeling Linear Systems - Activity A-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.

  2. Solving Linear Systems by Graphing-Compare a system of equations in standard form or in slope‑intercept form to its graph. Examine the graph and table of values. Determine the solutions to the system.

  3. Special Types of Solutions to Linear Systems-Compare a system of equations in standard form to its graph. Examine the graph and table of values. Determine the solutions to the system.

  4. Systems of Linear Equations - Activity A-Solve a system of linear equations by graphing and finding the intersection of the lines of the equations. Create a system of equations, examine its graph, matrix, and table of values, and determine the solution of the system.

     

 10. Solve quadratic equations with real roots by factoring, graphing, using the quadratic formula and with technology.

  1. Smart Board Lesson Created by :   LAURIE FOUTS  SB

  2.  Factoring A Difference Between Two Squares-This web site teaches about factoring a difference of squares and then has an interactive quiz to test what was learned.

  3. Factoring Trinomials -This study guide from Encyclopedia Britannica covers an examination of trinomial factoring, including multiplying binomials, factoring a difference of squares, factoring in pairs, and splitting the middle term.

  4. How the quadratic formula is derived -This animated slideshow explains step-by-step how the quadratic formula is derived. It has an audio explanation for each step so be sure to have your speakers on. The slideshow pauses after each step in case you wish to discuss the last step or share more information.

  5. Graphing Quadratic Equations-This web site uses an animated slideshow to demonstrate graphing a quadratic equation using a table of values and identifying the roots.

  6. Modeling the Factorization of ax2+bx+c-Factor a polynomial with a leading coefficient greater than 1 using an area model. Use step-by-step feedback to diagnose any mistakes.

  7. Modeling the Factorization of x2+bx+c-Factor a polynomial with a leading coefficient equal to 1 using an area model.  Use step‑by‑step feedback to diagnose any mistakes.

  8. Roots of a Quadratic-Find the root of a quadratic using its graph or the quadratic formula. Explore the graph of the roots and the point of symmetry in the complex plane. Compare the axis of symmetry and graph of the quadratic in the real plane.

     

 11. Add, subtract, multiply and divide monomials and polynomials (division of polynomials by monomials only).

  1. FOIL Method -This web site teaches about using the FOIL method to multiply two binomials, and then has an interactive quiz to test what was learned.
  2. Simplifying Using Distribution -This web site teaches about using the distributive property to simplify alegraic expressions, and then has an interactive quiz to test what was learned.
  3. Simplifying Multiplication -This web site teaches about simplifying expressions by multiplying algebraic terms with exponents, and then has an interactive quiz to test what was learned.
  4. Virtual Manipulatives - Algebra Tiles -This site lets you work with online algebra tiles, and includes sample activities for you to complete.
  5. Addition of Polynomials - Activity A-Add polynomials using an area model. Use step‑by‑step feedback to diagnose any problems in the polynomial models and the polynomial addition.
  6. Dividing Exponential Expressions-Choose the correct steps to divide exponential expressions. Use the feedback to diagnose incorrect steps.
  7. Dividing Polynomials Using Synthetic Division-Divide a polynomial by dragging the correct numbers into the correct positions for synthetic division. Compare the interpreted polynomial division to the synthetic division.
  8. Multiplying Exponential Expressions-Choose the correct steps to multiply exponential expressions. Use the feedback to diagnose incorrect steps.
  9. Simplifying Radicals - Activity A-Simplify a radical expression. Use step‑by‑step feedback to diagnose any incorrect steps.
     

 12. Simplify rational expressions by eliminating common factors and applying properties of integer exponents.

  1. Simplifying Multiplication -This web site teaches about simplifying expressions by multiplying algebraic terms with exponents, and then has an interactive quiz to test what was learned.
  2. Variables of Exponents -This web site teaches about simplifying exponential expressions involving variables, and then has an interactive quiz to test what was learned.
  3. Polynomial Exponents -This web site teaches about simplifying polynomial expressions involving exponents, and then has an interactive quiz to test what was learned.
  4. Simplifying Fractions With Negative Exponents
             This web site teaches about simplifying algebraic fractions involving exponents, and then has a quiz to test what was learned.
  5. Factoring by Finding a Common Factor -This study guide from Encyclopedia Britannica covers information on factoring, including equivalent fractions, reducing fractions, factoring into primes, and the distributive law.
  6. Exponents: Algebraic Powers -This study guide from Encyclopedia Britannica covers information on exponential notation. Covers identifying the base, equivalent expressions, coefficients, multiplication and division, and working with negative exponents.
  7. Dividing Exponential Expressions-Choose the correct steps to divide exponential expressions. Use the feedback to diagnose incorrect steps.
  8. Factoring Special Products-Choose the correct steps to factor a polynomial involving perfect‑square binomials, differences of squares, or constant factors. Use the feedback to diagnose incorrect steps.
     

 13. Model and solve problems involving direct and inverse variation using proportional reasoning.

  1. Determining a Spring Constant-Place a pan on the end of a hanging spring, and continue to add additional objects with mass to the pan. As the string stretches the length of the spring can be measured. Using the data points, a best? fit line can be used to find the spring constant.

  2. Direct Variation-Adjust the constant of variation and explore how the graph of the direct variation function changes in response.

  3. Direct and Inverse Variation-Adjust the constant of variation and explore how the graph of the direct or inverse variation function changes in response. Compare direct variation functions to inverse variation functions.

 14. Describe the relationship between slope and the graph of a direct variation and inverse variation.

  1. Determining a Spring Constant-Place a pan on the end of a hanging spring, and continue to add additional objects with mass to the pan. As the string stretches the length of the spring can be measured. Using the data points, a best?fit line can be used to find the spring constant.

  2. Direct Variation-Adjust the constant of variation and explore how the graph of the direct variation function changes in response.

  3. Direct and Inverse Variation-Adjust the constant of variation and explore how the graph of the direct or inverse variation function changes in response. Compare direct variation functions to inverse variation functions.

  4. Slope - Activity B-Explore the slope of a line, and learn how to calculate slope. Adjust the line by moving points that are on the line, and see how its slope changes.

 15. Describe how a change in the value of a constant in a linear or quadratic equation affects the related graphs.

  1. Function Flyer -A more advanced version of Slope Slider, this activity allows the manipulation of the constants and coefficients in any function thereby encouraging the user to explore the effects on the graph of the function by changing those numbers.  

  2. Conic Flyer -Similar to Function Flyer, but allows the manipulation of the constants and coefficients of all the types of conic section equations on a coordinate plane by changing those numbers using a slider bar.

  3. 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.

  4. Quadratic and Absolute Value Functions-

    Compare the graph of a quadratic or absolute‑value function to its equations. Vary the coefficients of the equation and explore how the graph changes in response.

  5. Quadratics in Factored Form

    Investigate the factors of a quadratic through its graph and through its equation. Vary the roots of the quadratic and examine how the graph and the equation change in response.

  6. Quadratics in Polynomial Form - Activity A-

    Manipulate two similar figures and vary the scale factor to see what changes are possible under similarity.

  7. Reflections of a Linear Function-

    Explore and compare the graphs of y = f(x), y = −f(x), y = f(‑x), and y = −f(‑x), for a linear function f(x) in slope‑intercept form. Vary the terms of f(x) and examine how the graphs change in response.
  8. Reflections of a Quadratic Function-Explore and compare the graphs of y = f(x), y = −f(x), y = f(−x), and y = −f(−x), for a quadratic function f(x) of the form f(x) = ax2 + bx + c. Vary the terms of f(x) and examine how the graphs change in response.
  9. Roots of a Quadratic-

    Find the root of a quadratic using its graph or the quadratic formula. Explore the graph of the roots and the point of symmetry in the complex plane. Compare the axis of symmetry and graph of the quadratic in the real plane.
  10. Translating and Scaling Functions-

    Vary the coefficients in the equation of a function and examine how the graph of the function is translated or scaled. Select different functions to translate and scale, and determine what they have in common.


     

 

Data Analysis and Probability

 

 1. Classify data as univariate (single variable) or bivariate (two variables) and as quantitative (measurement) or qualitative (categorical) data.

 

2. Create a scatterplot for a set of bivariate data, sketch the line of best fit, and interpret the slope of the line of best fit.

  1. Data Flyer -Similar to Function Flyer, but with the capability of plotting data points as well as a function. Then you can tweak the function to fit the data.

  2. Scatterplot Activity -This interactive activity from Encyclopedia Britannica is a statistical tool to explore the relationships between two data sets. Ranges can be set independently and data points entered by hand or loaded from sample sets. Displays an updated regression line and summary statistics.

  3. Scatter plot - Virtual Manipulative -This online activity allows the user to create scatter plot by adding points to a grid, and then calculates and displays the line of best fit. The grid size can be changed fit any activity, and one suggested activity is explained on the site.
  4. Scatter plots - Excel activity -This is an Excel spreadsheet activity for individual students or the whole class. As the user enters ordered pairs, the spreadsheet graphs a scatterplot, creates a line of best fit, and displays its equation (in linear or polynomial form).
  5. 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.
  6. Lines of Best Fit Using Least Squares - Activity A-Fit a line to the data in a scatter plot using your own judgment. Then compare the least squares line of best fit.
  7. Scatter Plots - Activity A-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.
  8. Solving Using Trend Lines-Examine the scatter plots for a 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.
     


     

3. Analyze and interpret frequency distributions based on spread, symmetry, skewness, clusters and outliers.

 

4. Describe and compare various types of studies (survey, observation, experiment), and identify possible misuses of statistical data.

  1. Misleading Graphs
            This is an Excel spreadsheet activity for the whole class or individual student use. Two different bar graphs are made from the same survey of favorite foods. The students need to determine which graph is more fair and why, by studying the graphs and altering the data.

 5. Describe characteristics and limitations of sampling methods, and analyze the effects of random versus biased sampling; e.g., determine and justify whether the sample is likely to be representative of the population.

  1. Polling: Neighborhood-Conduct a phone poll of citizens in a small neighborhood to determine their response to a yes-or-no question. Use the results to estimate the sentiment of the entire population. Investigate how the error of this estimate becomes smaller as more people are polled. Compare random versus non-random sampling.

6. Make inferences about relationships in bivariant data, and recognize the difference between evidence of relationship (correlation) and causation.

  1. 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.

7. Use counting techniques and the Fundamental Counting principle to determine the total number of possible outcomes for mathematical situations.

 

8. Describe, create and analyze a sample space and use it to calculate probability.

  1. Compound Independent Events-Compare the theoretical and experimental probabilities of compound independent events by drawing colored marbles from a bag. Record the results of successive draws with or without replacement of marbles to calculate the experimental probability.
  2. Compound Independent and Dependent Events-Compare the theoretical and experimental probability of a compound independent event by drawing colored marbles from a bag. Record the results of successive draws with or without replacement of marbles to calculate the experimental probability.
  3. Geometric Probability - Activity A-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
  4. Independent and Dependent Events-Compare the theoretical and experimental probabilities of a compound independent event by drawing colored marbles from a bag.  Record the results of successive draws with or without replacement of marbles to calculate the experimental probability.
  5. 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.
  6. 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.

 9. Identify situations involving independent and dependent events, and explain differences between, and common misconceptions about, probabilities associated with those events.

  1. Compound Independent Events-Compare the theoretical and experimental probabilities of compound independent events by drawing colored marbles from a bag. Record the results of successive draws with or without replacement of marbles to calculate the experimental probability.
  2. Compound Independent and Dependent Events-Compare the theoretical and experimental probability of a compound independent event by drawing colored marbles from a bag. Record the results of successive draws with or without replacement of marbles to calculate the experimental probability.
  3. Independent and Dependent Events-Compare the theoretical and experimental probabilities of a compound independent event by drawing colored marbles from a bag.  Record the results of successive draws with or without replacement of marbles to calculate the experimental probability.
     

10. Use theoretical and experimental probability, including simulations or random numbers, to estimate probabilities and to solve problems dealing with uncertainty; e.g., compound events, independent events, simple dependent events.

 

  1. Misleading Graphs
    This is an Excel spreadsheet activity for the whole class or individual student use. Two different bar graphs are made from the same survey of favorite foods. The students need to determine which graph is more fair and why, by studying the graphs and altering the data.
  2. Compound Independent Events-Compare the theoretical and experimental probabilities of compound independent events by drawing colored marbles from a bag. Record the results of successive draws with or without replacement of marbles to calculate the experimental probability.
  3. Compound Independent and Dependent Events-Compare the theoretical and experimental probability of a compound independent event by drawing colored marbles from a bag. Record the results of successive draws with or without replacement of marbles to calculate the experimental probability.
  4. Geometric Probability - Activity A-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. 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.
  6. 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.