11th Grade Math

 

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. Determine what properties hold for matrix addition and matrix multiplication; e.g., use examples to show addition is commutative and when multiplication is not commutative.

 

  1.  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.

  2. Solving Formulas for any Variable  Choose the correct steps to solve a formula for a given variable. Use the feedback to diagnose incorrect steps.

  3. Solving Two-Step Equations  Choose the correct steps to solve a two-step equation. Use the feedback to diagnose incorrect steps.

2. Determine what properties hold for vector addition and multiplication, and for scalar multiplication.

  1. Vectors Manipulate the magnitude and direction of two vectors to generate a sum and learn vector addition. The x and y components can be displayed, along with the dot product of the two vectors.

     

3. Represent complex numbers on the complex plane.

  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

4. Use matrices to represent given information in a problem situation.

 

5. Model, using the coordinate plane, vector addition and scalar multiplication.

  1.  Vectors Manipulate the magnitude and direction of two vectors to generate a sum and learn vector addition. The x and y components can be displayed, along with the dot product of the two vectors.

6. Compute sums, differences and products of matrices using paper and pencil calculations for simple cases, and technology for more complicated cases.

  1. Matrices: An Introduction  This study guide from Encyclopedia Britannica covers a discussion of the basic aspects of matrices, including labeling, equality of two matrices, and addition, subtraction, and multiplication of matrices.

7. Compute sums, differences, products and quotients of complex numbers.

  1.  Points in the Complex Plane - Activity A  Identify the imaginary and real coordinates of a point in the complex plane. Drag the point in the plane and investigate how the coordinates change in response.

8. Use fractional and negative exponents as optional ways of representing and finding solutions for problem situations; e.g., 272/3 = (271/3)2 = 9.

  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 

9. Use vector addition and scalar multiplication to solve problems.

  1. Vectors: An Introduction  This Study Guide from Encyclopedia Britannica discusses the topics of scalar and vector quantities, quality of vectors, vector addition and subtraction, multiplying a vector by a scalar, component form of vectors, algebraic vector arithmetic, and calculating magnitude and direction.

  2. Vectors Manipulate the magnitude and direction of two vectors to generate a sum and learn vector addition. The x and y components can be displayed, along with the dot product of the two vectors.

Measurement

1. Determine the number of significant digits in a measurement.

 

2. Use radian and degree angle measures to solve problems and perform conversions as needed.

  1.  Smart Board Lesson Created by :   LAURIE FOUTS  SB
  2.  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

3. Derive a formula for the surface area of a cone as a function of its slant height and the circumference of its base.

  1. Surface and Lateral Area 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.

  2. Surface and Lateral Area of Pyramids and Cones   Vary the dimensions of a pyramid or cone 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.

     

4. Calculate distances, areas, surface areas and volumes of composite three-dimensional objects to a specified number of significant digits.

  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 

5. Solve real-world problems involving area, surface area, volume and density to a specified degree of precision.

  1.  Density Experiment: Slice and Dice  Drop a chunk of material in a beaker of water and observe whether it sinks or floats. Cut the chunk into smaller pieces of any size, and observe what happens as they are dropped in the beaker. The mass and volume of each chunk can be measured as a clear understanding of density, buoyancy, and floatation is investigated.

  2. Density Laboratory  With a scale to measure mass, a graduated cylinder to measure volume, and a large beaker of liquid to observe floatation, the relationship between mass, volume, density, and floatation can be investigated. The density of the liquid in the beaker can be adjusted, and a variety of objects can be studied during the investigation

  3. Density via Comparison  Using four beakers of different liquids with a known density, try to determine the density of a variety of unknown objects. Compare the buoyancy of each object in each beaker to determine an approximate value of density without knowing the mass or volume of the objects.

  4. Determining Density via Water Displacement Drop objects in a beaker that is filled with water and measure the water that flows over the edge. Using Archimedes principle, the amount of water displaced by the floating objects and the water displaced when you force the object under water, will allow you to determine the density of the objects.

  5. Prisms and Cylinders - Activity A Vary the height and base‑edge or radius length of a prism or cylinder and examine how its three‑dimensional representation changes. Determine the area of the base and the volume of the solid. Compare the volume of a skew prism or cylinder to the volume of a right prism or cylinder.

  6. Pyramids and Cones - Activity A   Vary the height and base‑edge or radius length of a pyramid or cone and examine how its three‑dimensional representation changes. Determine the area of the base and the volume of the solid. Compare the volume of a skew pyramid or cone to the volume of a right pyramid or cone.

Geometry and Spatial Sense

1. Use polar coordinates to specify locations on a plane.

  1.  Points in Polar Coordinates Identify the polar coordinates of a point. Drag the point in the plane and investigate how its r and theta coordinates change in response. Compare its Cartesian coordinates.

2. Represent translations using vectors.

  1.  Rotations, Reflections and Translations  Rotate, reflect, and translate a figure in the plane. Compare the translated figure to the original figure.

  2. Translations Translate a figure horizontally and vertically in the plane and examine the matrix representation of the translation.

  3. Vectors  Manipulate the magnitude and direction of two vectors to generate a sum and learn vector addition. The x and y components can be displayed, along with the dot product of the two vectors.

3. Describe multiplication of a vector and a scalar graphically and algebraically, and apply to problem situations.

  1. Vectors: An Introduction
    This Study Guide from Encyclopedia Britannica discusses the topics of scalar and vector quantities, quality of vectors, vector addition and subtraction, multiplying a vector by a scalar, component form of vectors, algebraic vector arithmetic, and calculating magnitude and direction.

4. Use trigonometric relationships to determine lengths and angle measures; i.e., Law of Sines and Law of Cosines.

  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. Law of Sines
    This web site uses an animated slideshow to explain the Law of Sines, and then demonstrates using the property to solve a problem. Be sure to click the "Pause" button as needed if the slideshow moves too quickly.

  3. Law of Cosines for Obtuse Triangles  
    This web site uses an animated slideshow to explain the Law of Cosines for Obtuse Angles, and then demonstrates using the property to solve a problem. Be sure to click the "Pause" button as needed if the slideshow moves too quickly.

  4. Law of Cosines for Acute Triangles
    This web site uses an animated slideshow to explain the Law of Cosines for Acute Triangles. Be sure to click the "Pause" button as needed if the slideshow moves too quickly.

  5. The Sine Rule
    This is an excellent interactive tutorial that uses animations and audio explanations to clearly teach the Sine Rule and show several sample problems. Be sure to click the "Play Audio" button to hear the commentary.

5. Identify, sketch and classify the cross sections of three-dimensional objects.

  1. Slicing Platonic Solids - Virtual Manipulative
    This online activity allows you to slice five different platonic solids with a plane. The solids can be rotated and the plane's height changed. The resulting shape from the cross section is displayed to the side.

Patterns, Functions and Algebra

1. Identify and describe problem situations involving an iterative process that can be represented as a recursive function; e.g., compound interest.

 

2. Translate a recursive function into a closed form expression or formula for the nth term to solve a problem situation involving an iterative process; e.g., find the value of an annuity after 7 years.

 

3. Describe and compare the characteristics of the following families of functions: quadratics with complex roots, polynomials of any degree, logarithms, and rational functions; e.g., general shape, number of roots, domain and range, asymptotic behavior.

  1. Cubic Function Activity Explore a cubic function, along with the associated Center of Rotation. Vary the coefficients of the equation and examine how the graph changes in response. 

  2. Fourth-Degree Polynomials - Activity A Compare the equation of a fourth‑degree polynomial to its graph. Vary the coefficients of the equation and investigate how the graph changes in response.

  3. General Form of a Rational Function Compare the equation of a rational function to its graph. Multiply or divide the numerator and denominator by linear factors and explore how the graph changes in response.

  4. Logarithmic Functions - Activity A Compare the equation of a logarithmic function to its graph. Change the base of the logarithmic function and examine how the graph changes in response. Use the line y = x to compare the associated exponential function.

  5. Logarithmic Functions: Translating and Scaling Vary the values in the equation of a logarithmic function and examine how the graph is translated or scaled. Connect these transformations with the domain of the function, and the asymptote in the graph.

  6. 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.

  7. 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.

  8. 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.

  9. Rational Functions Compare the graph of a rational function to its equation. Vary the terms of the equation and explore how the graph is translated and stretched as a result. Examine the domain on a number line and compare it to the graph of the equation.

  10. 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.

4. Identify the maximum and minimum points of polynomial, rational and trigonometric functions graphically and with technology.

  1. Cosine Function Compare the graph of the cosine function with the graph of the angle on the unit circle. Drag a point along the cosine curve and see the corresponding angle on the unit circle.

  2. Cubic Function Activity Explore a cubic function, along with the associated Center of Rotation. Vary the coefficients of the equation and examine how the graph changes in response.

  3. Fourth-Degree Polynomials - Activity A Compare the equation of a fourth‑degree polynomial to its graph. Vary the coefficients of the equation and investigate how the graph changes in response.

  4. General Form of a Rational Function Compare the equation of a rational function to its graph. Multiply or divide the numerator and denominator by linear factors and explore how the graph changes in response.

  5. Rational Functions Compare the graph of a rational function to its equation. Vary the terms of the equation and explore how the graph is translated and stretched as a result. Examine the domain on a number line and compare it to the graph of the equation.

  6. 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.

  7. Sine Function Compare the graph of the sine function with the graph of the angle on the unit circle. Drag a point along the sine curve and see the corresponding angle on the unit circle

  8. Tangent Function Compare the graph of the tangent function with the graph of the angle on the unit circle. Drag a point along the tangent curve and see the corresponding angle on the unit circle.

5. Identify families of functions with graphs that have rotation symmetry or reflection symmetry about the y-axis, x-axis or y = x.

  1.  Holiday Snowflake Designer Fold paper and cut in a certain way to make symmetrical snowflakes with six sides (similar to what can be found in nature) or with eight sides (an easier folding method). This simulation allows you to cut virtual paper on the computer screen with round dot or square dot "scissors" of various sizes before using physical paper.

6. Represent the inverse of a function symbolically and graphically as a reflection about y = x.

  1. Absolute Value with Linear Functions - Activity B Explore and compare the graphs of y = |f(x)| and y = f(|x|). By comparing the graphs of these functions to the graph of y = f(x), you will see how absolute value can affect the input and output values of linear functions.

     

7. Model and solve problems with matrices and vectors.

  1. Matrices: An Introduction
    This study guide from Encyclopedia Britannica covers a discussion of the basic aspects of matrices, including labeling, equality of two matrices, and addition, subtraction, and multiplication of matrices.

  2. Matrices: Equations and Systems of Equations
    This study guide from Encyclopedia Britannica covers a discussion of inverse matrices, determinants, matrix equations, and simultaneous equations.

  3. Vectors  Manipulate the magnitude and direction of two vectors to generate a sum and learn vector addition. The x and y components can be displayed, along with the dot product of the two vectors

8. Solve equations involving radical expressions and complex roots.

  1.  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.

9. Solve 3 by 3 systems of linear equations by elimination and using technology, and interpret graphically what the solution means (a point, line, plane, or no solution).

  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. Describe the characteristics of the graphs of conic sections.

  1. 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.

11. Describe how a change in the value of a constant in an exponential, logarithmic or radical equation affects the graph of the equation.

 

Data Analysis and Probability

1. Design a statistical experiment, survey or study for a problem; collect data for the problem; and interpret the data with appropriate graphical displays, descriptive statistics, concepts of variability, causation, correlation and standard deviation.

 

2. Describe the role of randomization in a well-designed study, especially as compared to a convenience sample, and the generalization of results from each.

 

3. Describe how a linear transformation of univariate data affects range, mean, mode and median.

 

4. Create a scatterplot of bivariate data, identify trends, and find a function to model the data.

  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.

  2. 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.

  3. 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.

  4. 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.

  5. Scatterplot - Virtual Manipulative
    This online activity allows the user to create scatterplot 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.

  6. Scatterplots - 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. Use technology to find the Least Squares Regression Line, the regression coefficient, and the correlation coefficient for bivariate data with a linear trend, and interpret each of these statistics in the context of the problem situation.

  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.

  2. 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.

  3. 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.

6. Use technology to compute the standard deviation for a set of data, and interpret standard deviation in relation to the context or problem situation.

 

7. Describe the standard normal curve and its general properties, and answer questions dealing with data assumed to be normal.

 

8. Analyze and interpret univariate and bivariate data to identify patterns, note trends, draw conclusions, and make predictions.

  1.  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.

  2.  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.

9. Evaluate validity of results of a study based on characteristics of the study design, including sampling method, summary statistics and data analysis techniques.

 

10. Understand and use the concept of random variable, and compute and interpret the expected value for a random variable in simple cases.

 

11. Examine statements and decisions involving risk; e.g., insurance rates and medical decisions.