EngageNY
Directed Line Segments and Vectors
Investigate the components of vectors and vector addition through geometric representations. Pupils learn the parallelogram rule for adding vectors and demonstrate their understanding graphically. They utilize the correct notation and...
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Vectors and Stone Bridges
What does it take to build a stable arch? Pupils apply vectors and physics as they examine arched bridges and their structural integrity. They use vectors to represent the forces acting on the stone sections and make conclusions based on...
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Solving Equations Involving Linear Transformations of the Coordinate Plane
How can matrices help us solve linear systems? Learners explore this question as they apply their understanding of transformation matrices to linear systems. They discover the inverse matrix and use it to solve the matrix equation...
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Solving General Systems of Linear Equations
Examine the usefulness of matrices when solving linear systems of higher dimensions. The lesson asks learners to write and solve systems of linear equations in four and five variables. Using matrices, pupils solve the systems and apply...
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Solving Equations Involving Linear Transformations of the Coordinate Space
Explore methods for solving linear systems with your classes and introduce learners to using matrices as a viable method. Scholars are able to recognize situations where matrices are the efficient method of solving. Application...
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Using Matrix Operations for Encryption
Data encryption is an important security measure for sensitive data stored on computers. Pupils learn how to utilize matrices for creating code. They also get a great review of matrix multiplication, inverse matrices, and the identity...
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Matrix Addition Is Commutative
Explore properties of addition as they relate to matrices. Using graphical representations of vector matrices, scholars test the commutative and associative properties of addition. They determine if the properties are consistent for...
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Matrix Multiplication Is Distributive and Associative
Learn the ins and outs of matrix multiplication. After discovering the commutative property does not apply to matrix multiplication in a previous activity in the series, pupils now test the associative and distributive properties. The...
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Representing, Naming, and Evaluating Functions (Part 1)
Begin the discussion of domain and range using something familiar. Before introducing numbers, the instructional activity uses words to explore the idea of input and outputs and addresses the concept of a function along with domain and...
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The General Multiplication Rule
In the first installment of a 21-part module, scholars build on previous understandings of probability to develop the multiplication rule for independent and dependent events. They use the rule to solve contextual problems.
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Discrete Random Variables
You don't need to be discreet about using the resource on discrete variables. In the fifth installment of a 21-part module, scholars explore random variables and learn to distinguish between discrete and continuous random variables. They...
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Probability Distribution of a Discrete Random Variable
Learn how to analyze probability distributions. The sixth installment of a 21-part module teaches pupils to use probability distributions to determine the long-run behavior of a discrete random variable. They create graphs of probability...
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Expected Value of a Discrete Random Variable
Discover how to calculate the expected value of a random variable. In the seventh installment of a 21-part module, young mathematicians develop the formula for expected value. They connect this concept the dot product of vectors.
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Interpreting Expected Value
Investigate expected value as a long-run average. The eighth installment of a 21-part module has scholars rolling pairs of dice to determine the average sum. They find aggregate data by working in groups and interpret expected value as...
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Determining Discrete Probability Distributions 1
Learn how to determine a probability distribution. In the ninth installment of a 21-part module, future mathematicians use theoretical probabilities to develop probability distributions for a random variable. They then use these...
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Determining Discrete Probability Distributions 2
Investigate how long-run outcomes approach the calculated probability distribution. The 10th installment of a 21-part module continues work on probability distributions from the previous lesson plan. They pool class data to see how...
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Estimating Probability Distributions Empirically 1
What if you don't have theoretical probabilities with which to create probability distributions? The 11th installment of a 21-part module has scholars collecting data through a survey. The results of the survey provide empirical data to...
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Analyzing Decisions and Strategies Using Probability 2
Explore how to compare and analyze different strategies. In the 20th installment of a 21-part module, scholars continue their analysis of decisions and strategies from the previous activity. They then extend this concept to hypothesis...
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Games of Chance and Expected Value 2
Use expected values to analyze games of chance. The 15th installment of a 21-part module has young mathematicians looking at different games involving tickets and deciding which would be the best to play. They calculate expected payoffs...
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Making Fair Decisions
Life's not fair, but decisions can be. The 17th installment of a 21-part module teaches learners about fair decisions. They use simulations to develop strategies to make fair decisions.
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Fair Games
What constitutes a fair game? Scholars learn about fair games and analyze some to see if they are fair. They extend this idea to warranties and other contexts.
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Analyzing Decisions and Strategies Using Probability 1
Learn how to increase the probability of success. The 19th installment of a 21-part module teaches future mathematicians how to use probability to analyze decisions. They determine strategies to maximize the chances of a desired outcome.
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Special Triangles and the Unit Circle
Calculate exact trigonometric values using the angles of special right triangles. Beginning with a review of the unit circle and trigonometric functions, class members use their knowledge of special right triangles to find the value...
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Addition and Subtraction Formulas 2
Knowing the addition formulas allows for the calculations of double and half formulas. The fourth installment of 16 has the class use the addition formula to develop the double angle trigonometric formulas. Using the double formula,...