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First-Person Computer Games
How do graphic designers project three-dimensional images onto two-dimensional spaces? Scholars connect their learning of matrix transformations to graphic design. They understand how to apply matrix transformations to make...
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Linear Transformations of Lines
Discover the extension of parametric equations to model linear transformations. Scholars first write parametric equations to model lines through two points. They then find the parametric equations that represent a linear transformation.
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Why Are Vectors Useful? 1
How do vectors help make problem solving more efficient? Math scholars use vectors to represent different phenomenon and calculate resultant vectors to answer questions. Problems vary from modeling airplane motion to the path of a robot.
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Vectors and Translation Maps
Discover the connection between vectors and translations. Through the activity, learners see the strong relationship between vectors, matrices, and translations. Their inquiries begin in the two-dimensional plane and then progress to the...
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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 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 questions...
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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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The Hunt for Better Notation
The matrix — it's not just a movie. The lesson introduces the concept of 2 x 2 matrix multiplication as a way to represent linear transformations. Class members determine when a linear transformation represented as matrix multiplication...
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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. They pool class data to see how conducting...
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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 lesson. They then extend this concept to hypothesis...
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Games of Chance and Expected Value 1
There's a strong chance that class members enjoy learning math through engaging games. Scholars analyze games of chance to determine long-term behavior. They learn to calculate expected value to help with this assessment.
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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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Using Expected Values to Compare Strategies
Discover how mathematics can be useful in comparing strategies. Scholars develop probability distributions for situations and calculate expected value. They use their results to identify the best strategy for the situation.
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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.