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Linear Systems: Orthogonal Matrices
In this orthogonal matrices learning exercise, students explore characteristics of an orthogonal matrix. They use Gram-Schmidt to convert linearly independent vectors to orthonormal vectors. This three-page learning exercise contains...
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Systems of Inequalities
In this Algebra I/Algebra II learning exercise, learners determine the solution to a system of inequalities by graphing. The two page learning exercise contains explanation, instruction, and four worked problems.
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Practice: Word Problems
Congratulations, you've just hit the word problem jackpot! Covering an incredible range of topics from integers and fractions, to percents, geometry, and much more, this collection of worksheets will keep young mathematicians...
Barton Math Class
Parallel and Perpendicular Lines Worksheet
With the focus being on parallel, perpendicular, or neither type, practice with three different types of problem solving. Learners start with a simple skill of determining the relationship between slopes and then work towards creating...
National Council of Teachers of Mathematics
Over the Hill
Can you hear me from there? Pupils determine the place to build a cell tower on a hill. The class uses constraints and creates a scale drawing on a coordinate system to calculate the exact location of the base of the cell tower.
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Border Patrol ID: 11603
Incorporate technology in your classroom by teaching your students how to graph systems of linear inequalities as they apply to an area of land. The lesson provides an extension in which students are challenged to write a system of...
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Row-Echelon Matrices
In this algebra worksheet, students rewrite linear equations using matrices and solve using row-echelon form. There are 30 problems ranging from one equation to system of equations.
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Linear Systems: Vector Spaces
In this vector spaces worksheet, students explore the column and rowspace of a matrix. They find the basis of subspaces associated with a given matrix. Students observe the relationship between vectors and the nullspace. This...
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Linear Systems: Independence, Basis and Dimension
In this basis and dimension worksheet, students explore vector spaces associated with rectangular matrices. The two-page worksheet contains approximately 20 short answer questions.
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Linear Systems: Nullspace Matrix
In this linear systems learning exercise, students explore the dimensions of a matrix. They identify the independent rows and columns. This two-page learning exercise contains explanations, examples and four problems to solve.
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Linear Systems: Least Square Regression
In this least square regression worksheet, students find solutions to given linear systems. They draw pictures, draw a vector and prove the solution. This two-page worksheet contains eleven problems, with some examples and explanations.
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Using Gauss Jordon to Solve Linear Systems by Elimination
In this math worksheet, students practice using the method of elimination to find the solutions to the linear systems. They use the matrices to find the solutions.
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Linear Systems: Matrix Operations
In this matrix operations worksheet, students find the dot product of matrices. They use the elimination method to solve linear equations. This two-page worksheet contains explanations, examples and three problems.
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Linear Systems: Fundamental Theorem
In this fundamental theorem worksheet, student explore the nullspace and column space of given matrices. They explore the vectors needed to make it linearly independent and construct free variable columns. This two-page worksheet...
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Linear Systems: Fundamental Theorem
In this fundamental theorem worksheet, students show matrix multiplication, identify the vector in the nullspace and interpret equations. This two-page worksheet contains examples, explanations and three problems.
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Linear Systems: Elimination
In this elimination worksheet, students use the elimination process to transform a system into an equivalent form. This three-page worksheet contains three practice problems as well as examples and explanations.
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Math Applications
In this math applications worksheet, students solve one word problem that has two parts to it. First, they determine the expected value of a ticket for a prize. Then, student determine the fair price for the ticket purchased and explain...
Balanced Assessment
Telephone Service
Class members must determine the best phone plan for customers. by assessing three different phone plans. Each plan price depends not only the number of minutes, but also the location of the calls — bringing in a third variable. Scholars...
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Graphing Inequalities in Two Variables
This study guide is a great resource to help you present the steps to graphing linear inequalities. Show your class two different ways to graph an inequality and work on a real-world example together. The document could also be easily...
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How Much Does Sibyl Dibble Get Paid Per Hour?
In this problem solving word problems, students determine how much a person makes per hour. The solution is provided. Students can solve this problem in several ways.
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Numerical Analysis: Using the QR Algorithm
For this QR algorithm worksheet, students use the QR algorithm to solve an over-determined system of equations. This two-page worksheet contains 11 problems.
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Linear Systems: Rectangular Matrices
In this rectangular matrices worksheet, students complete solutions to given matrices. They identify the pivot columns and examine the nullspace of a matrix. This four-page worksheet contains examples, explanations and approximately...
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Modeling in Algebra
In this modeling in algebra activity, 8th graders solve ten different types of algebra problems, including 5 word problems. They first complete each table, describe the pattern used, and determine the 20th and nth term for each. Students...
College Preparatory Mathematics
Using Elimination To Find the Point of Intersection of Two Lines
Two example problems are solved on the first page using the elimination method with a pair of linear equations. Detailed explanations accompany the math. The second page provides 20 practice problems and their answers. This would be a...
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