Lesson Plan
Curated OER

A Special Relationship

For Teachers 6th - 8th
Middle schoolers discover the relationships of the lengths of the sides of right triangles and right triangles using a series of drawings on dot paper. They investigate and solve problems of standard (customary and metric units) and...
Lesson Plan
Curated OER

Count the Differences

For Teachers 9th - 12th Standards
Pupils find the difference between consecutive y-values on the calculator and write an equation that fits the data.  They continue finding the differences in consecutive y-values using lists on their calculator. Learners...
Worksheet
Curated OER

Linear Systems: Nullspace Matrix and Rank

For Students 11th - Higher Ed
In this nullspace matrix worksheet, learners observe the rank and number of independent rows and columns a matrix has. They compute the product of matrices and describe the column space of each. This two-page worksheet contains...
Lesson Plan
Curated OER

PLANETS IN PROPORTION

For Teachers 6th - 8th
Students discover scales for both the solar bodies' relative sizes and their distances from the sun. They find equatorial circumference and volumes of their solar bodies. Students apply estimation strategies and proportioanl reasoning to...
Worksheet
Curated OER

Linear Equations

For Students 8th - 12th
In this variables worksheet, students eliminate the x or y values in each of the equations. Students complete 5 equations total on this worksheet.
Lesson Plan
Curated OER

Solving Systems of Equations by graphing for Algebra One

For Teachers 7th - 11th
Students watch the teacher demonstrate on an overhead projector how to graph various equations before the students try them on their own. They start with pencil and paper; once they grasp the concept they move on to punching in the...
Worksheet
Curated OER

Point of Intersection

For Students 9th - 11th
In this algebra worksheet, students graph two linear equations identifying where they cross and how many solutions there are. There are 4 questions with an answer key.
Lesson Plan
Museum of Science

Linear Perspective: Painting Distance with Size

For Teachers 5th - 8th
Young scholars examine a simple set up to measure the change in the apparent size of an object as it moves away from them.
Worksheet
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Linear Systems: Permutations and Transposes

For Students 12th - Higher Ed
For this permutations worksheet, students identify a transpose matrix, and create a permutation matrix. This three-page worksheet contains six problems.
Worksheet
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Linear Systems

For Students 11th - Higher Ed
In this multiplication of vectors worksheet, students prove that the dot product operation is commutative. They normalize a vector so it has the same direction with a magnitude of one. Students use the angle formula to confirm...
Worksheet
Curated OER

Linear Systems: The Column Space

For Students 11th - Higher Ed
In this column space worksheet, students find the column spaces of given matrices. This two-page worksheet contains examples of and explanations. One problem is provided for students to complete.
Worksheet
Curated OER

Linear Systems: Applications of Eiginvalues

For Students 12th - Higher Ed
In this Eigenvalue and Eigenvector instructional activity, students examine the applications of matrix exponentiation. This four-page instructional activity provides explanations and examples, as well as three problems to complete.
Worksheet
Curated OER

Linear Systems: Geometric Interpretation of Eigenvalues

For Students 12th - Higher Ed
In this geometric interpretation worksheet, students prove the exponentiation of a matrix and the Eigenvalues of an inverse. This two-page worksheet contains explanations, examples, theorems and two problems for students to solve.
Worksheet
Curated OER

How Much Does Sibyl Dibble Get Paid Per Hour?

For Students 8th - 11th
For 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.
Worksheet
Curated OER

Linear Systems: Symmetric Matrices

For Students 12th - Higher Ed
For this symmetric matrices worksheet, students explore the characteristics of symmetric matrices. This two-page worksheet contains examples and explanations concerning symmetric matrices. Two problems are provided to solve.
Worksheet
Curated OER

Linear Systems: Orthogonality of Vector Spaces of a Matrix

For Students 12th - Higher Ed
In this vector spaces of a matrix worksheet, students decompose any vector into two orthogonal pieces. They identify the nullspace, row space, and find a reduced echelon. This two-page worksheet contains examples and two problems.
Lesson Plan
Curated OER

Equations and Systems of Equations

For Teachers 7th - 8th
Pupils practice using algebra to be applied to real world situational problems. The key concepts of translation of language to algebraic expressions is covered. They also look in depth at relationships between different quantities.
Lesson Plan
Curated OER

Review of Systems of Equations

For Teachers 10th - 12th
Students work to complete various algebraic equations using different methods. Given a word problem, students create a poster identifying the various parts of the equation as well as the solution to the problem. Posters are presented...
Worksheet
Curated OER

Linear Systems: LU Decomposition

For Students 12th - Higher Ed
In this LU decomposition worksheet, learners multiply matrices, identify the elimination matrices, and the inverse of a matrix. This three-page worksheet contains approximately six problems.
Worksheet
Curated OER

Linear Systems: Eigenvalues and Eigenvectors

For Students 11th - Higher Ed
For this "Eigenvalues and Eigenvectors" worksheet, students find the eigenvalue of a matrix and explore the properties of eigenvalues with a matrix. This two page worksheet contains two multi-step problems.
Worksheet
Curated OER

Linear Systems: Diagonalizing a Matrix

For Students Higher Ed
In this diagonalizing a matrix activity, students explore matrix factorization and use diagonal decomposition. This two-page activity contains examples, explanations and four practice problems.
Worksheet
Curated OER

Linear Systems: Applications of Determinants

For Students 12th - Higher Ed
In this determinant worksheet, students explore determinants, area and volume. This two-page worksheet contains explanations and examples. It provides two problems for students to solve.
Worksheet
Curated OER

Linear Systems: Vector Spaces and Subspaces

For Students 12th - Higher Ed
In this vector space worksheet, students find the column space of given matrices, the identify the vector space and determine if the matrix is invertible. This four-page worksheet contains approximately six multi-step problems.
Worksheet
Curated OER

Linear Systems: Definition of the Nullspace

For Students 11th - Higher Ed
In this nullspace worksheet, students find the nullspace of matrices, write a rectangular matrix upper-triangular form, and convert augmented matrix to echelon form. This six-page worksheet contains approximately 8 problems.

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