Students compute the length of time it will take to save enough money to purchase a yo-yo. For this math lesson, students create a design with pennies and write the associated linear equation. In this linear equations lesson, students...

Students identify, analyze, and multiply matrices. They determine if various indicated operations are possible through classroom discussion and practice. Finally, students determine matrix product dimensions through problem-solving...

Middle schoolers identify and interpret various ways of expressing probability as a decimal, fraction, percent, or ratio. They solve problems based on probability as they apply to real world applications.

In this differential equations instructional activity, learners solve systems of simultaneous differential equations using linear algebra. This six-page instructional activity contains approximately six problems, with explanations and...

In 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.

In this column space worksheet, learners find the column spaces of given matrices. This two-page worksheet contains examples of and explanations. One problem is provided for students to complete.

In this nullspace worksheet, learners 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.

In this linear algebra worksheet, students complete matrix multiplication. They find the row space and nullspace of given matrices. This two-page worksheet contains examples, explanations, and approximately four problems to complete.

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...

In this basis and dimension worksheet, students explore vector spaces associated with rectangular matrices. The two-page worksheet contains approximately 20 short answer questions.

In this linear system worksheet, students explore the characteristics of given matrices. They multiply matrices and determine pivots and multiply solutions. This four-page worksheet contains approximately seven problems.

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...

In this least squares approximation learning exercise, students use linear algebra to find the least square error and the equation of a line for given points. They find the equation of a parabola through provided points. This four-page...

In this orthogonal matrices activity, students explore characteristics of an orthogonal matrix. They use Gram-Schmidt to convert linearly independent vectors to orthonormal vectors. This three-page activity contains approximately six...

In this projection instructional activity, students determine the projections of a given matrix. This four-page instructional activity contains explanations and examples and approximately ten problems to complete.

In this review of vectors worksheet, students explore vectors and their uses. They multiply and subtract vectors and identify the linear combinations of given matrices. This two-page worksheet contains approximately ten problems.

In this graphical interpretation of vectors learning exercise, students execute operations of addition and multiplication by a scalar. They sketch results and determine the commutativity of vector addition. This three-page learning...

In this least squares approximation activity, students determine the number of solutions a given linear system has. They find the least square error and the equation of a line of best fit for a set of three points. Students find the...

In this interpretation of vectors and linear systems worksheet, students describe the geometric appearance of two vectors. They add the two vectors and sketch the sum as well as the vectors to determine the commutativity of vector...

In this matrix operations activity, students perform matrix addition and multiplication. This two-page activity contains six problems. Definitions, examples and explanations are also provided.

In this linear systems worksheet, students use matrix multiplication as an elimination technique to solve linear systems. They compare products and explore trends. This four-page worksheet contains explanations, examples and five...

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.

For this linear systems worksheet learners multiply matrices and find the coefficient matrix in the upper-triangular form. This four-page worksheet contains approximately four problems, with examples and explanations.

In this determinant worksheet, students find the determinants of matrices. They identify patterns and their relationship to the canonical matrix. This two-page worksheet contains approximately nine problems, as well as examples and...