EngageNY
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...
EngageNY
Linear Transformations as Matrices
Don't stop with two-dimensional learning, go to the next dimension! Learners verify that 3x3 matrices represent linear transformations in the third dimension. Additionally, they verify the algebraic properties that extend to vector...
EngageNY
Composition of Linear Transformations 2
Scholars take transformations from the second to the third dimension as they extend their thinking of transformations to include three-dimensional figures. They explore how to use matrices to represent compositions of transformations.
101 Questions
Styrofoam Cups
How many cups does it take to reach the top? Learners attempt to answer this through a series of questions. They collect dimension information and apply it to creating a function. The lesson encourages various solution methods and...
Curated OER
Linear Systems: Fundamental Theorem of Linear Algebra
In this linear algebra instructional activity, students complete matrix multiplication. They find the row space and nullspace of given matrices. This two-page instructional activity contains examples, explanations, and approximately...
Curated OER
Solving Nonlinear Systems of Equations
In this nonlinear systems of equations worksheet, students solve nonlinear equations through elimination. They read statements, write equations, and solve systems of equations. This two-page worksheet contains 20 multi-step problems.
Curated OER
Solving Linear Equations
Use this worksheet for practice or review solving linear equations in one variable. Problems range from multiple-step problems involving parentheses and combining like terms, to word problems, to equations with no solution or infinitely...
Mathematics Assessment Project
Evaluating Statements About Enlargements
Double, toil ,and double linear dimensions. Learners first complete an assessment investigating how doubling linear dimensions affects the area of pizzas and the volume of popcorn containers. They then complete an activity investigating...
Chapman University
Fundamental Theorems of Mathematics
There are four fundamental theorems of mathematics: arithmetic, algebra, calculus, and linear algebra listed here. Each one is described on this poster or handout. The challenge for a student of math is to figure out why they are true.
Curated OER
Linear Algebra
In this linear algebra worksheet, students solve 3 different sets of problems that include rank, dimension, nullspace and range of linear algebra. They determine the relation between the rank of a matrix and the dimension of its range....
Curated OER
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.
Curated OER
Dimension and Rank
Students determine the dimension of a subspace. In this dimension and rank lesson, students explore the dimension of a vector space. They compare and explore the relationship in a matrix.
Curated OER
Beginning Modeling for Linear and Quadratic Data
Pupils create models to represent both linear and quadratic equations. In this algebra lesson, students collect data from the real world and analyze it. They graph and differentiate between the two types.
Concord Consortium
Graphical Depictions
Parent functions and their combinations create unique graphical designs. Learners explore these relationships with a progressive approach. Beginning with linear equations and inequalities and progressing to more complex functions,...
EngageNY
Vectors and the Equation of a Line
Represent linear equations in both two and three dimensions using parametric equations. Learners write parametric equations for linear equations in both two and three variables. They graph and convert the parametric equations to...
Curated OER
Linear Systems
For this linear systems worksheet, students explore the effect of two identical columns in a matrix on the null space of the matrix. They consider the column space of a matrix. Students compare the column space of a matrix to the column...
Curated OER
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...
Curated OER
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.
Curated OER
Solving Linear Systems Using Matrices
Start with the definition of a determinant and how to evaluate a 2x2 determinant. Apply this skill to solve systems of two equations with two unknowns by using Cramer's rule. These four basic problems would be good for a quick review or...
Curated OER
Expressing Geometric Properties with Equations
Algebra and geometry are not interchangeable. Demonstrate why not with a series of problems that deal with the equations of circles and equations of lines that meet specific criteria.
EngageNY
Complex Numbers and Transformations
Your learners combine their knowledge of real and imaginary numbers and matrices in an activity containing thirty lessons, two assessments (mid-module and end module), and their corresponding rubrics. Centered on complex numbers and...
EngageNY
Why Are Vectors Useful? 2
Investigate the application of vector transformations applied to linear systems. Individuals use vectors to transform a linear system translating the solution to the origin. They apply their understanding of vectors, matrices,...
EngageNY
Modeling with Polynomials—An Introduction (part 2)
Linear, quadratic, and now cubic functions can model real-life patterns. High schoolers create cubic regression equations to model different scenarios. They then use the regression equations to make predictions.
02 x 02 Worksheets
Factoring
Factor in this resource when teaching how to factor polynomials. Scholars use algebra tiles to factor linear and quadratic expressions. They practice their skill by working on example problems from a worksheet.