Illustrative Mathematics
Distance across the channel
Here you will find a model of a linear relationship between two quantities, the water depth of a channel and the distance across the channel at water level. The cross section of the channel is the shape of an isosceles trapezoid. The...
Curated OER
Linear Systems: Fundamental Theorem of Linear Algebra
In this linear algebra worksheet, learners 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.
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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.
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Dimensions of Subspaces
In this math worksheet, students practice to find the dimensions of subspaces. They also find the solutions to the systems of equations using the matrices.
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...
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Linear Algebra
For 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....
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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.
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,...
Mathematics Common Core Toolbox
Golf Balls in Water
Here's a resource that models rising water levels with a linear function. The task contains three parts about the level of water in a cylinder in relationship to the number of golf balls placed in it. Class members analyze the data and...
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The Cartesian Plane
Learners solve and complete 22 various types of problems. First, they find the gradients of the lines and plot the given points. Then, they complete the table of values for each equation and use the table to draw the graph.
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Linear Systems
In this linear systems activity, 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...
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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: 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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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.
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.
Noyce Foundation
Between the Lines
Explore linear and square dimensions by comparing areas of similar figures. A creative set of five activities designed for elementary through high school classes asks young scholars to compare areas of specific polygons. The first two...
Curated OER
Linear Systems: Nullspace Matrix and Rank
In this nullspace matrix worksheet, students 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...
Curated OER
Linear Systems: Orthogonality of Vector Spaces of a Matrix
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.
Curated OER
Find the Shortest Distance
In this problem solving worksheet students solve two problems regarding finding the shortest route. One problem is finding the shortest linear length given dimensions and the other problem is finding the shortest route as defined...
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Regents Exam Questions G.G.12: Volume
In this volume worksheet, high schoolers solve 12 short answer and multiple choice problems. Students find the dimensions of prisms given their volume in terms of quadratic and a linear expression.
Curated OER
Numerical Analysis: Discrete Least Squares
In this discrete least squares instructional activity, students use a linear algebra approach to discrete last squares approximation. This two-page instructional activity contains approximately 10 problems.
Teach Engineering
Exploring Acceleration with an Android
Small groups use rubber bands to accelerate an Android device along a track of books. They collect the acceleration data and analyze it in order to determine the device's velocity.
Houston Area Calculus Teachers
Area and Volume
An AP calculus lesson begins with an activity to determine the volume of a solid using a cross-section. Next, learners review the ways to find the area between two curves , as well how to find the volume of a solid created...