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Illustrative Mathematics

Combined Fuel Efficiency

For Teachers 8th - 11th Standards
Practice simplifying complex fractions and long division of polynomials with this brief exercise. These four questions make a challenging warm-up activity or a short, but comprehensive, follow-up after a detailed lesson on algebraic...
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Lesson Plan
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Representing the Unknown

For Teachers 6th - 8th
Student use mental math to solve linear equations. For this algebra lesson, students solve one and two steps equations. They write expressions using variables to identify the unknown.
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Worksheet
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Factoring Test

For Students 9th - 12th
In this algebra worksheet, students simplify monomials, perform basic operations on two polynomials, and factor binomials and trinomials. There are 20 questions and a bonus.
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Worksheet
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Factoring Completely

For Students 10th - 12th
In this factoring worksheet, learners factor polynomial expressions to simplify them. Upon placing their answer in the appropriate box, students may receive immediate feedback. A link for step-by-step solutions is provided.
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Worksheet
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Chapter 6 - Objective 3.1 Multiplication

For Students 9th - 10th
In this multiplication instructional activity, students multiply algebraic expressions. This one-page instructional activity contains ten problems.
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Lesson Plan
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Order of Operations H

For Teachers 6th - 8th
In this math worksheet, learners solve the five problems using the order of operations to simplify the expression. The answers are found on page two.
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Lesson Plan
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Rules of Exponents

For Teachers 8th - 10th
Students simplify problems using the rules of exponents and practice translating word sentences to algebraic expressions. Through a teacher led lecture and demonstration of exponent rules, students take notes and observe how to simply...
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Lesson Plan
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Operations of Polynomials

For Teachers 9th - 10th
Students investigate the concept of manipulating polynomials. They go through the process of using algebra tiles in order to practice grouping of like terms and model the solving process.
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Lesson Plan
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Laws of Exponents

For Teachers 9th
Ninth graders identify the different laws of exponents. In this algebra lesson, 9th graders write the rules of exponents and use them to solve problems. They use the product, quotient laws to solve problems.
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Lesson Plan
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Function Tables

For Teachers 8th - 9th
Young scholars identify function using tables of data. In this algebra lesson plan, students create a tale of point and plot on a coordinate plane. They analyze the graph as being a function or not.
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Worksheet
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Chapter 9 - Objective 2.1 Exponents

For Students 11th - 12th
In this exponent worksheet, students simplify equations containing exponents, fractions, radical expressions. This one-page worksheet contains ten problems.
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Worksheet
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Distributive Property

For Students 9th
In this Algebra I worksheet, 9th graders use the distributive property to simplify algebraic expressions.  The one page worksheet contains twenty multiple choice problems. Answers are provided. 
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Worksheet
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Commutative Property

For Students 8th - 9th
In this commutative property activity, students solve and complete 10 different problems by applying the commutative property to each. They rewrite each equation using the commutative property. Then, students write the reversed order on...
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Lesson Plan
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Reciprocals

For Teachers 9th - 10th
Students factor rational expressions using their reciprocals. In this algebra lesson, students simplify rational equations by factoring the fraction vy its reciprocal. They use the distributive property and solve combining like terms.
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Lesson Plan
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Algebra I: A Draining Swimming Pool

For Teachers 8th - 12th
Students analyze and develop symbolic representations to describe the amount of water left in a pool being pumped out after a given amount of time, with various pumping rates and initial quantities of water in the pool.
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Worksheet
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Polynomial Functions

For Students 11th
In this Algebra II worksheet, 11th graders classify polynomials by degree, write in standard form, and describe the behavior of the graph. The two page worksheet provides explanation and examples along with thirteen practice problems....
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Worksheet
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Eighteen Matrix Operations Questions

For Students 11th - 12th
In this matrix operations worksheet, students use matrix operations (adding, subtracting, multiplying) to simplify eighteen matrices, if possible.  Solutions are provided.
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Worksheet
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Order of Operations

For Students 8th - 9th
In this algebra learning exercise, students solve problems following the order of operation. They identify the properties of integers. There are 3 questions with an answer key.
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Worksheet
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Operations with Complex Numbers

For Students 10th - 11th
In this complex numbers instructional activity, students simplify thirty complex number expressions and answer two critical thinking questions.  The solutions are provided.
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Lesson Plan
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Strong Arm Iteration

For Teachers 7th - 9th
Young scholars solve exponential functions and inequalities. In this algebra lesson, students find the roots of equations and use it to graph and evaluate exponential functions. They simplify exponents using the law of exponents.
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Worksheet
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Multiplication of Square-Root Radicals

For Students 9th - 11th
In this Algebra I/Algebra II worksheet, students multiply square-root radicals and express answers in simplest form.  The one page worksheet contains three problems.  Answers are provided. 
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Lesson Plan
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Two Step Equations

For Teachers 6th
Sixth graders solve multiple step math problems. In this problem solving lesson, 6th graders practice following step by step instructions such as making cookies or building a snowman. Students use algebra tiles and draw pictures to solve...
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Lesson Plan
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Limits

For Teachers 10th - 12th
Young scholars practice the concept of limits graphically, numerically and algebraically. They participate in an exploration lab, BINGO game and complete a puzzle.
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Worksheet
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Properties of Logarithms

For Students 11th
In this algebra worksheet, 11th graders apply the 3 properties of logarithms to solve equations by expanding or condensing them. There are 4 problems to solve.