Illustrative Mathematics
Calculating the square root of 2
Does a calculator give you the exact value of the square root of 2? Here, learners must decide if 1.414236 is equal to the square root of 2. They must also explain why the square root of 2 could never be equal to a terminating decimal....
Illustrative Mathematics
Operations on the Number Line
A different way to look at integers is on this number line with variables in place of numbers. Learners are to look at different expressions and describe why they think the answer would be positive or negative, depending on the location...
Curated OER
Interesting Integers and Exciting Equations
An 80-page resource provides four lessons and all associated worksheets to teach middle schoolers about expressions and equations. The lessons are hands-on, using games, "integer chips," a balance and cubes, and cut and paste activities....
Virginia Department of Education
Complex Numbers
Build on your class' understanding of real numbers as they begin working with complex numbers. Pupils begin with an exploration of i and the patterns in the powers of i. After developing a definition for i, they...
Curated OER
Summer Intern
Your young apprentices build a function describing the percent concentration of salt in a brine. The rational function is then related to the parent function, y= 1/x, and graphed. Finally, the apprentices predict the amount of fresh...
EngageNY
Using the Quadratic Formula
What is the connection between the quadratic formula and the types of solutions of a quadratic equation? Guide young mathematicians through this discovery as they use the discriminant to determine the number and types of solutions,...
Curated OER
Worksheet 9: Trig Functions
In this math worksheet, students are given 7 problems in which they write expressions for trig functions, compute limits and graph functions.
Curated OER
Simplifying Radicals
In this radical worksheet, students write given radical expressions in a square root form. Explanations and examples are provided at the beginning of the document. This two-page worksheet contains 24 problems. Answers are located at the...
West Contra Costa Unified School District
Derivative – Standard Definition
Making a clear connection to algebra concepts helps learners understand the definition of a derivative. The lesson begins with looking at limits of simple linear and rational functions, and leads to the definition of the...
CK-12 Foundation
Trigonometric Functions and Angles of Rotation: The Triangle in the Circle
Go around the unit circle and create triangles. Pupils move a point around the unit circles to visualize the triangle associated with the angle in standard position. The three main trigonometric functions are defined in terms of the legs...
Curated OER
Eloquent Experts
Students practice reading with fluency and expression in this lesson. Students work with a partner with a set of sentence strips. They take turns pulling sentence strips out of the envelope and reading them aloud to each other using...
Curated OER
Algebra Quiz
For this college level algebra worksheet, students simplify absolute value expressions and solve radical and rational equations. The two page worksheet contains six problems. Answers are not provided.
Curated OER
Arithmetic Mean and Geometric Mean
In this algebra activity, students solve rational expressions. They differentiate between arithmetic and geometric mean. These problems are interactive with a solution key.
Courseware Solutions
Integers: A Real World Rational Numbers Application
Given centigrade temperatures for pairs of cities, math-minded meteorologists determine which is either warmer or colder. The instructional activity is embedded in a website from which you can access an answer key or even change the...
Curated OER
Algebraic Fractions
In this Algebra I worksheet, 9th graders find the product or quotient of algebraic fractions and reduce to simplest form. The two page worksheet contains a combination of eleven multiple choice and free response questions. ...
Curated OER
Reducing Fractions to Lowest Terms
For this Algebra I/Algebra II worksheet, students reduce algebraic fractions to lowest terms. The one page worksheet contains a combination of eleven multiple choice and free response problems. Answers are provided.
Curated OER
Dividing Fractions
In this Algebra I/Algebra II worksheet, students multiply and divide algebraic fractions. The one page worksheet contains four free response questions. Answers are included.
Curated OER
Adding or Subtraction Algebraic Fractions
For this Algebra I/Algebra II worksheet, students add and subtract algebraic fractions and reduce the answer to lowest terms. The two page worksheet contains a combination of eleven multiple choice and free response...
Curated OER
Understanding Rational Numbers and Proportions
Students explore parts of a whole. In this fraction lesson, students determine what makes a fair share. Working with manipulatives, students solve mathematical problems containing fractions.
Curated OER
Solving Equations Containing Algebraic Fractions
For this algebraic fractions worksheet, students solve and complete 20 different problems that include solving equations that contain algebraic fractions. First, they determine the common denominator in each and use the product of all...
EngageNY
Comparing Methods—Long Division, Again?
Remember long division from fifth grade? Use the same algorithm to divide polynomials. Learners develop a strategy for dividing polynomials using what they remember from dividing whole numbers.
EngageNY
Linear Equations in Disguise
In the eighth segment of a 33-part unit, learners look at equations that do not appear to be linear at first glance. The equations are proportions where the numerators and denominators may have more than one term. To round out the...
Curated OER
Discovering Math: Computation
Middle schoolers add, subtract, multiply, and divide rational numbers. They find the square and the cube of numbers. They create a game incorporating computation on rational numbers. Everyone works together to write and evaluate...
PB Works
Numbers Lesson 3 - Hershey Bar Fractions
Talk about delicious math! Pupils solve problems involving rational numbers and analyze real-life problems to find solutions in a pre-algebra class. They discuss the sections of a Hershey's bar in terms of fractions and decimals before...