EngageNY
What Lies Behind “Same Shape”?
Develop a more precise definition of similar. The activity begins with an informal definition of similar figures and develops the need to be more precise. The class learns about dilations and uses that knowledge to arrive at a...
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Successive Differences in Polynomials
Don't give your classes the third degree when working with polynomials! Teach them to recognize the successive differences and identify the degree of the polynomial. The instructional activity leads learners through a process to develop...
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The Inverse Relationship Between Logarithmic and Exponential Functions
Introducing inverse functions! The 20th installment of a 35-part instructional activity encourages scholars to learn the definition of inverse functions and how to find them. The instructional activity considers all types of functions,...
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Modeling Riverbeds with Polynomials (part 2)
Examine the power of technology while modeling with polynomial functions. Using the website wolfram alpha, learners develop a polynomial function to model the shape of a riverbed. Ultimately, they determine the flow rate through the river.
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Why Call It Tangent?
Discover the relationship between tangent lines and the tangent function. Class members develop the idea of the tangent function using the unit circle. They create tables of values and explore the domain, range, and end behavior of the...
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Basic Trigonometric Identities from Graphs
Have young mathematicians create new identities! They explore the even/odd, cofunction, and periodicity identities through an analysis of tables and graph. Next, learners discover the relationships while strengthening their understanding...
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Graphs of Exponential Functions and Logarithmic Functions
Graphing by hand does have its advantages. The 19th installment of a 35-part module prompts pupils to use skills from previous lessons to graph exponential and logarithmic functions. They reflect each function type over a diagonal line...
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Newton’s Law of Cooling, Revisited
Does Newton's Law of Cooling have anything to do with apples? Scholars apply Newton's Law of Cooling to solve problems in the 29th installment of a 35-part module. Now that they have knowledge of logarithms, they can determine the decay...
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Deriving the Quadratic Formula
Where did that formula come from? Lead pupils on a journey through completing the square to discover the creation of the quadratic formula. Individuals use the quadratic formula to solve quadratic equations and compare the method to...
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Why Stay with Whole Numbers?
Domain can be a tricky topic, especially when you relate it to context, but here is a lesson that provides concrete examples of discrete situations and those that are continuous. It also addresses where the input values should begin and...
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The Zero Product Property
Zero in on your pupils' understanding of solving quadratic equations. Spend time developing the purpose of the zero product property so that young mathematicians understand why the equations should be set equal to zero and how that...
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Graphs of Piecewise Linear Functions
Everybody loves video day! Grab your class's attention with this well-designed and engaging resource about graphing. The video introduces a scenario that will be graphed with a piecewise function, then makes a connection to domain...
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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.
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Comparing Rational Expressions
Introduce a new type of function through discovery. Math learners build an understanding of rational expressions by creating tables and graphing the result.
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Adding and Subtracting Rational Expressions
There's a fine line between a numerator and a denominator! Learners find common denominators in order to add and subtract rational expressions. Examples include addition, subtraction, and complex fractions.
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Solving Rational Equations
What do fractions and rational expressions have in common? Everything! Learners use common denominators to solve rational equations. Problems advance from simple to more complex, allowing pupils to fully understand the material before...
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Integer Sequences—Should You Believe in Patterns?
Help your class discover possible patterns in a sequence of numbers and then write an equation with a lesson that covers sequence notation and function notation. Graphs are used to represent the number patterns.
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Solution Sets to Inequalities with Two Variables
What better way to learn graphing inequalities than through discovering your own method! Class members use a discovery approach to finding solutions to inequalities by following steps that lead them through the process and even include...
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Geometric Sequences and Exponential Growth and Decay
Connect geometric sequences to exponential functions. The 26th installment of a 35-part module has scholars model situations using geometric sequences. Writing recursive and explicit formulas allow scholars to solve problems in context.
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Solving Quadratic Equations by Completing the Square
Many learners find completing the square the preferred approach to solving quadratic equations. Class members combine their skills of using square roots to solve quadratics and completing the square. The resource incorporates a variety...
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The Graph of a Function
Mathematics set notation can be represented through a computer program loop. Making the connection to a computer program loop helps pupils see the process that set notation describes. The activity allows for different types domain and...
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Representing, Naming, and Evaluating Functions (Part 2)
Notation in mathematics can be intimidating. Use this lesson to expose pupils to the various ways of representing a function and the accompanying notation. The material also addresses the importance of including a domain if necessary....
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The General Multiplication Rule
In the first installment of a 21-part module, scholars build on previous understandings of probability to develop the multiplication rule for independent and dependent events. They use the rule to solve contextual problems.
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Distributions and Their Shapes
What can we find out about the data from the way it is shaped? Looking at displays that are familiar from previous grades, the class forms meaningful conjectures based upon the context of the data. The introductory lesson to descriptive...