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EngageNY

True and False Equations

For Students 9th - 10th Standards
What does English have to do with math? Teach your class the "grammar" of a number sentence. Sentences with correct grammar can be false! Understanding of a number sentence leads to a comparison with equations.
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Lesson Plan
EngageNY

Solving and Graphing Inequalities Joined by “And” or “Or”

For Students 9th - 10th Standards
Guide your class through the intricacies of solving compound inequalities with a resource that compares solutions of an equation, less than inequality, and greater than inequality. Once pupils understand the differences, the...
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Lesson Plan
EngageNY

Equations Involving Factored Expressions

For Students 9th - 10th Standards
Be ready mathematicians of every level. This instructional activity leads to the discovery of the zero product property and provides challenges for early finishers along the way. At conclusion, pupils understand the process of using the...
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Lesson Plan
EngageNY

Creating and Solving Quadratic Equations in One Variable

For Students 9th - 10th Standards
Give your classes practice at modeling using quadratic models with a resource that uses area and integer problems to allow individuals to create second degree polynomials. Young mathematicians solve equations using factoring and then...
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Lesson Plan
EngageNY

Exponential Growth—U.S. Population and World Population

For Students 9th - 10th Standards
Show how exponential growth can look linear. Pupils come to understand the importance of looking at the entire picture as they compare the US population to the world population. Initially, the populations look linear with the same rate...
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Lesson Plan
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EngageNY

Interpreting Residuals from a Line

For Teachers 9th - 10th Standards
What does an animal's gestation period have to do with its longevity? Use residuals to determine the prediction errors based upon a least-square regression line. This second lesson on residuals shows how to use residuals to create a...
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Lesson Plan
EngageNY

Modeling from a Sequence

For Teachers 9th - 10th Standards
Building upon previous knowledge of sequences, collaborative pairs analyze sequences to determine the type and to make predictions of future terms. The exercises build through arithmetic and geometric sequences before introducing...
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Lesson Plan
EngageNY

Multiplying and Factoring Polynomial Expressions (part 1)

For Students 9th - 10th Standards
Polynomial multiplication and factoring go hand in hand. Why not teach them together. This resource begins with an area model for distributing a monomial and then connects the process to factoring the GCF. Learners then advance to...
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Lesson Plan
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EngageNY

Solution Sets for Equations and Inequalities

For Students 9th - 10th Standards
How many ways can you represent solutions to an equation? Guide your class through the process of solving equations and representing solutions. Solutions are described in words, as a solution set, and graphed on a number line....
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Lesson Plan
EngageNY

Some Potential Dangers When Solving Equations

For Students 9th - 10th Standards
Need a less abstract approach to introducing extraneous solutions? This is it! Young mathematicians explore properties used to solve equations and determine which operations maintain the same solutions. They eventually find that squaring...
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Lesson Plan
EngageNY

Comparing Quadratic, Square Root, and Cube Root Functions Represented in Different Ways

For Students 9th - 10th Standards
Need a real scenario to compare functions? This lesson has it all! Through application, individuals model using different types of functions. They analyze each in terms of the context using the key features of the graphs. 
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EngageNY

Solution Sets to Simultaneous Equations (part 2)

For Students 9th - 10th Standards
Do you want your budding mathematicians to be able to explain 'why' and not just 'do'? This lesson encourages an understanding of the process of elimination. Pupils are expected to understand how and why the elimination method is a valid...
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Lesson Plan
EngageNY

The Graph of a Function

For Teachers 9th - 10th Standards
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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Lesson Plan
EngageNY

Representing, Naming, and Evaluating Functions (Part 1)

For Teachers 9th - 10th Standards
Begin the discussion of domain and range using something familiar. Before introducing numbers, the lesson uses words to explore the idea of input and outputs and addresses the concept of a function along with domain and range. 
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Lesson Plan
EngageNY

Analyzing a Graph

For Teachers 9th - 10th Standards
Collaborative groups utilize their knowledge of parent functions and transformations to determine the equations associated with graphs. The graph is then related to the scenario it represents. 
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Lesson Plan
EngageNY

Four Interesting Transformations of Functions (Part 2)

For Teachers 9th - 10th Standards
What happens to a function whose graph is translated horizontally? Groups find out as they investigate the effects of addition and subtraction within a function. This nineteenth lesson in a 26-part series focuses on horizontal...
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Lesson Plan
EngageNY

Modeling an Invasive Species Population

For Students 9th - 10th Standards
Context makes everything better! Groups use real data to create models and make predictions. Classmates compare an exponential model to a linear model, then consider the real-life implications. 
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Lesson Plan
EngageNY

The Zero Product Property

For Students 9th - 10th Standards
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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Lesson Plan
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EngageNY

Solving Basic One-Variable Quadratic Equations

For Students 9th - 10th Standards
Help pupils to determine whether using square roots is the method of choice when solving quadratic equations by presenting a lesson that begins with a dropped object example and asks for a solution. This introduction to solving by square...
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Lesson Plan
EngageNY

The Graph of the Equation y = f(x)

For Students 9th - 10th Standards
Math language? Set notation is used in mathematics to communicate a process and that the same process can be represented as computer code. The concept to the loop in computer code models the approach pupils take when creating a solution...
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Lesson Plan
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EngageNY

Solving Quadratic Equations by Completing the Square

For Students 9th - 10th Standards
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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Lesson Plan
EngageNY

Representing, Naming, and Evaluating Functions (Part 2)

For Teachers 9th - 10th Standards
Notation in mathematics can be intimidating. Use this instructional activity 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...
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Lesson Plan
EngageNY

Summarizing Deviations from the Mean

For Teachers 9th - 10th Standards
Through a series of problems, learners determine the variability of a data set by looking at the deviations from the mean. Estimating means of larger data sets presented in histograms and providing a way to calculate an estimate round...
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Lesson Plan
EngageNY

Analyzing a Data Set

For Teachers 9th - 10th Standards
Through discussions and journaling, classmates determine methods to associate types of functions with data presented in a table. Small groups then work with examples and exercises to refine their methods and find functions that work to...

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