EngageNY
An Application of Linear Equations
Just how far will the Facebook post go? Lead a discussion on how to manipulate the sum of a geometric series to figure out a formula to find the sum at any step. The plan contains an alternative to the discussion with more accessible...
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The Graph of a Linear Equation in Two Variables
Add more points on the graph ... and it still remains a line! The 13th installment in a series of 33 leads the class to the understanding that the graph of linear equation is a line. Pupils find several solutions to a two-variable linear...
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Fundamental Theorem of Similarity (FTS)
How do dilated line segments relate? Lead the class in an activity to determine the relationship between line segments and their dilated images. In the fourth section in a unit of 16, pupils discover the dilated line segments are...
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Informal Proofs of Properties of Dilations
Challenge the class to prove that the dilation properties always hold. The lesson develops an informal proof of the properties of dilations through a discussion. Two of the proofs are verified with each class member performing the...
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First Consequences of FTS
Challenge the young mathematicians to find the exact coordinates of a dilated point. The fifth segment in a 16-part series introduces the class to the converse of the Fundamental Theorem of Similarity. Scholars use the theorem to find...
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Informal Proof of AA Criterion for Similarity
What does it take to show two triangles are similar? The 11th segment in a series of 16 introduces the AA Criterion for Similarity. A discussion provides an informal proof of the theorem. Exercises and problems require scholars to apply...
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Proof of the Pythagorean Theorem
What does similarity have to do with the Pythagorean Theorem? The activity steps through the proof of the Pythagorean Theorem by using similar triangles. Next, the teacher leads a discussion of the proof and follows it by an animated...
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The Converse of the Pythagorean Theorem
Is it a right triangle or not? Introduce scholars to the converse of the Pythagorean Theorem with a lesson that also provides a proof by contradiction of the converse. Pupils use the converse to determine whether triangles with given...
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Exponential Notation
Exponentially increase your pupils' understanding of exponents with an activity that asks them to explore the meaning of exponential notation. Scholars learn how to use exponential notation and understand its necessity. They use negative...
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Informally Fitting a Line
Discover how trend lines can be useful in understanding relationships between variables with a instructional activity that covers how to informally fit a trend line to model a relationship given in a scatter plot. Scholars use the trend...
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Determining the Equation of a Line Fit to Data
What makes a good best-fit line? In the 10th part of a 16-part module, scholars learn how to analyze trend lines to choose the best fit, and to write equations for best-fit lines to make predictions.
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Numbers Raised to the Zeroth Power
What in the world is the zeroth power? Examine the patterns of exponents as they apply to the zeroth power. Scholars apply the zero property to simple exponential expressions in this fourth lesson plan in a series of 15. The examples...
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Negative Exponents and the Laws of Exponents
Apply the properties of exponents to expressions with negative exponents. The fifth lesson in the series explains the meaning of negative exponents through an exploration of the properties taught in the previous lessons of the series....
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Proofs of Laws of Exponents
Apply pupil understanding of exponent properties to prove the relationships. In the sixth instructional activity of the series, individuals are expected to prove relationships using mathematical statements and reasoning.
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Interpreting Rate of Change and Initial Value
Building on knowledge from the previous lesson, the second lesson in this unit teaches scholars to identify and interpret rate of change and initial value of a linear function in context. They investigate how slope expresses the...
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Magnitude
Build an understanding of the powers of 10. Pupils investigate the results of raising 10 to positive and negative powers. They relate this understanding to the magnitude these powers represent in this seventh lesson of 15.
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Operations with Numbers in Scientific Notation
Demonstrate the use of scientific notation within word problems. The lesson presents problems with large numbers best represented with scientific notation. Pupils use these numbers to solve the problems in the 11th installment in a...
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Association Between Categorical Variables
Investigate associations between variables with two-way tables. Scholars continue their study of two-way tables and categorical variables in the 15th installment of a 21-part module. The lesson challenges them to calculate relative...
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Choice of Unit
Explore using units with scientific notation to communicate numbers effectively. Individuals choose appropriate units to express numbers in a real-life situation. For this 13th lesson of 15, participants convert numbers in scientific...
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Comparison of Numbers Written in Scientific Notation and Interpreting Scientific Notation Using Technology
Examine numbers in scientific notation as a comparison of size. The 14th instructional activity in the series asks learners to rewrite numbers as the same power of 10 in scientific notation to make comparisons. Pupils also learn how to...
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Writing Equations Using Symbols
Build upon prior equation writing experience to create more complicated equations. Lesson one in a 33-part unit builds upon the class members' sixth and seventh grade experience of writing linear equations. Several examples provide...
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Linear Equations in x
What does it mean to solve an equation? The resource revisits the concept of making a linear equation true. Classmates use algebraic methods to transform sides of equations to expressions with fewer terms. They use substitution to...
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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...
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Translating Lines
Define parallel lines through transformations. The third lesson of 18 examines the result of the translation of a line. Two possible outcomes include coinciding lines and parallel lines.