EngageNY
Calculating Probabilities of Events Using Two-Way Tables
Tables are useful for more than just eating. Learners use tables to organize data and calculate probabilities and conditional probabilities.
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Calculating Conditional Probabilities and Evaluating Independence Using Two-Way Tables (part 1)
Being a statistician means never having to say you're certain! Learners develop two-way frequency tables and calculate conditional and independent probabilities. They understand probability as a method of making a prediction.
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Calculating Conditional Probabilities and Evaluating Independence Using Two-Way Tables (part 2)
Without data, all you are is another person with an opinion. Show learners the power of statistics and probability in making conclusions and predictions. Using two-way frequency tables, learners determine independence by analyzing...
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Sampling Variability in the Sample Proportion (part 1)
Increase your sample and increase your accuracy! Scholars complete an activity that compares sample size to variability in results. Learners realize that the greater the sample size, the smaller the range in the distribution of sample...
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Properties of Exponents and Radicals
(vegetable)^(1/2) = root vegetable? The fourth installment of a 35-part module has scholars extend properties of exponents to rational exponents to solve problems. Individuals use these properties to rewrite radical expressions in...
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Multiplying and Factoring Polynomial Expressions (part 1)
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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Percent Rate of Change
If mathematicians know the secret to compound interest, why aren't more of them rich? Young mathematicians explore compound interest with exponential functions in the twenty-seventh installment of a 35-part module. They calculate future...
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Buying a Car
Future car owners use geometric sums to calculate payments for a car loan in the 31st installment of a 35-part module. These same concepts provide the basis for calculating annuity payments.
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Buying a House
There's no place like home. Future home owners investigate the cost of buying a house in the 33rd installment of a 35-part module. They come to realize that the calculations are simply a variation of previous formulas involving car loans...
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Complex Numbers as Vectors
Show your math class how to use vectors in adding complex numbers. Vectors represent complex numbers as opposed to points in the coordinate plane. The class uses the geometric representation to add and subtract complex numbers and...
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Counting Rules—The Fundamental Counting Principle and Permutations
Count the benefits of using the resource. The second installment of a 21-part module focuses on the fundamental counting principle to determine the number of outcomes in a sample space. It formalizes concepts of permutations and...
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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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Fair Games
What constitutes a fair game? Scholars learn about fair games and analyze some to see if they are fair. They extend this idea to warranties and other contexts.
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Addition and Subtraction Formulas 2
Knowing the addition formulas allows for the calculations of double and half formulas. The fourth installment of 16 has the class use the addition formula to develop the double angle trigonometric formulas. Using the double formula,...
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Law of Sines
Prove the Law of Sines two ways. The ninth segment in a series of 16 introduces the Law of Sines to help the class find lengths of sides in oblique triangles. Pupils develop a proof of the Law of Sines by drawing an altitude and a second...
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Law of Cosines
Build upon the Pythagorean Theorem with the Law of Cosines. The 10th part of a 16-part series introduces the Law of Cosines. Class members use the the geometric representation of the Pythagorean Theorem to develop a proof of the Law of...
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Divisibility Tests for 3 and 9
Who knew the sum of a number's digits gives such interesting information? The 18th installment of a 21-part module has scholars investigate division by three and nine. After looking at several examples, they develop divisibility tests...
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Connecting Graphical Representations and Numerical Summaries
Which graph belongs to which summary statistics? Class members build upon their knowledge of data displays and numerical summaries to connect the two. Pupils make connections between different graphical displays of the same data in...
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How Do Dilations Map Segments?
Do you view proofs as an essential geometric skill? The resource builds on an understanding of dilations by proving the Dilation Theorem of Segments. Pupils learn to question and verify rather than make assumptions.
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What Are Similarity Transformations, and Why Do We Need Them?
It's time for your young artists to shine! Learners examine images to determine possible similarity transformations. They then provide a sequence of transformations that map one image to the next, or give an explanation why it is...
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Properties of Similarity Transformations
You can explain it, but can you do it? After learners view a sequence of transformations, the next logical step is creating the transformation. Challenge your classes to construct a composition of transformations and verify the...
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Special Relationships Within Right Triangles—Dividing into Two Similar Sub-Triangles
Why are right triangles so special? Pupils begin their study of right triangles by examining similar right triangles. Verifying through proofs, scholars recognize the three similar right triangles formed by drawing the altitude. Once...
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Applying Tangents
What does geometry have to do with depression? It's an angle of course! Learners apply the tangent ratio to problem solving questions by finding missing lengths. Problems include angles of elevation and angles of depression. Pupils make...
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How Do 3D Printers Work?
If we stack up all the cross sections of a figure, does it create the figure? Pupils make the connection between the complete set of cross sections and the solid. They then view videos in order to see how 3D printers use Cavalerie's...