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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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Probability Rules (part 2)
Ensure your pupils are rule followers! Learners add the addition rule to the set of probability rules examined in the previous lesson. Problems require both the multiplication and addition rule.
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Types of Statistical Studies
All data is not created equal. Scholars examine the different types of studies and learn about the importance of randomization. They explore the meaning of causation and when it can be applied to data.
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Experiments and the Role of Random Assignment
Time to experiment with mathematics! Learners study experimental design and how randomization applies. They emphasize the difference between random selection and random assignment and how both are important to the validation of the...
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Margin of Error When Estimating a Population Mean (part 1)
We know that sample data varies — it's time to quantify that variability! After calculating a sample mean, pupils calculate the margin of error. They repeat the process with a greater number of sample means and compare the results.
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Ruling Out Chance (part 3)
Pupils analyze group data to identify significant differences. They use simulation to create their own random assignment data for comparison.
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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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The Most Important Property of Logarithms
Won't the other properties be sad to learn that they're not the most important? The 11th installment of a 35-part module is essentially a continuation of the previous lesson, using logarithm tables to develop properties. Scholars...
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Choosing a Model
There's a function for that! Scholars examine real-world situations to determine which type of function would best model the data in the 23rd installment of a 35-part module. It involves considering the nature of the data in addition to...
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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.
Teach Engineering
Wetting and Contact Angle
Explore terminology related to water droplets. The sixth installment of a nine-part series teaches young scientists about wetting and contact angles between water droplets and surfaces. It also distinguishes between hydrophobic and...
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An Appearance of Complex Numbers 1
Complex solutions are not always simple to find. In the fourth lesson of the unit, the class extends their understanding of complex numbers in order to solve and check the solutions to a rational equation presented in the first lesson....
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An Appearance of Complex Numbers 2
Help the class visualize operations with complex numbers with a lesson that formally introduces complex numbers and reviews the visualization of complex numbers on the complex plane. The fifth installment of a 32-part series reviews...
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Distance and Complex Numbers 1
To work through the complexity of coordinate geometry pupils make the connection between the coordinate plane and the complex plane as they plot complex numbers in the 11th part of a series of 32. Making the connection between the two...
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Networks and Matrix Arithmetic
Doubling a network or combining two networks is quick and easy when utilizing matrices. Learners continue the network example in the second lesson of this series. They practice adding, subtracting, and multiplying matrices by a scalar...
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Designing Your Own Game
Your classes become video game designers for a day! They utilize their matrices, vectors, and transformation skills to create and design their own game images. The complex task requires learners to apply multiple concepts to create their...
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Vectors and Translation Maps
Discover the connection between vectors and translations. Through the lesson, learners see the strong relationship between vectors, matrices, and translations. Their inquiries begin in the two-dimensional plane and then progress to the...
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Solving Equations Involving Linear Transformations of the Coordinate Space
Explore methods for solving linear systems with your classes and introduce learners to using matrices as a viable method. Scholars are able to recognize situations where matrices are the efficient method of solving. Application...
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Special Lines in Triangles (part 2)
Medians, midsegments, altitudes, oh my! Pupils study the properties of the median of a triangle, initially examining a proof utilizing midsegments to determine the length ratio of a median. They then use the information to find missing...
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Congruence Criteria for Triangles—AAS and HL
How can you prove it? Guide classes through an exploration of two possible triangle congruence criteria: AAS and HL. Learners connect this criteria to those previous learned and also explore criteria that does not work. The instructional...
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Congruence Criteria for Triangles—ASA and SSS
How do you know if a pair of triangles are congruent? Use the lesson to help class members become comfortable identifying the congruence criteria. They begin with an exploration of ASA and SSS criteria through transformations and...
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Stretching and Shrinking Graphs of Functions
Why is that graph wider? Pupils learn about stretching and shrinking graphs of square root, absolute value, cubic, and quadratic functions. They study both vertical and horizontal stretches and shrinks in addition to reflections.
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Modeling with Quadratic Functions (part 1)
Relevance is key! The resource applies quadratic modeling by incorporating application of physics and business. Pupils work through scenarios of projectile motion and revenue/profit relationships. By using the key features of the graph,...
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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....