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Radicals and Conjugates
Make the irrational rational again! Continuing the theme from previous lessons in the series, the lesson relates the polynomial identity difference of squares to conjugates. Learners develop the idea of a conjugate through analysis and...
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Ferris Wheels—Using Trigonometric Functions to Model Cyclical Behavior
Have class members going in circles as they model the path of a Ferris Wheel using trigonometric functions. Building on the previous lesson in this series on transformations, learners use trigonometric functions to model wheels of...
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Ruling Out Chance (part 2)
Help your classes find the significance in this lesson! Learners analyze the probability of Diff values. They then determine if the difference is significant based on their probability of occurrence.
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Rational Exponents—What are 2^1/2 and 2^1/3?
Are you rooting for your high schoolers to learn about rational exponents? In the third installment of a 35-part module, pupils first learn the meaning of 2^(1/n) by estimating values on the graph of y = 2^x and by using algebraic...
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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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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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Wishful Thinking—Does Linearity Hold? (Part 1)
Not all linear functions are linear transformations — show your class the difference. The first lesson in a unit on linear transformations and complex numbers that spans 32 segments introduces the concept of linear transformations and...
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An Appearance of Complex Numbers 2
Help the class visualize operations with complex numbers with a activity that formally introduces complex numbers and reviews the visualization of complex numbers on the complex plane. The fifth installment of a 32-part series...
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Justifying the Geometric Effect of Complex Multiplication
The 14th lesson plan in the unit has the class prove the nine general cases of the geometric representation of complex number multiplication. Class members determine the modulus of the product and hypothesize the relationship for...
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Representing Reflections with Transformations
In the 16th lesson in the series of 32 the class uses the concept of complex multiplication to build a transformation in order to reflect across a given line in the complex plane. The lesson breaks the process of reflecting across a line...
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When Can We Reverse a Transformation? 2
The second lesson on finding inverse matrices asks class members to look for a pattern in the inverse matrix and test it to see if it works for all matrices. The teacher leads a discussion to refine the process in finding inverses,...
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Waves, Sinusoids, and Identities
What is the net effect when two waves interfere with each other? The lesson plan answers this question by helping the class visualize waves through graphing. Pupils graph individual waves and determine the effect of the interference...
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Scatter Plots
Scholars learn to create scatter plots and investigate any relationships that exists between the variables with a lesson that also show them that statistical relationships do not necessarily indicate a cause-and-effect...
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Numbers in Exponential Form Raised to a Power
Develop an understanding of the properties of exponents through this series of activities. This third lesson of 15 explores the patterns associated with the power property. Scholars expand the powers before applying the property.
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Definition of Translation and Three Basic Properties
Uncover the properties of translations through this exploratory instructional activity. Learners apply vectors to describe and verify transformations in the second installment of a series of 18. It provides multiple opportunities to...
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More on the Angles of a Triangle
Angles and triangles: they're all connected. Uncover the connections between angles in triangles. Scholars learn how to find both exterior and interior angle measures in triangles. The lesson emphasizes the vocabulary related to these...
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Informal Proof of the Pythagorean Theorem
Prove the Pythagorean Theorem using multiple informal proofs. Scholars first develop an understanding of the origins of the Pythagorean Theorem through proofs. They round out the lesson by using the theorem to find missing side lengths...
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Summarizing Bivariate Categorical Data in a Two-Way Table
Be sure to look both ways when making a two-way table. In the lesson, scholars learn to create two-way tables to display bivariate data. They calculate relative frequencies to answer questions of interest in the 14th part of the series.
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Nonlinear Models in a Data Context
How well does your garden grow? Model the growth of dahlias with nonlinear functions. In the lesson, scholars build on their understanding of mathematical models with nonlinear models. They look at dahlias growing in compost and...
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The Pythagorean Theorem
Class members explore the estimation of irrational numbers in association with the Pythagorean Theorem. The first activity of this module challenges pupils to use the Pythagorean Theorem to find unknown side lengths. When the length is...
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Decimal Expansions of Fractions, Part 2
Develop your pupils' understanding of fractions and their decimal equivalence using the 12th lesson in this series. Scholars learn an alternative to long division that results in converting fractions to decimals that emphasize fractional...
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The Division Algorithm—Converting Decimal Division into Whole Number Division Using Mental Math
Make math much simpler with mental math methods. The 16th installment in a series of 21 looks at ways scholars can apply mental math to convert division problems into easier problems with the same quotient. Multiplying or dividing both...
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The Relationship of Multiplication and Division
Take any number, multiply it by five, and then divide by five. Did you end up with the original number? In the same vein as the previous lesson, pupils discover the relationship between multiplication and division. They develop the...
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Describing the Center of a Distribution Using the Median
Find the point that splits the data. The instructional activity presents to scholars the definition of the median through a teacher-led discussion. The pupils use data lists and dot plots to determine the median in sets with even and odd...