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The Power of Algebra—Finding Primes
Banks are responsible for keeping our financial information safe. Mathematics is what allows them to do just that! Pupils learn the math behind the cryptography that banks rely on. Using polynomial identities, learners reproduce the...
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Modeling with Polynomials—An Introduction (part 2)
Linear, quadratic, and now cubic functions can model real-life patterns. High schoolers create cubic regression equations to model different scenarios. They then use the regression equations to make predictions.
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Systems of Equations
What do you get when you cross a circle and a line? One, two, or maybe no solutions! Teach learners to find solutions of quadratic and linear systems. Connect the visual representation of the graph to the abstract algebraic methods.
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Graphing Systems of Equations
Expand on learners' understanding of quadratic-linear systems. Building on the graphic understanding developed in the previous lesson, pupils learn algebraic methods of solving the systems.
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Are All Parabolas Similar?
Congruence and similarity apply to functions as well as polygons. Learners examine the effects of transformations on the shape of parabolas. They determine the transformation(s) that produce similar and congruent functions.
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Complex Numbers as Solutions to Equations
Quadratic solutions come in all shapes and sizes, so help your classes find the right one! Learners use the quadratic formula to find solutions for quadratic equations. Solutions vary from one, two, and complex.
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Modeling from a Sequence
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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Why Call It Tangent?
Discover the relationship between tangent lines and the tangent function. Class members develop the idea of the tangent function using the unit circle. They create tables of values and explore the domain, range, and end behavior of...
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Integer Exponents
Fold, fold, and fold some more. In the first installment of a 35-part module, young mathematicians fold a piece of paper in half until it can not be folded any more. They use the results of this activity to develop functions for the area...
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Graphing the Tangent Function
Help learners discover the unique characteristics of the tangent function. Working in teams, pupils create tables of values for different intervals of the tangent function. Through teamwork, they discover the periodicity, frequency, and...
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Irrational Exponents—What are 2^√2 and 2^π?
Extend the concept of exponents to irrational numbers. In the fifth installment of a 35-part module, individuals use calculators and rational exponents to estimate the values of 2^(sqrt(2)) and 2^(pi). The final goal is to show that the...
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Euler’s Number, e
Scholars model the height of water in a container with an exponential function and apply average rates of change to this function. The main attraction of the lesson plan is the discovery of Euler's number.
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Bacteria and Exponential Growth
It's scary how fast bacteria can grow — exponentially. Class members solve exponential equations, including those modeling bacteria and population growth. Lesson emphasizes numerical approaches rather than graphical or algebraic.
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The Zero Product Property
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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Solving Basic One-Variable Quadratic Equations
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...
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Using the Quadratic Formula
What is the connection between the quadratic formula and the types of solutions of a quadratic equation? Guide young mathematicians through this discovery as they use the discriminant to determine the number and types of solutions,...
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Solution Sets for Equations and Inequalities
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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Recursive Formulas for Sequences
Provide Algebra I learners with a logical approach to making connections between the types of sequences and formulas with a lesson that uses what class members know about explicit formulas to develop an understanding of...
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Building Logarithmic Tables
Thank goodness we have calculators to compute logarithms. Pupils use calculators to create logarithmic tables to estimate values and use these tables to discover patterns (properties). The second half of the instructional activity has...
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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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Solving Logarithmic Equations
Of course you're going to be solving an equation—it's algebra class after all. The 14th installment of a 35-part module first has pupils converting logarithmic equations into equivalent exponential equations. The conversion allows for...
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Why Were Logarithms Developed?
Show your class how people calculated complex math problems in the old days. Scholars take a trip back to the days without calculators in the 15th installment of a 35-part module. They use logarithms to determine products of numbers and...
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Graphing the Logarithmic Function
Teach collaboration and communication skills in addition to graphing logarithmic functions. Scholars in different groups graph different logarithmic functions by hand using provided coordinate points. These graphs provide the basis for...
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The Graph of the Natural Logarithm Function
If two is company and three's a crowd, then what's e? Scholars observe how changes in the base affect the graph of a logarithmic function. They then graph the natural logarithm function and learn that all logarithmic functions can be...