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Solving and Graphing Inequalities Joined by “And” or “Or”
Guide your class through the intricacies of solving compound inequalities with a resource that compares solutions of an equation, less than inequality, and greater than inequality. Once pupils understand the differences, 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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Families of Parallel Lines and the Circumference of the Earth
How do you fit a tape measure around the Earth? No need if you know a little geometry! Pupils begin by extending their understanding of the Side Splitter Theorem to a transversal cut by parallel lines. Once they identify the...
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How Do Dilations Map Angles?
The key to understanding is making connections. Scholars explore angle dilations using properties of parallel lines. At completion, pupils prove that angles of a dilation preserve their original measure.
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Modeling a Context from Data (part 2)
Forgive me, I regress. Building upon previous modeling activities, the class examines models using the regression function on a graphing calculator. They use the modeling process to interpret the context and to make predictions...
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Modeling with Exponential Functions
These aren't models made of clay. Young mathematicians model given population data using exponential functions. They consider different models and choose the best one.
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A Surprising Boost from Geometry
Working with imaginary numbers — this is where it gets complex! After exploring the graph of complex numbers, learners simplify them using addition, subtraction, and multiplication.
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Interpreting and Computing Division of a Fraction by a Fraction—More Models II
No more inverting and multiplying to divide fractions. Applying concepts of measurement division from the previous lesson, pupils consider partitive division using fraction bars and number lines. They first convert fractions to like...
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Why Do Banks Pay YOU to Provide Their Services?
How does a bank make money? That is the question at the based of a lesson that explores the methods banks use to calculate interest. Groups compare the linear simple interest pattern with the exponential compound interest pattern.
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Dilations on the Coordinate Plane
Dilations from the origin have a multiplicative effect on the coordinates of a point. Pupils use the method of finding the image of a point on a ray after a dilation to find a short cut. Classmates determine the short cut of being...
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Graphs of Piecewise Linear Functions
Everybody loves video day! Grab your class's attention with this well-designed and engaging resource about graphing. The video introduces a scenario that will be graphed with a piecewise function, then makes a connection to domain...
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Solving a Linear Equation
Solving an equation is the art of creating simpler equivalent equations using properties of equality. Here, classes see that solving an equation is not always as easy as guessing. The lesson presents linear equations that scholars must...
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Why Move Things Around?
Explore rigid motion transformations using transparency paper. Learners examine a series of figures and describe the transformations used to create the series. They then use transparency paper to verify their conclusions.
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Percent
Extend percent understandings to include percents less than one and greater than 100. A great instructional activity has pupils build upon their knowledge of percents from sixth grade. They convert between fractions, decimals, and...
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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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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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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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Ratios II
Pupils continue the study of ratios by creating ratios from a context. The contexts present more than two quantities, and scholars create contexts that match given ratios.
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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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Two Graphing Stories
Can you graph your story? Keep your classes interested by challenging them to graph a scenario and interpret the meaning of an intersection. Be sure they paty attention to the detail of a graph, including intercepts, slope,...
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Points of Concurrencies
You say that perpendicular bisectors intersect at a point? I concur! Learners investigate points of concurrencies, specifically, circumcenters and incenters, by constructing perpendicular and angle bisectors of various triangles.
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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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Definition of Congruence and Some Basic Properties
Build a definition of congruence from an understanding of rigid transformations. The lesson asks pupils to explain congruence through a series of transformations. Properties of congruence emerge as they make comparisons to these...
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From Rates to Ratios
Look at rates from a general perspective. The 17th part of a 29-part series provides problems that help pupils develop more general ratios from given rates. Scholars determine unit rates and ratios that are associated with given rates....