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Measuring Variability for Skewed Distributions (Interquartile Range)
Should the standard deviation be used for all distributions? Pupils know that the median is a better description of the center for skewed distributions; therefore, they will need a variability measure about the median for those...
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Interpreting the Standard Deviation
Does standard deviation work for non-symmetrical distributions, and what does it mean? Through the use of examples, high schoolers determine the standard deviation of a variety of distributions and interpret its meaning. Problems require...
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Interpreting Residuals from a Line
What does an animal's gestation period have to do with its longevity? Use residuals to determine the prediction errors based upon a least-square regression line. This second lesson on residuals shows how to use residuals to create a...
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Relationships Between Two Numerical Variables
Is there another way to view whether the data is linear or not? Class members work alone and in pairs to create scatter plots in order to determine whether there is a linear pattern or not. The exit ticket provides a quick way to...
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Ferris Wheels—Tracking the Height of a Passenger Car
Watch your pupils go round and round as they explore periodic behavior. Learners graph the height of a Ferris wheel over time. They repeat the process with Ferris wheels of different diameters.
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The Special Role of Zero in Factoring
Use everything you know about quadratic equations to solve polynomial equations! Learners apply the Zero Product Property to factor and solve polynomial equations. They make a direct connection to methods they have used with quadratic...
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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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The Remainder Theorem
Time to put it all together! Building on the concepts learned in the previous lessons in this series, learners apply the Remainder Theorem to finding zeros of a polynomial function. They graph from a function and write a function from...
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Equivalent Rational Expressions
Rational expressions are just fancy fractions! Pupils apply fractions concepts to rational expressions. They find equivalent expressions by simplifying rational expressions using factoring. They include limits to the domain of the...
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Word Problems Leading to Rational Equations
Show learners how to apply rational equations to the real world. Learners solve problems such as those involving averages and dilution. They write equations to model the situation and then solve them to answer the question — great...
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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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Proving Trigonometric Identities
Young mathematicians first learn the basics of proving trigonometric identities. They then practice this skill on several examples.
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Chance Experiments, Sample Spaces, and Events
Want a leg up on the competition? Show classes how to use mathematics to their advantage when playing games. Learners calculate probabilities to determine a reasonable scoring strategy for a game.
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Evaluating Reports Based on Data from a Sample
Statistics can be manipulated to say what you want them to say. Teach your classes to be wise consumers and sort through the bias in those reports. Young statisticians study different statistical reports and analyze them for misleading...
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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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Rational and Irrational Numbers
Back to the basics: learning how to add numbers. The 17th installment of a 35-part module first reviews addition techniques for rational numbers, such as graphical methods (number line) and numerical methods (standard algorithm). It goes...
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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...
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Bean Counting
Why do I have to do bean counting if I'm not going to become an accountant? The 24th installment of a 35-part module has the class conducting experiments using beans to collect data. Learners use exponential functions to model this...
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Recursive Challenge Problem—The Double and Add 5 Game
Math is all fun and games! Use a game strategy to introduce the concept of sequences and their recursive formulas. The activity emphasizes notation and vocabulary.
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Measuring Variability for Symmetrical Distributions
How do we measure the deviation of data points from the mean? An enriching activity walks your class through the steps to calculate the standard deviation. Guiding questions connect the steps to the context, so the process is not about...
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More on Modeling Relationships with a Line
How do you create a residual plot? Work as a class and in small groups through the activity in order to learn how to build a residual plot. The activity builds upon previous learning on calculating residuals and serves as a precursor to...
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Modeling Relationships with a Line
What linear equation will fit this data, and how close is it? Through discussion and partner work, young mathematicians learn the procedure to determine a regression line in order to make predictions from the data.
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Summarizing Bivariate Categorical Data
How do you summarize data that cannot be averaged? Using an exploratory method, learners complete a two-way frequency table on super powers. The subject matter builds upon 8th grade knowledge of two-way tables.