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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....
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The General Multiplication Rule
In the first installment of a 21-part module, scholars build on previous understandings of probability to develop the multiplication rule for independent and dependent events. They use the rule to solve contextual problems.
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Distributions and Their Shapes
What can we find out about the data from the way it is shaped? Looking at displays that are familiar from previous grades, the class forms meaningful conjectures based upon the context of the data. The introductory...
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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...
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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 instructional activity on residuals shows how to use...
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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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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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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 —...
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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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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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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.
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Solving Quadratic Equations by Completing the Square
Many learners find completing the square the preferred approach to solving quadratic equations. Class members combine their skills of using square roots to solve quadratics and completing the square. The resource incorporates a...
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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...
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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...
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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.
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Analyzing Residuals (Part 2)
Learn about patterns in residual plots with an informative math lesson. Two examples make connections between the appearance of a residual plot and whether a linear model is the best model apparent. The problem set and exit ticket...
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Relationships Between Two Numerical Variables
Working in small groups and in pairs, classmates build an understanding of what types of relationships can be used to model individual scatter plots. The nonlinear scatter plots in this lesson plan on relationships between two numerical...
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Graphs of Quadratic Functions
How high is too high for a belly flop? Learners analyze data to model the world record belly flop using a quadratic equation. They create a graph and analyze the key features and apply them to the context of the video.
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The Division of Polynomials
Build a true understanding of division of polynomials. Learners use their knowledge of multiplying polynomials to create an algorithm to divide polynomials. The area model of multiplication becomes the reverse tabular method of division.