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## Delving Deeper: What's So Special about 3?

A few years ago, I encountered two different problems in which the number 3 played surprising roles. I found myself wondering, “Why 3? What's so special about 3?” Further investigation led to continuous extensions involving exponents, logarithms, a parametric equation, maxmin problems, and some history of mathematics. As you read, pause to try the problems and play with the applets (the article's title is a big hint!)

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## Formative Assessment at Work in the Classroom

Assessment tools–a rubric, exit slips–inform instruction, clarify expectations, and support learning.

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## Strategically Fostering Dynamic Interactive Environments

Student interviews inform us about their use of technology in multiple representations of linear functions.

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Readers comment on published articles or offer their own ideas.

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## Exploring Function Transformations Using the Common Core

Tying your teaching approach to the Common Core Standard for Geometry and Congruence will help students understand why functions behave as they do.

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## An Unexpected Influence on a Quadratic

Using technology to explore the coefficients of a quadratic equation leads to an unexpected result.

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Students analyze items from the media to answer mathematical questions related to the article. This month's clips involve finding a mathematical error in an advertisement as well as working with ratios and proportions.

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## Galileo, Gauss, and the Green Monster

Using ideas of Galileo and Gauss but avoiding calculus, students create a model that predicts whether a fly ball will clear the famous left-field wall at Fenway Park.

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## Activities for Students: Connecting Probability and Algebra

Algebra, probability, and sequences—all important curricular material—can be connected by a question that will challenge students: What is the probability P that the function f(x) = x 2 + rx + s has real zeros when r and s are real numbers between 0 and 9, inclusive? This problem involves an infinite sample space, making it more interesting for students who have worked on probability problems with only finite sample spaces.

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## Errors in Mathematics Aren't Always Bad

We tell students that mathematical errors should be avoided, but understanding errors is an important tool in developing numerical methods.