In this lesson, students explore the mathematics of architecture by investigating the unusual shapes of some of the rooms in the White House, such as the Blue Room's elliptical shape. They use a graph to plot, draw and determine the equation of an ellipse.
In this lesson, students explore relationships between x-intercepts, factors, and roots of polynomial functions using the graphing calculator. Students also investigate rational functions, identifying the roots and the asymptotes as well as holes in the graphs. Students construct boxes of various dimensions using graph paper, collect height and volume data, and create a scatterplot in order to determine the height of the box with the maximum volume. Students can solve this problem using a graphing calculator or by using their own scatterplots drawn by hand. The use of questioning by the teacher, and the group work of the students are important features of this lesson.
In this lesson, students represent numbers in scientific notation, and use geometry to solve problems related to three-dimensional figures. They will also explore distance and capacity problems about planets in the solar system.