Resource Type: Instructional Resource -- Best Practice Discipline: Mathematics Ohio Standards Alignment: Grades 10–12 Professional Commentary: In this lesson students calculate terms of a geometric sequence to determine frequencies of the chromatic scale. They then compare sine waves to see and hear the trigonometry behind harmonious and dissonant note combinations. Explanations are fairly detailed, but a background in music is clearly helpful.... Resource Type: Instructional Resource -- Best Practice Discipline: Mathematics Ohio Standards Alignment: Grades 6–8 Professional Commentary: This lesson features two creative twists on the standard lesson of having students measure several circles to discover that the ratio of the circumference to the diameter seems always to be a little more than 3. This lesson starts with squares, so students can first identify a simpler constant ratio (4) of perimeter to length of a side, before moving to the more difficult case of the circle. The second good idea is to measure with a variety of units, so students can more readily see that the ratio of the measurements remains constant, not only across different sizes of figures, but even for the same figure with different measurements.... Resource Type: Instructional Resource -- Best Practice Discipline: Mathematics Ohio Standards Alignment: Grades 8–12 Professional Commentary: This lesson is a nice example of using geometric models to gain a deeper understanding of numerical relationships. Students are challenged to arrange towers of small squares that are the same height as a given large square.... Resource Type: Instructional Resource -- Promising Practice Discipline: Mathematics Ohio Standards Alignment: Grades 8–12 Professional Commentary: Students model successive discounts as a composition of functions and show that, in general, function composition is not commutative. They study the graphs of the discount functions to find the values for which different orders of successive discounts yield equal results. An activity sheet, discussion questions, lesson extensions, suggestions for assessment, and prompts for teacher reflection are included.... 1015 Supreme Court Welcome Resource Type: Instructional Resource -- Best Practice Discipline: Mathematics Ohio Standards Alignment: Grades 5–8 Professional Commentary: This two-lesson unit allows students to investigate the triangular numbers in an interesting, real-world context, the Supreme Court. Beginning with the classic handshake problem, students generate geometric and algebraic representations for the patterns they encounter and conclude with a formula for the nth triangular number.... Resource Type: Instructional Resource -- Promising Practice Discipline: Mathematics Ohio Standards Alignment: Grades 6–12 Professional Commentary: Each student constructs a tetrahedron and describes the linear dimensions, area, and volume using non-traditional units of measure. Four tetrahedra are combined to form a similar tetrahedron whose linear dimensions are twice the original tetrahedron.... 1017 Triangle Classification Resource Type: Instructional Resource -- Promising Practice Discipline: Mathematics Ohio Standards Alignment: Grades 8–12 Professional Commentary: This lesson focuses on a problem: Given a line segment AB in a plane, find all points C in the plane such that triangle ABC is (a) right, (b) acute, (c) obtuse, (d) isosceles, (e) scalene, or (f) equilateral. An applet, activity sheet, discussion questions, a lesson extension, suggestions for assessment, and prompts for teacher reflection are included.... Resource Type: Instructional Resource -- Promising Practice Discipline: Mathematics Ohio Standards Alignment: Grades 6–10 Professional Commentary: When one end of a wooden board is placed on a bathroom scale and the other end is propped on a textbook, students can "walk the plank" and record the weight measurement as their distance from the scale changes. The results are unexpected— the relationship between the weight and distance is linear, and all lines have the same x-intercept.... 1019 Using Cubes and Isometric Drawings: Finding Surface Area and Volume Resource Type: Instructional Resource -- Promising Practice Discipline: Mathematics Ohio Standards Alignment: Grades 6–8 Professional Commentary: Students discover that solids with the same volume can have different surface areas, and solids with the same surface area can have different volumes. Using the isometric drawing tool, students build three-dimensional figures and find the surface area and volume of each figure.... Resource Type: Instructional Resource -- Promising Practice Discipline: Mathematics Ohio Standards Alignment: Grades 6–8 Professional Commentary: Students use probability to examine a few games for fairness. Student groups become game designers who are asked to design a fair game for a toy company.... |