Teaching Math: A Video Library, 9-12
See how high school teachers use the National Council of Teachers of Mathematics standards and group learning to reach a broad range of students. In this library, teachers demonstrate the fine art of guiding students through reasoning and problem solving. Students comment on the new way of learning, often expressing frustration as well as the sense of accomplishment they feel when working through problems with peers.
1. Introduction — A 10-minute overview of the components of the video library.
2. Alice to the Moon — Alice in Wonderland is the focus of a lesson on algebra and functions for a tenth-grade class.
3. Group Test — Students work in groups to solve test problems on mathematical modeling and functions.
4. Exploring Functions — Students practice process standards such as reasoning and problem-solving as they work in groups to solve two equations using more than one method—such as graphing, algebra or geometry.
5. Bungee Jump — Students work with functions and statistics while they investigate the mathematics of bungee jumping.
6. Staircase Problem — Students are challenged to identify a pattern and then find a rule that determines the pattern.
7. Ferris Wheel — The concept of a ferris wheel is used as students work with functions, algebra, geometry and trigonometry.
8. Properties of Parallelograms — Geometry from a synthetic perspective and mathematical structure are the focus of this program where students create parallelograms. Students are encouraged to use mathematical vocabulary as they explain how their work illustrates the properties of a parallelogram.
9. Finding Proof — Students are introduced to the historical context of proofs and to Greek mathematician Thales, who sought proof for mathematical conclusions.
10. Exploring Congruence — Students focus on geometry from a synthetic perspective and mathematical structure as they draw triangles using specific measurements.
11. Enveloping Functions — Students review graphing in cases when the coefficient of the function is a number and the coefficient is a variable.
12. Calculator-Based Labs — Student groups learn how they will conduct two experiments using the Calculator-Based Laboratory (CBL) system—a temperature probe and a motion detector attached to graphing calculators.
13. Taxicabs — Students share their homework on the probability of taxicabs starting downtown and ending downtown after two fares.
14. Fish Derby — In a linear programming problem, students work in groups using the data they gathered and information on fishes’ breeding and feeding habits to determine optimal fish populations in a fictional pond.
15. Maximizing Profits — A class is divided into small groups to discuss problem-solving strategies, such as finding a verbal model, assigning labels and writing an algebraic model based on maximizing profit on sales of necklaces and bracelets.
16. Conjectures Through Graphing — Students work in groups to solve four problems on derivatives of exponential functions.
17. Problem Solving — Excerpts from 10 classrooms where students are learning mathematics through problem solving. Teachers use multilayered tasks to engage students in making conjectures, constructing meaning and developing strategies.
18. Communication — Excerpts of seven classrooms demonstrate communication about mathematical ideas in a range of formats, including whole-class discussions, small groups, writing and student presentations.
19. Reasoning — Excerpts of seven classrooms show students reasoning about mathematical ideas in whole-class discussions, small group work and class presentations.
20. Connections — In excerpts from eight classrooms, students make connections within mathematics, to other disciplines and to situations in the real world.
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