9-12
In this lesson students will calculate terms of a geometric sequence to determine frequencies of the chromatic scale. They will then compare sine waves to see and hear the trigonometry behind harmonious and dissonant note combinations.
9-12
This lesson introduces students to a common and practical use of modular arithmetic. First the barcode system is examined, specifically UPC and ISBN bar coding. Then, students will discover the applications of modular arithmetic as applied to credit card numbers.
9-12
Students learn about the repeated subtraction and repeated division methods for converting a decimal number
N to a numeral in base
b, provided
b
is an integer other than ‑1, 0, or 1. Students also learn about the
Fibonacci representation, which is a method for representing a numeral
as a sum of Fibonacci numbers. The Fibonacci representation will be
useful in later lessons in this unit when exploring Nim games.
9-12
Static Nim is a one-pile game between two players. In this game, the maximum number of tokens that can be removed on each turn remains constant throughout the game. In this lesson, students will learn to represent the positions as the vertices of a directed graph and the moves as the edges of the graph. Also, they will learn that solving a game means finding a partition of the vertices into two sets such that three important properties are satisfied.
3-5
There are many common objects that come in standard sizes. Students
will verify measurements for some of these objects, use these objects
to determine the size or spacing of other objects, and suggest
additional objects that can be included in the class’ list of
"makeshift measures."
6-8
This lesson allows students to use a variety of units when measuring
the side length and perimeter of squares and the diameter and
circumference of circles. From these measurements, students will
discover the constant ratio of 1:4 for all squares and the ratio of
approximately 1:3.14 for all circles.
9-12
Students are presented with a problem: two bowls are suspended from the ceiling by springs. One bowl is lower than the other. In one bowl, you can only place marbles; in the other bowl, you can only place bingo chips. How many items must be placed in each bowl so that the heights of the bowls are the same?
9-12
In many curricula, the Power of Points theorem is often taught as three separate theorems: the Chord-Chord Power theorem, the Secant-Secant Power theorem, and the Tangent-Secant Power theorem. Using a dynamic geometry applet, students will discover that these three theorems are related applications of the Power of Point theorem. They also use their discoveries to solve numerical problems.
Pre-K-2, 3-5
Students often view linear measurement as a procedure in which a number is simply read off a ruler. The goal of this lesson is to have students gain experience in linear measurement by using a variety of measuring instruments to measure the heights of classmates, to discover the error inherent in measurement, and to search for patterns in data that are represented on a table. In this lesson, students compare results of measuring the same height using different methods, and discuss measurement error. They measure the heights of classmates and the heights of older students in their school, and construct a table of height and age data. The lesson is also designed to serve as a springboard for a second lesson in which students relate measurement to algebra and data analysis concepts.
Pre-K-2, 3-5
A key goal for instruction on algebra at the elementary level is to analyze change, and to understand how change in one variable can relate to change in a second variable. The goal of this lesson is for students to explore how changes in students’ ages relate to changes in their heights.
