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### History of Populations

6-8

The activities at this level focus on studying a series of circle
graphs that report the population of the United States and of selected
states–Massachusetts, New York, and Pennsylvania–in fifty-year
intervals from 1800 to 1950. The students are asked to discuss and
describe the information and to explain why the percent of the total
population changed for the three states. They are asked to write a
justification for their explanation.### Averages and The Phantom Tollbooth

6-8

Students participate in activities in which they focus on connections between mathematics and children's literature. Using *The Phantom Tollbooth*as a literature basis, students explore the concept of averages.

### Football Finances

6-8

In this activity, students analyze pictures of football stands to make estimates related to the attendance at the Super Bowl. The students will realize that estimates must, at times, be made with little background information and that a range of answers might be correct. Students also make estimates about the television audience.### Airport Numbers

6-8

The activities at this level use an airport theme to investigate numbers. Students are encouraged to relate the numbers to familiar situations, for example, to use the dimensions of the classroom to describe an airplane.### Birthdays and the Binary System

6-8

This lesson is a collection of three activities, all of which revolve around patterns and place value in the binary system. Grades 5‑8 students are drawn into the mathematics by the "magical" ability to guess an unknown number and by the use of birthdays, something they find very relevant. This lesson plan is adapted from the September 1997 edition of *Mathematics Teaching in the Middle School*.

### Bouncing Tennis Balls

6-8

Students develop their skills in collecting and recording data using the real-world situation of a bouncing tennis ball. They use the data collected to formulate the relationship between the dependent and independent variable in their experiment.### Building Bridges

6-8

In this lesson, students transition from arithmetic to algebraic thinking by exploring problems that are not limited to single-solution responses. Values organized into tables and graphs are used to move toward symbolic representations. Problem situations involving linear, quadratic, and exponential models are employed. This lesson is based upon the article "Building Bridges to Algebraic Thinking" by Roger Day, which appeared in the February 1997 edition of *Mathematics Teaching in the Middle School*.

### The Game of SKUNK

6-8

In this lesson, students practice decision-making skills leading to a
better understanding of choice versus chance and building the
foundation of mathematical probability. ### Grid and Percent It

6-8

In this lesson, students use a 10 × 10 grid as a model for solving
various types of percent problems. This model offers a means of
representing the given information as well as suggesting different
approaches for finding a solution. This lesson is adapted from "A
Conceptual Model for Solving Percent Problems," which originally
appeared in *Mathematics Teaching in the Middle School*, Vol. 1, No. 1 (April 1994), pp. 20-25.

### Covering the Plane with Rep‑Tiles

6-8

Students discover and explore a special kind of tiling of the plane. Rep‑tiles are geometric figures such that *n*copies can fit together to form a larger, similar figure. Students experiment with various shapes and values of

*n*. Spatial sense is encouraged by the need to visualize and perform transformations with the shapes involved. This lesson was adapted from an article by Linda Fosnaugh and Marvin Harrell, which appeared in the January‑February 1996 edition of

*Mathematics Teaching in the Middle School.*