In this lesson, students use Cuisenaire Rods to build trains of different lengths and investigate patterns. Students make algebraic connections by writing rules and representing data in tables and graphs.

This lesson offers examples of inverse variation. Students collect data and generate graphs before finding specific equations for inverse variation relationships and examining their graphs.

By using sampling from a large collection of beans, students get a
sense of equivalent fractions, which leads to a better understanding of
proportions. Equivalent fractions are used to develop an understanding
of proportions.

This lesson can be adapted for lower-skilled students by using a
more common fraction, such as 2/3. It can be adapted for upper grades
or higher-skilled students by using ratios that are less instinctual,
such as 12/42 (which reduces to 2/7).

Scaffold the level of difficulty in this lesson by going from a simple
ratio such as 2/3 to more complicated ratios such as 2/7 or 5/9.

In this lesson, students experience an application of proportion that scientists actually use to solve real-life problems. Students learn how to estimate the size of a total population by taking samples and using proportions. The ratio of “tagged” items to the number of items in a sample is the same as the ratio of tagged items to the total population.

The Stomachion is an ancient tangram-type puzzle. Believed by
some to have been created by Archimedes, it consists of 14 pieces cut
from a square. The pieces can be rearranged to form other interesting
shapes. In this lesson, students learn about the history of the Stomachion, use the pieces to create other figures, learn about symmetry and transformations, and investigate the areas of the pieces.

When students play the Factor Trail game, they have to identify the
factors of a number to earn points. Built into this game is cooperative
learning — students check one another's work before points are awarded.
The score sheet used for this game provides a built-in assessment tool
that teachers can use to check their students' understanding.

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.

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.

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?

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.

Students discover the algorithm for solving linear programming problems and gain conceptual understanding by solving a real-world problem and using graphing calculator applications.

In this lesson, students will pretend to travel to the island of Ambergris Caye off the coast of Belize. Students will work together to complete the measurements needed for their scuba diving gear in preparation for the dives, and they will solve elapsed time problems.

In this lesson, students will view several websites and determine what mathematical ideas and concepts are involved in scuba diving. The emphasis is on using technology to help students gain an understanding of how math is used outside of a school setting.

Students will be introduced to modular arithmetic by first examining a five-hour analog clock and its mathematical properties. Then students will investigate patterns and relationships that exist in 12-hour addition and multiplication clock tables.

Given growth charts for the heights of girls and boys, students will use slope to approximate rates of change in the height of boys and girls at different ages. Students will use these approximations to plot graphs of the rate of change of height vs. age for boys and girls.

People come in all different sizes and can be measured in lots of different ways. In this lesson, students can make their own fascinating discoveries and become aware of the concepts of ratio and proportion as they relate to measuring features of their own bodies.

In this lesson, students build a three‑dimensional model from their two‑dimensional blueprint. In addition, they solve problems related to constructing and decorating their clubhouse.

In this lesson, students develop strategies for finding the perimeter and area for rectangles and triangles using geoboards and graph paper. Students learn to appreciate how measurement is a critical component to planning their clubhouse design.

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