Students learn how different characteristics of shapes—side lengths, perimeter and area—change when the shapes are scaled, either enlarged or reduced. Student pairs conduct a “scaling investigation” to measure and calculate shape dimensions (rectangle, quarter circle, triangle; lengths, perimeters, areas) from a bedroom floorplan provided at three scales. They analyze their data to notice the mathematical relationships that hold true during the scaling process. They see how this can be useful in real-world situations like when engineers design wearable or implantable biosensors. This prepares students for the associated activity in which they use this knowledge to help them reduce or enlarge their drawings as part of the process of designing their own wearables products. Pre/post-activity quizzes, a worksheet and wrap-up concepts handout are provided.

Students learn how to determine map distances and areas using the map scale. They get a feel for how much an area represents on the map in relation to the size they are suggesting for their underground caverns to shelter the Alabraska population.

In this Cyberchase video segment, the CyberSquad learns what happens to the area of a rectangle when the shape enclosed by the perimeter changes.

This interactive exercise focuses on working with the radius of various circles to find the circumference and area as well as challenging you to find the distance a square wheel travels around the track.

This short video and interactive assessment activity is designed to teach third graders an overview of area and perimeter.

Students analyze and begin to design a pyramid. Working in engineering teams, they perform calculations to determine the area of the pyramid base, stone block volumes, and the number of blocks required for their pyramid base. They make a scaled drawing of the pyramid using graph paper.

Students learn about contact stress and its applications in engineering. They are introduced to the concept of heavy loads, such as buildings, elephants, people and traffic, and learn how those heavy loads apply contact stress. Through the analysis of their own footprints, students determine their contact stress.

Students are introduced to the concepts of stress and strain with examples that illustrate the characteristics and importance of these forces in our everyday lives. They explore the factors that affect stress, why engineers need to know about it, and the ways engineers describe the strength of materials. In an associated literacy activity, while learning about the stages of group formation, group dynamics and team member roles, students discover how collective action can alleviate personal feelings of stress and tension.

Playing the role of engineers in collaborations with the marketing and production teams in a chocolate factory, students design a container for a jumbo chocolate bar. The projects constraints mean the container has to be a regular trapezoidal prism. The design has to optimize the material used to construct the container; that is, students have to find the dimensions of the container with the maximum volume possible. After students come up with their design, teams present a final version of the product that includes creative branding and presentation. The problem-solving portion of this project requires students to find a mathematical process to express the multiple variables in the prism’s volume formula as a single variable cubic polynomial function. Students then use technology to determine the value for which this function has a maximum and, with this value, find the prism’s optimal dimensions.

In this activity, students learn how engineers design faucets. Students will learn about water pressure by building a simple system to model faucets and test the relationship between pressure, area and force. This is a great outdoor activity on a warm day.

Conceptualize what area is by calculating the area of a rectangle by using unit squares and the area formula. [3:21]

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This short video and interactive assessment activity is designed to teach third graders about given the perimeter, find the side length and area - squares.

Find a quick, concise explanation of a parallelogram. An example is given and clearly explained.

Find a quick, concise explanation of what a trapezoid is. Examples are given and clearly explained.

Find a quick, concise explanation of area and the formulas for different shapes. An example is given to help you understand how find the area of a shape. The area formulas are listed for different types of shapes.

Take a look at this tutorial to learn how to use the formula for the area of a triangle to find the height if you already know the area and the length of the base. [6:09]

Explains how to calculate the area of a rectangle using the formula where area equals length times width. [2:56]

Take a look at this tutorial to discover how to find the area of a sector of a circle. [4:23]

You can use the formula for the area of a circle to find the radius. This tutorial shows you how to use that formula and the given value for the area to find the radius. [3:28]

Take a look at this tutorial to learn about circles and see the different parts of a circle. [3:54]