"Apples to Atoms" is a collection of activities focused on important concepts underlying nanoscience, developed for middle school science and math students. Each of the four chapters (Size and Scale, Measurement, Microscopy, and Surface Area to Volume Ratios) contains a series of linked activities, and readings which provide context for the concepts developed in the activities. Suggested assessment items are also included. The chapters are inter-related, but are designed so they may be taught independently or in any order.

In this activity, students construct their own rocket-powered boat called an "aqua-thruster." These aqua-thrusters will be made from a film canister and will use carbon dioxide gas produced from a chemical reaction between an antacid tablet and water to propel it. Students observe the effect that surface area of this simulated solid rocket fuel has on thrust.

In this lesson, the students will discover the relationship between an object's mass and the amount of space it takes up (its volume). The students will also learn about the concepts of displacement and density.

Rockets need a lot of thrust to get into space. In this lesson, students learn how rocket thrust is generated with propellant. The two types of propellants are discussed and relation to their use on rockets is investigated. Students learn why engineers need to know the different properties of propellants.

Students find the volume and surface area of a rectangular box (e.g., a cereal box), and then figure out how to convert that box into a new, cubical box having the same volume as the original. As they construct the new, cube-shaped box from the original box material, students discover that the cubical box has less surface area than the original, and thus, a cube is a more efficient way to package things. Students then consider why consumer goods generally aren't packaged in cube-shaped boxes, even though they would require less material to produce and ultimately, less waste to discard. To display their findings, each student designs and constructs a mobile that contains a duplicate of his or her original box, the new cube-shaped box of the same volume, the scraps that are left over from the original box, and pertinent calculations of the volumes and surface areas involved. The activities involved provide valuable experience in problem solving with spatial-visual relationships.

To display the results from the previous activity, each student designs and constructs a mobile that contains a duplicate of his or her original box, the new cube-shaped box of the same volume, the scraps that are left over from the original box, and pertinent calculations of the volumes and surface areas involved.

CK-12's Geometry delivers a full course of study in the mathematics of shape and space for the high school student, relating the ancient logic and modern applications of measurement and description to its essential elements, processes of reasoning and proof, parallel and perpendicular lines, congruence and similarity, relationships within triangles and among quadrilaterals, trigonometry of right triangles, circles, perimeter, area, surface area, volume, and geometric transformations.

This digital textbook was reviewed for its alignment with California content standards

In Counting on Art, students will explore the paintings of Horace Pippin and Wayne Thiebaud and the mobiles of Alexander Calder to discover and practice math and visual art concepts.In Pippin's Story, young children (grades K–3) focus on a painting by African American artist Horace Pippin. They will learn how to "read" the clues in a painting and write a story about the work. Students will also solve counting and time problems and create their own "secret number" painting.Calder's Balancing Acts focuses on math in the mobiles of Alexander Calder. Elementary- level students (grades 2–5) will learn about the artist and write equations based on Calder's art. Upper-level students (grades 6–8) will discover patterns and the Fibonacci sequence. Both levels will make their own math mobiles.Cake Math, based on a painting by California artist Wayne Thiebaud, features math challenges of many varieties. Elementary-level students (grades 2–5) will practice fractions, addition, subtraction, word problems, sorting, and classifying. Intermediate level students (grades 6–8) will find volume and surface area in Thiebaud's cakes.

In this activity, students investigate the simulated use of solid rocket fuel by using an antacid tablet. Students observe the effect that surface area and temperature has on chemical reactions. Also, students compare the reaction time using two different reactants: water and vinegar. Finally, students report their results using a bar graph.

This geometry lesson shows how to find the volume and surface area of a cylinder. [Geometry playlist: Lesson 20 of 31]

This lesson explores the drag force on airplanes. The students will be introduced to the concept of conservation of energy and how it relates to drag. Students will explore the relationship between drag and the shape, speed and size of an object.

In NASA CONNECT PSA: The Astronaut's Helper, students will be introduced to the Personal Satellite Assistant (PSA), a small, spherical robot that assists astronauts with their chores on space-based vehicles. Students will learn about different types of robots and the mechanical systems on the PSA that must work together for the PSA to function. In the web activity, students interact with a simulation of the PSA and learn how forces affect motion in a low-friction, microgravity environment. Students learn that scientists need to shrink the Paean they engage in a hands-on activity where they find the maximum surface area of a computer component that must fit into a smaller PSA. Grades 6-8.

Students find the volume and surface area of a rectangular box (e.g., a cereal box), and then figure out how to convert that box into a new, cubical box having the same volume as the original. As they construct the new, cube-shaped box from the original box material, students discover that the cubical box has less surface area than the original, and thus, a cube is a more efficient way to package things.