Students explore Hooke's law while working in small groups at their lab benches. They collect displacement data for springs with unknown spring constants, k, by adding various masses of known weight. After exploring Hooke's law and answering a series of application questions, students apply their new understanding to explore a tissue of known surface area. Students then use the necessary relationships to depict a cancerous tumor amidst normal tissue by creating a graph in Microsoft Excel.

Measuring the dimensions of nano-circuits requires an expensive, high-resolution microscope with integrated video camera and a computer with sophisticated imaging software, but in this activity, students measure nano-circuits using a typical classroom computer and (the free-to-download) GeoGebra geometry software. Inserting (provided) circuit pictures from a high-resolution microscope as backgrounds in GeoGebra's graphing window, students use the application's tools to measure lengths and widths of circuit elements. To simplify the conversion from the on-screen units to the real circuits' units and the manipulation of the pictures, a GeoGebra measuring interface is provided. Students export their data from GeoGebra to Microsoft® Excel® for graphing and analysis. They test the statistical significance of the difference in circuit dimensions, as well as obtain a correlation between average changes in original vs. printed circuits' widths. This activity and its associated lesson are suitable for use during the last six weeks of the AP Statistics course; see the topics and timing note below for details.

Learn how to approximate the decimal value of square root of 45 without using a calculator. [7:11]

Khan Academy learning modules include a Community space where users can ask questions and seek help from community members. Educators should consult with their Technology administrators to determine the use of Khan Academy learning modules in their classroom. Please review materials from external sites before sharing with students.

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.

Through a video lecture, students discover the visual side of the important applications of mathematics in practical life. More specifically, they will understand the relationship of mathematics and decoration or art.

This short video and interactive assessment activity is designed to teach third graders about creating largest and smallest numbers given digits.

This is an introduction to finding the arc length and area of sectors of circles. Students should have the formulas for Circumference and Area of circles.

The famous story of Archimedes running through the streets of Syracuse (in Sicily during the third century bc) shouting ''Eureka!!!'' (I have found it) reportedly occurred after he solved this problem. The problem combines the ideas of ratio and proportion within the context of density of matter.

Students create four-legged walking robots and measure how far they travel across different types of surfaces. They design and create "shoes" to add to the robots' feet and observe the effect of their modifications on the net distance traveled across the various surface types. This activity illustrates how the specialized locomotive features of different species help them to survive or thrive in their habitat environments. The activity is best as an enrichment tool that follows a lesson that introduces the concept of biological adaptation to students.

Students often wonder how two things so different can end up being the same, in this lesson students will be exploring the relevance and how to determine if fractions are equivalent through a variety of ways.

In this problem, students are given a picture of two triangles that appear to be similar, but whose similarity cannot be proven without further information. Asking students to provide a sequence of similarity transformations that maps one triangle to the other focuses them on the work of standard G-SRT.2, using the definition of similarity in terms of similarity transformations.

Students develop an understanding of areas as how much two-dimensional space a figure takes up, and relate it to their work with multiplication from Units 2 and 3.

Student-made monsters on grid paper are a great way to stimulate comparison problem-solving.

Use area models to show a visual representation of the product of two fractions. This interactive exercise focuses on multiplying fractions and reducing them when possible.

An interactive for investigating what fraction multiplication looks like. Students choose two fractions to multiply, then observe as one fraction bar model is overlaid on the second, showing the common grid area as the product. Students then simplify the fraction if need be.

Video lesson explores how to find the length and width of a rectangular table given the perimeter and area. [4:45]

Khan Academy learning modules include a Community space where users can ask questions and seek help from community members. Educators should consult with their Technology administrators to determine the use of Khan Academy learning modules in their classroom. Please review materials from external sites before sharing with students.

This short video and interactive assessment activity is designed to give fourth graders an overview of composite figures composed of squares and rectangles.

Students determine the area and perimeter of regular polygons and use that information to conduct a beginning investigation of limits.

Find the area and perimeter of quadrilaterals using their coordinates. Students receive immediate feedback and have the opportunity to try questions repeatedly, watch a video or receive hints.

Khan Academy learning modules include a Community space where users can ask questions and seek help from community members. Educators should consult with their Technology administrators to determine the use of Khan Academy learning modules in their classroom. Please review materials from external sites before sharing with students.