Students discover the mathematical constant phi, the golden ratio, through hands-on activities. They measure dimensions of "natural objects"—a star, a nautilus shell and human hand bones—and calculate ratios of the measured values, which are close to phi. Then students learn a basic definition of a mathematical sequence, specifically the Fibonacci sequence. By taking ratios of successive terms of the sequence, they find numbers close to phi. They solve a squares puzzle that creates an approximate Fibonacci spiral. Finally, the instructor demonstrates the rule of the Fibonacci sequence via a LEGO® MINDSTORMS® NXT robot equipped with a pen. The robot (already created as part of the companion activity, The Fibonacci Sequence & Robots) draws a Fibonacci spiral that is similar to the nautilus shape.

Students investigate the difference between qualitative and quantitative measurements and observations. By describing objects both qualitatively and quantitatively, they learn that both types of information are required for complete descriptions. Students discuss the characteristics of many objects, demonstrating how engineers use both qualitative and quantitative information in product design.

How much water do you use everyday? Find out in this engaging investigation, where you compare your water usage with your classmates and other people around the world. An exploration filled with lots of math and science that students are sure to enjoy.

Students use a watt meter to measure energy input into a hot plate or hot pot used to heat water. The theoretical amount of energy required to raise the water by the measure temperature change is calculated and compared to the electrical energy input to calculate efficiency.

Students use LEGO® motors and generators to raise washers a measured height. They compare the work done by the motor-generator systems with the energy inputs to calculate efficiency.

The CyberSquad must construct a clock of sorts in order to keep track of the amount of time they have to rescue Dr. Marbles in this video segment from Cyberchase.

This site is a series of video lectures and interactive exercises for teaching basic mathematics skills to first graders. It has separate addition and subtraction skills reviews numbers up to 10, 20, and 100; a section on telling time and reading clocks as well as course material on measurement and geometry.

This unit provides the framework for conducting an “engineering design field day” that combines 6 hands-on engineering activities into a culminating school (or multi-school) competition. The activities are a mix of design and problem-solving projects inspired by real-world engineering challenges: kite making, sail cars, tall towers, strong towers and a ball and tools obstacle course. The assortment of events engage children who have varied interests and cover a range of disciplines such as aerospace, mechanical and civil engineering. An optional math test—for each of grades 1-6—is provided as an alternative activity to incorporate into the field day event. Of course, the 6 activities in this unit also are suitable to conduct as standalone activities that are unaffiliated with a big event.

This Lesson provides two different activities that require students to measure energy outputs and inputs to determine the efficiency of conversions and simple systems. One of the activities includes Lego motors and accomplishing work. The other investigates energy for heating water. They learn about by products of energy conversions and how to improve upon efficiency. The teacher can choose to use either of these or both of these. The calculations in the water heating experiment are more complicated than in the Lego motor activity. Thus, the heating activity is suitable for older students, only the Lego motor activity suitable for younger students.

Students use simple materials to design an open spectrograph so they can calculate the angle light is bent when it passes through a holographic diffraction grating. A holographic diffraction grating acts like a prism, showing the visual components of light. After finding the desired angles, students use what they have learned to design their own spectrograph enclosure.

Video lesson provides practice with estimating the length of an object when given the length of another object. [2:02]

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.

Harry estimates how long it will take him to get to the front of a long ticket line in this Cyberchase video segment.

Students use their height and the length of the shadow to determine the height of buildings. A great outdoor activity to learn about proportions and ratios.

The CyberSquad tests which broom can travel the furthest in five seconds in this video from Cyberchase.

This task provides students the opportunity to make use of units to find the gas need (N-Q.1). The key point is for them to explain their choices. This task provides an opportunity for students to practice MP2, Reason abstractly and quantitatively, and MP3, Construct viable arguments and critique the reasoning of others.

Using the LEGO® NXT robotics kit, students construct and program robots to illustrate and explore the Fibonacci sequence. Within teams, students are assigned roles: group leader, chassis builder, arm builder, chief programmer, and Fibonacci verifier. By designing a robot that moves based on the Fibonacci sequence of numbers, they can better visualize how quickly the numbers in the sequence grow. To program the robot to move according to these numbers, students break down the sequence into simple algebraic equations so that the computer can understand the Fibonacci sequence.

If you like tackling formulas, then this math challenge is for you. See if you can calculate Helix's BMI (body mass index) and find out if his health is at risk. A one page NCTM Math Challenges for Families activity that engages learners in real-world skills.

Use your algebraic reasoning to solve this math challenge that explores the relationship between quantities and weights. Try this math challenge from the NCTM Math Challenges for Families series. Also, discover how mastering this skill would useful in real life situations.

Take the math challenge. Can you figure out how long you have to wait in line to buy a ticket? An estimation and time measurement challenge from the NCTM Math Challenges for Families collection. Based on real-world themes and application. Hints are included, if you need them.

In this video segment from Cyberchase, through addition and regrouping in base sixty, Matt helps Digit figure out what time his CyberSoufflŰ__ŒŰÖ will be done.