This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: In the picture below, points $A$ and $B$ are the centers of two circles and they are collinear with point $C$. Also $D$ and $E$ lie on the two respecti...

In this open-ended, hands-on activity that provides practice in engineering data analysis, students are given gait signature metric (GSM) data for known people types (adults and children). Working in teams, they analyze the data and develop models that they believe represent the data. They test their models against similar, but unknown (to the students) data to see how accurate their models are in predicting adult vs. child human subjects given known GSM data. They manipulate and graph data in Excel® to conduct their analyses.

Student teams use sensors—motion detectors and accelerometers—to collect walking gait data from group members. They import their collected position and acceleration data into Excel® for graphing and analysis to discover the relationships between position, velocity and acceleration in the walking gaits. Then they apply their understanding of slopes of secant lines and Riemann sums to generate and graph additional data. These activities provide practice in the data collection and analysis of systems, similar to the work of real-world engineers.

While students need to be able to write sentences describing ratio relationships, they also need to see and use the appropriate symbolic notation for ratios. If this is used as a teaching problem, the teacher could ask for the sentences as shown, and then segue into teaching the notation. It is a good idea to ask students to write it both ways (as shown in the solution) at some point as well.

In this activity, students study gas laws at a molecular level. They vary the volume of a container at constant temperature to see how pressure changes (Boyle's Law), change the temperature of a container at constant pressure to see how the volume changes with temperature (Charles’s Law), and experiment with heating a gas in a closed container to discover how pressure changes with temperature (Gay Lussac's Law). They also discover the relationship between the number of gas molecules and gas volume (Avogadro's Law). Finally, students use their knowledge of gas laws to model a heated soda can collapsing as it is plunged into ice water.

A gear is a simple machine that is very useful to increase the speed or torque of a wheel. In this activity, students learn about the trade-off between speed and torque when designing gear ratios. The activity setup includes a LEGO(TM) MINDSTORMS(TM) NXT pulley system with two independent gear sets and motors that spin two pulleys. Each pulley has weights attached by string. In a teacher demonstration, the effect of adding increasing amounts of weight to the pulley systems with different gear ratios is observed as the system's ability to lift the weights is tested. Then student teams are challenged to design a gear set that will lift a given load as quickly as possible. They test and refine their designs to find the ideal gear ratio, one that provides enough torque to lift the weight while still achieving the fastest speed possible.

In this lab activity students isolate genomic DNA from their cheek cells on the inside of their mouths. Students then remove the DNA from those cheek cells. It shows the DNA is in every cell in the body and can be extracted easily. Students use their DNA necklace which they proudly wear around school the rest of the day.

Workshop overview for the Data Carpentry genomics curriculum. Data Carpentry’s aim is to teach researchers basic concepts, skills, and tools for working with data so that they can get more done in less time, and with less pain. This workshop teaches data management and analysis for genomics research including: best practices for organization of bioinformatics projects and data, use of command-line utilities, use of command-line tools to analyze sequence quality and perform variant calling, and connecting to and using cloud computing. This workshop is designed to be taught over two full days of instruction. Please note that workshop materials for working with Genomics data in R are in “alpha” development. These lessons are available for review and for informal teaching experiences, but are not yet part of The Carpentries’ official lesson offerings. Interested in teaching these materials? We have an onboarding video and accompanying slides available to prepare Instructors to teach these lessons. After watching this video, please contact team@carpentries.org so that we can record your status as an onboarded Instructor. Instructors who have completed onboarding will be given priority status for teaching at centrally-organized Data Carpentry Genomics workshops.

This task presents students with some creative geometric ways to represent the fraction one half. The goal is both to appeal to students' visual intuition while also providing a hands on activity to decide whether or not two areas are equal.

Students complete a scientific research project including asking a question, developing methods, collecting data, analyzing and interpreting data, and communicating results. The research question begins "What do other students think about _____" and students fill in the blank with a topic that interests them from the class. Although it is geoscience education research, it involves students in the process of science while learning about a topic of their choosing, making it an effective learning tool for all students.

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Teachers and students come to school bringing a wide range of backgrounds, languages, abilities, and temperaments. Get things off to the best start by asking them to respect their differences and make the most of their similarities. By sharing information on their lives and dreams, students and teachers can build community in the classroom that will support literacy instruction throughout the school year.

Students investigate motors and electromagnets as they construct their own simple electric motors using batteries, magnets, paper clips and wire.

Students are introduced to gear transmissions and gear ratios using LEGO MINDSTORMS(TM) NXT robots, gears and software. They discover how gears work and how they can be used to adjust a vehicle's power. Specifically, they learn how to build the transmission part of a vehicle by designing gear trains with different gear ratios. Students quickly recognize that some tasks require vehicle speed while others are more suited for vehicle power. They are introduced to torque, which is a twisting force, and to speed the two traits of all rotating engines, including mobile robots using gears, bicycles and automobiles. Once students learn the principles behind gear ratios, they are put to the test in two simple design activities that illustrate the mechanical advantages of gear ratios. The "robot race" is better suited for a quicker robot while the "robot push" calls for a more powerful robot. A worksheet and post-activity quiz verify that students understand the concepts, including the tradeoff between torque and speed.

Students take part in a hypothetical scenario that challenges them to inform customers at a local restaurant of how their use and disposal of plastics relates/contributes to the Great Pacific garbage patch (GPGP). What students ultimately do is research information on the plastics pollution in the oceans and present that information as a short, eye-catching newsletter suitable to hand out to restaurant customers. This activity focuses on teaching students to conduct their own research on a science-technology related topic and present it in a compelling manner that includes citing source information without plagiarism. By doing this, students gain experience and skills with general online searching as well as word processing and written and visual communication.

This activity is a lab where the students try to make a lightbulb light up using two wires, a battery and a lightbulb.

Spreadsheets Across the Curriculum module/Geology of National Parks course. Students use foundational math to calculate such earthquake-related numbers as fault displacement rate and earthquake recurrence interval associated with the San Andreas Fault at Point Reyes National Seashore.

The first of these word problems is a multiplication problem involving equal-sized groups. The next two reflect the two related division problems, namely, "How many groups?" and "How many in each group?"

The purpose of this task is to show three problems that are set in the same kind of context, but the first is a straightforward multiplication problem while the other two are the corresponding "How many groups?" and "How many in each group?" division problems.