Students go on a GPS scavenger hunt. They use GPS receivers to find designated waypoints and report back on what they found. They compute distances between waypoints based on the latitude and longitude, and compare with the distance the receiver finds.

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 July 2013 issue of United Airlines' Hemisphere Magazine the following article appeared: Write down an equation that describes Captain Bowers' me...

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: Below is a picture of $\triangle ABC$: Draw a triangle $DEF$ which is similar (but not congruent) to $\triangle ABC$. How do $\frac{|DE|}{|DF|}$ and $\...

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 rectangle $ABCD$, $|AB|=6$, $|AD|=30$, and $G$ is the midpoint of $\overline{AD}$. Segment $AB$ is extended 2 units beyond $B$ to point $E$, and $F$...

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: Suppose we take a square piece of paper and fold it in half vertically and diagonally, leaving the creases shown below: Next a fold is made joining the...

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: Milong and her friends are at the beach looking out onto the ocean on a clear day and they wonder how far away the horizon is. About how far can Milong...

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: Below is a picture of a right triangle $ABC$ with right angle $C$ along with the point $D$ so that $\overleftrightarrow{CD}$ is perpendicular to $\over...

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 two triangles pictured below $m(\angle A) = m(\angle D)$ and $m(\angle B) = m(\angle E)$: Using a sequence of translations, rotations, reflectio...

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: Suppose $0 \lt a \lt 90$ is the measure of an acute angle. Draw a picture and explain why $\sin{a} = \cos{(90 -a)}$ Are there any angle measures $0 \lt...

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.

In this math activity, learners practice decision-making skills leading to a better understanding of choice versus chance and building the foundation of mathematical probability. SKUNK is a variation on a dice game also known as "pig" or "hold'em." The object of SKUNK is to accumulate points by rolling dice. Points are accumulated by making several "good" rolls in a row but choosing to stop before a "bad" roll comes and wipes out all the points. SKUNK can be played by groups, by the whole class at once, or by individuals.

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.

Presents the anatomy, physiology, biochemistry, biophysics, and bioengineering of the gastrointestinal tract and associated pancreatic, liver, and biliary systems. Emphasis on the molecular and pathophysiological basis of disease where known. Covers gross and microscopic pathology and clinical aspects. Formal lectures given by core faculty, with some guest lectures by local experts. Selected seminars conducted by students with supervision of faculty. Permission of instructor required. (Only HST students may register under HST.120, graded P/D/F.) The most recent knowledge of the anatomy, physiology, biochemistry, biophysics, and bioengineering of the gastrointestinal tract and the associated pancreatic, liver and biliary tract systems is presented and discussed. Gross and microscopic pathology and the clinical aspects of important gastroenterological diseases are then presented, with emphasis on integrating the molecular, cellular and pathophysiological aspects of the disease processes to their related symptoms and signs.

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.

This fill-in-the-blank timeline is a planning tool for teachers to use when figuring out when to begin the steps associated with conducting a two-generation artificial selection experiment using Fast Plants. Teachers preparing for any selection experiment will find this timeline helpful, including those planning for the AP Biology Lab 1 of Big Idea 1: Evolution, Artificial Selection.

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.

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.

This tool allows you to learn about various geometric solids and their properties. You can manipulate each solid, seeing it from every angle. You can also color each shape to explore the number of faces, edges, and vertices. With that information, you are challenged to investigate the following question: For any polyhedron, what is the relationship between the number of faces, vertices, and edges?