This Demonstration illustrates the concept of rotating a 2D polygon. The rotation …

This Demonstration illustrates the concept of rotating a 2D polygon. The rotation matrix is displayed for the current angle. The default polygon is a square that you can modify.

This unit on thermal energy transfer begins with students testing whether a …

This unit on thermal energy transfer begins with students testing whether a new plastic cup sold by a store keeps a drink colder for longer compared to the regular plastic cup that comes free with the drink. Students find that the drink in the regular cup warms up more than the drink in the special cup. This prompts students to identify features of the cups that are different, such as the lid, walls, and hole for the straw, that might explain why one drink warms up more than the other.

Students investigate the different cup features they conjecture are important to explaining the phenomenon, starting with the lid. They model how matter can enter or exit the cup via evaporation However, they find that in a completely closed system, the liquid inside the cup still changes temperature. This motivates the need to trace the transfer of energy into the drink as it warms up. Through a series of lab investigations and simulations, students find that there are two ways to transfer energy into the drink: (1) the absorption of light and (2) thermal energy from the warmer air around the drink. They are then challenged to design their own drink container that can perform as well as the store-bought container, following a set of design criteria and constraints.

In this unit, students develop ideas related to how sounds are produced, …

In this unit, students develop ideas related to how sounds are produced, how they travel through media, and how they affect objects at a distance. Their investigations are motivated by trying to account for a perplexing anchoring phenomenon — a truck is playing loud music in a parking lot and the windows of a building across the parking lot visibly shake in response to the music.

They make observations of sound sources to revisit the K–5 idea that objects vibrate when they make sounds. They figure out that patterns of differences in those vibrations are tied to differences in characteristics of the sounds being made. They gather data on how objects vibrate when making different sounds to characterize how a vibrating object’s motion is tied to the loudness and pitch of the sounds they make. Students also conduct experiments to support the idea that sound needs matter to travel through, and they will use models and simulations to explain how sound travels through matter at the particle level.

Esta animacion muestra cómo se absorben los herbicidas por las raíces, e …

Esta animacion muestra cómo se absorben los herbicidas por las raíces, e ilustra la ruta que sigue el herbicida a través de la raíz, para llegar al sistema vascular de la planta.

How do strong and weak acids differ? Use lab tools on your …

How do strong and weak acids differ? Use lab tools on your computer to find out! Dip the paper or the probe into solution to measure the pH, or put in the electrodes to measure the conductivity. Then see how concentration and strength affect pH. Can a weak acid solution have the same pH as a strong acid solution?

An interactive applet and associated web page that show the concept of …

An interactive applet and associated web page that show the concept of adjacent angles (two angles that share a common leg). The applet shows three line segments with a common endpoint. The user can move the center one and see that the angles on both sides (the adjacent angles) of it are affected. Applet can be enlarged to full screen size for use with a classroom projector. After use in the classroom, students can access it again from any web browser at home or in the library with no login required. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

An interactive applet and associated web page that demonstrate the alternate exterior …

An interactive applet and associated web page that demonstrate the alternate exterior angles that are formed where a transversal crosses two lines. The applets shows the two possible pairs of angles alternating when in animation mode. By dragging the three lines, it can be seen that the angles are congruent only when the lines are parallel. When not in animated mode, there is a button that alternates the two pairs of angles. The text on the page discusses the properties of the angle pairs both in the parallel and non-parallel cases. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

An interactive applet and associated web page that demonstrate the alternate interior …

An interactive applet and associated web page that demonstrate the alternate interior angles that are formed where a transversal crosses two lines. The applets shows the two possible pairs of angles alternating when in animation mode. By dragging the three lines, it can be seen that the angles are congruent only when the lines are parallel. When not in animated mode, there is a button that alternates the two pairs of angles. The text on the page discusses the properties of the angle pairs both in the parallel and non-parallel cases. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

Representatives from 10 sovereign Native American nations in Michigan, five State of …

Representatives from 10 sovereign Native American nations in Michigan, five State of Michigan agencies, two universities, and three private organizations collaborated to develop two short curriculum units, one for 3rd grade and one for 5th grade. Each grade level unit includes five lesson plans and support materials for teachers using information from two archaeological sites provided by MDOT and cultural, historical, environmental, and indigenous knowledge provided and vetted by Michigan Native American tribal partners participating in the project. The lesson plans use the Inquiry Arc of the College, Career, and Civic Life (C3) Framework and focus on specific Michigan Social Studies Standards. The lesson plans also provide links to Michigan English Language Arts (ELA) literacy standards, as well as science and math applications.

Create your own shapes using colorful blocks and explore the relationship between …

Create your own shapes using colorful blocks and explore the relationship between perimeter and area. Compare the area and perimeter of two shapes side-by-side. Challenge yourself in the game screen to build shapes or find the area of funky figures. Try to collect lots of stars!

An interactive applet and associated web page that demonstrate the area of …

An interactive applet and associated web page that demonstrate the area of a circle. A circle is shown with a point on the circumference that can be dragged to resize the circle. As the circle is resized, the radius and the area computation is shown changing in real time. The radius and formula can be hidden for class discussion. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

An interactive applet and associated web page that deals with the area …

An interactive applet and associated web page that deals with the area of a kite, (a quadrilateral with two distinct pairs of equal adjacent sides). The applet shows a kite and the user can reshape it by dragging any vertex. The other vertices move automatically to ensure it always remains a kite. As the vertices are dragged, the area is continuously recalculated and displayed. The kite is filled with a grid of unit squares so that the students can estimate the area. The on-screen calculation can be hidden until the estimates are done. The web page lists two different ways to compute the area of a kite. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

A web page and interactive applet showing the ways to calculate the …

A web page and interactive applet showing the ways to calculate the area of a parallelogram. The user can drag the vertices of the parallelogram and the other points change automatically to ensure it remains a parallelogram. A grid inside the shape allows students to estimate the area visually, then check against the actual computed area, which is continuously recomputed and displayed. The text on the page gives three different ways to calculate the area with a formula for each. The applet uses one of the methods to compute the area in real time, so it changes as the rhombus is reshaped with the mouse. A companion page is http://www.mathopenref.com/parallelogram.html showing the definition and properties of a parallelogram Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

A web page and interactive applet showing the ways to calculate the …

A web page and interactive applet showing the ways to calculate the area of a trapezoid. The user can drag the vertices of the trapezoid and the other points change automatically to ensure it remains a trapezoid. A grid inside the shape allows students to estimate the area visually, then check against the actual computed area. The text on the page gives three different ways to calculate the area with a formula for each. The applet uses one of the methods to compute the area in real time, so it changes as the trapezoid is reshaped with the mouse. A companion page is http://www.mathopenref.com/trapezoid.html showing the definition and properties of a trapezoid. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

An interactive applet and associated web page that explain the area of …

An interactive applet and associated web page that explain the area of a triangle. The applet shows a triangle that can be reshaped by dragging any vertex. As it changes, the area is continually recalculated using the 'half base times height' method. The triangle has a fixed square grid in its interior that can be used to visually estimate the area for later correlation with the calculated value. The calculation can be hidden while estimation is in progress. The text page has links to a similar page that uses Heron's Formula to compute the area. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

Remember your multiplication tables? ... me neither. Brush up on your multiplication, …

Remember your multiplication tables? ... me neither. Brush up on your multiplication, division, and factoring skills with this exciting game. No calculators allowed! The students will be given mutiplication and division problems which they must answer. They also have the option of being given a number then stating the factors of how that number was attained using either multiplication or division.

The simulation shows a ballistics cart. If the cart is at rest …

The simulation shows a ballistics cart. If the cart is at rest on a horizontal surface, it will shoot a ball straight up in the air, and catch the ball again. What if, as in this simulation, the cart is traveling at a constant velocity horizontally, instead? Will the ball land ahead of the cart, in the cart, or behind the cart? Note that the cart fires the ball straight up, with respect to the cart, when the middle of the cart passes the small vertical trigger on the track. Use the buttons to select the different modes (whether there is a tunnel or not, and whether to show the velocity vectors).

Experiment with a helium balloon, a hot air balloon, or a rigid …

Experiment with a helium balloon, a hot air balloon, or a rigid sphere filled with different gases. Discover what makes some balloons float and others sink.

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