An interactive applet and associated web page that demonstrate the properties of a 45-45-90 isosceles right triangle. The applet shows a right triangle that can be resized by dragging any vertex. As it is dragged, the remaining vertices change so that the triangle's angles remain 45 degrees, 45 degrees and 90 degrees The text on the page points out that the sides of a 45-45-90 triangle are always in the ratio of 1 : 2 : root 2 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.

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: Which of the polygons are right triangles? Choose a measuring tool to help you determine this. These are right trianglesThese are not right triangles 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: Look at each figure. Read each of the descriptions. Place an X in the box if it appears to describe the figure pictured. A. B. C. D. 4 vertices Four si...

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: Each shape below has a line of symmetry. Draw a line of symmetry for each shape. Not every shape has an line of symmetry. Which of the four shapes belo...

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: Letters can be thought of as geometric figures. How many line segments are needed to make the letter A? How many angles are there? Are they acute, obtu...

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: Say what a trapezoid is in your own words. Compare your definition with a partner. Is this parallelogram a trapezoid according to your definition? Expl...

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: Draw at least two examples and two non-examples of each of the quadrilaterals defined below. Parallelogram: A quadrilateral with 2 pairs of parallel si...

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: The students in Ms. Sun's class were drawing geometric figures. First she asked them to draw some points, and then she asked them to draw all the line ...

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: Draw an angle that measures 60 degrees like the one shown here: Draw another angle that measures 25 degrees. It should have the same vertex and share s...

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: Margie bought 3 apples that cost 50 cents each. She paid with a five-dollar bill. How much change did Margie receive?...

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: Mr. Liu asked the students in his fourth grade class to measure their heights. Here are some of the heights they recorded: StudentHeight Sarah 50 inche...

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: Maned wolves are a threatened species that live in South America. People estimate that there are about 24,000 of them living in the wild. The dhole is ...

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: Historians estimate that there were about 7 million people on the earth in 4,000 BCE. Now there are about 7 billion! We write 7 million as 7,000,000. W...

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: The tick marks on the number line are evenly spaced. Label them. Plot the following numbers on the number line: 85 940 2,316 5,090 7,784 Round each num...

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: Find a number greater than 0 and less than 1,000 that: Is closer to 500 than 0, and Is closer to 200 than 500. There are many correct answers to this p...

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: Cynthia is making her famous "Perfect Punch" for a party. After looking through the recipe, Cynthia knows that she needs to mix $4\frac58$ gallons of 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: How does the value of a fraction change if you double its numerator? Explain your answer. How does the value of a fraction change if you double its den...

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 aspects of the task and its potential use.

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: What fraction of the rectangle below is shaded? Laura says that $\frac14$ of the rectangle is shaded. Do you think she is correct? Explain why or why n...

This resource provides students with the opportunity to solve a multi-step contextual word problem with a degree of difficulty appropriate to Grade 4, requiring application of knowledge and skills.