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: During the 2005 Divisional Playoff game between The Denver Broncos and The New England Patriots, Bronco player Champ Bailey intercepted Tom Brady aroun...

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: Quadrilateral $ABCD$ is a trapezoid, $AD = 15$, $AB = 50$, $BC = 20$, and the altitude is 12. What is the area of the trapezoid?...

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: A spider walks on the outside of a box from point A to B to C to D and finally to point E as shown in the picture below. Draw a net of the box and map ...

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: Let $A$ be the area of a triangle with sides of length 25, 25, and 30. Let $B$ be the area of a triangle with sides of length 25, 25, and 40. Find $A/B...

This 8th grade Math parent guide explains the content in straightforward terms so they can support their children’s learning at home and will encourage caretaker engagement with lessons.

Our Teacher Guides are meant to support the use of our online course and unit content. Please use these to accompany the use of our content and for ideas to support struggling learners, those needing extension and for additional resources.

For this lesson, students apply the Pythagorean Theorem to real world and mathematical problems in two dimensions.

This problem is part of a very rich tradition of problems looking to maximize the area enclosed by a shape with fixed perimeter. Only three shapes are considered here because the problem is difficult for more irregular shapes.

For this lesson, students know how to compute the average rate of change in the height of water level when water is poured into a conical container at a constant rate.

For this lesson, students know how to determine the volume of a figure composed of combinations of cylinders, cones, and spheres.

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.

Discussion about how the Pythagorean Theorem works and what it does for us. This lesson was developed by Michael Tinker as part of their completion of the North Carolina Global Educator Digital Badge program. This lesson plan has been vetted at the local and state level for standards alignment, Global Education focus, and content accuracy.

The students will start to use the Pythagorean Theorem to calculate the hypotenuse of a given triangle. This lesson was developed by Michael Tinker as part of their completion of the North Carolina Global Educator Digital Badge program. This lesson plan has been vetted at the local and state level for standards alignment, Global Education focus, and content accuracy.

Students will now be given less in the way of instructions and will have to find what missing measure is being asked for. This lesson was developed by Michael Tinker as part of their completion of the North Carolina Global Educator Digital Badge program. This lesson plan has been vetted at the local and state level for standards alignment, Global Education focus, and content accuracy.

Students will use a variation of the Pythagorean Theorem to find the diagonal measure of a three dimensional figure. This lesson was developed by Michael Tinker as part of their completion of the North Carolina Global Educator Digital Badge program. This lesson plan has been vetted at the local and state level for standards alignment, Global Education focus, and content accuracy.

Students will use what they have learned to answer word problems related to the Pythagorean Theorem. This lesson was developed by Michael Tinker as part of their completion of the North Carolina Global Educator Digital Badge program. This lesson plan has been vetted at the local and state level for standards alignment, Global Education focus, and content accuracy.

This task gives students an opportunity to work with volumes of cylinders, spheres and cones. Notice that the insight required increases as you move across the three glasses, from a simple application of the formula for the volume of a cylinder, to a situation requiring decomposition of the volume into two pieces, to one where a height must be calculated using the Pythagorean theorem.

Students will learn about translations, reflections, and rotations in the plane and, more importantly, how to use them to precisely define the concept of congruence.

Students will learn about dilation and similarity and apply that knowledge to a proof of the Pythagorean Theorem based on the Angle-Angle criterion for similar triangles.