8G-Understand+and+apply+the+Pythagorean+Theorem

8.G.6. Explain a proof of the Pythagorean Theorem and its converse. 8.G.7. Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. 8.G.8. Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. || ===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Anchor Standard/Mathematical Practice(s)**=== 3.  Construct viable arguments and critique the reasoning of others.4. Model with mathematics.6. Attend to precision.7. Look for and make use of structure.G.7 # Make sense of problems and persevere in solving them. 4. Model with mathematics.5. Use appropriate tools strategically.6. Attend to precision.7. Look for and make use of structure.G.8 Model with mathematics.5. Use appropriate tools strategically.6. Attend to precision.7. Look for and make use of structure. || 8.TT.1 Use technology and other resources for assigned tasks. 8.SE.1 Analyze responsible behaviors when using information and technology resources. 8.SI.1 Evaluate information resources based on specified criteria. 8.TT.1 Use technology and other resources for assigned tasks. || ===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Revised Bloom's Level of thinking**=== Understanding Applying Analyzing Evaluating || ===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Learning Target/Task Analysis**=== legs is equal to the square of the hypotenuse in a right triangle. Students also understand that given three side lengths with this relationship forms a right triangle. mathematical problems in two and three dimensions. plane. Students build on work from 6th grade (finding vertical and horizontal distances on the coordinate plane) to determine the lengths of the legs of the right triangle drawn connecting the points. Students understand that the line segment between the two points is the length of the hypotenuse. Students find area and perimeter of two-dimensional figures on the coordinate plane, finding the distance between each segment of the figure. (Limit one diagonal line, such as a right trapezoid or parallelogram).
 * ===**Common Core Standards**===
 * G.6**
 * 1) Reason abstractly and quantitatively.
 * 1) Make sense of problems and persevere in solving them.
 * 2) Reason abstractly and quantitatively.
 * ===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Information Technology Standard**===
 * 8.G.6** Using models, students explain the Pythagorean Theorem, understanding that the sum of the squares of the
 * 8.G.7** Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and
 * 8.G.8** One application of the Pythagorean Theorem is finding the distance between two points on the coordinate

‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**I can...**
I can explain a proof of Pythagorean Theorem. I can demonstrate the converse of Pythagorean Theorem. I can apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems. I can apply the Pythagorean Theorem to find the distance between two points in a coordinate system.
 * 8.G.6**
 * 8.G.7**
 * 8.G.8**

‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Essential Vocabulary**
right triangle, hypotenuse, legs, Pythagorean Theorem, Pythagorean triple

‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Differentiation**
Station work for Pythagorean Theorem: Patty Paper Geometry Set 12, Looking at Lines page 204, Teaching Student-Centered Mathematics page 22**1**

‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Intervention:**
Hands-on activities book pages 227-232

‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Enrichment:**
Navigating through Geometry page 95

===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Instructional Resources**=== Carnegie Learning chapter 6 and lesson 8.2 Mathematics Stations pages 154 and 161
 * Quantile G.7**
 * Quantile G.8**

===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Notes and Additional Information**===
 * Refer to NC DPI unpacked content pages 33-35**
 * Refer to Arizona Academic Content standards pages 24 and 25**