# Wentzville School District Curriculum Development Template Stage 1 Desired Results

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1 Wentzville School District Curriculum Development Template Stage 1 Desired Results Integrated Math 8 Unit Four Geometry Unit Title: Geometry Course: Integrated Math 8 Brief Summary of Unit: In this unit students will apply geometric concepts to the coordinate plane and real world situations. They will create and analyze the properties of compositions of transformations. In addition, they will solve problems related to angles with polygons, parallel lines and transversals. Also, students will apply volume formulas for curved surfaces. Finally, the students will use the Pythagorean Theorem and and its converse to find distances for triangle side lengths both in real world problems and on the coordinate plane. Textbook Correlation: Pearson Algebra 1 chapter 10 section 1 (This unit will require supplementing for topics other than Pythagorean Theorem) (Use 7th Grade Pre-Algebra Book Chapters 11 and 12 include 8th grade standards) Time Frame: 3-4 weeks WSD Overarching Essential Question Students will consider How do I use the language of math (i.e. symbols, words) to make sense of/solve a How does the math I am learning in the classroom relate to the real-world? What does a good problem solver do? What should I do if I get stuck solving a How do I effectively communicate about math with others in verbal form? In written form? How do I explain my thinking to others, in written form? In verbal form? How do I construct an effective (mathematical) argument? How reliable are predictions? WSD Overarching Enduring Understandings Students will understand that Mathematical skills and understandings are used to solve real-world problems. Problem solvers examine and critique arguments of others to determine validity. Mathematical models can be used to interpret and predict the behavior of real world phenomena. Recognizing the predictable patterns in mathematics allows the creation of functional relationships. Varieties of mathematical tools are used to analyze and solve problems and explore concepts. Estimating the answer to a problem helps predict and evaluate the reasonableness of a

2 Why are patterns important to discover, use, and generalize in math? How do I create a mathematical model? How do I decide which is the best mathematical tool to use to solve a How do I effectively represent quantities and relationships through mathematical notation? How accurate do I need to be? When is estimating the best solution to a solution. Clear and precise notation and mathematical vocabulary enables effective communication and comprehension. Level of accuracy is determined based on the context/situation. Using prior knowledge of mathematical ideas can help discover more efficient problem solving strategies. Concrete understandings in math lead to more abstract understanding of math. Transfer Transfer Goal Students will be able to independently use their learning to Describe and analyze the relationships that exist between objects in the real world. Apply the Pythagorean Theorem and its converse in a real world situation (e.g. to make sure you have square corners, etc.) Meaning Essential Questions Students will consider Where are the geometric properties and measurement evident in the world around us? How do we recognize and apply transformations of shapes to solve problems? How are angle relationships used to find missing angle measurements? What are some examples in real life when we can apply the Pythagorean Theorem? How do I recognize transformations in the real world and use them to help me understand shape Understandings Students will understand that There are various relationships among angles formed by parallel lines and transversals There is a relationship between the number of sides a polygon has and the sum of the interior angles. The sum of the angle measures in any polygon can be derived from the Triangle Sum Theorem The resulting image from a sequence of transformations (rotations, reflections, translations) is congruent to the original figure

3 properties? How do I apply problem solving strategies to analyze real world situations involving volume? The resulting image from a sequence of transformations (which includes at least one dilation) is not congruent, but similar, to the original figure The Pythagorean Theorem and its converse can be used in various real world contexts to find the measure of missing lengths Formulas are functional tools used to solve complex real world situations/problems Acquisition Key Knowledge Key Skills *Skills that are italicized do NOT need to be emphasized in Integrated Math 8. These italicized skills will not be assessed in Integrated Math 8. Students will know The characteristics of vertical angles, supplementary and complementary angles, and reflex angles The characteristics of angles formed by parallel lines and transversals. The Triangle Sum Theorem The formulas to find the measures of interior and exterior angles of polygons How to identify the four transformations and a composition of the transformation Dilations cause similar (Use AA Similarity Theorem for Triangles) Reflections, Rotations, and Translations result in congruent. to use the prime symbol to represent the image of the figure. The Pythagorean Theorem and its converse The Pythagorean Theorem can be used on the coordinate grid to find distance. The volume formulas for cones, cylinders, and spheres Students will be able to. Find missing angle measures given intersecting lines Find missing angles when a set of parallel lines is cut by a transversal Determine the sum of the measures of the interior and exterior angles of a polygon. Find missing angle measures in polygons Identify and perform multiple transformations to the same point, line segment, or shape on the coordinate plane Describe the effect of transformations on points, line segments, and two-dimensional Apply the Pythagorean Theorem to twodimensional Apply the Pythagorean Theorem to threedimensional Apply the Pythagorean Theorem to find the distance between two points on a coordinate plane Apply volume formulas to curved surfaces

4 (cones, cylinders, spheres) Apply Pythagorean Theorem and volume formulas to real-world problems Standards Alignment MISSOURI LEARNING STANDARDS 8.G.1 Verify experimentally the properties of rotations, reflections, and translations: a. Lines are taken to lines, and line segments to line segments of the same length. b. Angles are taken to angles of the same measure. c. Parallel lines are taken to parallel lines. 8.G.2 Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent, describe a sequence that exhibits the congruence between them. 8.G.3 Describe the effect of dilations, translations, rotations, and reflections on two-dimensional using coordinates. 8.G.4 Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional, describe a sequence that exhibits the similarity between them. 8.G.5 Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so. 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. 8.G.9 Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.6 Attend to precision.

5 MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning. Goal 1: 1, 4, 5, 6, 7, 8 Goal 2: 2, 3, 7 Goal 3: 1, 2, 3, 4, 5, 6, 7, 8 Goal 4: 1, 4, 5, 6 Mathematics: 1, 2, 4, 5 SHOW-ME STANDARDS

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