4th 6 Weeks January 3 – March 1 38 days TEKS Reporting Category Days Instructional Scope Instruction Resources Assessment 8.7C Use pictures or models to demonstrate the Pythagorean Theorem. Supporting Standard 8.14C Select or develop an appropriate problem-solving strategy from a variety of different types, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem. Process Standard 8.15A Communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models. Process Standard 8.16A Make conjectures from patterns or sets of examples and non-examples. Process Standard 3 3 Use concrete models to develop the Pythagorean Theorem. Cut apart squares to show the relationship between the length of the sides of the squares and the triangle that is formed. Emphasize that the hypotenuse is always the longest side and its relationship to the placement of the right angle. Emphasize that Pythagorean Theorem is only true of right triangles. Use letters other than a, b, and c. Identify models of examples and of the Pythagorean Theorem. Make conjectures from patterns or sets of examples and non-examples. TAKS Mathematics Preparation Grade 8 (Region 4) “Pythagorean Theorem Lesson.” TAKS Mathematics Preparation Grade 8 (Region 4) “Objective 3 Selected Response Questions,” 6.
8.14B Use a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness. Process Standard 8.15A Communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models. Process Standard 8.16B Validate his/her conclusions using mathematical properties and relationships. Process Standard Include problems involving finding a leg when the length of a leg and the hypotenuse of the triangle. Example: How much farther does Karva walk if she walks from her house to school and then to the bookstore than if she walks from her house to the bookstore? Justify your answer. (about 0.8 mile) Evaluate solutions for reasonableness. 8.4A Generate a different representation of data given another representation of data (such as a table, graph, equation, or verbal description). Readiness Standard 8.6B Graph dilations, reflections, and translations on a coordinate plane. Supporting Standard 8.7D 2,3 4 Graph translations and reflections. Predict placement before graphing. Determine how an ordered pair changes under a specific translation or reflection (under a given rule). Example: If point A (–3, 2) is translated under the rule (x – 5, y), what will be the new coordinates of point A? Justify your answer. (–8, 2) TAKS Mathematics Preparation Grade 8 (Region 4) “Coordinate Translation Lesson.” TAKS Mathematics Preparation Grade 8 (Region 4) “Coordinate Reflection Lesson.” Rethinking Middle School Mathematics: Geometry Across the TEKS (TEXTEAMS) “Translations.” TAKS Mathematics Preparation Grade 8 (Region 4) “Objective 3 Selected Response Questions,” 4.
Locate and name points on a coordinate plane using ordered pairs of rational numbers. Supporting Standard 8.14D Select tools such as real objects, manipulatives, paper/pencil, and technology or techniques such as mental math, estimation, and number sense to solve problems. Process Standard 8.16A Make conjectures from patterns or sets of examples and nonexamples. Process Standard Example: If point B (5, –7) is reflected across the what will be the coordinates of ? (–5, –7) Determine the relationship (or rule) between given ordered pairs of the original image and the reflected or translated image. Example: What rule describes the translation of to ? Justify your answer. (x + 8, y – 5) Evaluate reasonableness of solutions. Rethinking Middle School Mathematics: Geometry Across the TEKS (TEXTEAMS) “Reflections.” 8.6B Graph dilations, reflections, and translations on a coordinate plane. Supporting Standard 8.7D 3 5 Graph the dilations on a coordinate plane (include rational numbers). Graph dilations (enlargements and reductions) on a coordinate plane. TAKS Mathematics Preparation Grade 8 (Region 4) “Coordinate Dilation Lesson.” TAKS Mathematics Preparation Grade 8 (Region 4) “Objective 3 Selected Response Questions,” 1, 2, 3.
Locate and name points on a coordinate plane using ordered pairs of rational numbers. Supporting Standard 8.14A Identify and apply mathematics to everyday experiences, to activities in and outside of school, with other disciplines, and with other mathematical topics. Process Standard 8.14B Use a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness. Process Standard 8.15A Communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models. Process Standard Determine the factor of a dilation given the original figure and the dilated figure on a coordinate plane. Example: Triangle ABC was dilated to form triangle DEF. What number represents the scale factor used to change triangle ABC into triangle DEF? Justify your answer. (The scale factor is 2.) Determine the relationship (rule) between ordered pairs of the original image and the dilated image. (Students should be able to explain the presence of the scale factor in the rule .) Evaluate reasonableness. 8.7A Draw three-dimensional figures from different perspectives. Supporting Standard 8.14D Select tools such as real objects, manipulatives, 3 2 Draw three-dimensional figures from different perspectives. Draw top, side, and view of a given three-dimensional figure. Sketch a figure when given the top, side, and front view. TAKS Mathematics Preparation Grade 8 (Region 4) “What’s Your View on This? Lesson.” TAKS Mathematics Preparation 8 (Region 4) “Objective 3 Selected Response Questions,” 5.
Validate his/her conclusions using mathematical properties and relationships Process Standard 8.1B Select and use appropriate forms of rational numbers to solve real-life problems including those involving proportional relationships. Supporting Standard 8.8B Connect models of prisms, cylinders, pyramids, spheres, and cones to formulas for volume of these objects. Supporting Standard 8.14A Identify and mathematics to everyday experiences, to activities in and outside of school, with other disciplines, and with other mathematical topics. Process Standard 1,4 2 Find volume of three-dimensional figures. Use concrete models and nets models) to find volume. Connect models to formulas. Include prisms and pyramids. Include cylinders and cones. Include spheres. Include problems in which students must measure the dimensions before finding the volume of the figure. Evaluate reasonableness of solutions. Making Connections with Measurement Grade 8 TAKS (Region 4) “Volume: Pyramids and Cones.” Making Connections with Measurement Grade 8 TAKS (Region 4) “Volume: Spheres.” 8.1B Select and use appropriate forms of rational numbers to solve real-life problems including those involving proportional relationships. Supporting Standard 8.7B Use geometric concepts and properties to solve problems 1,3,4 2 Solve application problems involving surface area and volume. Estimate solutions. Use formulas to find surface area and volume. Include lateral and total surface area. Include problems in fields such as art and architecture. TAKS Mathematics Preparation Grade 8 (Region 4) “Surface Area and Volume Lesson.” TAKS Mathematics Preparation Grade 8 (Region 4), “Objective 4 Selected Response Questions,” 3, 4, “Objective 6 Selected Response Questions,” 3, 10.
(such as a table, graph, equation, or verbal description). Readiness Standard 8.10A Describe the resulting effects on perimeter and area when dimensions of a shape are changed proportionally. Supporting Standard 8.14A Identify and apply everyday experiences, to activities in and outside of school, with other disciplines, and with other mathematical topics. Processing Standard 8.14B Use a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness. Processing Standard 8.15A Communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models. Processing Standard 8.16A Example: Juan drew Rectangle A and Samantha drew Rectangle B. What is the comparison between the lengths of the sides in Rectangle A and Rectangle B? (The width of B is twice the width of A.) How does the perimeter of Rectangle B compare to the perimeter of Rectangle A? (The perimeter of B is 2 more than A.) Change all dimensions and observe change in perimeter. Example: Toby drew Rectangle C, and Geneva drew Rectangle D. What is the comparison between the lengths of the sides in Rectangle C and Rectangle D? (The width and length of D are twice the width and length of C.) How does the perimeter of Rectangle D compare to the perimeter of Rectangle C? (The perimeter of D is the perimeter of C.)
Processing Standard 8.15A Communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models. Processing Standard 8.16A Make conjectures from patterns or sets of examples and nonexamples. Processing Standard Change all the dimensions, and observe the change in the volume of the solid. Organize the data in a table, and look for patterns. Connect an algebraic expression to the resulting change in the volume. Find one of the dimensions of a solid when given the volume and the proportional change. Evaluate reasonableness of solutions.