TEA Vertical Alignment 5 th Grade Algebra I. Sample Assessment Question

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1 Geometry in Algebra Title Big Ideas/Enduring Understandings 3 rd & 4 th Six Weeks 14 days Guiding Questions Suggested Time Frame Grade 8 MATH Unit 6 Geometric concepts and formulas are used to solve problems Why are formulas important in math and science? within mathematical relationships such as algebraic reasoning. How can you distinguish between lateral and total surface area from a realworld problem? Both a conceptual understanding of surface area and volume How do the formulas for surface area relate to the nets of the 3-D shapes? and the ability to compute using the appropriate formula is What are some key words that help us determine whether a problem requires necessary to solve mathematical and real-world problems. us to find surface area or volume? The relationship between cones and cylinders of congruent How is the volume of a cone related to the volume of a cylinder if both have base are and height is important to problem solving and congruent bases and congruent heights? What are the implications for the formulas? predicting solutions. Why is a cone not truly half full when it is filled to half of its height? Volume is a concept and a skill that is required from How are the formulas for volume used to solve real life problems that involve manufacturing to agriculture. cylinders, cones, and spheres? If volume is given, what is the process to solve for a missing radius, diameter, or height? Vertical Alignment Expectations Coming soon... *TEKS one level below* TEA Vertical Alignment 5 th Grade Algebra I Sample Assessment Question *TEKS one level above* The resources included here provide teaching examples and/or meaningful learning experiences to address the District Curriculum. In order to address the TEKS to the proper depth and complexity, teachers are encouraged to use resources to the degree that they are congruent with the TEKS and research-based best practices. Teaching using only the suggested resources does not guarantee student mastery of all standards. Teachers must use professional judgment to select among these and/or other resources to teach the district curriculum. Some resources are protected by

2 copyright. A username and password is required to view the copyrighted material. Portions of the District Specificity/Examples are a product of the TEKS Clarifying Documents provided by the Austion Area Math Supervisors. Ongoing TEKS Math Processing Skills To be embedded and used all year long throughout all concept student expectations Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to: (A) apply mathematics to problems arising in everyday life, society, and the workplace; Focus is on application (B) use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution; (C) select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems; (D) communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate; Students should assess which tool to apply rather than trying only one or all (G) display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication (E) create and use representations to organize, record, and communicate mathematical ideas; Students should evaluate the effectiveness of representations to ensure they are communicating mathematical ideas clearly Students are expected to use appropriate mathematical vocabulary and phrasing when communicating ideas (F) analyze mathematical relationships to connect and communicate mathematical ideas; and Students are expected to form conjectures based on patterns or sets of examples and nonexamples Precise mathematical language is expected.

3 Knowledge and Skills with Student Expectations 8.06 Expressions, equations, and relationships. The student applies mathematical process standards to develop mathematical relationships and make connections to geometric formulas. The student is expected to: (A) describe the volume formula V=Bh of a cylinder in terms of its base area and its height. (B) model the relationship between the volume of a cylinder and a cone having both congruent bases and heights and connect that District Specificity/ Examples 8.06(A) Students need to understand that B is the area of the base. The formula would be V=r 2 h. Know the formula does not mean memorization of the formula. To know means to have an understanding of why the formula works and how the formula relates to the measure (volume) and the figure. This understanding should be for all students. Students build on understandings of circles and volume from 7th grade to find the volume of cylinders, finding the area of the base and multiplying by the number of layers (the height). 8.06(B) Use models to determine the formulas for the volume of cylinders, spheres, and Vocabulary Area Base Cone Cylinder Formula cylinder volume (V=Bh) or (V=r 2 h) Formula cone volume (V=1/3 Bh) or (V=1/3 r 2 h) height volume Suggested Resources Resources listed and categorized to indicate suggested uses. Any additional resources must be aligned with the TEKS. McGraw-Hill Chapter 7 Lessons 1-6 Web Resources: Region XI: Livebinder NCTM: Illuminations

4 relationship to the formulas. cones. Use Volume Relationships (manipulative) to establish the relationship of the formula for volume of a cone to the formula for the volume of a cylinder. A cone having a congruent base and height to a cylinder is 1/3 the volume of the cylinder. A cylinder having a congruent base and height to a cone is 3 times the volume of the cone. Students understand that the volume of a cylinder is 3 times the volume of a cone having the same base area and height or that the volume of a cone is 1/3 the volume of a cylinder having the same base area and height Expressions, Equations, and Relationships. The student applies mathematical process standards to use geometry to solve problems. The student is expected to: (A)solve problems involving the volume of cylinders, cones, and spheres. (B) use previous knowledge of surface area to 8.07(A) Cylinder V=Bh or V=r 2 h Cones V=1/3 Bh or V=1/3 r 2 h Spheres V=4/3 r 3 Estimate answers to application problems involving volume. Distinguish between finding lateral and total surface area and volume of solids in problem situations. Use formulas and apply a problem solving model to solve multi-step application area of the base circumference cone cylinder diameter height lateral area length pi radius rectangular prism slant height sphere total surface area triangular prism volume

5 make connections to the formulas for lateral and total surface area and determine solutions for problems involving rectangular prisms, triangular prisms, and cylinders. problems involving volume. Clarify the meaning of B. Students should be familiar with 3-dimensional figures including cylinders, cones, and spheres and identify the attributes of the figure including Base, height, and/or radius. Know the formula does not mean memorization of the formula. To know means to have an understanding of why the formula works and how the formula relates to the measure (volume) and the figure. Misconceptions: Student thinks B and b are interchangeable. B stands for area of the base shape where b is used as a linear measurement. Students calculate r squared as r times 2. (r squared is not the same as the diameter) Students try to calculate the cone formula using a decimal (.3) for ⅓. Students may confuse the formula for the circumference of a circle and the area of a circle, especially when dealing with cylinders and cones. Students may mistakenly use the diameter as the radius. Students have difficulty trying to reduce in the problem (on cones). For example: simplifying before squaring when the radius in a multiple of 3, or trying to calculate the entire formula THEN dividing by three as the last part of the formula when very large numbers are involved. Students may use diameter rather than radius in calculations. 8.07(B) Estimate answers to application problems involving lateral and total surface area. Distinguish between finding lateral and total surface area and volume of solids in problem situations. Use formulas and apply a problem solving model to solve multi-step application problems involving lateral and total surface area. Clarify the meaning of B and P. Misconceptions: Students may not understand that B is actually the area of the base and not the length of the base. Students may not understand that P is actually the perimeter of the base of the shape.

6 Students may confuse the formula for the circumference of a circle and the area of a circle, especially when dealing with cylinders. Students have trouble identifying which shape is the base figure. They assume that what is the bottom figure is the base shape. Must reinforce that on a triangular prism, the triangle is the base; on a cylinder, the circle is the base shape. Students assume they are always finding the total surface area and not just the lateral surface area at times.