Anoka Hennepin K-12 Curriculum plan

Transcription

1 Anoka Hennepin K-12 Curriculum plan Department: Elementary Math Unit Title: Packages and Polygons (Blue Book, Geo and Measurement) Triangles and Beyond (Blue Book, Geo and Measurement) Everyday Math: Volume 1 Unit 3 Course/Grade Level: Grade 5 Transition Math Number of Lessons: 13 days Unit Summary: This unit focuses on shape, construction and developing students spatial sense. It deepens and formalizes students knowledge of the structure and characteristics of two-and three-dimensional geometric shapes. Students will investigate relationships of angles in polygons and those formed by intersecting lines. DESIRED RESULTS (STAGE 1) K-12 Program Understandings: Spatial Sense; Geometry and Measurement Students will understand that spatial reasoning, geometric and measurement representation is useful in solving problems and understanding our world. MN Standards: Geometry and Measurement 5.3.1: Describe, classify, and draw representations of three- dimensional figures : Determine the area of triangles and quadrilaterals; determine the surface area and volume of rectangular prisms in various contexts : Calculate perimeter, area, surface area & volume of 2D & 3D figures to solve real- world & mathematical problems : Understand and use relationships between angles in geometric figures. MN Benchmarks Addressed Geometry and Measurement Describe and classify three-dimensional figures including cubes, prisms and pyramids by the number of edges, faces or vertices as well as the types of faces Recognize and draw a net for a three-dimensional figure Develop and use formulas to determine the area of triangles, parallelograms and figures that can be decomposed into triangles Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms Develop and use the formulas V = lwh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a rectangular prism by breaking the prism into layers of unit cubes. 1

2 Geometry and Measurement (cont.) Calculate the surface area and volume of prisms and use appropriate units, such as cm 2 and cm 3. Justify the formulas used. Justification may involve decomposition, nets or other models. Calculate the area of quadrilaterals. Quadrilaterals include squares, rectangles, rhombuses, parallelograms, trapezoids and kites. When formulas are used, be able to explain why they are valid Solve problems using the relationships between the angles formed by intersecting lines Determine missing angle measures in a triangle using the fact that the sum of the interior angles of a triangle is 180. Use models of triangles to illustrate this fact Develop and use formulas for the sums of the interior angles of polygons by decomposing them into triangles. Overarching Understandings Students will understand different contexts require specific tools, units of measure and formulas to explain and solve mathematical problems. formulas, sketches and nets can be used to analyze and create regular and irregular two- dimensional and three-dimensional shapes to support mathematical arguments. Topical Understandings Students will understand Three-dimensional figures can be identified through descriptions, classifications, and drawings. Formulas for finding area, volume and surface area can be developed and justified through various informal strategies. There are relationships between angles in geometric figures. There are appropriate units of measurement for various types of mathematical situations. Different aspects of measurement can be used to solve real-world problems. Course Essential Questions To understand, students will need to consider: How do I choose the appropriate tool, unit and formula to solve problems accurately and efficiently? How can I use what I know about two-dimensional and threedimensional objects to solve problems and support my thinking? Topical Essential Questions To understand, students will need to consider: How do I best represent three-dimensional figures? How can justifying formulas help me to understand the characteristics of three-dimensional shapes? How can geometry and measurement help me to solve realworld problems? How are the angles formed by intersecting lines or within polygons related to each other? 2

3 know Students will need to know the following (e.g. facts, concepts, generalizations, rules, theories, principles) there are relationships among angles and how they are formed in polygons. the meaning of length, capacity and weight. there is a relationship between two and three-dimensional figures and how surface area and volume can be determined. To understand, students will need to be able to do Students will be able to do (e.g. skills, procedures, processes) Distinguish between the concepts of surface area and volume; Use two- dimensional representations of three- dimensional figures to visualize and solve problems involving surface area and volume; Use and justify formulas for surface area and volume using nets, decomposition, or other models; Find lengths from given areas or volumes; Estimate and solve simple equations involving formulas by using number sense, properties of operations, and the idea of maintaining equality on both sides of an equation. Use the relationships formed by angles of intersecting lines to solve problems (adjacent, complementary, vertical, supplementary, etc). Develop a formula and find sums of interior angles of polygons by decomposing them into triangles and using the fact the sum of the interior angles of any triangle is 180 o ; 3

4 Essential New Vocabulary: GRADE 5 MCA III Test Spec Vocabulary cube prism cylinder pyramid cone edge face base three-dimensional triangular rectangular formula volume surface area net height intersecting GRADE 6 MCA III Test Spec Vocabulary vertical (angles) adjacent (angles) interior exterior complementary supplementary straight hypotenuse leg diagonal Additional Unit Vocabulary sphere parallel regular polygon irregular polygon alternate interior angles families of parallel lines bar model capacity Common Misunderstandings: Students may have difficulty distinguishing the concepts of perimeter, area, and volume, resulting in the choice of inappropriate units; Students may know area and volume formulas, but are not able to link those formulas to the idea of covering a shape with same-size square units or filling a space with same-size cubic units without gaps or overlaps; Students may have difficulty visualizing the unseen faces of a three-dimensional figure, making it difficult to find the surface area; Students may have difficulty visualizing volume. Students may be confused about why square units are also used to measure area and cubic units to measure volume, especially when the shapes or objects being measured are not squares or cubes; Students may believe that if the volume of a three-dimensional figure is known, then its surface area can be determined. Students are unfamiliar with the symbolic notation used to identify angles and their measures. Students have difficulty distinguishing between angle as movement, as in rotation; angle as a geometric shape, a delineation of space by two intersecting lines; and angle as a measure. Students may use the point of intersection to name all angles formed by a pair of intersecting lines. For example, all angles formed by a pair of lines that intersect at point A may be referred to as angle A. Students confuse the terms supplementary and complementary. Students believe that complementary and supplementary angles must be adjacent. Students believe that all adjacent angles are either complementary or supplementary. 4

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