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Curriculum Development Overview th Unit Planning for 7 Grade Mathematics Unit Title 3-D Required Focusing Lens(es) Relationships Visualization Inquiry Questions (Engaging-‐ Debatable): • • Unit Strands Geometry Circumference, area, circle, diameter, π, ratio, radius, slice, three-dimensional figures, two-dimensional figures, scale factor, magnification, zoom level, scale drawings, characteristics, drawing, tools (rulers, protractors, compasses), complementary, supplementary, adjacent, vertical, angles, indirect measurement, additive property, area, volume, decomposition, composition Concepts Length of Unit Standards and Grade Level Expectations Addressed in this Unit MA10-GR.7-S.4-GLE.1 MA10-GR.7-S.4-GLE.2 Why is pi an important number? (MA10-GR.7-S.4-GLE.2-IQ.8) How many two-dimensional shapes can you make by slicing a three-dimensional object? Generalizations My students will Understand that… 5 weeks Mathematicians recognize the special relationship between the diameter and circumference of a circle as the ratio called π, and utilize this relationship to calculate the area, circumference, diameter or radius of a circle. b) in twoSlicing (MA10-GR.7-S.4-GLE.2-EO.a, three-dimensional figures results dimensional figures (MA10-GR.7-S.4-GLE.1EO.a.iv) Mathematicians represent scale factor in terms of magnification or zoom level. (MA10-GR.7-S.4-GLE.1EO.a.i) Mathematicians draw geometric figure using rulers, protractors, and compasses with precision (MA10GR.7- S.4-GLE.1-EO.a.ii, a.iii) Guiding Questions Factual What is the radius? What is the formula for finding the circumference of a circle? What is the formula for finding the area of a circle? What is π? What types of two-dimensional figures can be created when slicing a cone? How does scale factor affect length, perimeter, angle measure, area, and volume? (MA10GR.7-S.4-GLE.1- IQ.3) How is sketching different from drawing? When drawing triangles, when do provided characteristics lead to no triangle, exactly one or more than one possible triangle? Is there a geometric figure for any given set of attributes? (MA10-GR.7-S.4GLE.1-IQ.1) Authors of the Sample: Sarah Beesley (Aspen 1); Teresa Brown (Montrose County RE-1J); Terrell Price th Complete Sample Curriculum – Posted: February (Byers 32J) 7 Grade, 15, 2013 Mathematics Conceptual How are the circumference and diameter of a circle related? How does the derivation of the formula for the area of a circle rely on both the circumference and radius of the circle? How does slicing a 3-D shape parallel to the base differ from slicing the same 3-D shape diagonal to the base? Why is the scale factor for side lengths and perimeters different from the one for areas? Why are rulers, protractors and compasses necessary when drawing shapes? Page 12 of 21 Curriculum Development Overview th Unit Planning for 7 Grade Mathematics How can you indirectly determine the What are complementary measurement of an unknown angle formed by angles? What are two intersecting lines? supplementary angles? What How can geometric relationships among lines and are adjacent angles? What are vertical angles? angles be generalized, described, and How do line relationships affect angle relationships? quantified? What are examples of familiar shapes that are Why area and (MA10volume GR.7-S.4-GLE.2-IQ.1) both have additive The additive property of area and volume provides a means for deriving equations to find the surface helpful to recognize within larger objects when properties of composition and trying to find volumes or surface areas? decomposition? area and volume of two -and three-dimensional What do surface area and volume tell about an objects (MA10- GR.7-S.4-GLE.2-EO.d) How can two shapes have the same volume but object? different surface areas and vice versa? (MA10(MA10-GR.7-S.4-GLE.2-IQ.6) GR.7-S.4-GLE.2- IQ.2, 3) Key Knowledge and Skills: What students will know and be able to do are so closely linked in the concept-‐based discipline of mathematics. Therefore, in the mathematics samples what students should know and do are combined. My students will… Angle relationships such as complementary, supplementary, adjacent and vertical angles provide mathematicians an indirect means to solve for unknown angles in a figure (MA10-GR.7-S.4GLE.2-EO.c) Authors of the Sample: Sarah Beesley (Aspen 1); Teresa Brown (Montrose County RE-1J); Terrell Price th Complete Sample Curriculum – Posted: February (Byers 32J) 7 Grade, 15, 2013 Mathematics Page 13 of 21 Curriculum Development Overview th Unit Planning for 7 Grade Mathematics • Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. (MA10-GR.7-S.4-GLE.1-EO.a.i) • • Find the area and perimeter of geometric figures – rectangles, triangles, circles Compute actual lengths and areas from a scale drawing of geometric figures (square, rectangle, triangle, circle) Reproduce a scale drawing of a geometric figure at a different scale • • • Given three measures of angles or sides for a triangle, determine when the conditions would create a unique triangle, more than one triangle, or no triangle • Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. (MA10-GR.7-S.4-GLE.1-EO.a.iv) • Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids • Know the formulas for the area and circumference of a circle and use them to solve problems (MA10-GR.7-S.4-GLE.2-EO.a) • • Learn the formula for the area and circumference of a circle Use the formulas for the area and circumference of a circle to solve problems • • • Give an informal derivation of the relationship between the circumference and area of a circle. (MA10-GR.7-S.4-GLE.2-EO.b) • Apply properties of angle relationships o Use properties of complementary angles to solve problems o Use properties of supplementary angles to solve problems o Use properties of vertical angles to solve problems Apply properties of parallel lines o Use properties of corresponding angles to solve problems o Use properties of alternate interior angles to solve problems • Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given condition, with focus on triangles from three measures of angles or sides, noting when the conditions determine a unique triangle, more than one triangle, or no triangle. (MA10-GR.7-S.4-GLE.1-EO.a.ii, a.iii) Describe the relationship between the circumference and area of a circle Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. (MA10-GR.7-S.4-GLE.2-EO.c) • Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. (MA10-GR.7-S.4-GLE.2-EO.d) • Calculate the surface area and volume, given formulas for: o cubes, right prisms, pyramids, cylinders, sphere • Solve real-world and mathematical problems involving surface area and volume Critical Language: includes the Academic and Technical vocabulary, semantics, and discourse which are particular to and necessary for accessing a given discipline. EXAMPLE: A student in Language Arts can demonstrate the ability to apply and comprehend critical language through the following statement: “Mark Twain Authors of the Sample: Sarah Beesley (Aspen 1); Teresa Brown (Montrose County RE-1J); Terrell Price th Complete Sample Curriculum – Posted: February (Byers 32J) 7 Grade, 15, 2013 Mathematics Page 14 of 21 exposes the hypocrisy of slavery through the use of satire.” Curriculum Development Overview th Unit Planning for 7 Grade Mathematics Authors of the Sample: Sarah Beesley (Aspen 1); Teresa Brown (Montrose County RE-1J); Terrell Price th Complete Sample Curriculum – Posted: February (Byers 32J) 7 Grade, 15, 2013 Mathematics Page 15 of 21 A student in can demonstrate the ability to apply and comprehend critical language through the following statement(s): Academic Vocabulary: Technical Vocabulary: Curriculum Development Overview th Unit Planning for 7 Grade Mathematics The area of a circle is derived by cutting the circle like a pizza into successively smaller slices and rearranging to form a parallelogram with a base that is half the circumference and a height of the radius. Solve, draw, freehand, ruler, protractor, triangle, area, circle, angles, polygons cubes, slice, three-dimensional figures, two-dimensional figures, scale factor, magnification, zoom level, scale drawings, characteristics, volume, derive, parallelogram Circumference, diameter, π, ratio, radius, drawing, tools (rulers, protractors, compasses), complementary angles, supplementary angles, adjacent angles, vertical angles, indirect measurement, additive property, decomposition, composition, congruent quadrilateral, right prisms Authors of the Sample: Sarah Beesley (Aspen 1); Teresa Brown (Montrose County RE-1J); Terrell Price th Complete Sample Curriculum – Posted: February (Byers 32J) 7 Grade, 15, 2013 Mathematics Page 16 of 21