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Transcript
Wentzville School District Curriculum Development Template Stage 1 – Desired Results Unit 7 - Geometric Figures Unit Title: Geometric Figures Course: Integrated 7 Brief Summary of Unit: Students will use the properties that exist in and between angles and triangles to solve problems. Students will also examine properties of three-dimensional figures to describe the real-world. Finally, students will use the idea of scale factor to make enlargements and reductions of a given model. Textbook Correlation: Glencoe Math Course 2 Chapter 7 (including 7-3 lab - Create Triangles and Problem-Solving Investigation) Time Frame: 3.5 weeks Note: If you can get access to appropriate student technology, plan to include 7-3 lab - Draw Triangles (Geometer’s Sketchpad), 7-4 lab - Investigate Online Maps and Scale Drawings, and 7-4 lab - Scale Drawings (Geometer’s Sketchpad) 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 problem? 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 problem? 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? Why are patterns important to discover, use, and 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 solution. Clear and precise notation and mathematical ● ● ● ● ● 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 problem? 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 problem? ● ● ● 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 Students will be able to independently use their learning to… ● ● Reason and solve problems about two-dimensional and three-dimensional objects by knowing the attributes of geometric figures. Read and analyze maps, scale drawings, blueprints, etc. Meaning Essential Questions How does geometry help us describe realworld objects? Understandings Geometric shapes have specific attributes that are used to describe and solve problems about the shape.. What tools could best be used to draw geometric shapes? Triangles can be classified by angles and/or sides. How can knowing the properties of angles and triangles help us find missing measurements? The relationships between the angles made by intersecting lines can be used to solve problems. Angle relationships can be used to find unknown angle measurement in a figure. Three-dimensional figures’ cross sections are two-dimensional figures. By analyzing cross sections of a threedimensional figure, we can better understand How can angle relationships help us solve for unknown angle measurements? How can angle measurements be determined without using a protractor? What patterns are there in the measures of the angles that are formed when lines intersect? How are supplementary, complementary, vertical, and adjacent angles similar? How are they different? How can you use a scale factor to represent real-world objects on a piece of paper or model? How can you use a map to estimate the distance between two locations? How does drawing the different views of a three-dimensional figure help you have a better understanding of the figure? How does the slope and position of a plane cutting through a three-dimensional figure affect the resulting cross section? the properties of the figure. Scale is the relationship between an actual object and a drawing or model of that object. Scale drawings can be used to find real lengths and areas. Acquisition Key Knowledge Line segment acute triangle adjacent angles base complementary angles cone congruent congruent segments coplanar cross section cylinder diagonal edge equilateral triangle face isosceles triangle obtuse triangle plane polyhedron prism pyramid right triangle scale scale drawing scale factor Key Skills Classify angles, and identify vertical and adjacent angles. Use properties of vertical and adjacent angles to solve for missing angles and/or values. Classify angles, and Identify supplementary and complementary angles. Use properties of complementary and supplementary angles to solve for missing angles and/or values. Draw triangles using given angles or given side lengths. Identify and classify triangles and find missing angles. (Using triangle sum theorem.) Make a model in order to solve problems. Solve problems involving scale drawings (using scale factors, models, drawings, and actual dimensions). Draw three-dimensional figures given the top, side and front views and vice versa. scale model scalene triangle supplementary angles triangle sum theorem vertex vertical angle Identify and draw three-dimensional figures, including naming the specific parts of threedimensional figures. Name the two-dimensional cross-section when a three dimensional figure is sliced with a plane in various directions. Use protractors, rulers, and technology to create specified geometric shapes. Standards Alignment MISSOURI LEARNING STANDARDS Draw, construct, and describe geometrical figures and describe the relationship between them. (7.G.1) 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. (7.G.2) Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. (7.G.3) Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. Solve real-life and mathematical problems involving angle measure, area, surface area, and volume. (7.G.5) Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problems to write and solve simple equations for an unknown angle in a figure. 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. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning. SHOW-ME STANDARDS Goals: 1.1, 1.4, 1.5, 1.6, 1.7, 1.8 2.2, 2.3, 2.7 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, 3.8 4.1, 4.4, 4.5, 4.6 Performance: Math 1, 2, 5