Rigorous Curriculum Design Authentic Performance Tasks

Transcription

1 1 of 14 Rigorous Curriculum Design Authentic Performance Tasks Subject Grade/Course Unit of Study Duration of Unit Math 3 rd Grade Unit 6 Geometry 3 Weeks Engaging Scenario Directions: Incorporate the five elements of effective scenarios: current situation; student challenge; student role; intended audience; product or performance. The Rosedale School District has been hired to create some new geometry games. Third grade has been chosen to do this job. Operations and Algebraic Thinking Priority Standards 3.OA.8 SOLVE two step words problem USING the four operations. REPRESENT these problems USING equations with a letter standing for the unknown quantity. ASSESS the reasonableness of the answers USING mental computation and estimation strategies including rounding. Measurement and Data 3.MD.7.d Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems. 3.MD.8 Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. Geometry 3.G.1 Understand that shapes in different categories (e.g. rhombuses, rectangles, and others) may share attributes (e.g. having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.

2 2 of 14 Supporting Standards Measurement and Data 3.MD.5 Recognize area as an attribute of plane figures and understand concepts of area measurement. 3.MD.5.a A square with side length 1 unit, called a unit square, is said to have one square unit of area, and can be used to measure area. 3.MD.5.b A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units. 3.MD.6 Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). 3.MD.7 Relate area to the operations of multiplication and addition. 3.MD.7.a Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths. 3.MD.7.b Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning. 3.MD.7.c Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b+ c is the sum of a b and a c. Use area models to represent the distributive property in mathematical reasoning. Geometry 3.G.2 Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape. Writing Social Studies Interdisciplinary Connections

3 3 of 14 Unwrapped Concepts (students need to know) SOLVE 3.OA.8 USING 3.OA.8 REPRESENT 3.OA.8 USING 3.OA.8 ASSESS 3.OA.8 USING 3.OA.8 Recognize 3.MD.7.d Find 3.MD.7.d Decomposing 3.MD.7.d Adding 3.MD.7.d Applying 3.MD.7.d Solve 3.MD.7.d Solve 3.MD.8 Find(ing) 3.MD.8 Find(ing) 3.MD.8 Exhibit(ing) 3.MD.8 Understand 3.G.1 Unwrapped Skills (students need to be able to do) two step word problems 3.OA.8 the four operations 3.OA.8 problems 3.OA.8 equations with a letter standing for the unknown quantity 3.OA.8 the reasonableness of answers mental computation and estimation strategies including rounding 3.OA.8 Area as additive 3.MD.7.d Areas of rectilinear figures 3.MD.7.d Non-overlapping rectangles 3.MD.7.d Areas of the non-overlapping parts 3.MD.7.d Technique 3.MD.7.d Real world problems 3.MD.7.d Real world and mathematical problems 3.MD.8 Involving perimeters of polygons Perimeter given side length Unknown side length Rectangles With same perimeter and different area With same area and different perimeter 3.MD.8 Shapes in different categories may share attributes Rhombuses, rectangles, etc Having four sides, etc DOK Levels

4 4 of 14 Understand 3.G.1 Recognize 3.G.1 Draw 3.G.1 Shared attributes can define a larger category Quadrilaterals Rhombuses, rectangles, and squares as examples of quadrilaterals Quadrilaterals that do not belong to any of these subcategories3.g.1 Unit Vocabulary Terms Unwrapped Priority Standards Concepts Supporting Standards Concepts and Other Unit-Specific Terms Area Perimeter Polygon Quadrilateral Rhombus Trapezoid Rectangle Square Parallelogram Addition Subtraction Multiplication Division Performance Task Synopses Task 1: Students will draw shapes and identify all attributes of shapes. They can also play a Guess My Shape game. (This game is optional) Task 2: Students will answer and write polygon riddles. Task 3: Students will determine the perimeter and area of different tablets.

5 5 of 14 Performance Task # 1 In Detail S: Which standard(s) (priority/supporting) will the task address? 3.G.1 Understand that shapes in different categories (e.g. rhombuses, rectangles, and others) may share attributes (e.g. having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. Q: What essential Question(s) and corresponding Big Idea(s) will this task target? How do we classify geometric shapes?3.g.1 Shapes are classified by their attributes.3.g.1 U: Which unwrapped specific concepts and skills will this task target? Understand shapes in different categories may share attributes Understand shared attributes can define a larger category Recognize rhombuses, rectangles, and squares as examples of quadrilaterals A: How will the students apply the concepts and skills? What will they do and/or produce? Students will be able to identify polygons that could be classified as quadrilaterals and nonquadrilaterals. R: What resources, instruction, and information will students need in order to complete the task? Students will need instruction on polygons and their attributes. E: What evidence of learning will I look for to show that I know all of my students have conceptually learned the concepts and skills the standard(s)? 1. Students meet proficient level or higher on Task 1 rubric 2. Students respond to Essential Question with Big Idea in written or oral format. D: How can I differentiate the application and/or evidence to meet the varying needs of my students? Students may work in small groups if necessary. Task 1 Full Description: Students will draw and describe all attributes of the following shapes: rectangle, square, rhombus, triangle, trapezoid, quadrilateral, pentagon, hexagon, and circle.

6 6 of 14 Performance Task # 1 Scoring Guide Proficient Meets _8_ of the Proficient criteria Draw and list attributes of the following: Rectangle Square Rhombus Triangle Trapezoid Quadrilateral Pentagon Hexagon Circle Progressing Meets _5-7_ of the Proficient criteria Task to be repeated after re-teaching Beginning Meets _0-4_ of the Proficient criteria Task to be repeated after re-teaching Teacher s Evaluation: Comments regarding student s performance: Interdisciplinary Connections and Related Priority Standards Specific to Task #1 21 st Century Learning Skills Specific to Task #1 Check all those that apply for each task: Teamwork and Collaboration Initiative and Leadership Curiosity and Imagination Innovation and Creativity Critical thinking and Problem Solving Flexibility and Adaptability Effective Oral and Written Communication Accessing and Analyzing Information Other

7 7 of 14 Performance Task # 2 In Detail S: Which standard(s) (priority/supporting) will the task address? 3.G.1 Understand that shapes in different categories (e.g. rhombuses, rectangles, and others) may share attributes (e.g. having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. Q: What essential Question(s) and corresponding Big Idea(s) will this task target? How do we classify geometric shapes? 3.G.1 Shapes are classified by their attributes. U: Which unwrapped specific concepts and skills will this task target? Understand shapes in different categories may share attributes Understand shared attributes can define a larger category Recognize rhombuses, rectangles, and squares as examples of quadrilaterals A: How will the students apply the concepts and skills? What will they do and/or produce? Students will use riddle clues to identify the polygon. R: What resources, instruction, and information will students need in order to complete the task? Students will need completed work from Task 1. E: What evidence of learning will I look for to show that I know all of my students have conceptually learned the concepts and skills the standard(s)? 1. Students meet Proficient level or higher on Task 2 rubric. 2. Students respond to Essential Question with Big Idea in written. D: How can I differentiate the application and/or evidence to meet the varying needs of my students? Students may work in small groups if necessary. Task 2 Full Description: Students will determine the polygon by using the clues given in riddle form. Then they will write their own clues for a polygon that they draw.

8 8 of 14 Performance Task # 2 Scoring Guide Proficient Meets _5-6_ of the Proficient criteria Identify and justify each of the following polygons: Square Trapezoid Rhombus Hexagon Student Choice Progressing Meets _3-4_ of the Proficient criteria Task to be repeated after re-teaching Beginning Meets _0-2_ of the Proficient criteria Task to be repeated after re-teaching Comments: Interdisciplinary Connections and Related Priority Standards Specific to Task #2 21 st Century Learning Skills Specific to Task #2 Check all those that apply for each task: Teamwork and Collaboration Initiative and Leadership Curiosity and Imagination Innovation and Creativity Critical thinking and Problem Solving Flexibility and Adaptability Effective Oral and Written Communication Accessing and Analyzing Information Other

9 9 of 14 Performance Task # 3 In Detail S: Which standard(s) (priority/supporting) will the task address? 3.OA.8 SOLVE two step words problem USING the four operations. REPRESENT these problems USING equations with a letter standing for the unknown quantity. ASSESS the reasonableness of the answers USING mental computation and estimation strategies including rounding. 3.MD.7.d Recognize area as additive. Find areas of rectilinear figures by decomposing them into nonoverlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems. 3.MD.8 Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. Q: What essential Question(s) and corresponding Big Idea(s) will this task target? How/Why would decomposing a polygon be helpful in finding the area?3.md.7.d What is the difference between area and perimeter? 3.MD.8 What strategies will help me to solve for an unknown side when finding perimeter? 3.MD.8 Irregular shaped polygons can be broken apart to find the area. 3.MD.7.d The perimeter of a polygon can be calculated by adding the lengths of its sides. 3.MD.8 The area of a rectangle or square can be measured in square units. 3.MD.8 U: Which unwrapped specific concepts and skills will this task target? Find Areas of rectilinear figures Decomposing Non-overlapping rectangles Adding areas of the non-overlapping parts Find perimeter given side length Exhibiting Rectangles with same perimeter and different area Exhibiting Rectangles with same area and different perimeter A: How will the students apply the concepts and skills? What will they do and/or produce? Students will determine the perimeter and area of tablets. R: What resources, instruction, and information will students need in order to complete the task? Students will the task. Grid paper may be needed or used. E: What evidence of learning will I look for to show that I know all of my students have conceptually learned the concepts and skills the standard(s)? 1. Students meet Proficient level or higher on Task 3 rubric. 2. Students respond to Essential Question with Big Idea in written. D: How can I differentiate the application and/or evidence to meet the varying needs of my students? Students may work in small groups if necessary. Task 3 Full Description: Students will use information about the dimensions of a tablet to determine the perimeter and area. In the second question, students will use the answer from 2a to compute the answers for 2b.

10 10 of 14 Performance Task # 3 Scoring Guide Proficient Meets _5-6_ of the Proficient criteria Correctly find the perimeter and area for all problems. 1. Perimeter: 22 inches 1. Area: 28 sq. inches 2a. Perimeter: 30 inches 2a. Area: 54 sq. inches 2b. Perimeter: 42 inches 2b. Area: 108 sq. inches Progressing Meets _3-4_ of the Proficient criteria Task to be repeated after re-teaching Beginning Meets _0-2_ of the Proficient criteria Task to be repeated after re-teaching Comments: Interdisciplinary Connections and Related Priority Standards Specific to Task #3 21 st Century Learning Skills Specific to Task #3 Check all those that apply for each task: Teamwork and Collaboration Initiative and Leadership Curiosity and Imagination Innovation and Creativity Critical thinking and Problem Solving Flexibility and Adaptability Effective Oral and Written Communication Accessing and Analyzing Information Other

11 11 of 14 Task 1- Identifying Shapes Use the space below to draw and describe all attributes of each of the following shapes. Rectangle Square Rhombus Triangle Trapezoid Quadrilateral Pentagon Hexagon Circle

12 12 of 14 Task 1: Game Time (Optional) Guess My Shape Directions: 1. Using the information from Task 1, create game cards by drawing a shape and writing all of its attributes on an index card. 2-3 cards per student 2. Students draw a card and tape on the back of another student. Students should not look at the card that will be taped on their back. 3. Students can ask yes or no questions to other students to determine or guess the shape on their back. 4. Repeat as many times as you d like. Task 2: Polygons Answer each riddle. List all possible answers. Be sure to justify your answer with words or pictures. 1. I have 4 sides. My opposite sides are equal. I have 4 right angles. What shape am I? 2. I have 4 sides. I have only 1 pair of parallel sides. I have 4 corners. What shape am I? 3. I have 4 sides. My opposite sides are parallel. I do not have any right angles. What shape am I?

13 13 of Write three different clues for this shape: Clue 1: Clue 2: Clue 3: Answer: I am a. 5. Draw and name a shape. Then write three different clues for the shape: Task 3: Area and Perimeter 1. The new mini tablet is coming out. It is rectangular with the shorter sides measuring 4 inches and the longer sides measuring 7 inches. What is the perimeter and area of this new mini tablet? Justify your answer in the space below with pictures, words, or numbers. Perimeter Area inches sq. inches

14 14 of 14 2a. There is a new tablet that allows you to connect two like tablets or more for ultimate gaming. One rectangular-shaped tablet is 6 inches on one side and 9 inches on the other side. Find the area and the perimeter. Perimeter Area inches sq. inches b. Your friend comes over to play with their identical tablet. The tablets connect on the longest side. What is the area and perimeter when your tablets are connected? Perimeter Area inches sq. inches