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Understanding By Design Unit Template (Revised & adapted) Title of Unit Subject Developed By Area and Perimeter Grade Level Third Math Time Frame February 4 – March 1 Diana, Laura, Mona Stage 1 - Identify Desired Results Narrative about this Unit of Study: (including the Big Idea) This instructional bundle contains a task aligned to the Content Core standards and additional supports for diverse learners. The task is embedded in a 4-5 week unit on understanding concepts of area and perimeter using multiplication and addition to measure. Perimeter and area are two different measurements of the same shape and that each has its own kind of unit of measurement. Area is measured with square units and perimeter is measured in units of length. Learning Outcomes – Identified Primary Standards What relevant goals will this unit address? 3.MD.5 Recognize area as an attribute of plane figures and understand concepts of area measurement. 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. 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. 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. 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. 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. 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. Standards for Mathematical Practice: MP.1 Make sense of problems and persevere in solving them. MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. Understandings What understandings about the big ideas implied in the PLOs are desired? Essential Questions What provocative questions will foster inquiry into the content? Students will understand that (includes key vocabulary)... lationship between finding rectilinear area and multiplication/addition How to deconstruct a rectilinear space into non-overlapping rectangles to find the area of the entire space How to connect mathematical expression to word problems There are similarities and differences between the measurement of area and perimeter What is area? How is finding the area of a quadrilateral related to multiplication and addition? How can we express the area of a quadrilateral in a numerical expression? Why is calculating area important to us in our everyday life? How can we find the area of a rectilinear space that incorporates multiple rectangles? No essential questions that relate to perimeter Knowledge: What knowledge will student acquire as a result of this unit? Skills What skills will students acquire as a result of this unit? Students will know... Students will be able to… Using mathematics in real world contexts is the focus, specifically the measurement of area as it relates to multiplication and how perimeter relates to addition. They will know that being able to accurately measure the surface area is an essential skill for many professions. Key concepts that will be covered: • Measurement: measuring area using tiles and multiplication. • Number Operations: relating area to multiplication (length x width). understand that area is the amount of surface inside a twodimensional figure. (3.MD.5) understand that there are two ways to find the area of a square or rectangle: 1. Count the number of squares/tiles of a certain size that cover the inside of a shape. (3.MD.6) 2.Multiply side lengths a x b to find the area. (3.MD.7a) Students use tiles to create rectangular arrays that show a specific area. (3.MD.7a) Students use tiles to show that the area of a rectangular array is the same as would be found by multiplying the side lengths. (3.MD.7a) Students use tiles to find the area of a rectangle when provided with the side lengths, within the context of a word problem. (3.MD.7b) Students solve real-life problems related to area using multiplication and division (without tiles). (3.MD.7b) Stage 2 – Assessment Evidence Performance Task Through what authentic performance task will students demonstrate the desired understandings, knowledge, and skills? Brief Written Description of the Performance Task The NYC DoE has an area unit that has 3 examples of performance tasks with rubrics: 1. Ms. Smith’s Planting Predicament 2. Winter Vegetables 3. Fencing the Garden http://schools.nyc.gov/NR/rdonlyres/CD824F33-84DA-4D5F-8D4A-B450EA8C8000/0/NYCDOE_G3_Math_CityFarmers_Final.pdf Rubric for Assessment: Rubrics are included in the unit plan for the above tasks. Other Evidence Through what other evidence – student work samples, observations, quizzes, tests, self-assessment or other means – will students demonstrate achievement of the desired results? The pre-assessment (included below in the document) has been developed using the sequence of learning that is advocated in the CCLS, that is: 1. Student’s build and understanding about what area and perimeter are. 2. Students begin to establish how many square units fit into rectangles and squares by tiling or counting squares (building counting from skip counting and repeated addition to multiplication is a key focus of the unit). 3. Decomposing irregular shapes that have the square units identified. 4. Decomposing irregular shapes and calculating the area by using the dimensions of the shape 5. Decomposing irregular shapes, establishing some unknown dimensions from known dimensions and then calculating the area. From: Wiggins, Grant and J. McTighe. (1998). Understanding by Design, Association for Supervision and Curriculum Development, ISBN # 0-87120-313-8 (pbk) Objective(s) Related to knowledge, skills or both? Using U.S and Metric Units to measure length. What is perimeter? What is perimeter? What is perimeter? What is perimeter? What is perimeter? What is area? What is area? Listed Aim or Learning Intention of Each Lesson. - Review the length of units of measure (inch, foot, yard, centimeter and meter). - Establishing Measurement Benchmarks. - Understand perimeter as the measure around the outside edges of a 2-dimensional shape. - Use U.S standard units and metric units to accurately measure length. - Find the perimeter of a polygon given the side lengths. - Creating different shapes with the same perimeter. - Finding perimeter using standard units. - Understanding perimeter as the measure around the outside edges of a 2-dimensional figure. - Understanding perimeter as the measure around the outside edges of a 2-dimensional figure. - Finding perimeter using standard units. - Creating different shapes with the same perimeter. - Determine how the perimeter and area of the shape are related. - Determining the geometric moves needed (slides, flips, turns) to prove or disprove congruence between two shapes. - Understanding that area is measured in square units. - Understanding that when measuring area, the space being Assessment Are students using the measurement tools accurately? Are they making reasonable estimates for each unit of measure? Did students choose an appropriate tool to measure perimeter? Resources Unit 4 Investigations Lesson 1.1 (pg. 22) Unit 4 Investigations Lesson 1.2 (pg. 29) Do students add all of the sides to find perimeter? Do students accurately measure the perimeter of each shape? Are they able to explain why their predictions may differ from the actual order? As above. Robotic Racing. Lesson Plan in pdf saved on the server. Unit 4 Investigations Lesson 1.4 (pg. 45). This activity has 4 centers you can use with students. This could be undertaken over two days or just with students that need extra perimeter work. Unit 4 Investigations Lesson 1.5 (pg. 50) Ordering shapes based on perimeter How can I demonstrate my understanding of area and perimeter? Fence the Yard. Lesson Plan in pdf saved on the server (this lesson can go for 3-5 days). Are students able to make all five tetrominoes? Unit 4 Investigations Lesson 2.1 (pg. 62). How do they decide if the shapes are the same or not? Students explore all the possible arrangements of four squares. measured must be completely covered with no gaps or overlaps. What is area? What is perimeter? What is area? - determine if rectangles can have the same perimeter, but different area. - Understanding that when measuring area, the space being measured must be completely covered with no gaps or overlaps - Understanding that area is measured in square units What is the relationship between perimeter and area? Rectangle Rules. Lesson Plan in pdf saved on the server. How do students arrange the tetrominoes to cover squares? Unit 4 Investigations Lesson 2.2 (pg. 68). Do students find larger units they can use to cover the space? Students discuss the meaning of area and find the area of an 8 by 10 rectangle. Exploring Area - Understanding that when measuring area, the space being measured must be completely covered with no gaps or overlaps - Understanding that area is measured in square units The following link has an activity for students still building their understanding of area: http://www.k5mathteachingresources.com/supportfiles/exploringarea.pdf Exploring Area - Understanding that area is measured in square units Geoboard Areas. Lesson Plan in pdf saved on the server. Exploring Area - Understanding that area is measured in square units. Making different shapes that have an area of four square units on a Geobord: http://www.k5mathteachingresources.com/supportfiles/areaonthegeobaord.pdf Exploring Area - Understanding that area is measured in square units. - Students identify, create, and use square units to measure area. Tiling a Tabletop. Lesson Plan in pdf saved on the server. Exploring perimeter and area - determine how measures of length change when the unit of measure changes. - what methods can we use to determine the area of an object. - Developing strategies for measuring the area of rectangles. - Skip counting, repeated addition and multiplication. How big is a desk? Lesson Plan in pdf saved on the server. Calculating area Comparing rectangles: http://www.k5mathteachingresources.com/supportfiles/comparing-rectangles.pdf Calculating area Calculating area Calculating area Calculating area. Decomposing irregular shapes with the units identified Decomposing irregular shapes with the units identified Decomposing irregular shapes with just the dimensions Decomposing irregular shapes with just the dimensions Decomposing irregular shapes with just the dimensions - Developing strategies for measuring the area of rectangles. - Skip counting, repeated addition and multiplication. - Developing strategies for measuring the area of rectangles. - Skip counting, repeated addition and multiplication. - Determine the area of a rectangle by counting square units - Communicate the process of finding the area of a rectangle - students will use the dimensions of rectangles to determine their areas. - Students decompose shape and then apply compute the area of the shape. Rectangle Comparison 2. Lesson Plan in pdf saved on the server. - Find the area of a rectangle by breaking it into smaller rectangles - Discuss how they broke a rectangle into two smaller rectangles - Find the area of a large, rectilinear figure by decomposing it into smaller rectangles - Communicate their process of finding the area of a rectilinear figure Breaking Apart Arrays. Lesson Plan in pdf saved on the server. - Find the area of a large, rectilinear figure by decomposing it into smaller rectangles - Communicate their process of finding the area of a rectilinear figure Finding the Area of Complex Figures 2. Lesson Plan in pdf saved on the server. - Find the area of a large, rectilinear figure by decomposing it into smaller rectangles - Communicate their process of Finding the Area of Complex Figures 3. Lesson Plan in pdf saved on the server. Incomplete Rectangles. Lesson Plan in pdf saved on the server. Mowing for Money. Lesson Plan in pdf saved on the server. Sticker Stumper. Lesson Plan in pdf saved on the server. This activity from Illustrative mathematics is a good example of decomposing shapes with the units identified: http://www.illustrativemathematics.org/ illustrations/516 Finding the Area of Complex Figures 1. Lesson Plan in pdf saved on the server. Possible Performance Task finding the area of a rectilinear figure Decomposing irregular shapes with some unknown dimensions These activities still need to be developed. - Use clues to determine whether to find the area or the perimeter to solve a problem - Communicate how they solved problems involving area or perimeter Area or Perimeter. Lesson Plan in pdf saved on the server.