Geometry and Measurement

Transcription

1 Geometry and Measurement (Developmentally Appropriate Lessons for K-5 Students) Amanda Anderson Title I Teacher Lincoln Elementary aanderson@bemidji.k12.mn.us

2 Executive Summary This 10-day unit plan is constructed in a format that best fits my Title I teaching schedule. I have, on average, a total of 14 classes a day with groups, on average, of 6-8 students. Each class fits in a 25-minute time slot. Within these classes are students who range in age from kindergarten to fifth grade, and developmentally from struggling to advance. This unit plan teaches the concepts of geometry and measurement on a third grade level in 20-minute intervals. After each continued lesson is a category called Adaptations, which contains the alterations necessary to quickly adapt this unit for any other elementary grade K-5. The Minnesota state standards that this unit will address, for each grade level, can be found after the Unit Plan Outline and Overview section located below. Before, I will start this unit, the students will be given a pre-assessment in order to find out their prior knowledge on the following concepts which come from the third edition of the Everyday Math series: parallel lines, perpendicular lines, triangles, quadrangles, and polygons. It is important that before this unit, the students must also comprehend the concept of lines, segments, rays, and symmetry. Throughout this unit, each concept will be addressed over two weeks and on Fridays the students will be receiving post assessments over the new concepts they learned. This will be done through activities, formal and informal assessments, and through the use of technology. Standard Based Unit Plan Outline and Overview Day 1 Day 2 Day 3 Day 4 Day 5 Day 6 Day 7 Day 8 Day 9 Day 10 Launch, Explore, Share, and Summarize: parallel lines Launch, Explore, Share, and Summarize: perpendicular lines Launch, Explore, Share, and Summarize: triangles Launch, Explore, Share, and Summarize: triangles Activities and Post Assessment: parallel, perpendicular lines, and triangles Launch, Explore, Share, and Summarize: quadrangles Launch, Explore, Share, and Summarize: quadrangles Launch, Explore, Share, and Summarize: polygons Launch, Explore, Share, and Summarize: polygons Activities and Post Assessment: quadrangles and polygons

3 Standards Addressed in this Unit Kindergarten: Geometry and Measurement: Recognize and sort basic two-and three-dimensional shapes; use them to model real-world objects. K Recognize basic two-and three-dimensional shapes such as squares, circles, triangles, rectangles, trapezoids, hexagons, cubes, cones, cylinders, and spheres. First Grade: Geometry and Measurement: Describe characteristics of basic shapes. Use basic shapes to compose and decompose other objects in various contexts Describe characteristics of two-and three-dimensional objects, such as triangles, circles, rectangular prisms, cylinders, cones, and spheres. Second Grade: Geometry and Measurement: Identify, describe, and compare basic shapes according to their geometric attributes Identify and name basic two-and three-dimensional shapes, such as squares, circles, triangles, rectangles, trapezoids, hexagons, cubes, rectangular prisms, cones, cylinders, and spheres. Third Grade: Geometry and Measurement: Use geometric attributes to describe and create shapes in various contexts Identify parallel and perpendicular lines in various contexts, and use them to describe and create geometric shapes, such as right triangles, rectangles, parallelograms, and trapezoids Sketch polygons with a given number of sides or vertices (corners), such as pentagons, hexagons, and octagons. Fourth Grade: Geometry and Measurement: Name, describe, classify and sketch polygons Describe, classify, and sketch triangles, including equilateral, right, obtuse, and acute triangles. Recognize triangles in various contexts Describe, classify, and draw quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms and kites. Recognize quadrilaterals in various contexts. Fifth Grade: Geometry and Measurement: Determine the area of triangles and quadrilaterals; determine the surface area and volume of rectangular prisms in various contexts Develop and use formulas to determine the area of triangles, parallelograms and figures that can be decomposed into triangles.

4 Table of Contents 1. Grade 2-3 Assessment page 5 2. Day 1: Parallel Lines page 9 3. Day 2: Perpendicular Lines.page Lesson Adaptations.page Day 3: Equilateral and Right Triangles page Day 4: Isosceles and Scalene Triangles.page Lesson Adaptations page Day 5: Post-Assessment: Lines and Triangles page Day 6: Quadrangles.page Day 7: Continuing with Quadrangles.page Lesson Adaptations page Day 8: Regular Polygons page Day 9: Polygons page Lesson Adaptations page Day 10: Post-Assessment and Activities page Sources page 65

5 Name Date: What Do You Know? (Grade 2-3) 1. Can you show me a pattern using squares, rhombuses, kites, trapezoids, or hexagons? 2. What is one shape that has only one pair of parallel lines? Write the answer and draw a picture of this shape. 3. What type of triangles are these? How do you know? Label them.

6 4. What is one shape that has a pair of perpendicular lines? Write the answer and draw a picture of this shape? 5. Can you tell me what a quadrangle is? Can you draw a picture of a quadrangle? 6. Can you circle the polygons? 7. Can you circle the scalene triangle? How do you know it's a scalene triangle?

7 8. Fill in the blank spaces in the chart below. Name of Shape Number of Sides Number of Vertices Parallel Lines? (Yes or No) Perpendicular Lines? (Yes or No)

8 9. Can you draw me a picture that has parallel and perpendicular lines in it? 10. Can you draw triangles to make the following shapes? You're Done! Thank you for your hard work!

9 Day 1 Introduction to Parallel Lines Standard: Geometry and Measurement: Use geometric attributes to describe and create shapes in various contexts Identify parallel and perpendicular lines in various contexts, and use them to describe and create geometric shapes, such as right triangles, rectangles, parallelograms, and trapezoids. Objectives: The students will learn about the names of the following shapes; triangles, rectangles, parallelograms, trapezoids, squares, right triangle, and cube through an online geoboard activity. The students will increase their mathematic vocabulary through discussion and the use of technology. The students will solve a mathematics question that focuses on the concept of parallel lines and will be able to locate parallel lines found in a variety of shapes. Materials (located at the end of each continued lesson): Computers White Board Visualizer Online Geoboard Activity: panel=true&from=applets/controller/query/query.htm?qt=geoboard Procedure: Launch (4 min.): The students will first come to class and see a math question displayed on the white board through the use of a visualizer. The sample question is as followed: What do you notice about these two lines?

10 The teacher will then ask, How should we answer this question? (Possible student responses: We need to figure out what is the same or different about these two lines, think of times we've seen lines like these, the two lines aren t touching, they look like a road, etc.) Tell me what you see. Explore (4 min.): After discussing these lines as a group, the teacher will, then, put a second set of lines up on the board. Now what do you notice? (The lines still are not meeting, but they are different sizes, etc.) If I were to tell you that both sets of lines are parallel lines, what do you think I am meaning? (Possible student responses: That the lines do not touch, never meet, etc. ) Excellent detective skills! Parallel lines and line segments are lines that are in the same plane but never meet. They are the same distance apart at all points on each line. So, are these two lines parallel? (No.) But why? They are not touching. (They will eventually). The students, through the guidance of the teacher, will be working in pairs (six to eight students = three to four pairs) and making a variety of shapes that contain parallel lines. The name and picture of each shape will be found displayed on a white board through the use of a visualizer. The process will be as followed: 1. Display the shape on the visualizer. 2. Have the students construct the shape on their online geoboards. 3. Have the students fill in the shape using one of the side colors on the program so that they can see the shape, as a whole, clearly. 4. Display the name of the shape on the visualizer. 5. Talk about the shape, the number of sides, vertices (corners), and faces. Share (3 min.): While the students are working on their geoboards, the teacher will be asking questions to inspire a mathematical discussion. These questions will be based on having the students share different ideas on how they are using their detective skills to solve to find the parallel lines in each shape if they exist. How are you finding the different lines? (Possible student responses: I look for the two lines that will never touch, I remembered what we learned in class today, I was able to use the shapes on the visualizer to help me, etc.) By having the students share their ideas, it will give others new ways to solve and comprehend different ways to find

11 parallel lines. The teacher will also be asking the students for different ways they can use what they've learned about parallel lines to help them in the future (example: Where can we find parallel lines outside the classroom? etc.) Summarize (2 min.): Towards the end of class, the teacher will get the group's attention and ask, So, what did we learn about or try today? (Parallel lines.) Based on the students' responses, the teacher will be able to conclude whether or not the students truly comprehended today's activities. So, not only did we learn how to solve a math problem about parallel lines, but we also were able to create parallel lines using an online geoboard game, talk about where we could find other parallel lines, and learned the names of different shapes that have parallel lines. Excellent! Wonderful detective work!

12 Standard: Day 2 Introduction to Perpendicular Lines Geometry and Measurement: Use geometric attributes to describe and create shapes in various contexts Identify parallel and perpendicular lines in various contexts, and use them to describe and create geometric shapes, such as right triangles, rectangles, parallelograms, and trapezoids. Objectives: The students will expand upon their mathematical vocabulary through group discussion during the summary portion of this lesson. The students will locate objects with perpendicular lines and angles through a classroom scavenger hunt. The students will draw a picture using real-world objects and shapes that have perpendicular lines and angles. Materials: Scavenger Hunt Activity Sheet Shapes Scene Activity Sheet White Board Visualizer Launch (4 min.): When the students first come to class, the teacher will say, Remember how we learned about parallel lines, yesterday? Why do you think it's important that learn about parallel lines? (Possible student responses: so we know that they can be a part of a shape, so that we can find them outside of school, to learn about what the word parallel means, etc.) Excellent! Today we are going to learn about a new set of lines. But first, can you tell me what these two sets of lines have in common? The teacher displays the following drawing up on the white board through the use of a visualizer (Possible student responses: they are touching, they look like they could make a square, etc.). What do we notice at the vertices, or corners? What shape could fit between the two lines? (they line up perfectly, a square could fit there) Exactly! A square corner could fit between these two lines. A square corner is also called a right angle. Square corners, or right

13 angles, can also be seen on the edge of your journals and pieces of paper. How we mark right angles is to put a square in the corner where the two sides meet. This is to remind us that a right angle is also known as a square corner. The lines that make up these corners are known as perpendicular lines. The teacher then draws the appropriate right angle icon on all of the angles displayed through the visualizer. Explore (11 min.): The teacher will then ask, Do you know any shapes that have right angles or perpendicular lines in them? (square, rectangle, cube, rhombus, etc.) Exactly! Wow! Great detective work! You are going to be going on a classroom scavenger hunt. You will walk around the classroom and find any other shapes that have perpendicular lines in them. Remember, perpendicular lines are two lines that make a right angle. Then you will draw those shapes or objects you find during your scavenger hunt on your scavenger activity sheet. On the back of your scavenger sheet you will be drawing a picture using some of the different perpendicular lined shapes that we talked about today that are on the top of your activity sheet. The teacher will be walking around to provide guidance, role modeling, and assistance. Share (3 min.): After the students have had a chance to work on the activities mentioned above, the teacher will get the group's attention and ask, What did we learn about perpendicular lines? What did we need to look for in order to find them? (Possible student responses: We learned that perpendicular lines create a square corner, that we need to put a little square in where the two lines meet to show that they are right angles, that some shapes have perpendicular lines and sides, etc.) Who can give me an example of one shape or object you know of that had perpendicular lines or angles in it? (Possible student responses: a block, a map, a piece of paper, a square, etc.) Summarize (3 min): The teacher will ask, So, what was one main idea or big picture we've learned about over the last two days? (Goal response: parallel and perpendicular lines). From the students' responses, the teacher will be able to summarize this two day concept, while also showing the importance in recognizing that the students truly do comprehend the concept of parallel and perpendicular lines. So, from what you are telling me, not only did we learn about parallel and perpendicular lines, but we played a geoboard game to find parallel lines in shapes, practiced finding examples of perpendicular lines, created a picture with perpendicular lined objects, and can now recognize examples of parallel and perpendicular lines in the future. Wonderful! Give yourselves a pat on the back for all of your hard work, detectives! If time allows, they can color their pictures they ve made with the objects that have perpendicular lines and angles.

14 Lessons' Materials and Resources 1. Pre-Assessment: Found Above before the start of the lesson (pages 5-8) 2. Link to Geoboard website (page 9) 3. Geoboard Modeling Shape Activity Sheet (page 25) 4. Scavenger Hunt Activity Sheet (page 23) 5. Student Activity Sheet: Creating a Picture with Perpendicular Lines and Angles (page 24) 6. Lesson Adaptations (page 15) 7. Pre-Assessments for K-1 (page 16-18) 8. Pre-Assessment for 4-5 (page 19-22)

15 Parallel and Perpendicular Lesson Adaptations for K, 1, 2, 4, 5 K In order to make this lesson developmentally appropriate for kindergarten students, and to meet the requirements of the suggested Minnesota standard, simply have the students use actual plastic geoboards with string that they can use to wrap around the pegs since their muscle coordination is not defined at this stage. Using pictures to represent perpendicular and parallel lines is another way to help the students visually solve the different math equations. Also, use the alternative pre-assessment version that is suitable for students in grades K-1. This pre-assessment alternative can be found on page 16. In order to make this lesson developmentally appropriate for first grade students, and to meet the requirements of the suggested Minnesota standard, simply have the students use actual plastic geoboards with string that they can use to wrap around the pegs since their muscle coordination is not defined at this stage. Using pictures to represent perpendicular and parallel lines is another way to help the students visually solve the different math equations. Also, use the alternative pre-assessment version that is suitable for students in grades K-1. This pre-assessment alternative can be found on page 16. These two days of lessons are completely appropriate for students to work on in second grade and will meet the Minnesota standard selected. In order to make this lesson developmentally appropriate for fourth grade students, and to meet the requirements of the suggested Minnesota standard, simply change include the following shapes when creating parallel lines on the geoboards: equilateral, right, obtuse, and acute triangles, parallelograms and kites. Recognize quadrilaterals in various contexts. Use the alternative pre-assessment version that is suitable for students in grades 4-5. This pre-assessment alternative can be found on page 19. In order to make this lesson developmentally appropriate for fifth grade students, and to meet the requirements of the suggested Minnesota standard, simply take the geoboards and student activity sheet one step further by talking about the ways that they could determine the area of the triangles, and parallelograms. On the geoboard activity, not only should they make the shape but then draw the lines that show how some of the different shapes can be decomposed into triangles. Use the alternative pre-assessment version that is suitable for students in grades 4-5. This pre-assessment alternative can be found on page 19.

16 Name Date: What Do You Know? (Grade K-1) (Read this to the students.) 1. Can you show me a shape pattern? What shapes did you use? 2. I am going to say the name of a shape. I want you to put an X on the shape after I say it. 3. Can you tell me an example of a sphere? 4. Can you tell me an example of a rectangular prism? 5. Can you tell me an example of a cube?

17 6. Can you draw a picture using some of these shapes? 7. Can you draw a picture using some of these shapes?

18 8. The teacher should ask the following information and write the student s answers in the appropriate spaces. Name of Shape Number of Sides Number of Corners (Vertices)

19 Name Date: What Do You Know? (Grade 4-5) 1. Can you show me a pattern using squares, rhombuses, kites, trapezoids, hexagons, kites, or rectangular prisms? 2. What is one shape that has only a pair of parallel lines and perpendicular lines? Write the answer and draw a picture of this shape. 3. What types of triangles are there? How do you know? Draw and label them. 4. Can you find the area of the following shapes below? 22 ft. 6ft. 7 ft. 12 ft. 6ft. 18ft.

20 5. Can you tell me what a quadrangle is? Can you draw a picture of a quadrangle? 6. Can you circle the regular polygons?

21 7. Fill in the blank spaces in the chart below. Name of Shape Number of Sides Number of Vertices Perimeter if all the sides are the same and a a length of 5. What would the area of this shape be? Top Line Length: 7 Bottom Line Length: 4 Slanted Line: 5 Height: 6 Top Line: 8 Slanted Line: 5 Height: 6 Top Line: 15 Side Line: 6

22 8. Can you draw triangles to make the following shapes? You're Done! Thank you for your hard work!

23 Name: Shape Scavenger Hunt Date: Find this shape. Fill in the table below. Name this shape. Draw an example. What did you draw? or or

24 Name: Date: Shape Scenes Make a picture using shapes that have perpendicular lines and angles (squares, rectangles, cubes, rectangular prisms, right triangles).

25 Geoboard Shapes with Parallel Lines Name of Shape Number of Sides Number of Corners (Vertices)

26 Day 3 Introduction to Equilateral and Right Triangles Standard: Geometry and Measurement: Use geometric attributes to describe and create shapes in various contexts Identify parallel and perpendicular lines in various contexts, and use them to describe and create geometric shapes, such as right triangles, rectangles, parallelograms, and trapezoids Sketch polygons with a given number of sides or vertices (corners), such as pentagons, hexagons, and octagons. Objectives: The students will be able to identify equilateral and right triangles through a variety of picture activity sheets. The students will be able to identify the number of sides and vertices (corners) of triangles through a variety of discussion questions and answers. The students will be working in pairs in order to effectively communicate and discuss the location of various equilateral and right triangles. Materials: Equilateral Triangle Activity Sheet Right Triangle Activity Sheet Equilateral and Right Triangle Activity Sheet Pencil White board Visualizer Procedure: Launch (4 min.): The students will first come to class and see two triangles displayed on the white board through the use of a visualizer. The teacher will then ask, What do you notice about these two shapes? Look at them carefully. (Possible student responses: They are both triangles, one has a right angle sign, one looks like a hat, etc.) Great! I can see those detective hats are on. You re right! They are both triangles, which means they have three sides and three vertices, or corners. Do you

27 remember how we learned about perpendicular angles and lines yesterday? You will notice that one of our triangles has a right angle sign on it. This is where two of the lines in the triangle are perpendicular and meet to form that right angle. This triangle is called a right triangle. Are the sides of this right triangle all the same length? (No.) What do we notice about the other triangle up on the board? (The sides are all the same.) Great! This triangle is called an equilateral triangle. The part lateral means side and the prefix equi means the same, or equal, so an equilateral triangle means that all three sides are the same. The students will then look in their student reference book on page, 107. Explore (10min.): The teacher will then say, You have been such wonderful detectives in learning about equilateral and right triangles. Let s use our detective skills even more by trying to find as many equilateral and right triangles we can in the following pictures. The students will then break apart into groups and help each other count, and discover the variety of equilateral and right triangles in three pictures. The teacher will be walking around for guidance. With each picture that is completed the teacher and students will then discuss the pictures as a group in order to make sure all of the triangles are discovered. Share (3 min): What did we learn about equilateral and right triangles? (Possible student responses: The sides of an equilateral triangle are all the same size/length, a right triangle has the little square on it to tell us it s a right triangle, the sides of a right triangle are not all the same size/length, etc.) Who can give me an example of one way you solved the different triangle pictures? (Possible student responses: I used the pictures on the board to help me, I talked with my partner to make sure I didn t miss any triangles, etc.) Summarize (3 min.): The teacher will focus the group's attention and ask, So, what was one main idea or big picture we've learned about today? (Goal response: Equilateral and right triangles). Student responses may vary but the goal of their responses is to see whether or not they truly understand the concept of equilateral and right triangles and if they would be able to recognize and solve these types of triangles in the future. So not only did we learn about equilateral and right triangles, but we compared and contrasted the two, and was able to locate the different triangles in a variety of pictures. What wonderful ideas! You are all becoming great math detectives!

28 Day 4 Introduction to Isosceles and Scalene Triangles Standard: Geometry and Measurement: Use geometric attributes to describe and create shapes in various contexts Sketch polygons with a given number of sides or vertices (corners), such as pentagons, hexagons, and octagons. Objectives: The students will be able to identify isosceles and scalene triangles through discussion and through creating triangles with manipulatives. The students will be able to identify the number of sides and vertices (corners) of triangles through a variety of discussion questions and answers. The students will be working in pairs in order to effectively communicate and discuss how to create a variety of scalene, and isosceles triangles. Materials: Straws Pipe Cleaners (cut into fourths) White board Visualizer Crayons or Colored Pencils Procedure: Launch (4 min.): The students will first come to class and see two triangles displayed on the white board through the use of a visualizer. The teacher will then ask, What do you notice about these two shapes? Look at them carefully. (Possible student responses: They are both triangles, they both have three sides and three vertices, one triangle has three different sides, etc.) Great! I can see those detective

29 hats are on. You re right! They are both triangles, which means they have three sides and three vertices, or corners. But, they are not equilateral or right triangles. The triangle on the left is called an isosceles triangle, which means it is a triangle where two of the sides are the same length. The triangle on the right is called a scalene triangle, meaning that each side is a different length (no two lengths are the same). Explore (10min.): The teacher will then say, Let's use our detective skills, to practice making isosceles and scalene triangles by using straws that have been cut at different lengths and pipe cleaners that we will use to attach the straws together. The teacher will then model, with the students following along, an example of a scalene and isosceles triangle. After the teacher can see, through the students' own constructions, that they know how to make a scalene and isosceles triangle, the students will practice making more of these types of triangles with a partner for guidance. The teacher should also encourage the students to try making equilateral and right triangles as well. Share (3 min): What did we learn about isosceles and scalene triangles? (Possible student responses: no sides on a scalene triangle are the same, isosceles triangles have two sides that are the same length, both have three sides and vertices, etc.) Who can show me an example of a scalene triangle by using the visualizer? An isosceles triangle? (student name sticks will be used) Summarize (3 min.): The teacher will then focus the group's attention and ask, So, what was one main idea or big picture we've learned about today? (Goal response: Isosceles and scalene triangles). Student responses may vary but the goal is to see whether or not they truly understand the concept of scalene and isosceles triangles and if they would be able to recognize and create these types of triangles in the future. So not only did we learn about scalene and isosceles triangles, but we compared and contrasted the two, and we were able to create examples of each type of triangle using straws and pipe cleaners. Fabulous! Congratulations detectives on your hard work!

30 K Triangle Lesson Adaptations for K, 1, 2, 4, 5 In order to make this lesson developmentally appropriate for kindergarten students, and to meet the requirements of the suggested Minnesota standard, simply make sure during the scavenger hunt that they try to write the name of the shape, but as long as they can read their findings to a teacher or another student, spelling should not be the main focus. The different types of triangles can be discussed, but as long as the student can identify the four types of triangles as triangles, that s the most important part. In order to make this lesson developmentally appropriate for first grade students, and to meet the requirements of the suggested Minnesota standard, simply make sure during the scavenger hunt that they try to write the name of the shape, but as long as they can read their findings to a teacher or another student, spelling should not be the main focus. The different types of triangles can be discussed, but as long as the student can identify the four types of triangles as triangles, that s the most important thing. These two days of lessons are completely appropriate for students to work on in second grade and meet the Minnesota standard selected. In order to make this lesson developmentally appropriate for fourth grade students, and to meet the requirements of the suggested Minnesota standard, simply expand the two triangle lessons a step further by introducing the following terminology: obtuse, and acute. In order to make this lesson developmentally appropriate for fifth grade students, and to meet the requirements of the suggested Minnesota standard, simply expand the two triangle lessons a step further by introducing the following terminology: obtuse, and acute. Also, talk about how the students could find the area of the various triangles and how a parallelogram can be broken down into triangle sections in order to find the total area of the parallelogram. Lessons' Materials and Resources 1. Equilateral Triangle Find Activity Worksheet (page 31) 2. Right Triangle Find Activity Worksheet (page 32) 3. Equilateral and Right Triangle Find Activity Worksheet (page 33)

31 Equilateral Triangles Mystery How many Equilateral Triangles are in this picture? (You can use different colored crayons or pencils if it would help.) Answer:

32 Right Triangles Mystery How many right triangles are in this picture? (You can use different colored crayons or pencils if it would help.) Make sure to add the right angle sign for each triangle. Answer:

33 Equilateral and Right Triangles Mystery How many equilateral and right triangles are in this picture? (You can use different colored crayons or pencils if it would help.) Answer:

34 Day 5 Post-Assessment on Parallel and Perpendicular Lines; Equilateral, Right, Scalene, and Isosceles Triangles Standard: Geometry and Measurement: Use geometric attributes to describe and create shapes in various contexts Identify parallel and perpendicular lines in various contexts, and use them to describe and create geometric shapes, such as right triangles, rectangles, parallelograms, and trapezoids Sketch polygons with a given number of sides or vertices (corners), such as pentagons, hexagons, and octagons. Objectives: The students will be using prior knowledge of parallel and perpendicular lines and triangles by completing a short post-assessment written activity. The students will be using their prior knowledge of isosceles, scalene, right, and equilateral triangles by completing a drawing activity. The students will be using their prior knowledge of perpendicular and parallel lines by completing a drawing activity. The students will be given an informal assessment while they are working on various activities in order to check for skill mastery and comprehension. Materials: Post-Assessment Student Questions (pages 36, 37) Parallel, Perpendicular, Triangle Drawing Activity Sheet (page 38) Pencils Post-Assessment Checklist (page 35) Organizing Triangles Online Activity: Procedure: The students will be working at three learning stations (One station focuses on completing post-assessment questions on this week's geometric concepts, another station focuses on creating a picture using the triangles and lines learned this week, and a third station will have the students working on an online activity of sorting the four triangle types into a variety of Venn diagrams. While the students are working at the different learning stations, the teacher will be walking around with a checklist to informally and formally assess the students on their comprehension of parallel and perpendicular lines and triangle. This form of assessment takes about 5 minutes to complete for each student

35 Name of Student Date: Classroom Teacher Grade Level: Assessment Questions Regarding Parallel Lines, Perpendicular Lines, and Triangles Yes, fully mastered! Mastery Level Understands the majority of this concept. Needs Additional Help and Guidance Provide Example: Additional Comments 1. Is the student able to draw parallel lines correctly? 2. Is the student able to draw perpendicular lines correctly? 3. Is the student able to draw isosceles, equilateral, scalene, and right triangles correctly? 4. Can the student provide reasoning in how to locate perpendicular and parallel lines correctly? 5. Does the child use different strategies to create and locate different triangles, parallel, and perpendicular lines? 6. Is the student able to correctly answer the questions located on the post-test? 7. Is the student able to provide reasoning on how to locate isosceles, right, scalene, and equilateral? 8. Does the child use different strategies when creating the shape scene activity? 9. Would the student be able to explain the concepts of perpendicular and parallel lines to another person? 10. Would the student be able to explain the different types of triangles to another person?

36 Name Date: What Do You Know Now? (Grade 2-3) 1. What is one shape that has only one pair of parallel lines? Write the answer and draw a picture of this shape. 2. What type of triangles are these? How do you know? Label them. 3. What is one shape that has a pair of perpendicular lines? Write the answer and draw a picture of this shape?

37 4. What type of triangles are these? How do you know? Label them. 5. Can you draw me a picture that has parallel and perpendicular lines in it? You're Done! Thank you for your hard work!

38 Name: Date: Shape Scenes Directions: On the back of this piece of paper you are going to make a picture of your choice using the shapes and lines we've learned about this week. Your picture must have at least one of the following shapes or lines: 1. a scalene triangle 2. a right triangle 3. an equilateral triangle 4. an isosceles triangle 5. a pair of parallel lines 6. a pair of perpendicular lines Your parallel and perpendicular lines can be a part of a shape. Make sure to label each shape or pair of lines in your picture. Use your detective skills to make your picture exciting. These will be displayed on the white board.

39 Day 6 Introduction to Quadrangles Standard: Geometry and Measurement: Use geometric attributes to describe and create shapes in various contexts Identify parallel and perpendicular lines in various contexts, and use them to describe and create geometric shapes, such as right triangles, rectangles, parallelograms, and trapezoids Sketch polygons with a given number of sides or vertices (corners), such as pentagons, hexagons, and octagons. Objectives: The students will be able to locate parallel and perpendicular lines by identifying various quadrangles through a licorice tracing activity and a quadrangle recognition activity. The students will be able to identify polygons (quadrangles/quadrilaterals) while recording the number of sides, angles and vertices (corners) of each quadrangle through a licorice tracing activity and a quadrangle recognition activity. The students will be working in pairs in order to effectively communicate and discuss the attributes of various polygons (quadrangles/quadrilaterals) through a recognition activity. Materials: Quadrangle Recognition Activity sources/elementary/touchandmatchquadrangles.doc+quadrangle+touch&cd=1&hl= en&ct=clnk&gl=us Quadrangle Shape Activity Sheet (needs to be laminated) Pull-and-Peel Licorice Brown Package Envelopes (to put quadrangle shapes in) Quadrangle Shapes: Square, Rhombus, Rectangle, Kite, Trapezoid (either through wooden blocks, plastic pieces, or laminated paper) Pencils White board Visualizer

40 Procedure: Launch (3 min.): The students will first come to class and see the following shapes displayed on the white board through the use of a visualizer: The teacher will then ask, What do you notice about these shapes? Look at them carefully. (Possible student responses: They all have four sides, they all have angles, some of them have parallel lines, the last shape does not have any parallel lines, etc.) Great ideas! I can see that you are trying to find out what all of these shapes have in common. Do you remember how we learned about triangles last week and how the term tri means three, thus the word triangle means three angles? If I were to tell you that each of these shapes are quadrangles, and the term quad means four, what do you think I am meaning? (they each have four angles) You've got it! We will be learning about different types of quadrangles over the next two days. Explore Part 1 (3 min.): The teacher will then say, I am going to be passing out a quadrangle shape template and we are going to be tracing these shapes with pull and peel strings as we learn about them. You will be able to eat the pull-and-peel licorice strings when we are done going over each shape. The teacher will then pass out a quadrangle shape activity sheet. As the teacher and students discuss each shape, the students will receive a stick of pull-and-peel licorice. The students will pull the licorice apart into strings and use one string to trace the shape of the each quadrangle while they are discussed one at a time. Explore Part 2 (8 min.): The teacher will then say, Now that we have gone over the different types of quadrangles, you are going to work with a partner (matched through student name sticks) and take turns guessing the different quadrangle shapes that can be found in each brown package envelope. Make sure to read the directions on the activity sheet so that you will know what to do. I will be checking your reading fluency as you and your partner read the directions together, but I will be walking around to help with any words you may not know or any questions you may have. The students will then begin the quadrangle recognition activity.

41 Share (3 min): What did we learn about quadrangles? (Possible student responses: There are four angles in a quadrangle, there are different types of quadrangles, some quadrangles have parallel lines, some quadrangles have perpendicular lines, etc.) Who can give me an example of one way you figured out a quadrangle in the mystery quadrangle activity? (Possible student responses: I used the pictures on the board and licorice sheet to help me, I talked with my partner to make sure I didn t miss anything when trying to figure out the quadrangle, I remembered that a square had the same four sides, etc.) Summarize (3 min.): The teacher will focus the group's attention and ask, So, what was one main idea or big picture we've learned about today? (Goal response: Quadrangles). Student responses may vary but the goal of their responses is to see whether or not they truly understand the concept of quadrangles and if they would be able to recognize and create these types of quadrangles in the future. So not only did we learn about quadrangles, but we compared and contrasted the different types, and we were able to trace and recognize them based on what we learned today. What great geometry detectives! You are becoming quadrangle experts!

42 Day 7 Continuing with Quadrangles Standard: Geometry and Measurement: Use geometric attributes to describe and create shapes in various contexts Identify parallel and perpendicular lines in various contexts, and use them to describe and create geometric shapes, such as right triangles, rectangles, parallelograms, and trapezoids. Objectives: The students will be able to locate parallel and perpendicular lines by identifying various quadrangles through a triangle shading activity. The students will be able to identify polygons (quadrangles/quadrilaterals) while identifying the number of sides, angles and vertices (corners) of specific quadrangles/quadrilaterals through a triangle shading activity. The students will be working in pairs in order to effectively communicate and discuss the attributes of various polygons (quadrangles/quadrilaterals) through a triangle shading activity. Materials: Shading Shapes Activity Sheet Shading Shapes Reference Page Pencils Procedure: Launch (4 min.): The students will first come to class and see the following quadrangles displayed on the white board through the use of a visualizer. The teacher will then ask, Can anyone tell me the names of these four quadrangles? (In order from left to right: square, rectangle, trapezoid, parallelogram) Wonderful! The teacher will then talk about how not all trapezoids or parallelograms may look the same. The teacher will then pass out a shading shapes reference page. You will see on this reference page that how a

43 few examples of how trapezoids and parallelograms can look differently. Explore (10min.): The teacher will then say, You are going to be working with a partner to create these types of shapes by taking turns and shading one small triangle at a time. The person that shades the last triangle to make one of these shapes, gets one point for each triangle that makes up the finished shape. The person with the most points at the end wins. Make sure that you and your partner shade the triangles in different colors so that you can keep track of who completes each finished shape. The students will be paired up with a partner using student name sticks. The students are allowed to help each other. The teacher will be walking around to answer questions, role model, and provide guidance. Share (3 min): What did we learn about quadrangles, today? (Possible student responses: That you can use a different shape like a triangle and make a quadrangle, some quadrangles can change in how they look, etc.) Who can show me an example of one quadrangle you made with your partner? Another quadrangle? A third quadrangle? (student name sticks will be used) Summarize (3 min.): After sharing, teacher will focus the group's attention and ask, So, what was one main idea or big picture we've learned about over the last two days? (Goal response: Quadrangles). Student responses may vary but the goal of their responses is to see whether or not they truly understand the concept of quadrangles and if they would be able to recognize and solve these types of triangles in the future. So not only did we learn more about how to make different quadrangles using triangles, but about how not all quadrangles have to stay exactly the same all the time, and how to work with a partner cooperatively in finding new ways to make quadrangles! Your quadrangle detective skills are soaring! Congratulations! Quadrangle Lesson's Materials 1. Quadrangle Shape Activity Sheet Teacher s Version (page 45) 2. Quadrangle Shape Activity Sheet Blank Version (needs to be laminated) (page 46) 3. Shading Shapes Activity Sheet Reference Page (page 48) 4. Shading Shapes Activity Game Board (page 47) 5. Lesson Adaptations (page 44)

44 Quadrangle Lesson Adaptations for K, 1, 2, 4, 5 K In order to make this lesson developmentally appropriate for kindergarten students, and to meet the requirements of the suggested Minnesota standard, simply make sure that the shapes they focus on are square, rectangle, trapezoid, parallelogram, and rhombus. The different types of quadrangles can be discussed that are in the brown package envelopes, but they don't need to do the written partner activity worksheet since their letter to word recognition has not developed strongly yet. As long as the students can recognize the different quadrangles, that is the most important thing. In order to make this lesson developmentally appropriate for first grade students, and to meet the requirements of the suggested Minnesota standard, simply make sure that the shapes they focus on are square, rectangle, trapezoid, parallelogram, and rhombus. The different types of quadrangles can be discussed that are in the brown package envelopes, but they don't need to do the written partner activity worksheet since their letter to word recognition has not developed strongly yet. As long as the students can recognize the different quadrangles, that is the most important thing. These two days of lessons are completely appropriate for students to work on in second grade and meet the Minnesota standard selected. In order to make this lesson developmentally appropriate for fourth grade students, and to meet the requirements of the suggested Minnesota standard, simply expand the quadrangle lessons a step further by including the dimensions on the shapes in the quadrangle recognition activity so that they would need to find the area of the various quadrangles. In order to make this lesson developmentally appropriate for fifth grade students, and to meet the requirements of the suggested Minnesota standard, simply expand the quadrangle lessons a step further by including the dimensions on the shapes in the quadrangle recognition activity so that they would need to find the area of the various quadrangles.

45 July 17,

46 Quadrangles (Quadrilaterals) parallelogram 2 pairs of parallel sides rectangle 1. 2 pairs of equal sides 2. 4 right angles rhombus 1. 4 equal sides 2. opposite sides parallel square 1. 4 equal sides 2. 4 right angles trapezoid 1. only 2 sides parallel 2. parallel sides not equal kite 1. 2 pairs of adjacent equal sides 2. opposite sides not equal

47 Shading Shapes Game Board July 17, 2009

48 July 17, 2009 Shading Shapes Reference Page Example 48

49 Day 8 Introduction to Regular Polygons Standard: Geometry and Measurement: Use geometric attributes to describe and create shapes in various contexts Sketch polygons with a given number of sides or vertices (corners), such as pentagons, hexagons, and octagons. Objectives: The students will be creating regular polygons through an online geoboard program. The students will be creating and labeling regular polygons through a polygon identification worksheet and drawing activity sheet. The students will understand the names of a variety of regular polygons through small group discussion and modeling. Materials: Geoboard Online Activity panel=true&from=applets/controller/query/query.htm?qt=geoboard Polygon Picture Activity Sheet Colored Pencils or Crayons Regular Polygon Shapes Guideline Worksheet Procedure: Launch (4 min.): The students will first come to class and see an activity sheet where there is a chart of regular polygons at each student's spot. After the students have had a chance to look at the chart, the teacher will then ask, What is this chart telling me? What am I suppose to be learning here? (Possible student responses: We are learning about different shapes, we are learning about something called regular polygons, we are learning about how to make polygons, etc.) You're right! We are learning about regular polygons. Regular polygons are shapes where all sides of the shape are the same length and where all the angles are the same size. We've worked with some regular polygons already. Can anyone think of two regular polygons we've worked with over the last two weeks? (square, triangle) Excellent! When we are showing a shape's sides are all the same length, we put a dash on each line (the teacher models this) and when all the angles are the same we mark each angle the same way with a small curve in each corner (the teacher models this). Show me how we can mark each of these regular polygons and let's talk about the number of sides and vertices each of these regular polygons have.

50 Explore (10 min.): After the teacher and students have discussed the different regular polygons and how to mark them appropriately, the students will be making regular polygons through an online geoboard activity program. The students will each have their own computer to work on, but they will be sitting with a partner so that they have the ability to help each other if any questions within their group come up. The teacher will be walking around to assist, mentor, provide guidance, and answer questions. After the students have practiced making regular polygons on the computer, the students will be given an activity sheet where they will make a picture using the regular polygon shapes they learned about today. They should be encouraged to include colors in their polygon pictures. Share (3 min.): When the majority of students have finished their regular polygon pictures, the teacher will say, Now that we have finished our drawings, we are going to have a silent walk around for everyone to see the wonderful creativity each one of you has shown in your regular polygon drawings. After the students have had a chance to walk around, the teacher and students will then have a group discussion about regular polygons and what that means. Who can give me an example of a regular polygon? (Possible student responses: octagon, triangle, square, hexagon, etc.) How do we know when a polygon is a regular polygon? (Possible student responses: when all the sides are the same length, and when all the angles are the same, when the sides and angles have been marked a certain way, etc.) By having the students share their ideas, it will give others new ways to recognize and comprehend regular polygons when they come across this concept again in the future. Summarize (3 min.): Towards the end of class, the teacher will get the group's attention and ask, So, what did we learn about or try today? (Regular Polygons) Based on the students' responses, the teacher will be able to conclude whether or not the students truly comprehended today's activities. Not only did we learn how about regular polygons, but we were able to create different regular polygons through a geoboard and drawing activity, and we learned how to correctly mark a shape to show that it's a regular polygon. What a great group of math detectives! I can tell that you will be able to recognize regular polygons in the future. Keep your eyes open!