Assessment Plan Subject: Geometry Class: K/1 Class size: Approximately 20 students Unit Length: 8 single-­‐day lessons + 1 two-­‐day lesson * Please note: For ease of marking each of the “big 6” assessment strategies have been color coded when they appear throughout the lessons of this unit. The coding operates as follows: Orange = Learning Intentions Pink = Descriptive Feedback Green = Developing Criteria Blue = Self and Peer Assessment Purple = Questioning Red = Ownership Three Initial Lessons Lesson 1 Topic / Concept : Introducing Cylinders, Cones and Cubes Learning Intentions (Lesson Objectives): This lesson is designed to introduce students to cylinders, cones and cubes. On one level, the lesson is designed to help students connect new vocabulary (for example, the word “cube”) to everyday objects with which they are already familiar (for example, an “ice cube”). On another level the lesson also serves to facilitate the exploration of these 3D objects and the attributes which define them. Math PLO Describe 3D objects (C3 for Kindergarten) = “I can name some 3D objects and also talk a little bit about these objects” Resources: “The Three Doors”: an interactive oral story I have created for this lesson Story Props: 22 plastic bags and a collection of percussive instruments (to simulate the sound of rain), a collection of 3D shapes, three puppets Mnemonic props: 1 pine cone, one ice cube, one stick Lesson Activities: Introduction (4 min): Begin with a short predicting activity. Show students the “magical shapes” you will be using as props during the story and ask students what they notice about these shapes. “Does anyone know the names of these shapes?” Lesson Focus (15 min): Tell students the story of “The Three Doors” have students create sound effects for the story. Students will also participate by choosing which 3D objects will act as “keys” to open the three doors that they will encounter over the course of the story. This process will introduce students to the names of the objects, their attributes and examples of these objects in real life. During the story the teacher will also present the 3D objects (cube, cone cylinder) alongside props (an ice cube, a pine cone and a stick) that will help students remember the names of these 3D objects. Conclusion: See evaluation/assessment Assessment for Learning: Lesson as Pretest 1) Fundamentally, the “Introduction” section of this lesson is designed to serve as a pretest to help determine student knowledge surrounding 3D solids. This information can then be used when implementing further lessons. To guide this process the teacher may wish to use an assessment sheet such as that contained in appendix G. 2) (3 min) After the story has been read, you should also ask students if they can remember the names of the 3D objects used in the story. Ask students if they can also remember the mnemonic prop which helps them determine the names for these shapes. Ask students what criteria make these shapes distinct. Integration with other subjects: Kindergarten ELA: A2, A4, A8, B2 Grade One ELA: A1, A6, A7, B5 Developing Questions for the Unit (15 min) Some-­‐time between lessons one and two, you should focus on the open ended questions that will function within this unit. As students have experienced lesson one, they will have already been exposed to some of the key ideas of the concepts we will be working with. This process may have peaked some specific curiosities that students would like to explore further. To begin this process display on the smart board the three open ended questions that you would like to focus on: 1) How can we label and define 3D shapes? 2) How are 3D shapes related to 2D shapes? 3) How can we put different 3D objects into groups? Once you have modeled your questions, ask students to talk with a partner about any questions they have about geometric shapes and objects. Emphasize that these questions may be open or closed. After speaking with a partner, have students write their question down as a journal entry. Your 3 open questions will reappear within the lessons that follow. You will also have students reconsider their own questions during lesson 6 and during the end-­‐of-­‐unit student conference. Lesson 2 Topic / Concept: Seeing 2D shapes in 3D objects. Learning Intentions (Lesson Objectives): This lesson introduces students to the idea that 2D shapes exist within 3D objects through a free exploration learning model. . In doing so, students may also begin to understand that the 2D shapes which comprise an object offer one means of classifying that object (as a cube, prism, pyramid etc). Math PLO Compare 2D shapes to parts of 3D objects (C4 for grade one) = “ I understand that 3D objects are made up of shapes that I know like squares, triangles etc.” Resources 22 blank pieces of paper A collection of 3D shapes (at least 20) Washable paint, pencils, and pencil crayons. Models of the type of pictures that students will be making (see appendix D) Lesson Activities Day One: Introduction (5 min): Show students the pictures (on a smart board) which model the ones we will be making (see appendix D). Ask students what kinds of 2D shapes they see in the pictures. Developing Criteria: 1) (4 min) After looking at the model paintings (found in appendix D), ask students to talk with a partner about their favorite parts of these paintings (in other words “Choose a painting that you both like and decide on what you like most about that painting”). 2) (10 min) After partners have shared their ideas with each other have one person from each group share their thoughts with the rest of the class. During this process the teacher will write down these thoughts on the smart board. After all ideas have been written down, find ideas that look similar to you and ask the class if they consider these ideas to be similar as well. Use this strategy to narrow down the criteria on the smart board until you are left with 6 ideas (See appendix J). 3) Overnight, each of these written criteria on a giant (about 3’ x 3’ x 3’) cardboard die with one criteria item per side. Lesson Activities Day Two: (5 min) During the next day’s class, show students the giant die and roll it twice. Then explain that for today’s lesson the students will be focusing on the two criteria that were rolled when they do their own paintings (See appendix J). Represent both of these criteria down on the smart board [using both words and images (for example by utilizing an app like communicate in print)] Save this giant die as it will be used in further painting and drawing lessons. Lesson Focus (20 min): Explain to students that we will be making our own “shape pictures” by tracing and stamping 3D objects. Students may make any design or picture they choose by tracing faces of 3D objects and then coloring them in or by painting the faces of the 3D objects and then using the object as a stamp. Students will work around large art tables while the teacher circulates the room questioning and assisting students. Assessment as Learning (self and peer assessment) 10 min: After all students have finished making their paintings, have them regroup with the partner that they had during the criteria development section of this lesson. Have students show the paintings they have made to each other. Then have students consider their paintings in relation to the two criteria that were established. Do they believe they were able to meet the criteria? To facilitate this process, have students individually complete a worksheet such as that found in appendix f. During the concluding activity, observe students’ abilities to describe how they made their pictures. Ask questions like “what 3D shape did you use to make that?”. Record anecdotal notes in your notebook (See Appendix I). Modification: If students do not know what they want to make, draw a geometric image on the blackboard (such as a house) which they can try to replicate. Extension: If a student is easily able to recognize which 3D objects will make which 2D shapes, encourage them to think about how a 3D object could be defined by its constituent 2D shapes. Integration with other subjects: Kindergarten Art: A2 (create images featuring shape) Grade One Art: A2 (create images featuring shape) Lesson 3 Topic / Concept : A 2D “Eye Spy” Adventure Learning Intentions (Lesson Objectives): This lesson once again focuses on having students recognize 2D shapes that exist within 3D figures. In doing so students will begin to understand that the 2D shapes which comprise an object offer one means of classifying that object (as a cube, prism, pyramid etc). Math PLO Compare 2D shapes to parts of 3D objects (C4 for grade one) = “I understand that 3D objects are made up of shapes that I know like squares, triangles etc.” Resources: 22 Eye Spy Charts (see appendix A), Pencils, a hard surface for students to write on when outside. Models of 2D objects, to scaffold the Eye Spy Activity Models of 3D objects (for concluding activity) Lesson Activities: Lesson Focus (10-­‐12 minutes per group): During playtime take students outside in groups of 5. Lead 3 rounds of “Eye Spy” (“I spy a 3D object (such as an electrical box) that has a square as part of it”) and have students fill out their Eye Spy Chart as you play. When the whole group is back together (after playtime) play a few rounds of this version of Eye Spy –this time with the students leading the game (5 min). Questioning within the Context of a Concluding Activity (6 min): As a class, discuss the connections between 3D objects and their constituent 2D shapes. Ask guiding questions such as “If we see an object made up of only squares, does that mean it might be a cube?” or “Do pyramids have triangles in them?”. Use models of these 3D objects to facilitate this discussion. Assessment for Learning and Differentiation: Take anecdotal notes (in your notebook) during the discussion which occurs within the concluding activity. The discussion should be indicative of whether or not some students are beginning to understand that the 2D shapes within a 3D object may help define that object as a specific geometric entity. Try utilizing questioning techniques to identify students who are having the most difficulty in grasping this concept. Then, design small scale remedial activities that these students can do with the assistance of an E.A. Such activities could include: a) folding 3D objects from nets, and b) making model 3D objects using mediums like straws and playdough. Additionally, examine students’ Eye Spy charts once completed. Combine the information gathered from these charts with the info you have gathered from your questioning during the concluding activity (see appendix I). This should help confirm reliably which students will benefit from remedial instruction. Store these charts in student portfolios for later reference. Outline of the Remainder of Lessons Lesson 4 Topic / Concept : “Cubes and Cones” P.E Game Learning Intentions (Lesson Objectives): This lesson is deigned to help students differentiate 3D objects on the basis of single attributes. In particular it is designed to help students differentiate between cubes and cones using ideas that have been introduced in previous lessons such as what 2D shapes compose the 3D object. Again this lesson also encourages students to connect these shapes with real life exemplars. Math PLO Sort 3D objects using a single attribute (C2 for Kindergarten and Grade 1) = “I know that different 3D objects are made up of different shapes” Resources: 1 giant die made from cardboard [face 1: picture of cube, face 2: picture of a cone, face 3: “has a (image of a circle)”, face 4: “has a (image of a square), face 5 and 6 –see appendix B] Model of a cube and cone (for concluding activity and assessment) Lesson Activities: Preliminary Step (5 min): Begin by playing a few rounds of crows and cranes with the students. The only difference will be that team names will become “cubes” and “cones” Lesson Focus (15 min): Introduce students to the giant die, explain to them that instead of having their team name called, they will have to determine this information by examining the die. Before playing, go over each side of the die to ensure that students know how to respond appropriately. For example, if the die were to land face up on a picture of a conical tower, the students would have to determine that this image represents a cone, -­‐therefore the cone team will chase the cube team for this round. Conclusion: See Assessment Assessment for Learning and Descriptive Feedback (3 min): 1) After students have played a few rounds of the game, assess which sides of the die are presenting the most difficulty for students to figure out. 2)Pause the game and show students the models of the cube and cone that you have with you. Use these models to orally reinforce concepts that the class may be having difficulty understanding [for example, if the dice says (or shows in pictures) “has a square in it” it is probably pointing to a cube because when you look at a cube you can see its square faces] 3) Resume the game and continue to assess participants’ comprehension in order to offer further descriptive feedback as needed. Ownership: Later in the week have your class teach this game to another k/1 class in the school. To maximize teaching time, divide your class into groups of three and match them with groups of three from the other class. Then have your students explain the game to the groups of students from the other class. Once this is complete have both classes regroup and play a few rounds of the game together. Lesson 5 Topic / Concept : Building 3D representations of local plants Learning Intentions (Lesson Objectives): This lesson allows students to practice replicating composite 3D images while also allowing them to contemplate the structure and needs of local plants. Some of the 3D objects which are used in this lesson (pine cones and cylindrical sticks) are designed to reinforce the mnemonics introduced in lesson 1. Math PLO Replicate composite 2D shapes and 3D objects (C3 for Grade One) = “I can make my own version of 2D and 3D patterns that I see” Resources: A collection of: pine cones, cylindrical sticks and circular rocks. Drawn depictions of: 3 cedar trees and 3 dandelions. Lesson Activities: Introduction (4 min): As a class, brainstorm the common structural characteristics of plants. Write down students’ ideas on the chalkboard. Lesson Focus (15 min): Take students outside. Divide students into 6 groups. Assign each group to a collection of pine cones, sticks and rocks (laid out in a pile) and give each group a drawn depiction of a dandelion or cedar tree. Have students recreate the drawn images using the pine cones, sticks and rocks. Circulate between groups as they do their work. Conclusion: See assessment Assessment as Learning (self and peer assessment) 10 min: 1) After all groups are finished their replicas, have groups observe each others’ work such that group a is observing group b’s work and group b is observing group a’s work. 2) Have students examine the work of the other group and think of a) two things they really like about it and b) one thing that could have been done differently in order to have the replica be a closer representation of the original. 3) Have groups communicate their feedback orally to each other. 4) After oral feedback has been received have the groups return to the replica they made and modify their replica in accordance with the feedback they received. Assessment for Learning and Descriptive Feedback: As groups are working on their replicas circulate the area assessing each group’s ability to make their replica similar to the drawing they have. Offer descriptive feedback such as “Hi everybody, I noticed that in the drawing the tree has roots that look like long strait lines. In your replica I noticed you are using pine cones to represent the roots. Do you think that there might be another object you could use (i.e. the sticks) to represent the roots?” Photograph the replicas that each group has made. Then place these photographs side by side the drawings that they were intended to represent. Examine each group’s replica and ensure that each group was able to produce a replica that reasonably represented the original. If one group was unable to do this, closely observe these students during lessons 8 and 9 which also involve creating 2D and 3D replicas. Lesson 6 Topic / Concept : Partner sorting Learning Intentions (Lesson Objectives): This lesson designed to give students hands on practice in creating and deducing sorting rules for 3D objects. As opposed to previous activities, this lesson emphasizes interpersonal communication using mathematical language and ideas. Math PLO Sort 3D objects using a single attribute and explain sorting rule (C2 for Kindergarten and Grade 1) = “I can put 3D objects into different groups using rules I have invented” Resources: Premade bags containing 5-­‐10 3D objects. Each pair gets one bag. Lesson Activities: Introduction (8 min): Begin by showing students two sets of 3D objects which I have sorted. Have students take turns trying to guess the sorting rule before I draw a cat on the chalk board (like hangman). This will be done as a class with students sitting at their desks. Lesson Focus (10 min): Divide students into pairs, giving each pair a bag of 3D objects. Have students take turns sorting the objects while the other person tries to guess the sorting rule used. Assessment for Learning: While visiting pairs of students, ask what sorting rules they are using. Take note (see appendix I) if students are using the component 2D shapes as a basis for their sorting or deductions and record which students have and have not grasped this concept. Conclusion (4 min) Questioning: Have students refer to the individual questions that they recorded in their journals near the beginning of the unit. Ask students, “have they been able to answer their question yet?” If so, have them record the answer in their journal. If their question has not been answered, encourage them to focus on it in the lessons that follow. Modification: Some groups may require you to give more examples of how to sort 3D objects before grasping the concept of sorting based on attribute. You may also allow students to sort based on non-­‐conventional attributes such as the shape having sharp points, being able to roll etc. Lesson 7 Topic / Concept : 3D shape scavenger hunt done in teams Learning Intentions (Lesson Objectives): This lesson is designed to augment students’ abilities to describe 3D shapes, by focusing on the qualities of these shapes. Math PLO Describe 3D objects (C3 for kindergarten) = “I can talk about a 3D object by using the shapes that it is made out of” Resources: 5 Scavenger Hunt check lists (one list for every group of 4). See appendix C Models of the hidden objects (for modification) Lesson Activities: Preliminary Step: Hide the following items in the playground and school yard: 5 cubes, 5 pyramids, 5 cones and 5 cylinders. Lesson Focus: Take students outside. Do a think-­‐aloud to model how one might go about finding the first item on the check-­‐list, before beginning scavenger hunt. Then divide students into groups of 4 and give each group one check list before beginning the scavenger hunt. Conclusion: See Assessment Assessment for Learning (1 min per group): Go over the completed checklists and ask each group to show their example for each clue. Ask individual students how they knew what shape to look for. When doing this you can utilize some of the open questions you presented at the beginning of this unit Record the responses of individual students in your notebook. Modification: If some groups are having trouble with the clues, go over the clue with them and show them the models. Ask which model looks like it fits this clue? Lesson 8 Topic / Concept : Replicating 2D Images Learning Intentions (Lesson Objectives): This lesson allows students to practice replicating composite 2D images. Additionally working in pairs encourages students to use mathematical terminology while learning to express their thinking with greater clarity. Math PLO Replicate composite 2D shapes and 3D objects (C3 for Grade One) = “I can make my own version of 2D and 3D patterns that I see” Resources: A collection of 2D pattern blocks. Photographs of patterns made from these blocks. Samples of pattern block images (see appendix E) Hinged Mirrors (if available) Lesson Activities: Preliminary Steps: Create 3 different images out of the pattern blocks. Photograph the images and give each pair photographs of all three images. These images should be of varying levels of complexity Introduction (6 min) : Using the pattern blocks as models, review the names for the different 2D shapes with the class. This is intended to help students use this vocabulary when doing the main activity. Lesson Focus (12 min): Have students replicate the photographed images by working together in pairs. Assessment for Learning: Observe individual students’ abilities to replicate the patterns and to use mathematical dialogue when describing the pattern blocks. Record this information anecdotally and save it for use in the unit’s summative assessment rubric. Modification: If a pair is having difficulty replicating the images, have students take turns making a simple image while the other copies it. Lesson 9 Topic / Concept : Creating a 3D representation of a flower Learning Intentions (Lesson Objectives): This lesson allows students to further explore the structural characteristics of plants by having them construct a 3D paper flower from a model. In doing so students gain practice in replicating multifaceted 3D objects. Math PLO Replicate composite 2D shapes and 3D objects (C3 for Grade One) = “I can make my own version of 2D and 3D patterns that I see” Resources: 1 cube net, 6 pyramid nets, 1 rectangular prism net and 2 eliptical 2D shapes for each student. Several demonstration flowers will also be required Card stock paper (to print the nets onto) Paint, paint brushes and glue. Lesson Activities: Preliminary Step (to be completed on a previous day): Hand out the pyramid and prism nets to students and have students paint them any way they wish. Have students write their names on their nets. After the nets have dried the teacher will fold them all up. Introduction (5 min): Review with students the components of the dandelions that were constructed last class. After writing some of these structural components on the board, explain that today we will be making our own 3D flowers by focusing on the stem, leaf and flower components. Lesson Focus (20 min): Show students the model flowers. Have students construct their own flower by folding and then combining the nets provided Conclusion: see assessment Assessment for Learning : After the flowers have been made, ask individual students what similarities exist between the different 3D objects that compose the flower. For example you may wish to encourage students to think about how the pyramid and the cube both contain 2D squares, which is why they fit so well together when making the flower. Record student responses anecdotally in your notebook for use in the final assessment of learning. Modification: Some students who have difficulty with fine motor skills may benefit from doing this lesson with the assistance of a partner. Unit Conclusion: Assessment of Learning Using the products that students have created in lessons 2, 3, 5 and 7 begin to tentatively fill out the summative rubric found in Appendix H. The information which you gather from these products should also be augmented by the anecdotal observations you made in lessons 3, 6, 8 and 9. Additionally, hold a five minute conference with each student during which the following types of questions will be asked: 1) Closed questions designed to elicit student understanding of the learning objectives 2) Open questions about what activity students enjoyed most in the unit and what activity they felt helped them learn most effectively. 3) Were you able to answer the geometry question you had at the beginning of this unit? If not, why not? What are some ways that your teacher or your parents could help you find this answer? Responses from the first type of questions will allow you to finish filling in the rubric contained in appendix H. Responses from the second type of questions will provide the teacher with valuable feedback to inform their future teaching practice. Appendix A: I Spy Adventure 2D Shape Place Found (invented spelling okay) Object that the 2D shape is part of Cube Prism Cone Appendix B The large die: Appendix C 3D Object Scavenger Hunt 1) Has a 2) Has a 3) Has a 4) Looks like Appendix D: Painting Samples Appendix E: Replicating 2D Patterns Appendix F: Self Assessment Criteria One “………………………………………………………” Criteria Two “………………………………………………………” (Students draw the symbol that matches their self assessment for criteria one here) (Students draw the symbol that matches their self assessment for criteria two here) I did a good job of using this idea = I did an okay job of using this idea = I could have done a much better job using this idea = Appendix G: Pretest Hold up a cube, ask students: “How many people (Here, record approximate number of students who think they know what this shape might be put their hands up. Then ask some of these students called?” what they believe the answer is. Record these responses here as well) Ask students, “How many people can think of an (Record student responses here) example of a cube shape in everyday life?” Hold up a cylinder, “How many people think that this object is called a cone?” (Record number of students that believed this information to be true) Hold up a cone, “Does anyone know what this object might be called?” (Record student responses here) Hold up the cone again, “Can anyone think of any objects in everyday life that look like this?” (Record student responses here) Appendix H: Summative Rubric Student: Approaching Expectations Meets Expectations Exceeds Expectations “I can name some 3D objects and also talk a little bit about these objects” “ I understand that 3D objects are made up of shapes that I know like squares, triangles etc.” “I know that different 3D objects are made up of different shapes” “I can make my own version of 2D and 3D patterns that I see” “I can put 3D objects into different groups using rules I have invented” Appendix I Sample Anecdotal Notes from Teacher Notebook Student: Hugo C. -­‐During lesson 2 Hugo recognized that cubes will make a 2D square shape when traced or stamped on paper. -­‐In lesson 8 Hugo showed a grade level ability to replicate 2D patterns Student: Fidel C. -­‐During lesson 3, Fidel showed an above grade level understanding of the relation between 2D shapes and 3D objects Student: Evo M. -­‐After making his painting is lesson 2, Evo had a hard time remembering what 3D objects he had used to produce the triangles and squares on his page. -­‐After speaking with Evo and examining his work at the end of lesson 3, I determined Evo was still having a very hard time and would benefit from remedial instruction -­‐During lesson 6 Salvador demonstrated a grade level ability in sorting 3D objects according to a single attribute Student: Salvador A. etc. etc. etc. etc. Appendix J: Steps of criteria development 1) Initial input of what students like about the model paintings -­‐Colourful -­‐Detailed -­‐Organized -­‐Lots of shapes -­‐Bright -­‐Pretty -­‐Looks happy -­‐Carefully coloured -­‐Clean lines -­‐Not messy -­‐Thoughtful -­‐Made with care 2) Narrow input down to six qualities and define on T-­‐Chart Quality Colourful Thoughtful Detailed Etc. Definition -­‐Uses more than two colours -­‐Care and thought have been put into making this -­‐Has many shapes and lines -­‐Etc. These six qualities will then be painted on to a giant die. The next day the die will be rolled twice so students know which two qualities to focus on when making their painting. These qualities will be displayed in large print on the smart board: 1) Colorful: Uses more than two colors 2) Detailed: Has many shapes and lines