1 THE UNIVERSITY OF TRINIDAD AND TOBAGO SCHOOL FOR STUDIES IN LEARNING, COGNITION AND EDUCATION BACHELOR OF EDUCATION PROGRAMME LESSON PLAN- MATHEMATICS SPECIALIZATION ( SECONDARY) INTRODUCTORY BACKGROUND NAME: DATE: CLASS: SUBJECT: MATHEMATICS AGE RANGE: ABILITY LEVEL: NO. IN CLASS: 21 NO. PRESENT: TOPIC/CONCEPT: DURATION: SPECIFIC OBJECTIVES/ LEARNING OUTCOMES: CLASSIFICATION: 2 At the end of the lesson students will be able to: (Cognitive Domain) 1. Identify items in real life that are shaped like cubes 2. Identify the attributes/properties of a demonstrated cube 3. Describe what is the net of a cube 4. Explain how to derive the net of a given cube 1 2 3 4 5 Knowledge Analysis Knowledge Comprehension Synthesis / Precision 6 Synthesis / Precision 7 Responding (Cognitive & Psychomotor Domain) 5. Accurately create more than one distinct net of a cube using concrete cube manipulatives, in a group activity (Affective Domain) 6. Participate willingly in a group activity to discover the net of a cube PREVIOUS KNOWLEDGE, SKILLS AND EXPERIENCES: 1. Students are able to identify prototypes of the 3 dimensional figures: cubes, cuboids, cylinders, prisms, cones and pyramids. 2. Students know the properties of a square. 3. Students are familiar with the following terms related to a cube: face, edge, vertex/vertices MATHEMATICAL PROCESSES: 1. The students have to engage in the activity, in a given amount of time, of creating more than one examples of net of a cube. Students cooperate to discover ways to get multiple 3 nets. This task involves the problem solving process with the use of concrete manipulative where students engage in visualisation and inventiveness among other skills to find more than one solution to the same problem (more than one net of a cube). Students have the freedom to use more than one strategy to solve the problem. 2. The activity to create more than one net of a cube requires the students to recognize structures of the nets which may or may not result in a cube. Students are required to give reason(s) in attempting to distinguish which net gives a cube. This develops their reasoning skills. The group activity encourages students to critique each other’s suggestions in their groups and formulate full-proof methods in proving their answers. Since each group is required also to explain their solutions reasoning skill is further developed. 3. The lesson builds on students’ prior knowledge of understanding the nature of 3 dimensional figures and how it makes it possible to derive a net from a cube. By referring to cardboard boxes, which are items in their real life, students will make connections to what they already know and effectively develop their mathematical understanding. The new knowledge of “nets of a cube” is not learnt in isolation and will most likely be imbedded in long term memory. 4. The use of multiple representations of the cardboard box by demonstration (concrete manipulative) and the diagram of it on the whiteboard provide students with more than one way of deriving the attributes of a cube. Drawing the discovered nets on the checkered grids provided when they are given the 3” X 3” cubes provides them with the opportunity to use representations to record the idea of “nets of a cube” 4 5. Demonstration of solution(s) in the activity and including the journals in the lesson provides the students with experiences of multiple ways of expressing mathematical understanding. Apart from demonstrating, students communicate their ideas when they write and explain their method(s) used in deriving nets of a cube. RESOURCES: 1 large cardboard box – (cube-shaped) 25 prepared paper cubes – 3”X3”X3” Large demonstration cube Adhesive Tape 6 Pairs of Scissors White board & White board markers Prepared Written Assessment Prepared Activity Worksheets Laptop Multimedia Projector Relevant software Two dice A Rubik’s Cube THE LEARNING ENVIRONMENT: The desks will be arranged linearly however it should accommodate cooperative learning groups of four or five students. It should also be arranged so that all students are able to see on the 5 whiteboard. The room has proper lighting, good ventilation and an air condition unit. Space is readily available. The environment includes the following resources: 1 large cardboard box – (cube-shaped), 25 prepared paper cubes – 3”X3”X3”, large demonstration cube, adhesive tape, 6 Pairs of Scissors, white board & white board markers, prepared written assessment, prepared activity worksheets, laptop, multimedia projector, relevant software, two dice and A Rubik’s Cube. CLASSROOM MANAGEMENT STRATEGIES: ENERGISERS: THEORETICAL UNDERPINNINGS: 6 SET INDUCTION: TIME ALLOCATION 1: 3 Minutes Bring students to the floor. Ask, “Who can say what an attribute is?” Confirm that an attribute describes a quality, property, or characteristic of somebody or something. Call on a student to stand in front of the class and state an attribute/property of the child (the color of their hair, eyes, shoes, etc.). Ask students, “What are some other attributes (or properties) of … (name of student). Students contribute suggestions. MAIN IDEAS/ UNDERSTANDINGS/FOCUS The properties of a cube are: Cubes have twelve edges, eight vertices and six faces which are squares The net of a 3 dimensional object is STEP- BY STEP PROCEDURES/ACTIVITIES IN THE LESSON SECTION ONE – 12 Minutes Introduce the alternative words to “attributes”: properties, characteristics, qualities. Ask students, “Who can recall the names of the different three dimensional figures you learnt about in last class?” Pause a few seconds then call on student(s) in class to list them. Let students know that the main focus of the lesson is on Cubes, their properties, and their nets. Show students Figure 1 on the slide show (see Appendix) which shows various 3D shapes and ask, “Which shape shown is a cube?” Ask a student who raises his/her hand to give an answer. 7 Reveal to students a large cube- shaped cardboard box to demonstrate an example of where in the real world a cube can be found. Ask students, “What else (in the real world) has the shape of a cube?” List at least Three (3) examples given by students on the whiteboard. If students are unable to give examples, three are Die (plural Dice) Ice cubes Rubik’s Cube Distribute one cube each to the students and ask them to identify the different properties of the cube, making sure they call the “sides” faces, and “corners” vertices. Prompt students with the questions, “What can you tell me about the faces of the cube the edges of the cube the vertices of the cube?” As students identify the properties compile a list on the whiteboard. When all properties are listed allow students to write them in their math notebooks. Ensure the following properties are included: Cubes have twelve edges, eight vertices and six faces all faces are squares To reinforce the properties of a cube show a number of projected images of mixed examples and non-examples of cubes. Students must analyse which are cubes/not cubes, and say why. Pose questions to the entire class then randomly choose students to give responses. Ask the following questions for each image: 1. Is this a cube? 2. Why do you say so? 8 SECTION TWO – 20 Minutes Activity Place students in groups of three’s for the purpose of the activity. State the objective of the activity – To Investigating the Net of a Cube Give students the definition of what is a Net. Then ask students, “Given the definition of a Net, what do you think is the net of a cube?” Write their definition at the top of the Whiteboard. Allow students to take note of the definition in their notebooks. Let students know that they will now follow three simple steps in which you start with a cube and derive its net. They will work in their groups of three’s and use ONE cube per group. Use the prepared comprehensive steps shown on the power point slides for students who cannot understand clearly by listening. An instruction sheet is distributed as well for each student. INSTRUCTIONS: Step 1. Place the cube on a flat surface (the desktop/table-top). Identify the top flat face of the cube. Using a pair of scissors, cut three edges around the face to make a flap (see Step 1 diagram) Step 2. Cut along the four vertical edges downwards until you reach the base of the cube. Hold the flap and open outwards (see diagram) Step 3. The cube can now be opened completely to the form of its net (see diagram) Demonstrate how the net is formed back into a cube by folding. Let students know that it is possible to get eleven (11) distinct nets of a cube. Students in each group now work together to create different nets of a cube, Each group is allowed three cubes. Instructions given: Students can cut ONLY edges ALL faces must be joined together by at least one edge each 9 Every student must participate Groups are given five (5) minutes to create their nets. Observe students on-task Presentation of Findings Students, in their groups, display their nets by sticking them on different sections of the whiteboard. Label each group’s work. Possible questions to ask group members: How do you know that you have created a net of a cube? Was there any special method that you used to arrive at your nets? Did you make any other observations when you Can you draw a net of a cube without using the cube? Is it possible to create a new net of a cube without using the cube? How? Why do you think we need to learn about Nets? Confirm that all nets are accurate. Allow students to draw the different nets of a cube that they created, on the Grid Sheet provided. QUESTIONING STRATEGIES 10 SECTION 1: Teaching TIME ALLOCATION 2: CONTENT METHODOLOGY TEACHING POINTS TEACHING STRATEGIES An attribute is a property or CLASS DISCUSSION characteristic of an object (person, thing etc). The teacher asks the students what LEARNING ACTIVITIES Students contribute suggestions of what they think an attribute is. they think an attribute is. After discussion the class confirms that an attribute describes a quality, property or characteristic of something or someone. The teacher then asks a student to stand at the front of the class and the class then states an attribute of that student. The teacher now establishes other synonyms for “attributes” and lets Other synonyms for “attribute” students know that the main focus are quality, characteristic, trait, of the lesson is on Cubes, their feature aspect and element. “attributes”, and their nets. Cubes found in the real world are : Television Dice Blocks Ice block DEMONSTRATION The teacher will reveal to students a large cube- shaped cardboard box to demonstrate an example of Students give examples of cubes found in the real be found. At least three examples of world. where in the real world a cube can cubes found in the real world, given by students, will be displayed on the whiteboard. 11 USE OF MANIPULATIVES The properties of a cube It is a three – dimensional solid It bounded by six square faces, twelve edges, with three meeting at each vertex. It has eight vertices It has eleven nets Distribute one cube each to the students and ask them to identify the different properties of the cube, making sure they call the “sides” faces, and “corners” vertices. A list of the properties will be complied on the whiteboard. When Students will identify different properties of the cube and write them in their math notebooks. all properties are listed, students will be allowed to write them in their math notebooks. USE OF VISUALS Show students on the slide show, various 3D shapes consisting of examples and non- examples of Students answer questions based on examples and nonexamples of cubes. cubes. Pose questions to the entire class based on the various 3D shapes then randomly choose students to give responses. QUESTIONING -“Who can recall the names of the different three dimensional figures you learnt about in last class?” Students actively participate in formative questioning 12 -“What are some other attributes (or properties) of … (name of student). -“What else (in the real world) has the shape of a cube?” -“What can you tell me about the faces of the cube, the edges of the cube, the vertices of the cube?” -Is this a cube? -Why do you say so? 13 SECTIONAL REVIEW 1/ VERIFICATION OF LEARNING DURING THE LESSON 1: SECTION 2: Activity TIME ALLOCATION 3: CONTENT TEACHING POINTS METHODOLOGY TEACHING STRATEGIES COOPERATIVE LEARNING Students will be placed in groups of four or five A net is a twodimensional figure that can be cut out and folded up to make a threedimensional solid. LEARNING ACTIVITIES Allow students to take note of the definition in their notebooks. Teachers will give students the definition of a net and then ask them what they think the net of the cube is. Their definition will be written on the whiteboard. Teacher will let students know that they will now follow three simple steps to derive the net of a cube. They will work in their groups and use ONE cube per group. After deriving one net, they will try to derive other nets of the cube. Each group is allowed three cubes. Teacher will demonstrate how the net is Working in cooperative learning groups students will start with a cube and derive its net. Students, in their groups, display their nets by sticking them on different sections of the whiteboard. formed back into a cube by folding. They will also observe students on-task and confirm that all nets are accurate. Allow students to draw the different nets of a cube that they created, 14 on the Grid Sheet provided. EXPLANATION Students accurately Teacher will use the procedure shown on the follow teacher’s power point slides for students who cannot instructions understand clearly by listening. An instruction sheet will also be provided for each student. QUESTIONING How do you know that you have created a net of a cube? Was there any special method that you used to arrive at your nets? Did you make any other observations when you Can you draw a net of a cube without using the cube? Is it possible to create a new net of a cube without using the cube? How? Why do you think we need to learn about Nets? 15 CLOSING ACTIVITIES: - 5 Minutes SUMMARY &CLOSURE Pay special attention to the presentation of materials on the whiteboard which serves as a visual representation of the concepts learned. Students can take notes in their journals in a similarly organized fashion. ASSESSMENT ACTIVITIES: ADAPTATIONS OF THE LESSON: TEACHER’S LESSON APPRAISAL/ REFLECTION ON THE LESSON: 16 CONTINUATION/ FOLLOW –UP: CO-OPERATING TEACHER’S COMMENTS: PRACTICUM ADVISOR’S COMMENTS: 17 APPENDIX: FOUR COLUMN LESSON PLAN Overall goal: Materials needed: Steps of the Lesson: Expected student Teacher’s Responses Goals and Method(s) Learning Activities Reactions or to Student of Evaluation and Key Questions Responses Reactions/ Things to Remember 18 Steps of the Lesson: Expected student Teacher’s Responses Goals and Method(s) Learning Activities Reactions or to Student of Evaluation and Key Questions Responses Reactions/ Things to Remember 19 Matthew, M.E. et al (2009). Using Lesson Study and Four- Column Lesson Planning with Pre-service Teachers. Mathematics Teacher 102(7).pp.504-509.