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# Standard A: Plans Curriculum and Instruction

## on Jun 23, 2011

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This document provides five lesson plans that were part of a unit on geometry that I planned and taught. There is also a reflective essay about my experience planning curriculum.

This document provides five lesson plans that were part of a unit on geometry that I planned and taught. There is also a reflective essay about my experience planning curriculum.

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## Standard A: Plans Curriculum and InstructionDocument Transcript

• Standard APlans Curriculum and InstructionUnit: Geometry o What is a Polygon o Tangrams o Review and Formative Assessment o Lines o Geometry Scavenger HuntReflective Essay
• Grade 4 – MathematicsFrameworks and Standards This unit is built on the Massachusetts Mathematics Curriculum Frameworks for Geometry Grades 3-4 Standards 4.G.1 – 4.G.9 (page 40) and Grades 3-4 Standards for Measurement 4.M.1 and 4.M.4 (page 48) Thus unit is also built on the Braintree Public Schools Grade 4 Mathematics Geometry Module which follows the MA FrameworksEssential Questions (Goals) What is geometry? How can it help me solve real world math problems? How can I describe and tell the difference between 2-D and 3-D shapes? How can I name angles that look different and how can I use that to help me classify triangles and quadrilaterals? What’s the difference between parallel, intersecting and perpendicular lines? What happens when I move shapes in different ways? Can all shapes and figures be cut in half equally? When do I need to find perimeter, area or volume? What do I need to know to find those?The geometry unit that I planned and implemented in the classroom was done over a five weekperiod. The following five lesson plans are a sampling of the types of lessons I taught to create aproductive, creative and cooperative learning environment to meet the standards and answerthe essential questions as focusing goals.
• What is a Polygon?Grade 4 MathFebruary 28, 2011 (Monday)85 minutesMassachusetts Curriculum Framework:Mathematics – Geometry – 4.G.1 Compare and analyze attributes and other features (e.g., number ofsides, faces, corners, right angles, diagonals and symmetry) of two and three dimensional geometricshapesMathematics – Geometry – 4.G.2 Describe, model, draw, compare and classify two and threedimensional shapes, e.g. circles, polygons – especially triangles and quadrilaterals – cubes, spheres, andpyramidsObjective:The objective of this lesson is for students to build a foundation for understanding polygons and howthey can be classified. One goal is that students will be able to determine whether a figure is a polygonand describe why or why not. Another goal is that students will be able to classify polygons by thenumber of sides a figure has.Expected Student Outcomes:At the completion of this lesson, students will be able to: Explain the difference between an open and closed figure Define a polygon as a two-dimensional, closed figure with straight sides Determine whether a particular figure is a polygon or not Classify a polygon by the number of sides it hasInstructional Procedures: I will introduce this lesson by giving each student a half sheet of paper with two rows of figures drawn on it. One row has open figures and one row has closed figures. I will ask the students to look at the figures and jot down in their journals what differences and similarities they see between the figures. The students will then turn and talk about what they wrote in their journals. I will then ask volunteers to discuss with the whole class their thoughts on the figures. I will use their thoughts and ideas to build the definition of open and closed figures. The students will label the figures as open or closed and keep the sheet in their journals.
• I will then draw a circle and a square on the whiteboard. The students will draw a circle and square in their journals and we will have a class discussion on the similarities and differences. Through the discussion, we will arrive at the conclusion that they are both closed figures but only one has straight sides. (I will use the student comments to guide them to reach this conclusion, but I only want to guide, not tell.) I will write the word polygon on the board and write the definition as a two-dimensional, closed figure with straight sides. I will ask the students whether they think the square can be a polygon and whether the circle can be a polygon. In their journals, I will have them label the square as a polygon and label the circle as not a polygon. I will draw the figure from page 436 #26 on the board. I will have the students copy the figure in their journals and independently write whether it can be a polygon or not. We will have a whole class discussion about it after a couple minutes of writing. I will then list the words triangle, quadrilateral, pentagon, hexagon and octagon on the board. The students will copy the words into their journals and try to draw what they think each figure looks like. I will have volunteers come up to the board to draw each figure. I will correct misunderstandings and clarify as we progress. The students will then work independently on Reteach 19-2 and page 435 numbers 1-5. I will assign the homework; Practice Sheet 19-2Materials and Resources: Each student’s math journal Math book for each student Copy of open and closed figure sheet for each student Copy of 19-2 Reteach and Practice sheets for each student Whiteboard and dry-erase markersAssessment of Student Achievement: This lesson includes many opportunities for informal assessment to check what students alreadyknow and how they are progressing during the lesson. I will assess what the students already knowabout open and closed figures by watching what they are writing in their journals and listening to theturn and talk time and whole class discussion. I will check what the students already know aboutclassifying polygons by watching what they are drawing for each classification listed. I do not want to
• just tell the students how many sides each figure has before I see what they already know about it. Thiswill allow me to focus instruction on the figures they are confused on. During the lesson, I will check for student understanding by walking around and monitoringwhether they are editing the ideas in their journals to match what is being taught. I want the journals tocapture thinking, but I also want them to capture how their thinking should be modified. I will also checkfor understanding by monitoring how individual students are performing on the Reteach sheet and bookproblems. If the students can work through these problems with ease, I will know they are successful.Students will also have the opportunity to show what they know through the homework sheet whichwill also be a way for me to assess what they have understood in the lesson.Student Evaluation: Students will be evaluated in this lesson through formative measures. The worksheets andjournal work provide me with ample opportunities to measure understanding and see if the objectivesare being met as we go through the lesson. I will collect the journals at the end of the unit and gradethem based on a rubric. The overall journal grade will be counted in as a quiz grade for math. The inclass work and homework are not graded with a formal grade to be entered into the grade-book, butthey serve as practice for the students and a check for me to see what they are understanding and whatneeds more time to be worked on.
• Tangrams – Polygon PuzzlesGrade 4 MathMarch 1, 2011 (Tuesday)85 minutes (Morning work 8:45-9:55 Math 10:15 – 11:30)Massachusetts Curriculum Framework:Mathematics – Geometry – 4.G.9 Predict and validate the results of partitioning, folding, and combiningtwo and three dimensional shapesMathematics – Geometry – 4.G.7 Describe and apply techniques such as reflections (flips), rotations(turns), and translations (slides) for determining if two shapes are congruentObjective:The objective of this lesson is for students to understand how polygons can be combined and moved toform other polygons and figures. It is a scaffold to examining flips, turns and slides in more detail in alater lesson.Expected Student Outcomes:At the completion of this lesson, students will be able to: Use two tangram pieces to form one polygon Arrange the seven tangram pieces to form one quadrilateral Arrange the tangram pieces to form other figures (bird, lion etc. from sheet)Instructional Procedures: During the Morning Work time, the students will reinforce yesterday’s polygon lesson by completing a vocabulary sheet and gluing it into their journals. The students are well accustomed to coming into the classroom in the morning and getting right down to work. I will begin the 10:15 – 11:30 block by reviewing the homework from yesterday and fielding any lingering questions from yesterday’s lesson. I will then tell the students that today we will be exploring shapes by using tangrams. I will explain that tangrams are a kind of puzzle. On the overhead projector, I will display each of the seven pieces of the tangram. I will ask students whether each piece is a polygon and if so how can it be classified.
• The students will be working in groups so I will split the class into six groups and give each group a tangram puzzle. I will tell the students that their first challenge is to make a quadrilateral using two triangles. The students will work in their groups to decide how to arrange the triangles to do this. I will give the students a minute or two to display it on their desks. I will then demonstrate the solution on the overhead. I will then tell the students that their next challenge is to use all seven pieces to make one quadrilateral. I will have the students work for about fifteen to twenty minutes to solve the puzzle (more or less time depending on their progress). It is challenging to complete, so I want to allow for ample time. Before starting, I will ask the students why they think we are working with the puzzles today. I will build on their responses to come to the conclusion that we are working with the pieces to see how polygons can work together and see how turning and flipping changes them. As the students are working, I will circulate among the groups and check on progress and observe strategies. I will encourage the students to keep trying and keep working because it is challenging but can be done. I will try to avoid giving hints unless the students are making no progress. The first group who completes the puzzle will come up to the front and display the solution on the overhead projector for the whole class to see. I will then give each student a copy of the solution that they can take home and cut out the pieces to try at home. I will also give each student a copy of the tangram packet. The packet includes figures such as animals and people that can be built with the tangrams. The students will continue to work in their groups to arrange the pieces into the figures. The students who finish all of the figures early will draw a picture of anything they would like using as many polygons as they can. I will conclude the lesson by assigning and explaining that the homework is to make a list of polygons they find at home and classify what type of polygon it isMaterials and Resources: Six tangram puzzles and one tangram puzzle that can be displayed on an overhead projector Overhead projector and screen Copy of 2-D vocabulary sheet for each student Copy of tangram solution sheet for each student Copy of tangram figure packet for each student Homework sheet with chart to list polygons discovered at home
• Assessment of Student Achievement: This lesson includes opportunities to informally assess student achievement. I will assess whatstudents already know by reviewing the homework on polygons and asking the students to identify whattype of polygon each piece of the tangram puzzle is. I will also assess what they already know by askingthe students to use two triangles to form a quadrilateral. I will be able to quickly see whether thestudents already know that shapes can be turned and flipped and combined. I start with this simplechallenge to get a sense of where students’ understanding is at the beginning of the lesson. I will check for understanding during the lesson by watching the students work together to solvethe puzzle of using the seven pieces to make a quadrilateral. I will know if they are successful if I seethem turning, flipping and rotating the pieces to form different combinations and shapes. I will alsoknow if they are successful if they can solve the puzzle. While they are working on combining pieces toform the figures in the packet I will also check on their progress. I will know if they are successful if theycan complete the figures with ease because making these figures is less challenging than the singlequadrilateral.Student Evaluation: This lesson focuses mainly on informal assessment as the students work. A more formalevaluation of this lesson will be how well students perform on later cumulative assessments.
• Review and Formative AssessmentGrade 4 MathMarch 4, 2011 (Friday) (On Wed. 3/2/11 and Thurs. 3/3/11 3-D shapes and nets were covered)80 minutesMassachusetts Curriculum Framework:Mathematics – Geometry – 4.G.1 Compare and analyze attributes and other features (e.g., number ofsides, faces, corners, right angles, diagonals and symmetry) of two and three dimensional geometricshapesMathematics – Geometry – 4.G.2 Describe, model, draw, compare and classify two and threedimensional shapes, e.g. circles, polygons – especially triangles and quadrilaterals – cubes, spheres, andpyramidsObjective:The objective of this lesson is to give students a fun way to review geometry concepts learned so far andto have students take a formative assessment to check for understanding up to this point. The objectiveof a formative assessment is to be able to use the results to guide instruction.Expected Student Outcomes:At the completion of this lesson, students will be able to: Extend their knowledge of polygons to a real life example Understand which ideas and concepts from the topics of polygons, two-dimensional and three- dimensional shapes are most important to know Demonstrate their understanding of these concepts through a formative assessmentInstructional Procedures: During the morning work time (8:40 – 9:00) students will choose one of the polygons found for homework on Tuesday night and draw a picture of it. They will then cut construction paper into the shape of the polygon and glue their picture on. I will use their polygons to put up on a bulletin board. I will begin the math block (10:30 – 11:30) with a BINGO review. I will give each student a blank BINGO sheet and explain that we are going to fill in the blanks with geometry words that they think will be important to know for the assessment. I will ask volunteers to say words while I write them on the whiteboard. Students will fill in their sheets by writing the words in whichever
• block they choose. I will then randomly call out words as the students try to get BINGO. When a student does get BINGO, before they can win they must tell the whole class the definition of or explain the words that they have gotten a BINGO with. I will continue with BINGO for about twenty to twenty five minutes. After BINGO, the students will take the formative assessment. When they are finished, they may read silently or finish up any other work from the week that needs to be completed.Materials and Resources: White drawing paper and construction paper Blank BINGO sheet for each student Handful of plastic BINGO markers for each student Copy of Geometry Quiz for each student Crayons, expo markersAssessment of Student Achievement: In this lesson, I will assess what students already know by reviewing with BINGO. I will be able totell how well they have understood what’s important from the topics by which kinds of words they giveand also by how well they can explain the words when they win BINGO. This will allow me to clear upany confusion or misunderstandings before the students take the quiz.Student Evaluation: This lesson includes a formative assessment that covers polygons, two-dimensional shapes,three-dimensional shapes and nets. The quiz includes various types of questions to test how well thestudents have understood the concepts. It is important to do this assessment now before getting too farinto geometry and realizing the students are not grasping the topics. I will be able to evaluate thequizzes and then decide if the students are ready to move on to the topic of lines or if they need morework on these topics.
• Name:__________________________________________________________Date:_______________ GEOMETRY QUIZDirections: Use the word bank below to complete numbers 1 -13. WORD BANK closed figure quadrilateral open figure triangle polygon base hexagon 2-dimensional figure pentagon octagon vertex edge face1) A shape with length and width is called a ________________________________________2) Closed 2-D shapes that have straight sides are called _______________________________3) A face on which a figure sits is the ______________________________________________4) Figures that do not start and end at the same point are _____________________________5) A three sided figure is a _______________________________________________________6) Two faces meet at the _______________________________________________________7) An eight sided figure is a _____________________________________________________8) The flat side of a 3-D figure is called a ___________________________________________9) A four sided figure is a _______________________________________________________
• 10) A six sided figure is a _______________________________________________________11) A five sided figure is a _______________________________________________________12) Three or more faces meet at the ______________________________________________13) Figures that start and end at the same point are __________________________________14) Draw any polygon and classify which kind it is Type of polygon___________________________________________15) Draw a figure that is NOT a polygon and write why it is not a polygon This is not a polygon because ___________________________________________
• Directions: Circle the best answer to each question.16) What shape is the base of a triangular pyramid? square circle triangle17) How many faces does a cylinder have? five three two18) How many edges does a cone have? zero three five19) Draw the net for a square pyramid20) Draw the net for a rectangular prism
• LinesGrade 4 MathMarch 7, 2011 (Monday)35 minutes 9:00 – 9:35Massachusetts Curriculum Framework:Mathematics – Geometry 4.G.5 Describe and draw intersecting, parallel, and perpendicular lines.Objective:One goal of this lesson is for students to understand the difference between a line, line segment andray. Another goal is for students to be able to define and identify what parallel, intersecting andperpendicular lines are.Expected Student Outcomes:At the completion of this lesson, students will be able to: Explain the difference between a line, line segment and ray and draw each appropriately Define what parallel, intersecting and perpendicular lines are and identify them in various “real life” applicationsInstructional Procedures: I will introduce the concept of lines by asking the students to draw a line in their math journals. I expect that all students will draw what they consider to be a line. I will tell them that I actually asked them to do something impossible. I will ask if anyone knows why it is impossible. I will then explain that the geometry definition of a line is that it is infinite. I will demonstrate on the board that to show a line going on for infinity you need two arrows at the ends. I will explain that what they drew in their journals was actually a line segment. I will show on the board the different way of depicting this by using points instead of arrows. I will then ask the students if they can think of what a ray is and how they could depict that. I will have them try it in their journals then I will demonstrate on the board. Next, I will draw on the board a set of parallel lines, a set of intersecting lines and a set of perpendicular lines. I will have the students copy these into their journals and then independently jot down the similarities and differences they see between the sets of lines. After a few minutes, I will have the students turn and talk to one another about what they jotted down in their journals. I will then bring the class together as whole to discuss their thoughts and ideas about the sets of lines. I will use their ideas to construct the definitions of each set. (At this point, I will not have the students write out the definitions in their journals because on the next day, the students will begin math with a fill in the blank sheet with definitions that they will glue into their journals).