Original AVA2 Task 2-2 LP Solid Geo PDF

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Download Original AVA2 Task 2-2 LP Solid Geo PDF

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C. DAVIS #000729160

BMM1 — BMM TASK 2: UNDERSTANDING AND TEACHING SOLID GEOMETRY OR MEASUREMENT OF SOLID FIGURES GEOMETRY AND STATISTICS — AVA2 PRFA — BMM1

Portfolio Response Sheet: Solid Geometry Course Code and Title: (GR, AVA2-0718) Course Module: Statistics and Geometry AVA2 Performance Task #: AVA Task 2 GENERAL INFORMATION

Lesson Title & Subject(s): Fill It Up Inside Topic or Unit of Study: Geometry & Measurement of Solid Figures Grade/Level: 5 Instructional Setting This lesson takes place in the regular classroom setting. The objective and class schedule is written on the dry erase board daily (objective 5.4H, Do Now, Fill It Up Inside, Everyday Math Pg. 67-68 problems 1-10, Exit Ticket) My students will begin as whole groups which will eventually break up into groups of twos and/or threes based on their IEPs and learning abilities. Bulletin boards will display a variety of categorized two- and three-dimensional geometric figures charts and posters. Formula charts which emulate the 5th Grade STAAR Resource Manual will also be exhibited along with student made anchor charts and frayer model. The “walls that talk” will be covered with group rules and responsibilities posters along with diverse 3-dimensional shapes and their property charts, including real-world examples. The word walls will hold both review and unit vocabulary and pictures. Student work examples from last year will also be displayed only to be replaced with the work my current will produce for this lesson. Also, positive messages will be displayed.

STANDARDS AND OBJECTIVES

STATE STUDENT ACHIEVEMENT STANDARD 5.4H – represent and solve problems related to perimeter and/or area and related to volume

Lesson Objective(s): Given ten volume equations, TLW find the answers to of the problems with at least 70% accuracy. Students will demonstrate competency on this objective by earning at least 7 out of 10 points on the school lab and classroom computers.

MATERIALS

Instructional Materials: 1. Math Journals 2. Filling Prisms Handout 3. Smart Board/dry erase markers/erasers 4. How to Describe 3D Shapes Video and Projector 5. Center Manipulatives (boxes, cm blocks, paper clips, marbles, tile blocks, unifix blocks) 6. Pencils/scissors/gluesticks 7. Previous Vocabulary Handout

8. Lesson directions Handout for ESL/SpED 9. Graph Paper Nets on cardstock 10. 3D Geometric Poster/Pictures/Anchor Charts/Real World/Attributes 11. Everyday Math Textbook Pg. 67-68 problems #1-10 12. 5th Grade STAAR Formula Chart (reduced to fit in journal)

INSTRUCTIONAL PLAN NOTE: Because my mathematics classroom schedule is 90 minutes, this lesson plan is written to correspond with that time limit. However, depending on student prior knowledge, I may have to spend two class periods on volume of geometric figures. DO NOW: (3-5 MINUTES) After students complete their daily TEKS spiral review, which is to determine the area of a two-dimensional shape in a real-world situation problem, I will do a “thumbs up” routine to evaluate the assignment. This can also be a great place flow into the main concept of today’s lesson because some students have either forgotten or missed this plane geometry concept which is needed to move into solid geometric figure measurement. Once we have spent a reasonable amount of time. Immediate feedback and quick scoring is achieved by thumbs up grading. Sometimes I call on volunteers to read and work the problem on the smartboard. Depending on time constraints, sometimes I go ahead and work it myself, especially if the majority of the class does not understand the concept. Student must show all steps and labels as needed. As a student works the problem on the smartboard, I am able to monitor the class as I walk around the room checking responses, whether they followed instructions by showing their work and to see if adjustments are needed . As you can see, this time varies from concept to concept, depending on student understanding.

I DO: INTRODUCTION OF THE LEARNING TARGET: (10-15 MINUTES) Once I have assisted my students in recalling and reviewing key concepts of perimeter and area of 2-dimensional polygons, including some of their properties and characteristics for grouping. This is where I use the “Walls That Talk.” “When the coach has you to run around the playground during P.E., what geometric term describes the area where you are running?” Name something else that you can think of which requires something around its perimeter. (varying answers) “What formula would we use to find the perimeter of the playground?” (P = 2l + 2w) and square (P = 4s). “What about when someone is mowing their yard?” “Do they only mow around the outside edge of it?” “Oh really, so what geometric vocabulary do we use to describe all of the

part that must be mowed?” “What if I wanted to paint a wall in our classroom; would I paint around this edge or world I paint this part too?” “And what is that part called again?” Very good! “What is the formula for area?” (A = l x w or A = bh). “What is the special formula for the area of a square or cube?” (A = s x s) Alright class, today we’re going to extend your knowledge of geometry of 2-dimensional figures into finding the volume of 3-dimensional figures. NOTE: Students must have a clear understanding of perimeter and area before they can clearly comprehend the concept of volume. (real world examples assist w/ comprehension: discuss the total amour of trim/border they would need for decorating your bulletin board vs the total amount of butcher paper you would need to cover your entire bulletin board.) Also, students need to be reminded that the solution for area is signified by square units or units squared because two sides have been multiplied. “Does anyone already know what the definition of volume is?” “If not that’s just fine because, “what do we come to school for?” “That’s right, to learn!” Let’s explore some more interesting information about 3 dimensional geometric figures that we see every day by watching this quick video, How to Describe 3-D Shapes https://youtu.be/3-QwWFkz5hw.

NOTE: I chose this video because it illustrates a variety of 3-dimensional geometric figures that students are familiar with, as well as some very interesting ones from around the world which they probably have never seen. The video also delves into the properties and characteristics of these figures, which will help them to realize the relationship between two- and three-dimensional shapes. This will assist them in building their learning for later grades since they will have to find the surface area and volume several other three-dimensional figures, measures of angles, study vertices, learn the concept of congruency and maintain a working knowledge of the characteristics and properties a diverse number of geometric shapes. My goal of showing this video is to help them to realize that math is not just inside of the classroom, as well as to help the to attain a deeper understanding of the geometric concept of volume. NOTE: Assist them in discovering the difference in the units of measure for two- and three-dimensional geometric figures and why.

WE DO/REVIEW VOCABULARY TERM(S) (10-15 MINUTES) With a partner, students will be allowed to three minutes to discuss and write, in their journals, at least one real world applications of the shapes in the video. I will assist students in reviewing of old and attaining new vocabulary. They already have enough frayer models pasted in their journals for the new vocabulary. Students will use the frayer model to define and display the new key vocabulary in their math journals. For the sake of time, I will give them a printed list of previous content vocabulary to be pasted into their journals. I will direct students to observe the word wall to discuss any of the vocabulary they may not understand. I would then instruct my students to write each word, represented using the vocabulary Frayer model, into their math notebooks and to complete them. By this time of year student should know how to use the frayer

model, therefore I allow them to work with a partner so that they can be tutored on the process by their peers, as I walk around the room prompting and assisting special students and new arrivals. This model has 4 squares for different sections including, the definition, characteristics, an example and a non-example. Note: Some misconceptions to watch for are that a few of the students might get the formulas mixed up and confuse area for the perimeter concept. Others only think of the area of a figure as the length times the width rather than the space a figure takes up or occupies. This one reason why I always incorporate the outside world into every lesson so they can visualize the math and not just think numbers and formulas.

Frayer Model Example:

Rectangular Prism: A solid (3-dimensional) object which has six faces that are rectangles. It has the same cross-section along a length, which makes it a prism. It is also a "cuboid". Picture: I will supply this picture example

Non-Example:

KEY VOCABULARY Perimeter the outer edge of a two-dimensional geometric figure. It is the measure of the is a linear distance around the outside or outer rim/edge of a two-dimensional shape. Area is defined as the measure which describes the region covered. This attribute of measure is represented in square units.

Volume is the amount of space that a substance or object occupies or that is enclosed within a container, especially when great. Volume can be defined as the amount of space a three-dimensional object takes up or volume is the measure of how much space a solid object takes up Two Dimensional is described as having only two dimensions, such as width and height but no thickness. Squares, Circles, Triangles, etc are two-dimensional objects. Also known as "2D". Square Units signify that two quantities measured in the same units, have been multiplied together (sq or 2. For example, to find the area of a square or a rectangle, their length or breadth are multiplied together to give the area, which is measured in square units. Three Dimensional Having three dimensions (such as height, width and depth), like any object in the real world. Example: your body is three-dimensional. Three dimensional figures are measured in cubic units, also known as "3D". Cubic Units (cu or 3) This signifies when three quantities, measured in the same solid geometric figure with the same units, are multiplied together. Example: A rectangular prism is a three-dimensional object which has length, breadth(width) and height. If these units of measure for each side are the same, then they can be multiplied to find the volume of the figure, which is then measured in units cubed. Prism The characteristics of a prism are two faces that are identical in shape and are parallel. These two faces are sometimes called the bases of the prism. The rest of the prism sides lie between these two faces, which are usually rectangles. Cube In mathematics, a cube a three dimensional geometric shape with six sides of which each is a square. It is shaped like a cube of ice or a di. is a number multiplied by itself three times. It is also defined as multiplying a numbe by itself to the third power or three times. Example: 3 cubed or to the third power is 27 (3 x 3 x 3). A vertex is a corner of a three-dimensional geometric figure. The point where two sides meet. An edge is a line segment between the faces of a three-dimensional geometric figure. A face is a single flat surface of a three-dimensional geometric figure. Side is a line segment which creates the edge or boundary of a two-dimensional geometric figures Length is the attribute of measure which describes a continuous distance from one end to another.

Liquid volume is the attribute of measure that describes the amount of space that a dry or liquid, pourable material will use. Liquid measure is normally measured with standard capacity units. Mass is the attribute of measure which describes the amount of matter within an object (regardless of its location, mass will remain the same/constant) Weight is the attribute of measure which describes the heaviness of an object., This is determined by the earths gravitational pull upon the object (it also depends on the location of the object). RELATED VOCABULARY: Base, Centimeter, Dimensions, Feet, Figure, Formula, Height, Inch, Linear units, Measure, Meter, Metric units, Miles, Millimeter, Rectangle, Square, Square units, Unit, Width Attribute, Capacity, Elapsed time, Formula, Interval, Polygon For the next activity students will be involved in a hands-on activity which involves different shaped rectangular prisms and various items with which to fill them. They will work with small shipping boxes, soap boxes, earring boxes and brad boxes, which will be located in mobile math centers. The centers will also contain filler items such as pattern blocks, paper clips, marbles unifix cubes and cm cubes. Since my students are already seated in groups of four on a daily basis, these will be their study partners for this exercise. Each student will use the handout given and work with their group to complete the tasks. As they are working, I will walk around the room, monitoring progress and asking guided questions. I will read the assignment aloud so that my ESL, 504 and SpEd students will be accommodated. “Are there any questions?” I will then release the students to begin so that I can go to each group to check for understanding. Students discover how many of each item it takes to complete each facet of this activity allows as they investigate and fill the boxes. I will briefly draw the class back into a whole group discussion before allowing them to use the unifix and cm cubes to fill the boxes. I want to know what they discovered about the marbles, paperclips and pattern blocks when they tried to fill the boxes. (Gaps? Overlaps?)

THEY DO (30-35 MINS) Note: Throughout the years, I have found that the most beneficial way to teach volume, for my students, has been by using counting cubes and nets. The students seem to gain a deeper comprehension of the concept while enjoying the task. “Our next task is to build our own rectangular prisms.” “If you will recall, you’ve already created two dimensional shapes and arrays using graph paper so this activity may be familiar to some of you.” On my smartboard, guide students through the steps of building a rectangular net and then I’ll model filling it with 1cm counting cubes in order to find its volume. Students will be reminded

throughout the work time to alleviate gaps and overlaps and to explain why this is important when finding volume of 3D geometric figures. Their answers to the related volume problems will be written on the Filling Prisms handout. NOTE: For more detail about this activity see Instructional Strategy below. I will briefly introduce students to the volume formulas and give them a copy of the 5 th grade STAAR Mathematics Chart so that they can begin to become familiar with using it. Note: This chart will be kept in their math journals for frequent reference. Students are to write these formulas in their math journals: Volume = length x width x height or V=lxwxh Also, Volume = area of the base x the height or V = B x h (B = l x w) I call this Big which is the base of the geometric figure And Special cubic formula is V = s × s × s.

EVALUATING UNDERSTANDING “Turn to page 67 in your Everyday Math books.” You will continue to practice solving volume problems by solving problems 1-10 in your book.” “Show all of your work, including writing which volume formula you used to solve the problem.” “Read the instructions and solve the problems listed on the board.” The Everyday Math textbook book has a variety of practice problems which will allow students to experience diversity with the concept of volume of geometric figures. At this time, I will pull out students, who may be having difficulty, and work with them in small groups or one to one (especially ELL, 504 and SpEd). I also am able to allow my more responsible Target students to peer tutor some of my regular students who are having minor issues with the concept. During this time, I have a chance to monitor, assess and adjust for my students, deciding whether to reteach the whole class, small groups or to assign certain ones to after school/lunch tutorials. I will also add this concept to the STAAR spiral for continued practice. . EXAMPLE QUESTIONS AND STATEMENTS What process do we use to find the perimeter of a polygon? What if I have a rectangle with three side lengths given and one missing side length; how do I find the one that is missing, if they also give me the perimeter? (Is there any other way to find the length of the side?) How can the perimeter of a polygon process be written as an equation? Explain, to the class, how the formula P = 2l + 2w relates a rectangles perimeter. Please explain, how formula P = 4s is related to a square.

What process do we use to find the area of a rectangle? What process were you taught last year for finding the area of a square? If you are given the area and the other side length of a rectangle, what process must you use to find the length of the missing side? (What shape did the question I just asked refer to? How do you know?) (Is there any other way to find the length of the side?) How is the area of a square and a rectangle process alike? (How are the two processes different) How are the Area formula A = bh and A = l x w processes related? How do we determine the area of a rectangular prisms base? Explain the relationship between how many times the area is stacked up or layered and the actual area. Can you find a relationship between the formula V = Bh, the volume, the base areas number of layers and the area of the base? What dimensions doe a cubic unit have? Explain the reason we volume is measured using cubic units. Why do we not want to leave any gaps or have overlaps when finding volume? If we have gaps or overlaps, of the unit cubes, what happens to the volume? How are we using our pictorial and concrete models to better understand the volume formula of rectangular prisms? How can these models be used to better comprehend the volume formula of a cube? What is the formula for finding a rectangular prisms volume? How did we find the length of the missing side of a rectangular prism when we were given the volume and length of the other side length? What is the formula for finding a cubes volume? Compare and contrast the cube and rectangular prism formulas. (differences/similarities) Is a cube a rectangular prism? (Is it a special one? Why?) Expound on the relationship between the formulas V = l x w x h and V = Bh as related to finding a rectangular prisms volume. What does the B in V = Bh formula represent? Expound on the process you used with the formula V = s x s x s in the relation to a cubes volume.

EXTRA CREDIT: Students may play the Pump Up the Volume computer game and send their results to my computer or the printer for extra credit. They may also complete practice tasks which pertain to volume of rectangular prisms, located in the classroom learning centers. EXIT TICKET (10-15 MINUTES) IXL Computer Evaluation (All word problems as they will appear on the STARR exam)https://www.ixl.com/math/grade-5/volume-of-cubes-and-rectangular-prisms-wordproblems SpEd (Volume made of unit cubes)https://www.ixl.com/math/grade-5/volume-ofrectangular-prisms-made-of-unit-cubes

ELL/504 (mixture of models and word problems as they will appear on the STARR exam) https://www.ixl.com/math/grade-5/volume-of-cubes-and-rectangular-prisms-withdecimal-side-lengths contains ten problems with which have word problems, real world situations, decimals and whole numbers. Note: Students know how to use the computers, take their tests and send the results to my printer. I can also verify their results on my computer. The place where my students take the quiz depends upon the classes grasp of the concept. We will transition to the computer lab to take these quizzes.

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