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E XPLAINING A REA AND C IRCUMFERENCE OF A C IRCLE,LEARNING MAP INFORMATION. 7 G 4 Know the formulas for the area and circumference of a circle and solve problems give an informal derivation of. the relationship between the circumference and area of a circle. calculate the,area of a represent,explain explain polygon by equations. decomposing explain ratio with numbers,perimeter diameter it into and or. rectangles variables,calculate the construct,explain explain area of a simple. parallelogram equations to,circumference radius with the represent.
formula problems,real world,explain pi equations,nonnegative. explain the,explain the,formula for,circumference,the area of a. use the use the,formula for formula for,the area of a circumference. circle to to solve,solve problems,explain the,relationship. circumference,and the area,of a circle, The Dynamic Learning Maps including node names descriptions and connections have been developed by the Achievement and Assessment Institute.
etc that a ratio represents a multiplicative comparison of two quantities or. EXPLAIN RATIO the joining of two quantities into a composed unit For example the ratio. of eyes to nose on a person is 2 1 because for every two eyes there is one. Make known your understanding through words drawings manipulatives. EXPLAIN THE CIRCUMFERENCE FORMULA, etc that the formula of the circumference of a circle is 2 pi r or pi d. EXPLAIN THE FORMULA FOR THE AREA OF A Make known your understanding through words drawings manipulatives. CIRCLE etc that the formula for the area of a circle is pi r 2. EXPLAIN THE RELATIONSHIP BETWEEN Make known your understanding through words drawings manipulatives. CIRCUMFERENCE AND THE AREA OF A CIRCLE etc of the relationship between circumference and area of a circle. REPRESENT EQUATIONS WITH NUMBERS Through writing or an appropriate assistive technology represent equations. AND OR VARIABLES with numbers variables or both,SOLVE REAL WORLD PROBLEMS USING. Use equations with nonnegative rational numbers to solve real world. EQUATIONS WITH NONNEGATIVE RATIONAL, USE THE FORMULA FOR THE AREA OF A Use the formula for area of a circle to solve real world or mathematical. CIRCLE TO SOLVE PROBLEMS problems, USE THE FORMULA FOR CIRCUMFERENCE TO Use the formula for circumference to solve real world or mathematical. SOLVE PROBLEMS problems, The Dynamic Learning Maps including node names descriptions and connections have been developed by the Achievement and Assessment Institute.
and are copyrighted by the University of Kansas Center for Research Learning map information is available for use by educators but may not be used. for commercial purposes including being shared without cost when bundled in a commercial transaction without written permission Dynamic Learning. Map nodes and connections may not be altered by anyone other than the staff of the Achievement and Assessment Institute at the University of Kansas. ADDITIONAL NODES RELATED TO THIS UNIT OF INSTRUCTION. Node Name Node Description Related Node,Make known your understanding. through words drawings, EXPLAIN AREA manipulatives etc that area is a two Postrequisite of EXPLAIN LENGTH. dimensional quantity representing the,amount of space in a surface. The Dynamic Learning Maps including node names descriptions and connections have been developed by the Achievement and Assessment Institute. and are copyrighted by the University of Kansas Center for Research Learning map information is available for use by educators but may not be used. for commercial purposes including being shared without cost when bundled in a commercial transaction without written permission Dynamic Learning. Map nodes and connections may not be altered by anyone other than the staff of the Achievement and Assessment Institute at the University of Kansas. E XPLAINING A REA AND C IRCUMFERENCE OF A C IRCLE,TEACHER NOTES. This unit includes the following documents,u Learning Map Information.
essential understanding of geometry for teaching mathematics in grades 6 8 pp 7 68 Reston VA NCTM. Van de Walle J Bay Williams J Karp K Lovin L 2014 Exploring measurement concepts Teaching. student centered mathematics Developmentally appropriate instruction for grades 6 8 Volume I Second ed pp. 298 324 Upper Saddle River NJ Pearson Education Limited. The Dynamic Learning Maps including node names descriptions and connections have been developed by the Achievement and Assessment Institute. and are copyrighted by the University of Kansas Center for Research Learning map information is available for use by educators but may not be used. for commercial purposes including being shared without cost when bundled in a commercial transaction without written permission Dynamic Learning. Map nodes and connections may not be altered by anyone other than the staff of the Achievement and Assessment Institute at the University of Kansas. E XPLAINING A REA AND C IRCUMFERENCE OF A C IRCLE,INSTRUCTIONAL ACTIVITY. LEARNING GOAL, Students will develop an understanding of diameter radius circumference and pi and the relationships. among them and will solve problems using the circumference formula. PRIMARY ACTIVITY, Students will measure circular objects and create definitions to support their understanding of diameter. radius circumference and pi,OTHER VOCABULARY,Students will need to know. u Distance,u Perimeter, u Several circular objects of different sizes up to 10.
u Rulers or tape measures with centimeter markings. u I NSTRUCTIONAL ACTIVITY S TUDENT H ANDOUT,IMPLEMENTATION. Begin the lesson by having students measure the circular objects available and record their results as described. in the I NSTRUCTIONAL ACTIVITY S TUDENT H ANDOUT The following table is an example row of. student work, The Dynamic Learning Maps including node names descriptions and connections have been developed by the Achievement and Assessment Institute. and are copyrighted by the University of Kansas Center for Research Learning map information is available for use by educators but may not be used. for commercial purposes including being shared without cost when bundled in a commercial transaction without written permission Dynamic Learning. Map nodes and connections may not be altered by anyone other than the staff of the Achievement and Assessment Institute at the University of Kansas. DISTANCE AROUND THE,DISTANCE FROM THE DISTANCE ACROSS THE. DISTANCE AROUND CIRCLE DISTANCE,OBJECT CENTER OF THE CIRCLE WIDEST PART OF THE. THE CIRCLE ACROSS THE WIDEST,TO THE EDGE CIRCLE,PART OF THE CIRCLE.
about 3 218, small paper plate 9 centimeters 17 9 centimeters 57 6 centimeters. centimeters, Emphasize the importance of measuring in centimeters as accurately as possible for each object. Students should measure each object to the nearest tenth of a centimeter. Model the measurements students will make using a circular object Tape measures or string can be. used to measure the distance around the circle circumference and to measure straight distances. from the center of the circle to the edge radius or across the widest part of a circle diameter. Check the students work as they fill in the table to ensure their measurements are accurate. particularly in the column where students divide the circumference by the diameter to calculate. approximations of pi Note that the value in this column should be close to pi approximately. 3 14159 but will not be exact due to human error in calculation. Require students to answer Questions 1 7 to summarize their work in the table and look for. patterns in their data in pairs Students should write either d 2r or r d for Question 3 C d. for Question 6 and C 2 r for Question 7, Provide scaffolding when necessary using the following guiding questions As students describe and. show the diameter and radius of a circle they should articulate the fact that both the diameter and. radius pass through the center of the circle When students describe how to determine the distance. around an object it is important that they describe a process that measures the entire continuous. distance no gaps and does not measure any portion of the perimeter more than one time no. The Dynamic Learning Maps including node names descriptions and connections have been developed by the Achievement and Assessment Institute. and are copyrighted by the University of Kansas Center for Research Learning map information is available for use by educators but may not be used. for commercial purposes including being shared without cost when bundled in a commercial transaction without written permission Dynamic Learning. Map nodes and connections may not be altered by anyone other than the staff of the Achievement and Assessment Institute at the University of Kansas. GUIDING QUESTIONS,Elicit student thinking,u What can you tell me about this circle. u Can you describe different properties of this circle. Determine if the student can EXPLAIN DIAMETER, u What do you picture when you hear the word diameter.
u Can you show me where the diameter of this circle is. u How would you describe the diameter of a circle in your own words. Determine if the student can EXPLAIN RADIUS, u What do you picture when you hear the word radius. u Can you show me where the radius of this circle is. u How would you describe the radius of a circle in your own words. Determine if the student can EXPLAIN PERIMETER,u What do we call the distance around a rectangle. u How can you determine the distance around a shape. u Can you show me the perimeter of this circle, The Dynamic Learning Maps including node names descriptions and connections have been developed by the Achievement and Assessment Institute. and are copyrighted by the University of Kansas Center for Research Learning map information is available for use by educators but may not be used. for commercial purposes including being shared without cost when bundled in a commercial transaction without written permission Dynamic Learning. Map nodes and connections may not be altered by anyone other than the staff of the Achievement and Assessment Institute at the University of Kansas. GUIDING QUESTIONS, Determine if the student can EXPLAIN CIRCUMFERENCE. u What shape are we referring to when we talk about circumference. u What is the difference between perimeter and circumference. u How would you describe the circumference of a circle in your own words. Determine if the student can EXPLAIN PI,u How did we determine the value of pi.
world and mathematical problems,GUIDING QUESTIONS, Determine if the student can USE THE FORMULA FOR CIRCUMFERENCE TO SOLVE. u What information do you have about this circle, u What are you trying to determine Can you describe this measurement in. relation to the circle, u What equation or process is most efficient for answering this question. u How would you simplify solve this equation or carry out this process. Students should be required to show all work as they complete the I NSTRUCTIONAL ACTIVITY S TUDENT. H ANDOUT and write their answers in complete thorough well thought out sentences. At the end of the activity teachers should provide students with an example requiring them to use either C. d or C 2 r to solve a problem as an exit ticket for the day. The Dynamic Learning Maps including node names descriptions and connections have been developed by the Achievement and Assessment Institute. and are copyrighted by the University of Kansas Center for Research Learning map information is available for use by educators but may not be used. for commercial purposes including being shared without cost when bundled in a commercial transaction without written permission Dynamic Learning. Map nodes and connections may not be altered by anyone other than the staff of the Achievement and Assessment Institute at the University of Kansas. E XPLAINING A REA AND C IRCUMFERENCE OF A C IRCLE, For each object make the measurements described in the following table Use the string to help measure. when needed Be sure to measure in centimeters and be as precise as possible. DISTANCE AROUND,DISTANCE FROM THE DISTANCE ACROSS,DISTANCE AROUND THE CIRCLE DISTANCE.
OBJECT CENTER OF THE CIRCLE THE WIDEST PART OF,THE CIRCLE ACROSS THE WIDEST. TO THE EDGE THE CIRCLE,PART OF THE CIRCLE,Copyright 2015 by The University of Kansas 1. 1 What do you notice about the distance across the widest part of the circle and the distance from the. center of the circle to the edge, 2 The distance across the widest part of the circle is called the diameter Write a definition of diameter in. your own words, 3 The distance from the center of the circle to a point on the edge is defined as the radius What is the. relationship between the length of the radius and the length of the diameter in each row of your. table Write an equation that relates the diameter d to the radius r. 4 What do you notice about the distance around the circle divided by the diameter of the circle These. numbers are in the last column of the table, 5 The ratio of the distance around the circle to the diameter of the circle is defined as pi Using the.

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