# Number, Operation, and Quantitative Reasoning - ?· Number, Operation, and Quantitative Reasoning Grade…

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<ul><li><p>Mathematics TEKS Refinement 2006 K-5 Tarleton State University </p><p>Number, Operation, and Quantitative Reasoning Grade 2 How Big Am I? Page 1 </p><p>Number, Operation, and Quantitative Reasoning Activity: How Big Am I? TEKS: (2.2) Number, operation, and quantitative reasoning. The student </p><p>describes how fractions are used to name parts of whole objects or sets of objects. </p><p> The student is expected to: (A) use concrete models to represent and name fractional parts of a </p><p>whole object (with denominators of 12 or less); (B) use concrete models to represent and name fractional parts of a </p><p>set of objects (with denominators of 12 or less); and (C) use concrete models to determine if a fractional part of a whole </p><p>is closer to 0, 12</p><p>, or 1. </p><p> Overview: According to Van de Walle (2007), the most important reference points for </p><p>fractions are 0, 12</p><p>, and 1. Once this new concept is introduced, the game </p><p>in the following lesson can be used as a center activity to help students gain an understanding of the importance of comparing concrete objects to determine reference points. As soon as the concept has been taught and practiced, this game can be used as a performance assessment. </p><p> Materials: Prior to lesson: </p><p>Dessert paper plates Scissors Colored card stock Fraction Bars master How Big Am I? game board master How Big Am I? Directions master Fraction Number Cards master Lesson: Apple Fractions by Jerry Pallotta or a fraction-based literature book Fraction Estimators Fraction Number Cards Fraction circles or fraction squares Double-sided counters Paper bags Fraction Bars (Size of pieces is determined by the TEKS (2.2) Number, </p><p>operation, and quantitative reasoning, parts A and B.) How Big Am I? game board (one per pair of students) How Big Am I? Directions (one per pair of students) Second Grade Fraction Anecdotal Assessment Checklist </p></li><li><p>Mathematics TEKS Refinement 2006 K-5 Tarleton State University </p><p>Number, Operation, and Quantitative Reasoning Grade 2 How Big Am I? Page 2 </p><p>Grouping: </p><p>Day 1 Day 4: Whole Group and Small Groups Day 5: Pairs </p><p> Time: </p><p>30 minutes </p><p>Lesson: Procedures Notes 1. Prior to Lesson </p><p>Prepare Fraction Estimators a. Purchase two 7" dessert paper </p><p>plates per child. These plates should be two different colors. </p><p>b. Cut each plate to the center. Be sure not to cut plates all the way through. </p><p>c. Slide cut edges together and turn so that plates intersect. (See examples in Notes.) </p><p>d. Turn plates so that contrasting colors will show reference </p><p>points close to 0, 12</p><p>, and 1. </p><p>This inexpensive tool can be used as a form of assessment in understanding childrens grasp of fractions less than 1. </p><p> Prepare How Big Am I game. a. Run copies of fraction bar </p><p>pieces on multi-colored cardstock. You do not want students to associate a particular fraction with a specific color. </p><p>b. Cut out pieces to varying lengths. </p><p>c. Make copies of game board and directions for each pair of students in the class. </p><p>d. Laminate these pieces for durability. </p><p> Prepare Fraction Number Cards. a. Copy numerous sets of Fraction </p><p>Number Cards onto cardstock. b. Cut out the sets. The teacher </p><p> . </p></li><li><p>Mathematics TEKS Refinement 2006 K-5 Tarleton State University </p><p>Number, Operation, and Quantitative Reasoning Grade 2 How Big Am I? Page 3 </p><p> Procedures Notes will use one set, while the other sets are for various center activities. How many you make depends on how many center activities will need the cards. </p><p> 2. Day 1 Day 2: </p><p>Read Apple Fractions by Jerry Pallotta (2003) as a review of fractions. Have students participate as much as possible in the reading of the story. Divide students into small groups. Complete the following activity with a small group of students at the teacher center: a. Give each student a Fraction </p><p>Estimator. b. As you read the book again, </p><p>have students model the fractions using their Fraction Estimators. After the students have modeled a fraction, ask: </p><p>Is this fraction closer to 0, 12</p><p>, </p><p>or 1? c. Have the students explain why </p><p>they think it is closer to 0, 12</p><p>, or </p><p>1. </p><p> Read the book to the whole class before dividing the students into small groups. If you do not have the suggested book, use a book that will review fractions less than a whole. The teacher may want to refer to the Childrens Literature Booklist provided with the MTR training. Work with small groups on Fraction Estimators while other students are reviewing various fraction concepts in centers. The teacher will be considered one of the centers. Have students spend 15-20 minutes in each center. When working with Fraction Estimators, one color needs to be designated as the answer color. This will allow for quick assessment of the students understanding. Use Fraction Anecdotal Assessment Checklist to document students understanding. If students are struggling with this concept, reteach what the whole is and in this case, it is the paper plate. Have the students demonstrate for you whether the designated color is closer to filling the whole plate, half the plate, or almost none of the plate. This portion of the lesson should take two days. Students need time to process the new concept and review previously taught concepts. </p></li><li><p>Mathematics TEKS Refinement 2006 K-5 Tarleton State University </p><p>Number, Operation, and Quantitative Reasoning Grade 2 How Big Am I? Page 4 </p><p> Procedures Notes You may develop your center activities based on student needs, but suggested centers for lesson are: 1. Have students draw a number card and </p><p>practice building that fraction using Fraction Bars. </p><p>2. Have students draw a number card and practice building that fraction using Fraction Circles or Fraction Squares. </p><p>3. Have students draw a number card and practice building that fraction using double-sided counters. </p><p> 3. Day 3 Day 4 </p><p>Divide students into small groups. Teacher will work with small groups on identifying whether fractional parts of a set are closer </p><p>to 0, 12</p><p>, or 1. While the teacher is </p><p>working with one group, the other students are reviewing various fraction concepts in centers. Teacher draws a fraction number card and has students build that fraction with the double-sided counters. </p><p> Have enough double-sided counters so that each child can have twelve. This portion of the lesson should be a review and should be completed quickly. If students have not had much experience with the set model of fractions, spend time instructing the students. This will lengthen the amount of days necessary for instruction but is well worth the effort. </p><p>If 23</p><p> is drawn from the stack of number </p><p>cards, students would build the following fractional representation. First students would build the denominator with all red counters. </p><p>Then the students would turn over the counters to demonstrate the numerator. </p></li><li><p>Mathematics TEKS Refinement 2006 K-5 Tarleton State University </p><p>Number, Operation, and Quantitative Reasoning Grade 2 How Big Am I? Page 5 </p><p> Procedures Notes Once the review has been completed, continue the previous process, but now have students identify whether the represented </p><p>fraction is closer to 0, 12</p><p>, or 1. </p><p>If 9</p><p>12 is drawn from the stack of number </p><p>cards, students would build the following fractional representation. </p><p>Use the Fraction Anecdotal Assessment Checklist while working with small groups of children to assess their understanding of the concept. Another Suggested Center Activity Fraction Estimators should now be an independent center. Have students take turns being the teacher and the students. Have one student draw a fraction number card while the other students in the group show the fraction using their Fraction Estimators. Have the students identify whether it is closer to 0, </p><p> 12</p><p>, or 1. </p><p> 4. Day 5 </p><p>Students are grouped in pairs. The students will play How Big Am I? game. The shortest student goes first. Game Procedures: 1. Student 1 draws a fractional bar </p><p>piece out of the paper bag and places it on the game board indicating whether it is closer to </p><p>0, 12</p><p>, or 1. </p><p> 2. If Student 1 is correct, he or she </p><p> Use Marked Fraction Bar pieces. You will need to make several copies of the document. Cut out pieces so that you have </p><p>1, 12</p><p>, 13</p><p>, 23</p><p>, 33</p><p>, 14</p><p>, 24</p><p>, 34</p><p>, 44 , etc.) </p><p> As children master this game, you may wish to use unmarked fraction bars and require the students to estimate the value of the bar. The students must decide among themselves if the pieces are placed correctly. At the end of the game, the teacher will check to see if they are placed </p></li><li><p>Mathematics TEKS Refinement 2006 K-5 Tarleton State University </p><p>Number, Operation, and Quantitative Reasoning Grade 2 How Big Am I? Page 6 </p><p> Procedures Notes places the piece on the board according to the reference number which it is closer to. </p><p> 3. If the student is incorrect, the </p><p>piece must go back into the paper bag. </p><p> 4. Next is Student 2s turn. 5. The process continues until all </p><p>pieces have been placed on the board. </p><p>correctly. Some discussion will occur </p><p>regarding fractions equivalent to 14</p><p> and 34</p><p>. </p><p>Allow the students to discuss and justify their answers. </p><p> Resources: Pallotta, J. (2003). Apple fractions. New York: Scholastic Books. </p><p> Van de Walle, J. (2007). Elemenatry and middle school mathematic: </p><p>Teaching developmentally (6th ed.). Boston, MA: Allyn and Bacon. Modifications: You may wish to continue small groupings to first instruct students </p><p>how to play How Big Am I? game. Even if you teach this in small group, students should work in pairs. </p></li><li><p>Mathematics TEKS Refinement 2006 K-5 Tarleton State University </p><p>Number, Operation, and Quantitative Reasoning Grade 2 How Big Am I? Page 7 </p><p>Fraction Number Cards </p><p>1 1 </p><p>1 2 </p><p>2 2 </p><p>3 3 </p><p>1 3 </p><p>2 3 </p><p>4 4 </p><p>3 4 </p><p>2 4 </p><p>1 4 </p><p>5 5 </p><p>4 5 </p><p>3 5 </p><p>2 5 </p><p>1 5 </p><p>6 6 </p><p>5 6 </p><p>4 6 </p><p>3 6 </p><p>2 6 </p><p>1 6 </p><p>7 7 </p><p>6 7 </p><p>5 7 </p><p>4 7 </p></li><li><p>Mathematics TEKS Refinement 2006 K-5 Tarleton State University </p><p>Number, Operation, and Quantitative Reasoning Grade 2 How Big Am I? Page 8 </p><p>3 7 </p><p>2 7 </p><p>1 7 </p><p>8 8 </p><p>7 8 </p><p>6 8 </p><p>5 8 </p><p>4 8 </p><p>3 8 </p><p>2 8 </p><p>1 8 </p><p>9 9 </p><p>8 9 </p><p>7 9 </p><p>6 9 </p><p>5 9 </p><p>4 9 </p><p>3 9 </p><p>2 9 </p><p>1 9 </p><p>10 10 </p><p>9 10 </p><p>8 10</p><p>7 10</p><p>6 10</p></li><li><p>Mathematics TEKS Refinement 2006 K-5 Tarleton State University </p><p>Number, Operation, and Quantitative Reasoning Grade 2 How Big Am I? Page 9 </p><p>5 10 </p><p>4 10 </p><p>3 10</p><p>2 10</p><p>1 10</p><p>11 11 </p><p>10 11 </p><p>9 11</p><p>8 11</p><p>7 11</p><p>6 11 </p><p>5 11 </p><p>4 11</p><p>3 11</p><p>2 11</p><p>1 11 </p><p>12 12 </p><p>1112</p><p>1012</p><p>9 12</p><p>8 12 </p><p>7 12 </p><p>6 12</p><p>5 12</p><p>4 12</p></li><li><p>Mathematics TEKS Refinement 2006 K-5 Tarleton State University </p><p>Number, Operation, and Quantitative Reasoning Grade 2 How Big Am I? Page 10 </p><p>3 12 </p><p>2 12 </p><p>1 12</p><p>0 1 </p><p>0 2 </p><p>0 3 </p><p>0 4 </p><p>0 5 </p><p>0 6 </p><p>0 7 </p><p>0 8 </p><p>0 9 </p><p>0 10</p><p>0 11</p><p>0 12</p></li><li><p>Mathematics TEKS Refinement 2006 K-5 Tarleton State University </p><p>Number, Operation, and Quantitative Reasoning Grade 2 How Big Am I? Page 11 </p><p>How Big Am I? </p><p>1 </p><p> 1 2</p><p> 0 </p><p>Game Board </p></li><li><p>Mathematics TEKS Refinement 2006 K-5 Tarleton State University </p><p>Number, Operation, and Quantitative Reasoning Grade 2 How Big Am I? Page 12 </p><p>How Big AM I? Directions </p><p> 1. Students are grouped in pairs. The oldest </p><p>student goes first. </p><p>2. Student 1 draws a fractional bar piece out of the paper bag and places it on the game board indicating whether it is closer to 0, </p><p> 12</p><p>, or 1. </p><p> 3. If Student 1 is correct, he or she places the </p><p>piece on the board on the reference number to which is closer. If he or she is incorrect, the piece must go back into the paper bag. Next is Student 2s turn. The process continues until all pieces have been placed on the board. </p><p>4. The students must decide between them if the pieces are placed correctly. At the end of the game, the teacher will check to see if they are placed correctly. </p></li><li><p>Mathematics TEKS Refinement 2006 K-5 Tarleton State University </p><p>Number, Operation, and Quantitative Reasoning Grade 2 How Big Am I? Page 13 </p><p>Fraction Bars 1 </p><p>1 2 </p><p>1 2 </p><p>1 3 </p><p>1 3 </p><p>1 3 </p><p>1 4 </p><p>1 4 </p><p>1 4 </p><p>1 4 </p><p>1 5 </p><p>1 5 </p><p>1 5 </p><p>1 5 </p><p>1 5 </p><p>1 6 </p><p>1 6 </p><p>1 6 </p><p>1 6 </p><p>1 6 </p><p>1 6 </p><p>1 7 </p><p>1 7 </p><p>1 7 </p><p>1 7 </p><p>1 7 </p><p>1 7 </p><p>1 7 </p><p>1 8 </p><p>1 8 </p><p>1 8 </p><p>1 8 </p><p>1 8 </p><p>1 8 </p><p>1 8 </p><p>1 8 </p><p>1 9 </p><p>1 9 </p><p>1 9 </p><p>1 9 </p><p>1 9 </p><p>1 9 </p><p>1 9 </p><p>1 9 </p><p>1 9 </p><p>1 10 </p><p>1 10 </p><p>1 10 </p><p>1 10 </p><p>1 10 </p><p>1 10 </p><p>1 10 </p><p>1 10 </p><p>1 10 </p><p>1 10 </p><p>1 12 </p><p>1 12 </p><p>1 12 </p><p>1 12 </p><p>1 12</p><p>1 12</p><p>1 12</p><p>1 12</p><p>1 12</p><p>1 12 </p><p>1 12 </p><p>1 12</p></li><li><p>Mathematics TEKS Refinement 2006 K-5 Tarleton State University </p><p>Number, Operation, and Quantitative Reasoning Grade 2 How Big Am I? Page 14 </p><p>Fraction Bars Unmarked </p></li><li><p>Mathematics TEKS Refinement 2006 K-5 Tarleton State University </p><p>Number, Operation, and Quantitative Reasoning Grade 2 How Big Am I? Page 15 </p><p>Second Grade Fraction Anecdotal Assessment Checklist Student Name Model </p><p>Fraction Explain Answer </p><p>Use Correct Vocabulary </p><p>Teacher Observation Notes </p><p> Grading Scale </p><p>S - Struggling: Student does not demonstrate the understanding of how to model </p><p>fractional representations and is unable to explain why a fraction is closer to 0, 12</p><p>, or 1. </p><p>E - Emerging: Student has an understanding of how to model fractional representations but is unable to model them correctly or consistently and has difficulty explaining why a </p><p>fraction is closer to 0, 12</p><p>, or 1. </p><p>D - Developed: Student demonstrates how to model fractional representations and is </p><p>able to explain why a fraction is closer to 0, 12</p><p>, or 1. </p></li></ul>

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