Task 4
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Western Governors University *
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Jan 9, 2024
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Kyle Clinedinst Student 1D-001029234 AOA2 BNM2-Task 4: Understanding and Teaching Fractions, Decimals, or Percentages A. Study the fractions, decimals, or percentages content standards for your state and do the following: 1. List three content standards from your state that apply to fractions, decimals, or percentages for grades K-6. The three selected standards must represent three different grade levels. Grade 3: "3.NF.1 Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a part of size 1/b.” -Ohio Learning Standards/Mathematics Grade 3 Grade 4: “4.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. c¢. Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie? ” -Ohio Learning Standards/Mathematics Grade 4 Grade 5: “5.NF.6 Solve real-world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.” -Ohio Learning Standards/Mathematics Grade 5
2. Write a sample problem for each of the three standards to illustrate the evolution of student understanding. Grade 3: 3.NF.1 Rachel is making a cake for her and her seven friends. She wants to divide the cake so that everyone gets an equal piece. a. If Rachel and her seven friends are eating the cake, how many people will have a piece? b. How many pieces of cake will there be? c. Draw a picture of the cake. d. What fraction of the cake will each person get? Grade 4: 4.NF.4 Rachel is making cupcakes for a birthday party. The recipe calls for ¥ cup of flour for each batch of cupcakes. If Rachel wants to make 7 batches of cupcakes, how many cups of flour will she need? Use the model to help solve. IR NN PR PR TN N Ao a. How many ¥ cups will Rachel need? b. Write an equation that represents this problem. c. Solve your equation and write your answer as a fraction. Grade 5: 5.NF.6 A bundle of bananas weighs 3 3% pounds. Tom wants to buy 4 %2 bundles of bananas and must find the total weight. How much would 4 %2 bundles of bananas weigh? Use the area model to solve. 4 Yo Ya
3. Provide a solution for each problem that demonstrates each step or explains the thinking process involved in determining the solution. Grade 3: 3.NF.1 Rachel is making a cake for her and her seven friends. She wants to divide the cake so that everyone gets an equal piece of cake. a. If Rachel and her seven friends are eating the cake, how many people will have a piece? 8 people b. How many pieces of cake will there be? 8 pieces c. Draw a picture of the cake. or d. What fraction of the cake will each person get? Each person will get ¥ of the cake. Thinking: For this problem, the first thing students will need to find is the number of people. Rachel and her seven friends equal eight people. Next, they will need to think about how many pieces of cake each person will receive. If there are eight people, and each person will receive one piece, this goes back to their prior knowledge of 8x1. Then, the students will need to draw a “cake” and split it into 8 pieces. There are multiple ways they can do this. Finally, they will need to understand how part “d” is asking for the unit fraction. Each person will get 1 of the 8 pieces or %.
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Grade 4: 4.NF.4 Rachel is making cupcakes for a birthday party. The recipe calls for ¥ cup of flour for each batch of cupcakes. If Rachel wants to make 7 batches of cupcakes, how many cups of flour will she need? Use the model to help solve. IR IR PN PN TN I[N I a. How many ¥ cups will Rachel need? 7 fourths b. Write an equation that represents this problem. Yax 7= or7xva= c. Solve your equation and write your answer as a fraction. 7/4 Thinking: For this problem, | set it up so that each part (a,b,c,) helps the students solve the problem step by step. For part a, the students will first need to find the number of batches of cupcakes Rachel is making. She is making 7 batches of cupcakes so she will need 7, ¥4 cups of flour. Next, they will take their thinking from part a to write an equation in partb. 7x%¥ =___ . Finally, they will multiply 7 x ¥4, to get 7/4, or they can count the number of fourths in the model to find 7 fourths. Grade 5: 5.NF.6 A bundle of bananas weighs 3 3% pounds. Tom wants to buy 4 %2 bundles of bananas and must find the total weight. How much would 4 %2 bundles of bananas weigh? Use the area model to solve. X 4 5 3 12 11 % |12/4 or 3B 3 12+1+3=16 Yo+ = 4/8 +3/8="7 16 + 75=16 7 Thinking- For this problem, students will need to rely on their prior knowledge of multiplying fractions by whole numbers and multiplying fractions by fractions. To start, students need to know the operation of this problem. Once they know they need to multiply, students can use the “area” model to help them solve. For this
guestion, | put the numbers in the area model for the students. First, students will multiply the whole numbers, 3x4=12. Next, they will multiply the whole numbers by the fractions, 3xY¥2=1%and 4 x 3% = 12/4 or 3. The last multiplication step is to multiply the fractions. This will rely on prior knowledge. % x 3 = 3. Once they multiply, students will add starting with the whole numbers, then the fractions. When adding the fractions, students will need to find a common denominator. Y = 4/8. They will add 4/8 + 3 to get 7. Finally, add 16 + 7 to get 16 7. 4. Discuss how the chosen standards and problems build student understanding of fractions, decimals, or percentages across the three K-6 grade levels selected in part Al. | chose these standards because they build on the previous year’s study of fractions from grades 3-5. In third grade, students learn that fractions are part of a whole. They learn the numerator is the amount being counted, and the denominator is the total parts of a whole or group. In fourth grade students learn to add fractions and multiply fractions by whole numbers. Finally in 5th grade, they take it a step further and learn how to multiply mixed numbers by mixed numbers. Part B: B. Watch the “Understanding Fractions through Real-World Tasks” video and do the following: 1. Describe how the teacher is a facilitator in this video lesson. The teacher did a great job of being the facilitator in this lesson. She supplied the example and gave a question dealing with common denominators. Then she asked them to think about a plan to “attack” this problem. She didn’t tell them what plan they should use, she let them discuss a plan with a partner. She let the students figure out plans and strategies without support from the teacher. “You can support student thinking without evaluation.” -(Van De Wallie & Karp & Bay-Williams, 2012, p.54) In the video, she even said, “students came up with their own ideas that may be different from my own.” 2. Describe how the teacher designed the lesson to deepen student understanding of fractions, using examples from the video. The teacher designed the lesson to deepen the students' understanding of fractions by first giving a real-world example. She brought in two watermelons and right away the students were excited. In the video, you can hear some student’s gasp. They are already invested in this lesson. Next, she had the students talk amongst themselves to
come up with a plan. This lets the students learn from each other. “Peer-assisted learning” -(Van De Wallie & Karp & Bay-Williams, 2012, p.100) Finally, she had one student show their work to the class. As the video said, this promotes a community of learners. 3. Explain how the teacher uses the final summary to reinforce student learning. The teacher used the final summary to reinforce the students' learning by having them first think about the task and their own strategies to solve. This gives the students a chance to reflect on their work. Next, the students talked to their neighbor about everything they have done and how they justified their strategy. While this was happening, the teacher could walk around and listen for a quick formative assessment. 4. Describe two formative assessment methods that were used in the lesson, using specific examples from the video. The first form of formative assessment the teacher used was a “check-in” with the students as they were working with their partners. She was going around asking the students “can you tell me what you did right here?” This allowed her to notice the students' math thinking. The first little boy was able to explain his thinking about how his “tape diagram” helped find a common denominator. She also did this at the end of the lesson when she summarized the main idea of the lesson. She again walked around the room and listened to the students' conversations to see if they understood how to find common denominators. The second form of formative assessment was when the teacher says, “thumbs up if you agree with Isaac.” This was briefly shown in the video. Most students put their thumbs up while one student said “it is correct” also showing that he agrees. a. Explain the value of each assessment method described in part B4. The “check-in" assessment was a quick way for the teacher to check her students' understanding. She asked the little boy to explain what he was doing and why. He told her his strategy and she could see that he drew a tape diagram to represent the fraction. The teacher also said, “I know he knows how to do his representation of a fraction.” This was effective in allowing her to see who understood the concept and if she had “supported” her students enough.
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The “thumbs up” assessment is very quick and easy to do. A teacher can quickly see who agrees or disagrees with a question or problem. The teacher can scan the room to see who understands and who doesn’'t. The problem with this assessment is that if used too often, students who do not understand will put their thumbs up just to make it look like they understand. | have found that you must “keep them on their toes” when asking these questions. | will do so by showing a wrong solution that | did, not a wrong solution from a student as to not embarrass them and ask if they agree. This will make them think about the solution and not just go along with the crowd. 5. Describe an activity that would aid in clarifying the need for common denominators for students who struggle with understanding the concept. Another activity that would clarify the need for common denominators would be to give another real-world example but provide struggling students with models. For this activity, | would start by giving a similar real-world example. Suzie eats %2 of the watermelon. John cuts his watermelon into 4ths and wants to eat the same amount as Suzie. | would then show them these models. The model on the left represents the part of the watermelon Suzie ate. Next, | would have the students shade in the watermelon on the right so that the same amount of the watermelon was shaded. | would have to clarify that it's not the same number of pieces, but the same amount total. After they shade in 2/4, | would have them discuss how they knew how much to shade in. Then | would have them discuss what fraction would equal the same as ¥2. This would lead us into finding a common denominator. Students who struggle are obviously missing some prior knowledge. | would use visuals like this to help aid them.
Part c: Prepare to create an original lesson plan on fractions, decimals, or percentages by doing the following: 1. Describe an evidence-based instructional strategy that will be incorporated into your original lesson plan. The evidence-based instructional strategy that | will incorporate into this lesson is called a “scoot”, and more specifically a “comparing fractions scoot”. For this strategy, the teacher first reviews the concept and has the students practice a few problems on a white board or with a partner. Next, the teacher distributes the scoot recording sheet and puts a scoot problem at everyone’s desk. For this example, I'll simulate having 20 students in the class. The recording sheet will have 20 boxes for students to show and record their work. Each scoot problem will be numbered 1-20 and have a 3rd grade comparing fractions question. The students will start with the numbered problem that is on their desk or if they are with a partner, the numbered problem that is on their partner's desk. The students will first work on the fraction problem on their desk and record the answer on the recording sheet. Then, once everyone has had ample time to solve, the teacher will say “scoot”. The students will move to the next problem taking their recording paper with them but leaving the comparing fractions problem on their desk. Ex- students go from their desk to their neighbors in numeric order. Once they are on problem #20, the students will go back to problem #1. They will continue this until all the problems have been solved. a. Explain why the chosen instructional strategy would be beneficial in a lesson on fractions, decimals, or percentages, using evidence from a credible source to support your selection. This is a strategy that has differentiation and a formative assessment built in. First, | would pair students that struggle with comparing fractions with students who understand and can explain the concept. (The students that are “above” level enjoy helping their peers and it gives them a chance to expand their knowledge by explaining their thinking. Also, the students who are “below” level get a chance to learn from their peers.) | also chose this strategy because it gets the students up and moving. Finally, this has a formative assessment built in. As the students are “scooting” | will circulate the classroom listening to their ideas and strategies. This will allow me to “support student thinking without evaluation.” -(Van De Wallie & Karp & Bay-Williams, 2012, p.54) Part E: Acknowledge sources, using in-text citations and references, for content that is quoted, paraphrased, or summarized.
Ohio Learning Standards Mathematics. (2017). Ohio Department of Education. https://education.ohio.gov/getattachment/Topics/Learning-in-Ohio/Mathematics/ Ohio-s-Learning-Standards-in-Mathematics/MATH-Standards-2017.pdf.aspx? lang=en-US Bay-Williams, J.V.D.W.K.S.K.J. M. (2012). Elementary and Middle School Mathematics: Teaching Developmentally, VitalSource for Western Governors University (8th Edition). Pearson Learning Solutions. https://wgu.vitalsource.com/books/9781256957669
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