Faye Schmidt Lesson 8
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Dakota State University College of Education Lesson 10: Mixed Numbers and Improper Fractions Name: Faye Schmidt Grade Level: 4th Grade School: Sioux Valley Elementary Date: Monday, March 18th, 2019 Time: 9:00-10:00 AM Reflection from prior lesson: ● In the previous lessons, students have been working with fractions. Although students who have been ill are slowing joining the class again, I still plan to take about 15 minutes to go over the concepts and strategies that were previously learned so that everyone can be as caught up as possible. The most recent lesson introduced mixed numbers, and this one will go even more in-depth when working with mixed numbers and will introduce improper fractions. The previous lessons in this chapter have gone very well, and the students have been able to successfully meet the set objectives each day. These students have been completing examples during class as a group and individually, submitting informal exit tickets, and handing in a Math Workbook homework page to be graded for each lesson so far in this chapter. Students are being assessed in various ways, both informally and formally, and the results are being used to construct future lessons. Lesson Goal(s) / Standards: ● Domain: Number and Operations - Fractions ● Major Cluster: Build fractions from unit fractions by applying and extending previous understanding of operations on whole numbers. ○ 4.NF.3 - Understand a fraction a/b with a > 1 as a sum of fractions 1/b. ● Math Practice Standards: ○ MP1: Make sense of problems and persevere in solving them. ○ MP2: Reason abstractly and quantitatively. ○ MP3: Construct viable arguments and critique the reasoning of others. ○ MP4: Model with mathematics. ○ MP5: Use appropriate tools strategically. ○ MP6: Attend to precision. ○ MP8: Look for and express regularity in repeated reasoning. Lesson Objectives: Faye Schmidt TWS Lesson 10: Mixed Numbers and Improper Fractions Chapter 8: Fractions
Page 1
● By the end of the lesson, students will write mixed numbers and improper fractions correctly with 70% accuracy. Materials Needed: ● Each Student will need their: ○ Math Notebook ○ Pencil ○ Math Workbook ● Teacher will need: ○ Promethean Interactive Board ○ Projector ○ Whiteboard marker and eraser ○ Paper to complete example problems on ○ Pencil ○ List of example problems to complete during lesson ○ Exit tickets to check for understanding after the lesson (attached) Contextual Factors/ Learner Characteristics: ● This classroom is made up of 28 total 4th-graders, aged 9-11. 27 of these students will be in the classroom to complete this math lesson as a large-group, teacher-led learning experience. When it comes to independent work time, 2 students work on their homework assignments in an alternative setting, and 25 complete their work independently in the general classroom. I, the student teacher, will be leading this lesson, and my cooperating teacher, who is the classroom’s primary teacher, will be observing and assisting students. This diverse classroom is made up of students from a various backgrounds and learning levels, which have been considered when planning this lesson. ● This lesson will be begin at about 9:00 AM, right after students are finished with their Morning Meeting. This lesson will end at about 10:00, when the students will leave the classroom to attend Library and Computer. Flex seating is also utilized in this classroom, with several different options available each week for the students to choose. In this classroom, there is a strict seating chart, and students are expected to find their seats and remain in their assigned seats for the lesson. Because of the size of the group and the arrangements of the desks, the teacher is to remain mindful of unnecessary behaviors, such as irrelevant conversations. These situations should be approached immediately if any issues arise during the lesson. Faye Schmidt TWS Lesson 10: Mixed Numbers and Improper Fractions Chapter 8: Fractions
Page 2
A. The Lesson 1. Introduction (10 min) ● First, the teacher should ask the students about what they have learned so far in the previous lessons in this chapter. This class discussion should take a few minutes, and should be used to review content or clear up any misunderstandings or confusion before moving on. Students will provide definitions and other information about fractions that they have learned thus far. The following review questions or prompts could be asked to the class if they need help recalling some of the things that have been addressed in prior lessons. Volunteers will raise their hands to be called on to share their definitions and other information regarding these terms or concepts. ○ What are the parts of a fraction? What is a numerator and denominator? ○ What does a numerator represent? denominator? ○ What is a mixed number? ● After this brief review is complete, remind the students that the information that was learned in the last couple of days will help us with this lesson, and the ones that follow. Today, our focus is to continue to work with mixed numbers and introduce improper fractions. ● The teacher will then share the objective with the class, and then begin the lesson. ○ “By the end of the lesson, students will write mixed numbers and improper fractions correctly.” 2. Content Delivery (30 min) ● Since the goal of this lesson is introduce mixed numbers to the students, a definition should be provided and shared with them as they begin thinking about what a mixed number really is and looks like. ○ An improper fraction is a fraction that has a numerator that is greater than its denominator. ■ Example: 32 , 74 , etc. ● After giving the students this definition and explaining it, make sure to emphasize that like mixed numbers, improper fractions have a value greater than 1. ● To begin the guided practice, the following example will be shown. To complete this problem, the teacher will read it aloud to the class and then model the steps on how to solve it. Since it is a new concept for these students, the teacher is to make sure that they are clear when explaining the reasoning of these problems. Faye Schmidt TWS Lesson 10: Mixed Numbers and Improper Fractions Chapter 8: Fractions
Page 3
○ First, the students will identify how many parts make up one whole. ■ 8 ○ Next, the students will write fractions under each image that represent the shaded amount. ■ 88 and 38 ○ Then, you must add these fractions together. When you add fractions, you must keep the denominator the same and add the numerators together to make an improper fraction. ■ 88 + 38 = 11 8 ○ So, ■ 1 38 written as an improper fraction is
11 8
● The next example will allow the students to practice converting an improper fraction to a mixed number. ○ First, the students must analyze the image. Later, they will need to draw their own model, so they must understand how to create a model that matches the fraction or mixed number. ○ Then, the class should dicuss how this is similar to what they were practicing in the last lesson, when they were writing mixed numbers. ○ Just like in the previous lesson, they must first count all of the “wholes.” ■ 2 ○ Then, notice that the last part of the model is incomplete, and they should count the remaining shaded parts of this section. ■ 14 ○ Lastly, they add these together to identify the mixed number shown in the model of the original improper fraction. Faye Schmidt TWS Lesson 10: Mixed Numbers and Improper Fractions Chapter 8: Fractions
Page 4
■ 2 14 ● Next, the students should complete the next set of examples independently, and then raise their hands to volunteer to answer and ask questions when everyone is finished and ready to share and compare. ● Follow the same steps as the first example to complete this series of problems. ○ Mixed Number ■ 1 46 ○ Improper Fraction ■ 66 + 46 = 10 6 ○ Mixed Number: ■ 1 25 ○ Improper Fraction: ■ 55 + 25 = 75 ● Mixed Number: 2 23 ● Improper Fraction:
3 Mixed Number: 2 10 3 3
+
3 3
+ 23 =
8 3
Improper Fraction:
10 10
10 3 + 10 + 10 =
23 10
Faye Schmidt TWS Lesson 10: Mixed Numbers and Improper Fractions Chapter 8: Fractions
Page 5
● Mixed Number: 2 12 ● Improper Fraction:
2 2
+ 22 + 12 =
5 2
Mixed Number: 3 34 Improper Fraction: 15 4
● For the next set of examples, the students will practice creating models for mixed numbers. The first example should be modelled by the teacher, and then the students should practice independently before reviewing the correct answers. ● The model should contain two shapes, each divided into 5 pieces. One should be completely shaded, and the other should have 3 of the 5 pieces shaded. ○ Improper Fraction: 85 ○ The first model should contain three shapes, each divided into 4 pieces. Two should be completely shaded, and the other should have 3 of the 4 pieces shaded. ■ Improper Fraction: 11 4 ○ The next model should contain two shapes, each divided into 10 pieces. One should be completely shaded, and the other should have 7 of the 10 pieces shaded. 17 ■ Improper Fraction: 10 Faye Schmidt TWS Lesson 10: Mixed Numbers and Improper Fractions Chapter 8: Fractions
Page 6
● For the next set of examples, the students will practice creating models for improper fractions. The first example should be modelled by the teacher, and then the students should practice independently before reviewing the correct answers. ● The model should contain two shapes, each divided into 8 pieces. One should be completely shaded, and the other should have 3 of the 8 pieces shaded. ○ Mixed Number: 1 38 ● The first model should contain two shapes, each divided into 6 pieces. One shape should be completely shaded, and the other should have 3 of the 6 pieces shaded. ○ Mixed Number: 1 36 ● The next model should contain three shapes, each divided into 3 pieces. Two shapes should be completely shaded, and the other should have 1 of the 3 pieces shaded. ○ Mixed Number: 2 13 ● Next, the students will practice some word problem examples, where they will need to carefully read each problem to identify what the question is asking, and problem solve how how complete. ○ Jason ran 11 miles. How many whole miles did he run? What portion of an 3 additional mile did he run? ■ 11 = 3 23 3 ■ 3 whole miles, 23 of a fourth mile ○ Jenny was on a horseback riding tour. She reached the end of the trail in 2 hours and 15 minutes. Write the amount of hours she spend on the trail as a mixed number and an improper fraction. Faye Schmidt TWS Lesson 10: Mixed Numbers and Improper Fractions Chapter 8: Fractions
Page 7
15 ■ 3 60 or 3 14 =
13 4
3. Closure (20 min, including work time) ● At this time, the teacher will ask the students if they have any questions regarding the new information from the lesson. If there are any concerns or confusion, these should be addressed as a group so that all students can benefit. ● Now, the teacher will ask the following questions to the class to discuss. Students will then volunteer to share their answers to these prompts. ○ What is a mixed number? What is it made up of? ○ What is an improper fraction? Name an example? ○ How are improper fractions and mixed numbers alike? ● After this class sharing and discussion, the teacher will review correct answers and clear up any confusion regarding these concepts. The teacher will then ask the students to show a quiet thumbs up if they feel confident with their understanding of the lesson or a thumbs down if they feel like they could use more practice. ● After the informal assessment of thumbs up/down, each student will be given an exit ticket (attached below) to complete before beginning their homework assignment for the day. ● As soon as the students begin working on their exit ticket, the teacher will write their Math Workbook assignment on the whiteboard (pg. 547-548). As soon as their exit ticket is handed in, they can begin to work on their assignment with the remaining class time available. B. Assessments Used ● Informal Assessment: Observations ○ Observations were gathered when working with students during the guided practice questions and also while walking around and working one-on-one during independent practice. ● Informal Assessment: Thumbs up/Thumbs down ○ By asking students to demonstrate their comfort level in using this method, you can get a better understanding of how confident they may be in this skill. If many showed that their thumbs were up and they were getting it, use that to plan more advanced lessons. However, if many showed a lack of confidence, you know that more work and support is needed to reach proficiency in this skill. ● Informal Assessment: Exit Ticket Faye Schmidt TWS Lesson 10: Mixed Numbers and Improper Fractions Chapter 8: Fractions
Page 8
○ Exit tickets will be collected upon completion at the end of the lesson, but not graded for correctness. These will be analyzed by the teacher to identify which students may need more assistance or any common problem areas that could use more explanation the following day. ● Formal Assessment: Collection of Workbook Assignment ○ Assignments completed from the Math Workbook are to be finished and handed in the following day for grading. These grades are entered and used to determine students’ midterm and quarter grades in math class. C. Differentiated Instruction ● For those needing additional support: ○ Work one-on-one with students needing more help to ensure that they are learning foundational skills to help them with math later on. The specific students who showed a quiet thumbs down at the end of the lesson could be invited to the front table to work with a teacher on more examples to gain more practice and confidence. ● For those in need of enrichment/challenging: ○ Offer more complex or additional problems to them, or ask them to explain their thinking and reasoning more in depth. ○ Also, have them work with those who may need more support. Pair them with struggling students so that both parties may benefit from this interaction. ● For those in need of specific language support: ○ Provide additional wait time for students who take a bit longer to complete the exercises. Make sure to speak slowly and articulate vocabulary and steps to the strategy, and use multiple phrases to describe and explain the same idea or concept. D. Resources Adapted from: McGraw-Hill Education. (2014). My math. Lesson 8.10 Mixed Numbers and Improper Fractions (p.543A-548). Columbus, OH: McGraw-Hill Education. Faye Schmidt TWS Lesson 10: Mixed Numbers and Improper Fractions Chapter 8: Fractions
Page 9
Lesson 10 Exit Ticket ____________________ Part 1: Write a mixed number and an improper fraction for each shaded model. Mixed number: _______ Mixed number: _______ Improper fraction: _______ Improper fraction: _______ 11 Part 2: Ava ran 4 miles. How many whole miles did she run? What portion of an additional mile did she run? Draw a model to represent this mixed number. _____________________________________________________________________
Faye Schmidt TWS Lesson 10: Mixed Numbers and Improper Fractions Chapter 8: Fractions
Page 10
Page 1
● By the end of the lesson, students will write mixed numbers and improper fractions correctly with 70% accuracy. Materials Needed: ● Each Student will need their: ○ Math Notebook ○ Pencil ○ Math Workbook ● Teacher will need: ○ Promethean Interactive Board ○ Projector ○ Whiteboard marker and eraser ○ Paper to complete example problems on ○ Pencil ○ List of example problems to complete during lesson ○ Exit tickets to check for understanding after the lesson (attached) Contextual Factors/ Learner Characteristics: ● This classroom is made up of 28 total 4th-graders, aged 9-11. 27 of these students will be in the classroom to complete this math lesson as a large-group, teacher-led learning experience. When it comes to independent work time, 2 students work on their homework assignments in an alternative setting, and 25 complete their work independently in the general classroom. I, the student teacher, will be leading this lesson, and my cooperating teacher, who is the classroom’s primary teacher, will be observing and assisting students. This diverse classroom is made up of students from a various backgrounds and learning levels, which have been considered when planning this lesson. ● This lesson will be begin at about 9:00 AM, right after students are finished with their Morning Meeting. This lesson will end at about 10:00, when the students will leave the classroom to attend Library and Computer. Flex seating is also utilized in this classroom, with several different options available each week for the students to choose. In this classroom, there is a strict seating chart, and students are expected to find their seats and remain in their assigned seats for the lesson. Because of the size of the group and the arrangements of the desks, the teacher is to remain mindful of unnecessary behaviors, such as irrelevant conversations. These situations should be approached immediately if any issues arise during the lesson. Faye Schmidt TWS Lesson 10: Mixed Numbers and Improper Fractions Chapter 8: Fractions
Page 2
A. The Lesson 1. Introduction (10 min) ● First, the teacher should ask the students about what they have learned so far in the previous lessons in this chapter. This class discussion should take a few minutes, and should be used to review content or clear up any misunderstandings or confusion before moving on. Students will provide definitions and other information about fractions that they have learned thus far. The following review questions or prompts could be asked to the class if they need help recalling some of the things that have been addressed in prior lessons. Volunteers will raise their hands to be called on to share their definitions and other information regarding these terms or concepts. ○ What are the parts of a fraction? What is a numerator and denominator? ○ What does a numerator represent? denominator? ○ What is a mixed number? ● After this brief review is complete, remind the students that the information that was learned in the last couple of days will help us with this lesson, and the ones that follow. Today, our focus is to continue to work with mixed numbers and introduce improper fractions. ● The teacher will then share the objective with the class, and then begin the lesson. ○ “By the end of the lesson, students will write mixed numbers and improper fractions correctly.” 2. Content Delivery (30 min) ● Since the goal of this lesson is introduce mixed numbers to the students, a definition should be provided and shared with them as they begin thinking about what a mixed number really is and looks like. ○ An improper fraction is a fraction that has a numerator that is greater than its denominator. ■ Example: 32 , 74 , etc. ● After giving the students this definition and explaining it, make sure to emphasize that like mixed numbers, improper fractions have a value greater than 1. ● To begin the guided practice, the following example will be shown. To complete this problem, the teacher will read it aloud to the class and then model the steps on how to solve it. Since it is a new concept for these students, the teacher is to make sure that they are clear when explaining the reasoning of these problems. Faye Schmidt TWS Lesson 10: Mixed Numbers and Improper Fractions Chapter 8: Fractions
Page 3
○ First, the students will identify how many parts make up one whole. ■ 8 ○ Next, the students will write fractions under each image that represent the shaded amount. ■ 88 and 38 ○ Then, you must add these fractions together. When you add fractions, you must keep the denominator the same and add the numerators together to make an improper fraction. ■ 88 + 38 = 11 8 ○ So, ■ 1 38 written as an improper fraction is
11 8
● The next example will allow the students to practice converting an improper fraction to a mixed number. ○ First, the students must analyze the image. Later, they will need to draw their own model, so they must understand how to create a model that matches the fraction or mixed number. ○ Then, the class should dicuss how this is similar to what they were practicing in the last lesson, when they were writing mixed numbers. ○ Just like in the previous lesson, they must first count all of the “wholes.” ■ 2 ○ Then, notice that the last part of the model is incomplete, and they should count the remaining shaded parts of this section. ■ 14 ○ Lastly, they add these together to identify the mixed number shown in the model of the original improper fraction. Faye Schmidt TWS Lesson 10: Mixed Numbers and Improper Fractions Chapter 8: Fractions
Page 4
■ 2 14 ● Next, the students should complete the next set of examples independently, and then raise their hands to volunteer to answer and ask questions when everyone is finished and ready to share and compare. ● Follow the same steps as the first example to complete this series of problems. ○ Mixed Number ■ 1 46 ○ Improper Fraction ■ 66 + 46 = 10 6 ○ Mixed Number: ■ 1 25 ○ Improper Fraction: ■ 55 + 25 = 75 ● Mixed Number: 2 23 ● Improper Fraction:
3 Mixed Number: 2 10 3 3
+
3 3
+ 23 =
8 3
Improper Fraction:
10 10
10 3 + 10 + 10 =
23 10
Faye Schmidt TWS Lesson 10: Mixed Numbers and Improper Fractions Chapter 8: Fractions
Page 5
● Mixed Number: 2 12 ● Improper Fraction:
2 2
+ 22 + 12 =
5 2
Mixed Number: 3 34 Improper Fraction: 15 4
● For the next set of examples, the students will practice creating models for mixed numbers. The first example should be modelled by the teacher, and then the students should practice independently before reviewing the correct answers. ● The model should contain two shapes, each divided into 5 pieces. One should be completely shaded, and the other should have 3 of the 5 pieces shaded. ○ Improper Fraction: 85 ○ The first model should contain three shapes, each divided into 4 pieces. Two should be completely shaded, and the other should have 3 of the 4 pieces shaded. ■ Improper Fraction: 11 4 ○ The next model should contain two shapes, each divided into 10 pieces. One should be completely shaded, and the other should have 7 of the 10 pieces shaded. 17 ■ Improper Fraction: 10 Faye Schmidt TWS Lesson 10: Mixed Numbers and Improper Fractions Chapter 8: Fractions
Page 6
● For the next set of examples, the students will practice creating models for improper fractions. The first example should be modelled by the teacher, and then the students should practice independently before reviewing the correct answers. ● The model should contain two shapes, each divided into 8 pieces. One should be completely shaded, and the other should have 3 of the 8 pieces shaded. ○ Mixed Number: 1 38 ● The first model should contain two shapes, each divided into 6 pieces. One shape should be completely shaded, and the other should have 3 of the 6 pieces shaded. ○ Mixed Number: 1 36 ● The next model should contain three shapes, each divided into 3 pieces. Two shapes should be completely shaded, and the other should have 1 of the 3 pieces shaded. ○ Mixed Number: 2 13 ● Next, the students will practice some word problem examples, where they will need to carefully read each problem to identify what the question is asking, and problem solve how how complete. ○ Jason ran 11 miles. How many whole miles did he run? What portion of an 3 additional mile did he run? ■ 11 = 3 23 3 ■ 3 whole miles, 23 of a fourth mile ○ Jenny was on a horseback riding tour. She reached the end of the trail in 2 hours and 15 minutes. Write the amount of hours she spend on the trail as a mixed number and an improper fraction. Faye Schmidt TWS Lesson 10: Mixed Numbers and Improper Fractions Chapter 8: Fractions
Page 7
15 ■ 3 60 or 3 14 =
13 4
3. Closure (20 min, including work time) ● At this time, the teacher will ask the students if they have any questions regarding the new information from the lesson. If there are any concerns or confusion, these should be addressed as a group so that all students can benefit. ● Now, the teacher will ask the following questions to the class to discuss. Students will then volunteer to share their answers to these prompts. ○ What is a mixed number? What is it made up of? ○ What is an improper fraction? Name an example? ○ How are improper fractions and mixed numbers alike? ● After this class sharing and discussion, the teacher will review correct answers and clear up any confusion regarding these concepts. The teacher will then ask the students to show a quiet thumbs up if they feel confident with their understanding of the lesson or a thumbs down if they feel like they could use more practice. ● After the informal assessment of thumbs up/down, each student will be given an exit ticket (attached below) to complete before beginning their homework assignment for the day. ● As soon as the students begin working on their exit ticket, the teacher will write their Math Workbook assignment on the whiteboard (pg. 547-548). As soon as their exit ticket is handed in, they can begin to work on their assignment with the remaining class time available. B. Assessments Used ● Informal Assessment: Observations ○ Observations were gathered when working with students during the guided practice questions and also while walking around and working one-on-one during independent practice. ● Informal Assessment: Thumbs up/Thumbs down ○ By asking students to demonstrate their comfort level in using this method, you can get a better understanding of how confident they may be in this skill. If many showed that their thumbs were up and they were getting it, use that to plan more advanced lessons. However, if many showed a lack of confidence, you know that more work and support is needed to reach proficiency in this skill. ● Informal Assessment: Exit Ticket Faye Schmidt TWS Lesson 10: Mixed Numbers and Improper Fractions Chapter 8: Fractions
Page 8
○ Exit tickets will be collected upon completion at the end of the lesson, but not graded for correctness. These will be analyzed by the teacher to identify which students may need more assistance or any common problem areas that could use more explanation the following day. ● Formal Assessment: Collection of Workbook Assignment ○ Assignments completed from the Math Workbook are to be finished and handed in the following day for grading. These grades are entered and used to determine students’ midterm and quarter grades in math class. C. Differentiated Instruction ● For those needing additional support: ○ Work one-on-one with students needing more help to ensure that they are learning foundational skills to help them with math later on. The specific students who showed a quiet thumbs down at the end of the lesson could be invited to the front table to work with a teacher on more examples to gain more practice and confidence. ● For those in need of enrichment/challenging: ○ Offer more complex or additional problems to them, or ask them to explain their thinking and reasoning more in depth. ○ Also, have them work with those who may need more support. Pair them with struggling students so that both parties may benefit from this interaction. ● For those in need of specific language support: ○ Provide additional wait time for students who take a bit longer to complete the exercises. Make sure to speak slowly and articulate vocabulary and steps to the strategy, and use multiple phrases to describe and explain the same idea or concept. D. Resources Adapted from: McGraw-Hill Education. (2014). My math. Lesson 8.10 Mixed Numbers and Improper Fractions (p.543A-548). Columbus, OH: McGraw-Hill Education. Faye Schmidt TWS Lesson 10: Mixed Numbers and Improper Fractions Chapter 8: Fractions
Page 9
Lesson 10 Exit Ticket ____________________ Part 1: Write a mixed number and an improper fraction for each shaded model. Mixed number: _______ Mixed number: _______ Improper fraction: _______ Improper fraction: _______ 11 Part 2: Ava ran 4 miles. How many whole miles did she run? What portion of an additional mile did she run? Draw a model to represent this mixed number. _____________________________________________________________________
Faye Schmidt TWS Lesson 10: Mixed Numbers and Improper Fractions Chapter 8: Fractions
Page 10
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