Faye Schmidt Lesson 8

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Dakota State University  College of Education    Lesson 4: Equivalent Fractions  Name: ​Faye Schmidt  Grade Level: ​4th Grade  School: ​Sioux Valley Elementary  Date: ​Friday, March 1st, 2019  Time: ​9:00-10:00 AM    Reflection from prior lesson:  ● In the previous lesson, students used learned about modelling equivalent  fractions using fraction tiles and number lines. Using these manipulatives,  especially the number line resource, they were successfully able to compare two  fractions and identify if they were equal. They completed examples during class as  a group and individually, submitted and informal exit ticket, and handed in a Math  Workbook homework page to be graded. Students were assessed in various  ways, both informally and formally, and the results were used to construct future  lessons. Overall, the students have done well on the previous lessons in this  chapter and have met the objectives set in the previous lesson plans. As a class,  they seem to have a good grasp on the knowledge needed to move forward onto  this next part, which dives even deeper into equivalent fractions.     Lesson Goal(s) / Standards:    ● Domain: ​Number and Operations - Fractions  ● Major Cluster: ​Extending understanding of fraction equivalence and ordering.   ○ 4.NF.1 ​- Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b)  by using visual fraction models, with attention to how the number and size  of the parts differ even though the two fractions themselves are the same  size. Use this principle to recognize and generate equivalent fractions.  ○ 4.NF.5​ - Express a fraction with denominator 10 as an equivalent fraction  with denominator 100, and use this technique to add two fractions with  respective denominators 10 and 100. For example, express 3/10 as 30/100,  and add 3/10 + 4/100 = 34/100.  ● Math Practice Standards:  ○ MP1​: ​Make sense of problems and persevere in solving them.  ○ MP2​: ​Reason abstractly and quantitatively.  ○ MP4​: ​Model with mathematics.  ○ MP7: ​Look for and make use of structure.   Faye Schmidt TWS Lesson 4: Equivalent Fractions Chapter 8: Fractions

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○ MP8​: ​Look for and express regularity in repeated reasoning. 

  Lesson Objectives:  ● By the end of the lesson, the students will be able to define the term ​equivalent  fractions​ in their own words verbally and in writing​.   ● By the end of the lesson, the students will identify equivalent fractions correctly  with 70% accuracy without the use of manipulatives.    Materials Needed:   ● ​Each Student will need their:  ○ Math Notebook  ○ Pencil  ○ Whiteboard marker and eraser  ○ Number line handout inside a plastic sheet (27 total) (attached)  ○ 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 9:15 AM, right after students are finished with  their Morning Meeting and complete a brief multiplication fact assessment. At this  time, the students should begin to get settled in to their normal daily math routine.  Faye Schmidt TWS Lesson 4: Equivalent Fractions Chapter 8: Fractions

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Also, this class will take a break at about 10:00, when the students leave the  classroom for their scheduled Library check out time. The students return to the  classroom at about 10:15, and will spend the remainder of the class time working  on their assignment and fact fluency before using the restrooms and washing for  Lunch. 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.     A. The Lesson   1. Introduction (10 min)    ● First, the teacher should ask the students about what they learned the previous  days in the first few lessons, as it will likely be helpful as they begin today’s lesson.  Students will provide definitions and other information about factors, multiples,  prime and composite numbers, and what they learned about modelling equivalent  fractions from the lesson the day before. They will also have the opportunity to  share information that they have withheld from the previous days.  ● Before beginning the lesson, the teacher will ask the following review questions to  the class, and call on volunteers to share their definitions and other information  regarding these terms.   ○ What is a numerator?  ○ What is a denominator?  ○ What are equivalent fractions?  ● After this brief discussion, the students will then be instructed to take out their  Math Notebooks, a pencil, number line handout, and a whiteboard marker.   ● ​As a quick review, the teacher will show the following question on the  Promethean board by using the projector for the students to answer as a  refresher. The students will record their answers on the next open page in their  Math Notebooks, and show the teacher that they are finished by putting their  pencil down. The teacher will read the problem to the students, and encourage  them to use their number line handout from the previous lesson if they need extra  assistance. When finished, they will then volunteer to share their answers and  explain their thinking. Additional examples may be provided to the class if more  review is needed.  Faye Schmidt TWS Lesson 4: Equivalent Fractions Chapter 8: Fractions

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○ Betty needs 12 cup of milk for her recipe. How many fractions can you find  to represent 12 ?  ■ 24 , 36 , 48 , etc..  ● 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 learn about equivalent fractions, but  to try to rely less on manipulatives and other resources.   ● The teacher will then share the objective with the class, and then begin the  lesson.  ○ “By the end of the lesson, the students will identify equivalent fractions  correctly without the use of manipulatives.”     2. Content Delivery (35 min)    ● Since the goal of this lesson is to draw back the students’ reliance on  manipulatives, the number line fraction chart that the student have been using will  gradually be used less and less throughout the lesson. To begin, they will be  allowed to use this chart as a guide.   ● 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 ask what they think  would be a good strategy to use to solve this problem. After taking suggestions,  slowly and clearly write out the fraction, and explain how you can multiply the  numerator and the denominator by the same number to get a new equivalent  fraction. Some students may have noticed this in the previous day’s lesson as well.  Use this method to find at least two fractions equal to 34 .   ○ A recipe for spaghetti and meatballs calls for 34 pound of ground beef. Find  two fractions that are equivalent to 34 .  9 ■ Answer: 68 and 12   ● After learning this multiplication strategy to find equivalent fractions, complete a  few more examples with the class. At this time, any manipulatives and the number  line handout should be put away. Also, discuss that you can also divide to find  equivalent fractions as well, as long as you use the same number to divide both  the numerator and the denominator of a fraction. Challenge students to find one  smaller equivalent fraction and one larger equivalent fraction for the third and  forth examples listed below.   ○ Find two equivalent fractions of 13   ■ 26 , 39 , etc.  ○ Find two equivalent fractions of 25   Faye Schmidt TWS Lesson 4: Equivalent Fractions Chapter 8: Fractions

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4 10

,

6 15

, etc. 

○ Find two equivalent fractions of 8 ■ 12 , 16 , etc. 

4 8

○ Find two equivalent fractions of

6 10



3 5

,

12 20

   

, etc.  

● Next, challenge the students even more by providing practice questions with  “mystery numbers.” To solve, they will have to identify what the given fraction is  multiplied or divided by to get the new number provided in the problem. Then,  they will have to find the other number that goes in the empty space to create the  equivalent fraction. Complete the following examples with students as guided  practice.   ? ○ 38 = 16   ○

7 10

■ Answer: 6  = 70   ?

■ Answer: 100  ● For this next set of questions, the students will work independently to solve the  missing number. After questions are given, the teacher will walk around the room  to work with students as they solve the problems. After everyone is finished,  volunteers will raise their hands to share and explain their answers.   ○ 37 = 9?   ○

■ Answer: 21  8 ? = 81   9



■ Answer: 72  11 = 2?   22



■ Answer: 1  25 = 5?   35

■ Answer: 7  ● Lastly, the class will work through two word problems together so that they are  more familiar with it when they see it on their assignment. For the first one, the  teacher should help guide the students in solving, and ask prompting questions to  encourage critical thinking. The second question should be given to the students  to complete on their own, and volunteers will raise their hands to answer.  ○ There are 10 cars in a parking lot. 6 of the cars are white. First, rewrite this  information in the form of a fraction, then find two equivalent fractions.   6 12 ■ Answer: White cars: 10 , 35 or 20 etc.  

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○ There are 15 marbles in a bowl. 5 of the marbles are blue, 9 of the marbles  are red, and 1 marble is green. Write two fractions that describe the fraction  of marbles that are blue.   5 10 15 ■ Answer: Blue marbles: 15 = 13 = 30 = 45 etc.     3. Closure (15 min)    ● 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 terms.   ○ What is a numerator?  ○ What is a denominator?  ○ What are equivalent fractions?  ○ How do we find equivalent fractions using math facts?  ● 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. 509-510). 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,  Faye Schmidt TWS Lesson 4: Equivalent Fractions Chapter 8: Fractions

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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  ○ 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 8.4 Equivalent Fractions  (p.505A-510). Columbus, OH: McGraw-Hill Education.        Faye Schmidt TWS Lesson 4: Equivalent Fractions Chapter 8: Fractions

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Lesson 4 Exit Ticket ____________________    1. How can we find equivalent fractions without using manipulatives?    _____________________________________________________________________  2. Write the fraction for the shaded part of the shape. Then, find one equivalent  fraction for each.   a.   b.       ____ = ____ ____ = ____          3. Identify two equivalent fractions for each fraction:    1 3 a. 5 b. 6        

   

Faye Schmidt TWS Lesson 4: Equivalent Fractions Chapter 8: Fractions

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