Curriculum Design – Case Scenario
6th Grade Math – Fractions
Grade: 6th Subject: Math Topic: Fractions
For my five day unit I have decided to use a Math lesson with a focus in fractions. I have chosen to work with the sixth grade level as it is where I am more comfortable with my teaching abilities. The students will be studying fractions for one hour a day for a five day school week. The material will be covered in the designated math period for each student. Through this curriculum the students will learn the skills of identifying, comparing/contrasting and solving factions; as well as decimal values. Students will be able to demonstrate through the use of various materials their understanding of fractions in comparison to everyday life and the subject of Math.
Through the use of a five day curriculum on fractions, as the teacher, I am going to have to pick and choose what information will be focused on in more detail and what material will be taught in a more general sense. The curriculum will start out with a very general overview and introduction into the material and as the day’s progress, the information will start involving much more information and steps to solving the problems assigned. Therefore it is my belief that the curriculum I have chosen will emphasize both depth and breadth depending on the material being covered in each class period.
I have chosen to have my students study this topic because the use of fractions in everyday life is vital. We as a society use fractions every day in life through the use of money, cooking, measuring, telling time, etc. Similar to my group curriculum simulation project on telling time, the use of fractions is also a universal skill. No matter what country or language, the use of currency, measurement and time are all the same. Every society is using some form of currency to pay for or trade for products, some form of measurement to build things and everyone is using a clock to tell time; therefore this skill is vital. We are able to relate this topic to the Social Efficiency Ideology because the skill needs to be taught in a sequential order for the students to understand the information. In order to progress to the next subtopic, the student must first master the basic information. Going along with the previous statement, we can also relate this lesson to the Scholar Academic Ideology since we are grooming the students to master the information. Finally we can also relate this curriculum to the Social Reconstruction Ideology because we are teaching various skills that can be related to future jobs that may combat some of the issues of our society (i.e. – economic crisis and tardiness).
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Grade Level: 4 Time: 40 minutes Subject: Math Topic: Dividing and Multiplying to Find Equivalent Fractions NY State Learning Standards: Mathematics, Science, and Technology Standard 1: Analysis, Inquiry, and Design Students will use mathematical analysis and scientific inquiry to seek answers and develop solutions. Materials: Mathematics Textbooks (page 401) Notebooks Pencils Different colored ...
The curriculum chosen will emphasize content followed by skills. The students need to understand the content and basic information of how to read and identify fractions before they can put to use the skills of simplifying and converting fractions. The use of content followed by skills once again relates back to the Social Efficiency and Scholar Academic Ideologies since we are teaching the information in a sequential manner and requiring the students master the material before moving forward to the next step. The students will be gaining the knowledge of the content and a more focused understanding of the skills through the curriculum. On the other hand, unfortunately the students will be losing the ability to create their own learning experiences. Students are losing the ability to create their own experiences because we are focusing on the skills. The materials that will be used throughout this curriculum include, the state curriculum, school Math textbook, worksheets, calculator, overhead projector and overhead worksheets, flashcards and candy.
As Tyler suggests, I will first determine my objectives and then acquire and organize the learning experiences each day for the students. Once again I am relating my curriculum to the Social Efficiency Ideology and the Scholar Academic Ideology since I am teaching to my students in an sequential manner as well asking them to master the material presented each day before being able to go on to the next step. I am able to assess whether or not my students are master the material I am asking them to master through the use of an exit ticket each day and a review through the opening activity at the beginning of each class period. It is easy to see through the below breakdown of my five day curriculum how the material is being taught sequentially.
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Foremost, I would like to express my sincere gratitude to my teacher Sir Edgardo M. dela Cruz for the continuous support of my research, for his patience, motivation, enthusiasm, and immense knowledge. His guidance helped me in all the time of research and writing of this thesis. I could not have imagined having a better teacher and mentor for my Thesis Writing. I thank my fellow classmates who ...
1. Day 1 – Introduction to Fractions
a. Students will be introduced to fractions.
b. Students will be able to relate fractions to everyday use in the world.
c. Students will be able to interpret information using a chart.
The opening activity for day one will involve asking students what they know about fractions previous to explaining any information for the day. Once this has been discussed I will draw a circle on the board and ask the students to relate the circle to a pie (flavor of their choice).
The students will be asked to imagine the pie being sliced into 16 pieces. Finally I will ask them, “If Johnny ate 3 pieces of the pie, what fraction of the pie is left for Katy to eat?” After this, depending on their level of understand we will either move on with the main activity or remain here and attempt more practice problems similar to the above. The main activity will involve a worksheet and the individual sized bags of M&M candy. Students are asked to open the M&M candy and separate the colors into piles. The students are then asked to fill out the information regarding each color M&M on the chart provided via the worksheet. One column is asking for the total number of a certain color and the second column is asking for the total number of M&M’s in the entire package. In order to leave the class that day, the students have to complete an exit ticket. This exit ticket is their completed worksheet that displays various fractions that are indicating the number of each color of M&M’s over the total number.
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2. Day 2 – Exploring Equivalent Fractions
d. Students will be able to express what fractions are equivalent fractions
e. Students will be able to explain why fractions are equivalent
The opening activity for day two will relate back to day one but also introduce the lesson for day two. Students will be given the following scenario and asked to solve the problem; “Johnny has a candy bar but was told by his father that he has to share the candy with his sister. Johnny told Katy that he would give here 2/4 of the candy bar. Is 2/4 of the candy bar half of the bar?” Students will be asked to explain how they came to their answer. The main activity will involve the worksheet with various fractions on it. Each student will be assigned a set of fractions and will be asked to stand up and tell the class what fractions they have (they may have halves, tenths, thirds, etc.).
The students should begin to recognize that although the fractions are broken up different, they have the same values. The students will then be asked to match up with the fellow student who has the equivalent fraction. The next activity will involve me showing the students the procedure for finding equivalent fractions, followed by example problems. In order to leave class that day, the students will be asked to complete an exit ticket. For the exit ticket, I will be asking the students to write down the fraction on the board and provide me with three equivalent fractions.
3. Day 3 – Reducing and Simplifying Fractions
f. Students will be able to reduce / simplify fractions.
g. Students will be able to compare decimal values to find equivalences.
The opening activity for day three will once again relate to the two previous days but also introduce the day’s lesson. Students will be asked, “Would you prefer 2/8 or 4/16 of the cake?” The main activity for the day will involve the rainbow fraction worksheets. I will display my version of the worksheet on the overhead for the class to see. Students will be able to see how the open activity examples are equal to one another. Using the same fractions students will then be introduced to simplifying fractions. Students will learn the use of factors to assist in the simplifying of fractions. As done in previous days, students will be required to complete an exit ticket in order to leave the class for the day. For the exit ticket students are being asked to take the two fractions written on the board and simplify them using the techniques learned in today’s class.
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Young people these days are less interested in studying than in earning money. ' This has been said by many people, and to a certain extent, is absolutely true. The bad thing is, people take this as bad, but this has always been the case since the invention of currency. People just see what's on the outside, and don't care to dig inside on these types of matters, thus making uneducated comments. ...
4. Day 4 – Comparing Fractions
h. Students will be able to compare fractions by determining if the fractions are less than, greater than, or equal to.
i. Students will be able to explain why a fraction is larger or smaller than another fraction.
The opening activity for day four will review the previous day’s lesson while also introducing today’s lesson. Students will be asked the question, “I have $167 and you have the choice to take either 4/7 or 5/8 of the amount.” Students will then be given time to figure out which portion of the money they would like to take. Through the main activity of the day students will be reminded that in order to decide which of the two portions is bigger they would need to find the common denominator (which was learned in yesterday’s lesson).
Students will be introduced to two methods in order to find the answer to question. Students are asked to use the method that is most comfortable to them. We will then review greater than, less than and equal to signs. Using the fraction circle worksheet, students will be asked to compare fractions using the information learned in the class. As an exit ticket for the day students will be asked to convert fractions to decimals and then compare which is greater than, less than or equal to another (with use of a calculator).
5. Day 5 – Adding and Subtracting Fractions
j. Students will be able to manipulate fraction bars to add and subtract fractions with common and unlike denominators.
k. Students will be able to add and subtract fractions with common and unlike denominators without using manipulative.
The opening activity for the day will involve materials previously learned as well as an introduction to the day’s lesson. Students will be shown a recipe for baking cookies. Students will then be shown how much of each ingredient the teacher has with her that day. The students will be asked to determine if the teacher has enough of each ingredient to bake the cookies or if she needs to purchase more. If she is required to get more of a particular ingredient, the students are asked to determine how much more she will need. Next students will be paired in groups and given the fraction bar worksheets once again. Students are asked to in their pair figure out what color is represented by what denominator for each fraction. Students will then be able to use this information when adding and subtracting with common denominators. Students are then taught the technique used to adding and subtracting fractions. After completing the assigned worksheets for the day, we will return to the opening activity question and us it as an exit ticket for the day. Students are asked to check their work after the days lesson to see if their original answer was correct.
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When sequencing my curriculum I will be once again be using content followed by skills. In order for my students to understand the information I am requiring of them, I need to first explain the content and then go into more depth on the skills. I would sequence the information I am placing in the curriculum as follows:
Simple to complex → Chronological
Easy to Difficult → Developmental
Simple to complex (chronological) and easy to difficult (developmental) would be the most fitting for my curriculum as it is a math curriculum. As in any subtopic in math, one must understand the basic, general overview of the topic before they can get into the more difficult steps. I cannot expect my students to understand how to add and subtract fractions before I teach them how to find common denominators. Also each day I will be revisiting the previous days learned information. At this point I am able to determine if my students have grasped the information I had asked them to learn the day before or not. If it is determined through the opening activity that the students have not fully understood the information, I must then revisit the lesson before moving forward to the next step in the curriculum. The use of continuity can be seen throughout the year in other subtopics in the subject matter. As discussed earlier, the use of fractions is used in many places in life. When we visit the subtopic of measurements later in the year, we will revisit the ideas learned in this lesson in order to help the students better understand the new material being introduced to them. By using these types of sequencing I am once again supporting the Social Efficiency and Scholar Academic Ideologies. As I have stated time and time again in this paper, I am asking my students to master one topic before they can move onto the next topic (scholar academic); as well as teaching them the information in a logical and sequential format for them to understand (social efficiency).
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I am a strong believer in the idea of an integrated curriculum. As in many aspects of life, it is my belief that everything relates back to everything else at some point. Therefore I would take time each day to relate our activities, whether as fractions as a whole or each days lesson, to students lives inside and outside of school. One of the easiest connections to see is money and fractions. It is important to give examples to the students of how learning these objectives in class can be related to their lives in the long run; also relating the use of fractions to other subjects that the students are enrolled in throughout the school year. Listed below are a few examples:
* Social Studies: ratio of populations, number of deaths in a war compared to population
* Physical Education: comparing sit and reach results
* Science: measuring out chemicals
* Technology Education: measuring of wood/building measurements
The ideology that best relates to an integrated curriculum in my opinion would be the Social Reconstruction Ideology. The ideology identifies an issue and works to educate students to correct this issue in order to create a better society then the current one. By educating students in a way that enables them to be able to relate information to each subject matter, we are able to educate students to see ways to better issues.
Throughout this paper I have used three of the four ideologies to relate to my five day curriculum and to my view on integration in the classroom. I think it is important to note that all four of the ideologies are useful in the classroom; it just depends on what information is being taught. Also it is important to realize that each of the ideologies is very similar to the next one although the emphasis is placed on different importance. All of them are important in their own right.
