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Students learn strategies for adding common fractions with like denominators here without provided pictures
3, 4, 5
Title – Adding Common Fractions with Like Denominators without Pictures
By – Whitney Robertson, Brittney Whitewood, & Marie Banchy
Primary Subject – Math
Grade Level – 3-5
- Description of students’ prior knowledge or the focus of the previous lesson:
- Before this lesson, students need to already know how to add and subtract fractions with common denominators. This lesson is going to focus on a specific test-taking technique to help students solve problems involving fractions that do not have a picture. Students will learn different ways to draw out fractions, either circles or squares, when there is no picture provided to give them a visual aide. This will become very crucial when students start ordering fractions and working on fractions that are greater than, less than, or equal to.
- Explanation of how this lesson relates to the unit of study and the goals for teaching about the topic:
- This lesson relates to the unit of study because it goes back to review the concept of adding and subtracting fractions, in case it has been a while. It will also provide students with a technique to use in the future when they will no longer have pictures to look at, instead they can make their own. Hopefully, by the end of this lesson, students will be able to draw fractions out in multiple ways, see a way that fractions are used in everyday life, and use manipulatives to visualize the addition and subtraction concepts since this age is more into visual learning.
- Explanation of what is needed from this lesson for the next lesson:
- In the next lesson, we are going to work on reducing fractions and finding common denominators. Once students know how to add and subtract fractions, with and without a manipulative, they will also be able to do it with reduced fractions. At times, some fractions will be in reduced form and can not be added together without the common denominator. This will take the concept of easily being able to add fractions because they have like denominators and making it more difficult because they will now see that there are some fractions out there that can be reduced more once the answer is achieved.
- Critical student characteristics or attributes that will affect student learning (including details about modifications needed for students with an IEP, GSSP, or LEP, 504 Plan, Title I, ethnic, cultural, or racial diversity, or achievement gaps):
- A characteristic that may affect student learning is any comprehension problems. This may cause a difficulty in how students perceive the information they are being taught and may confuse them, as well. Students with an IEP, may need more one-on-one instruction to make sure that they are understand the topic and to make sure they are benefiting, like the other students. When there are students with an LEP in the classroom, there may be a cultural or language barrier. The student(s) may not understand everything that is said by the teacher, because they don’t have the same native language. It is also important to remember cultural differences so every student is comfortable in the classroom. GSSP students need to be constantly challenged. It is important to make sure that there are alternate assignments available in case these students finish early, as well as opportunities for them to use their knowledge to work with and help other students. Overall, it is important that every student is comfortable in the classroom and learning to their highest potential. Make sure that all objectives and goals in mind are achievable. That may mean that certain students are held to different standards.
- Students will be able to add common fractions with like denominators using manipulatives.
- Students will be able to solve real-world problems involving adding and subtracting fractions.
- Students will be able to display fractions pictorially.
Curriculum Focal Points:
- Students will understand the meanings and use of fractions to represent parts of a whole and parts of a set.
Program of Studies – Skills and Concepts:
- MA-P-NPO-S-NS2: Students will apply multiple representations (e.g., drawings, manipulatives, base-10 blocks, number lines, expanded form, symbols) to describe and compare whole numbers and fractions (e.g., halves, thirds, fourths) in mathematical and real-world problems.
- MA-P-NPO-S-NO9: Students will add common fractions with like denominators using manipulatives.
- MA-P-NPO-S-NS5: Students will develop beginning fractional concepts (e.g., dividing an object into equal parts and naming the equal parts [e.g., halves, thirds, fourths]).
Core Content for Assessment:
- MA-EP-1.3.1: Students will analyze real-world problems to identify appropriate representations using mathematical operations, and will apply operations to solve real-world problems with the following constraints: add and subtract fractions with like denominators less than or equal to four. DOK 2
Resources, Media and Technology:
- manipulative pieces
- rubric for adding fractions
- open response
- paper and pencil
- worksheet with circles
- expo board and markers
- name tags
- teacher set of fractions
- Greet students.
- “Today we are going to start on our first lesson of our unit on fractions. Before this lesson, you are going to have to be able to add and subtract fractions with common denominators. To help you remember what you already know, we are going to do a quick review and hand out name tags. To get started, we are going to look at a few addition and subtraction problems involving common denominators. We are going to pull a name tag out and call that student up. Once the student comes up to the front, we will ask the other students to stand up if they have the matching first letter of their name. (For example, if we call up “Mark,” he will come to the front of the class. Then we will ask the other students with the matching first letter to come up, and “Maria,” “Michael,” “Manuel, and “Malcolm” will stand behind him.) Those name tags will be handed out and the student at the front of the room will count the students and tell us how many have similar starting letters of their first name, out of the 21 students in class. This will be continued for other topics such as wearing tennis shoes, boys, and girls until we have four fractions with common denominators. We will then construct addition and subtraction problems out of these fractions for students to solve. For example, 10/21 students are boys subtracted from 11/21 girl students. What is the difference? (1/21) This should take 10 minutes.”
- Send students back to their desks. Remind them that the main thing to remember is that fractions are used in everyday life outside of school. For example, “Who cooks?” (Students raise hands.) “This is something that will often involve a fraction of a whole that needs to be measured out precisely.”
- “By the end of this lesson, we will all be able to add fractions with common denominators, solve real-world problems involving adding and subtracting fractions, and demonstrate the meaning and use of fractions.”
- “From the pre-assessment we noticed that some students are having trouble visualizing what the fraction looks like when there is not a picture provided. Today we are going to focus on how important it is to draw things out if you need to. We are going to work with adding and subtracting fractions, since this is something that you have already mastered, and on how to draw this out when you don’t have a picture provided.”
- Give students their manipulative pieces and three minutes to “play” with them to see what kind of fractions they can create. This is solely for them to get comfortable with the manipulatives and let their mind wander in a structured way. Once their three minutes are up, as a class complete one addition and one subtraction problem with the manipulative. (Addition: 3/4 + 1/4 = 4/4 and Subtraction: 2/3 – 1/3 = 1/3) This takes about 5 minutes.
- “We are going to split up into three groups, each with a designated teacher. We are going to start off by adding the fractions using manipulatives, then drawing out the fractions on a circle provided, and then you will have to draw the circle and split it into parts on your own.” There will be manipulatives that the students will use to add and subtract specific fractions. The teacher focuses solely on adding fractions, from using manipulatives to drawing their own picture, then come back and start the same process with subtraction. Make a chart with the students’ names and a fraction on the top to have them add. Have them add different fractions each time they are working with a new method. The teacher leads the students and asks prompting questions since not already having a picture is new to them. (15 to 20 minutes)
- Have the students come back together as a class and distribute an open response to the students. This will use the adding and subtracting fractions in word terms because this is also another area that the students struggle or completely avoid on the pre-assessment. Make sure that students know every part needs to be completed as thoroughly as possible. They will have 5 to 10 minutes to complete it, but no more unless there are other circumstances.
- Have the students come back together again as a whole class to solve one last addition and subtraction problem. This time they will not use the manipulatives, instead they will have to draw out their own picture under the specific fraction on the board. The addition problem is: 1/2 + 1/2 (a whole or 1) and the subtraction problem is: 4/6 – 2/6 (2/6). Under each fraction, a different student is given the opportunity to draw it out and then the answer is written and drawn in, as well. Once the answer has been written out, ask the students if there is anything else that can be done to the answer (such as reducing). If there is a student who is willing to try to reduce it, they will come up to the board. If not, that is what the focus of your next lesson should be on. (5 minutes)
- “During this lesson, who can tell me what we learned (gather student answers)? Good! We focused on adding and subtracting fractions with like denominators using manipulatives, how to solve real-world problems using addition and subtraction of fractions, and the meaning and use of fractions.
- In our next lesson, on Wednesday, we are going to work on reducing fractions and how to find a common denominator. We will see you then and thanks for being so wonderful today.”
Completed by Brittney Whitewood, Marie Banchy, & Whitney Robertson.
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