I chose this question because I want to see if the students will apply their learning of benchmark fractions. Students should recognize that 2/3 is greater than 1/3 and that the solution 3/7 is less than a ½ so therefore the solution could not be true. Additionally, adding denominators is a common misconception with students when computing with fractions. In this lesson, students will see that we can't add uncommon parts together because the answer makes no sense and that creating common parts helps us get answer that we can understand.
I’m going to begin my lesson showing the students why just adding the numerator and denominator doesn’t work and I’m doing this through a model. In the first slide, it shows 1/3 + ¼ = and there is a model here showing the two parts joined together. Ask the students how much the solution is worth? They should be able to tell you that we don’t know because the parts are not equal. With that, I’m going to go into a discussion about making the equal parts. I will explain to them that I’m going to change each third into 4 equal parts and each fourth into 3 equal parts making each fraction circle 12 equal parts. Once I have the equal parts, I can add them all together and find my solution.
In the beginning, I have them modeling, writing the number sentence, re-writing (model and new number sentence with common denominator) and then finding the solution. By using this method, students will be working on mathematical practices 2,4,5,6. I will model with them slides 2,3,4, and 5. Starting with slide 6, I gave the students the common denominator and not the model. I’m going to have the students tell me how I got 20 for a common denominator? Then, I’m going to ask them to apply their knowledge of equivalent fractions to find the numerator. We will be doing this problem as a whole class, with them giving me the input.
As a side note, I’m having them write the number sentence from the model so they make the connection between the model and the number sentence. Also, since I will be writing on the board, I will be writing the fractions vertically instead of on a slant. I just feel it is much easier to read that way, but too much work to do on the computer!
I’ve chosen 4 problems purposefully for this activity. Problem 1 has them multiplying the denominators to find the common denominator. Problem 2 has a least common denominator and I want to see who will be finding this. Problem 3 has one of the denominators as the least common denominator. Problem 4 also has a least common denominator.
I’m asking the students to find a common denominator. If they find the least common denominator, that’s great, but not necessary.
I chose roundtable because the students are checking each other’s work as they go along. It will be interesting to see and hear the discussion when one student has found the LCD and the other found a common denominator.
Again, the students will be modeling, writing the number sentence, re-writing, and finding the solution for subtraction problems. I will want them to model it so they can visualize what the problem looks like. I’m anticipating that some students will be able to find the common denominator and work the problem out, but it is always a good idea to represent the problem in another way. I call this their back up plan.
The students will be working through 4 problems in this roundtable: 2 addition and 2 subtraction. For each problem, I want them to model, write the number sentence, re-write and solve. During the re-write, they do not have to model it, they can use equivalent fractions if they feel comfortable doing that. Also, I’m not worrying about simplifying. I just want them to feel comfortable with the computation.
The students will be completing a Connect 3. They will be making a connection between common denominators, adding fractions and subtracting fractions. Each line segments requires a one sentence connection between the two words and then in the middle, they will use their three sentences to develop a brief summary of the concept. This is a nice activity to get students thinking about the patterns in math along with using self-assessment to think about their learning. This tool supports MP 1 by monitoring and evaluating progress and MP 6 by creating carefully formulated explanations.