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PJ is a 3rd grade student at Amelia County Elementary School.

PJ is a African American, male student.

His parents are supportive and involved in his education.

He receives Title 1 services at the school.

He gets pulled out of class for additional help with math and reading.

He has trouble focusing in class, and often gets off task by talking to others.

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1. Teacher interview

In the interview that I had with my CT, she said that he can identify improper fractions and mixed numbers with a picture, and another strength is identifying it in both forms on a number line. She says that he struggles actually changing the fraction from an improper fraction into a mixed number and vice versa.

2. Homework
After reviewing his homework assignment on changing improper fractions to mixed numbers and vice versa, and representing that fraction, I found that there is no specific error pattern. He received a 52% this homework assignment. It seems as if he has no conceptual knowledge of how to change improper fractions to mixed numbers and vice versa. There is no consistency in the errors.

3. Student Interview
After I conducted my interview with PJ, I found that there is still no specific error pattern. To change an improper fraction into a mixed number he has no conceptual or procedural knowledge of changing the fraction. For changing and mixed number into an improper fraction, he has some sort of procedural knowledge with multiplying the whole number and denominator but doesn’t know what to do after that.

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In this planning tool you will see the SOL standards incorporated in the lesson, the objectives, what his conceptual and procedural knowledge will be at the end of the intervention, real world application of the content, and disposition of using mixed number and improper fraction.

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Math 3.2 The student will

a) name and write fractions and mixed numbers represented by a model

b) represent fractions and mixed numbers, with models and symbols

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For the first session, I will start by asking him what he knows about improper fractions.

Once he does that, I will go over how an improper fraction is different than a proper fraction. An improper fraction has a bigger number as the numerator.

I will use the mini-poster to show him what an improper fraction looks like and how to represent it in a picture.

I will model examples

I will have him think of an example of an improper fraction and have him represent it using the cut-out manipulatives or drawing it.

After that, I will give him either an improper fraction that he has to represent, or a representation and he has to write the improper fraction.

Exit ticket

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For the second session, I will start by reviewing what we learned last time about improper fractions. I will have him write a few examples and represent them using cut-out manipulatives.

I will then ask what he knows about mixed numbers.

Once he does that, I will go over how a mixed number has a whole number and a proper fraction.

I will use the mini-poster to show him what a mixed number looks like and how to represent it in a picture.

I will model examples

I will have him think of an example of a mixed number and have him represent it using the cut-out manipulatives or drawing it.

After that, I will give him either a mixed number that he has to represent, or a representation and he has to write the mixed number.

Exit ticket

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For the third session, I will start by reviewing everything we’ve learned so far about improper fractions and mixed numbers. What is the difference, how to write and represent them.

I will ask him if he knows how to make an improper fraction a mixed number

Once he does that, I will explain to him that you can use division to change an improper fraction into a mixed number.

I will use the mini-poster to show him how to set up the division using the numerator and denominators, how to use the answer to the division as a mixed number, and how the representation of the improper fraction and the new mixed number are the same.

I will model examples of this process.

I will have him think of an example of an improper fraction to change into a mixed number, he will do the division using a white board and then represent it using the cut-out manipulatives.

After that, I will give him either an improper fraction or a representation and he will have to use that to change it into a mixed number.

Exit ticket

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For the fourth session, I will start by reviewing everything we’ve learned so far about improper fraction and mixed numbers. What the difference is, how to write and represent them, and how to change an improper fraction into a mixed number.

I will ask him if he knows how to make a mixed number into an improper fraction

Once he does that, I will explain to him that you can use multiplication and addition to change a mixed number into an improper fraction.

I will use the mini-poster to show him that to change a mixed number into an improper fraction you first multiple the denominator and the whole number. With that answer, add the numerator together to give you the numerator of your new improper fraction. Then use the same denominator as the mixed number in the new improper fraction. He will be able to see how the representation of the mixed number and the new improper fraction are the same.

I will model examples of this process.

I will have him think of an example of a mixed number to change into an improper fraction, he will do the multiplication and addition process using a white board and then represent it using the cut-out manipulatives.

After that, I will give him either a mixed number or a representation and he will have to use that to change it into an improper fraction.

Exit ticket

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Representation

o  The student will use cut-out manipulatives to represent the improper fraction or mixed number

o  The student will use a white board to write out his thinking process, change between fractions, and draw representations of the fractions.

Student Engagement

o  Using fractions in everyday life.

o  Making up his own improper fraction and mixed numbers

Expression of Understanding

o  The student will use cut-out fraction circles to show their understanding of improper and mixed numbers.

o  The student will use a white board to show their procedural understanding.

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I used mini posters with the content that was being taught each day on it, fraction circle manipulatives, and a white board for him to write on.

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During each session, I will monitor the student’s work to see if he is understanding the material or not. I will guide him if I see that he is not procedurally or conceptually understanding a concept during the session. I will also be giving him an exit ticket at the end of each session for him to do individually, without my help, and that will help inform my instruction for the next session. In the attach document is the exit ticket for each day that I gave PJ.

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I saw that over the span of my 4 days of tutoring that my student was able to conceptually and procedurally understand what improper and mixed number are, and how to change from an improper fraction to a mixed number (and vice versa).

There were a few things that worked really well in my lessons and I continued to use throughout. One thing that worked in my lessons was that I started each session reviewing what we learned in the last one, that way all of the information is being refreshed in his mind and he can build off of that information in the next lesson. I broke up the lessons in a scaffolding way so that each new lesson builds off of the last. I would also start teaching new content by asking him what he already knew about it. That way I could go off of whatever his prior knowledge was. By using cut-out fraction circles, he was able to work hands on and visually see the representations of the improper fractions or mixed number. Another thing that worked in my lessons was when I allowed him to come up with his own improper fraction or mixed numbers when doing example problems. He really liked it when I gave him that choice and I continued to use it throughout the lessons. Lastly, when I saw that he wasn’t understanding something, I would go back and re-explain and model again. I would ask him “how” or “why” questions throughout the learning process to get him to think on higher levels.

His overall progress shows that he did master the content taught in the tutoring sessions. On the pre-assessment homework sheet on improper and mixed numbers he received an 11/21, which is equal to a 52%. I gave him an exit ticket to complete individually each day to assess what he learned during that session. There were 4 questions each exit ticket and he got all of them right each day. My objective was for him to get 3 out of 4 correct, and he exceeded that getting 4 out of 4 correct each day. The post assessment was given on the 5thday and was a cumulation of all the content that was taught over the 4 days of tutoring. He also got all of the questions correct on that assessment. The intervention with PJ was a smooth and successful experience, and I’m confident that he now has the conceptual and procedural knowledge of improper and mixed numbers and how to interchange them.