Week 12 Blog EDET 637: Differentiating Instruction through Technology Instructor: Dr. Lee Graham

By Aleta May

Essential question: What evidence am I collecting for my final project – and for what purpose?

The most obvious **evidences** are: pre- post- tests, a few screenshots of computer gaming levels / playing for padlet.com link, observation notes, and daily worksheets. On task behavior was not formally tracked, but was noted in observation notes.

We went from adding and reducing to subtracting & reducing fractions. Focused on a specific game.

As of 4-13-16, Students are getting the concept of adding and subtracting fractions with unlike denominators; but they are still having trouble with reducing. I will continue working on this with them next week, even though I know they are improving.

The kinds of **evidence** of contributing to individual learning paths are as follows: First, I have a small group, so it is easier to go from student to student. Second, checking their paper/pencil work regularly as soon as they leave gives me feedback for what to emphasize the next day. Third, I watch them as they play the reducing fractions game to see them move on to different game levels.

Evidence that students are being given **individualized learning paths** are staying on the same basic concept of adding fractions with unlike denominators; then gradually going into subtraction, all the while reducing. Some students seem to want to complete the entire sheet, even knowing they will be asked to go back to reduce these the next day. They are not penalized for this, since the entire concept of adding/subtracting fractions with unlike denominators was either new to them, they forgot what they had learned in the past, or they simply added denominators to get the same denominator in their answers. Then reducing fractions is yet another step for them. As long as they are focused, the pressure is not who gets what first, rather, the focus is on learning and progressing daily.

The pillar that bears the most weight of evidence of learning are the pre- and post-tests; as well as the fact that they are staying so on task! **On task behavior** is one definition of **engagement and learning**.

One way I am **scaffolding learning** is to have three students who need to learn their multiplication tables fluently are working on these to prepare them for adding and subtracting fractions with unlike denominators. As they learn multiplication tables, they will now, start multiplying fractions and using their multiplication chart to assist with this. Further, scaffolding is allowing students to focus on the process of creating like denominators; then the process of reducing after—either one problem at a time or step one for all the problems then step two.

The kind of growth I expect on my post-test, based on observation and daily worksheet checks is; with such a short time frame for the unit, they will grow in creating common denominators—and hopefully reducing fractions as well.

This is how the unit is set up:

Day One PreTest

Day Two Multiplication Facts/Practice

Day Three Computer Fractions Game

Day Four Adding Fractions Worksheet

Day Five Computer Reducing Fractions

Day Six Reducing/Adding Fractions Worksheet

Day Seven Computer Adding Fractions Game

Day Eight Subtracting Fractions

Day Nine Computer Subtracting Fractions Game

Day Ten PostTest

**Evidence** is collected daily through worksheets; teacher observation and reflections of the help needed; pre- post-test; and a padlet.com wall with screenshots of their Sheppardsofware.com fractions game.

http://www.sheppardsoftware.com/mathgames/fractions/mathman_reduce_fractions.htm

See level screenshots at: http://padlet.com/aleta_57/tq5v224rfbuk

**3-28-16**

Pre-Test: 20 problems possible

Turn in assignment, then practice identifying types of fractions at: http://coolmath-games.com/0-fraction-splat

J. W.: 6/20

P. J.: 14/20

M. C.: 15/20

A. I.: 6/20

T. E.: 4/20

**4-4-16**

Students will go onto an internet site to practice math skills: shepherdsoftware.com choose ‘math games’

Students practiced reducing fractions with the computer software program. They challenged each other to try to get to level 7

During the allotted time students remained on task and improved with practice.

Ongoing Concept the students are learning: We don’t have to reduce any more because you cannot reduce 5/8.

* Weekly summary notes *for

**the dates 3-28 through 4-1 and 4-4-4-8 are in the blog for Week 11.****Monday, 4-11-16**

Math Has Problems:

3/6= 1/2 1/3 + 1/7 = __7+ 3__ /2

2/4= 1/2 1/2+ 1/5 = __5 + 2__ /10

8/10 = __4/5__ 4/8 + 1/8 = 5/8

Practice and review

T.E. is getting his multiplication skills up in order to prepare for fractions reducing. Sheppardsofware.com

J. W. 2 goes into 2 how many times so right here we put 2 over 2; what number goes into these; what number goes into those; how many times does this number go into this? Multiply the bottom; now we need to multiply the top. He got to level 4 on Math Man, then restarted (WTL18) 18 possible, 3 errors= 15/18 83%

P. J. This number reduces further; this number has to be the same, if you divide the top, then the same for both numbers; this reduces further; (Mac 2). On the Math Man program. P. J. stayed at level 1. 18 possible 8 errors= 10/18 56%

M. C. Let’s look at this again and do it the other way; multiply and multiply; 4 goes into both those. 2 X 4 goes into there 3 times. M. C. Has a very difficult time transitioning to the computer activity without getting sidetracked, however, he did begin working on Mac Man—he appeared to enjoy it and did not want to stop when class time was over. (P.C. Mac Pam’s). 18 possible, 3 errors= 15/18 83%

The students will **make corrections** on Tuesday, then access the Math Man reducing fractions game.

P. J. will get **individualized assistance** in making corrections.

**Tuesday, 4-12-16**

Today the students made corrections on their worksheets from the previous day. They enjoy using the game after making corrections, so this was motivational to them to finish their work.

On Day 7: students came to class and reviewed yesterday’s work, making any needed corrections and then logged onto Sheppardsoftware.com; Math Games and played Fractions Games.

When asked how they could use Fractions, some of their reply were: Measuring things, calculating how much is needed for something, money has fractions (cents of a dollar), how much to order….

**Wednesday, 4-13-16**

How to subtraction Fractions:

4/3 – __3__/4_ = __16 -_ __ /12

First multiply the two denominators (3×4=12) put a line above the 12. Second multiply the top first numerator (4) by the second denominator (4) and put the answer (16) on the line above the 12, followed by a subtraction sign. Thirdly, multiply the first denominator (3) times the second numerator (3), and put the answer (9) above the 12, after the subtraction sign. Fourthly, subtract the numerators and put the answer over the denominator:

__ 16-9__ / 12 = __7__/12

Then for reducing ask: Is there number that can fit into both the numerator and denominator evenly?

Another Problem:

__5__ /6- 1/3 = __15 – 6___ /18 = 9/18 = 1 /2

Reduce: The **biggest number** that can fit into both the numerator and denominator evenly is 9.

M. C.—Is very focused on completing the radial fraction worksheet. It is common for M. C. to get off track; but not today. M. C. will need to reduce tomorrow.

J. W.—Is pushing himself to be fast at radial fractions; subtraction. J. W. needs to reduce several problems tomorrow.

P. J.—Is very focused on completing the radial fraction worksheet—at a slower pace. (**Home factors; health of grandpa**.) Preston / Joseph need occasional support; 3 goes into this and 3 goes into that. P. J.–is focusing on completing the process of creating like denominators. He finished half the page, and plans to finish and reduce them tomorrow. His Uppi (grandpa) whom he lives with is experiencing serious health problems, and P. J. came to school tired; napped earlier. He helps take care of his Uppi.

They are not familiar that reducing is part of the process. They get correct answers, but in trying to complete the pages in a hurry, they reduce quickly.

J. E.—multiply to get ready for fractions. (Serious attendance problems lately.)

T. E.—multiply to get ready for fractions.

A. I.—Came in 20 minutes late; multiply to get ready for fractions.

As a side note: Older students: 9^{th} grade students also participated in the radial math fraction activities; from a separate group. This is helping them to build their fluency and skill in reducing fractions. A. A., C. C., N. A.

On Thursday, April 14, the students will go back to these same math problems to reduce fractions they completed on Wednesday.

Students will go onto an internet site to practice math skills: shepherdsoftware.com and choose Math Man (reducing fractions) in ‘math games.’ This allows them time to practice reducing fractions fluently.

Students practiced reducing fractions with the computer software program. They challenged each other to try to get to level 7.

During the allotted time students remained on task and improved with practice.

**Updating notes on Thursday, 4-14-16:**

Students have earned time to play Math Man for tomorrow, 4-15-16.

First, M. C., P. J., & J. W., created common denominators on 4-13-16.

Second, M. C., P. J., & J. W., reduced fractions using the following process:

To scaffold learning for M. C., P. J., & J. W., I provided a color coded multiplication chart that is set up in a linear way visually so students could refer to it when they ask themselves the following question: How many times does 6 go into 42? Looking at the linear chart, with each multiplication set up in rectangles and divided up by colors for each (6x is green; 7x is yellow, etc.), it is visually easy to find the highest number that will go into a numerator and denominator to reduce.:

6 X 0= 0

6 X 1= 6

6 X 2 = 12

6 X 3 = 18

6 X 4 = 24

6 X 5 = 30

6 X 6 = 36

6 X 7 = 42

etc.

M. C. Finishing radial fractions, subtraction page and reducing problems he had created common denominators for yesterday. He was able to stay on task and really looks forward to raising his reducing fractions game time tomorrow using Math Man. He is at level 5 in the game.

P. J. When he came in, he completed the steps for creating common denominators, then reduced fractions. P. J. looks forward to using Math Man to reduce fractions tomorrow. He is at level 1 in the game.

J. W. When he came in, he was surprised at first to have his page handed back to him from yesterday. He apparently completed the page on 4-13 forgetting that creating common denominators and subtracting was not the final step, unless that fraction answer could not be reduced further. He is working to complete level 4 with a higher score and reaching level 5.

**To Scaffold learning for T.E. & A.I.:**

T. E. & A. I. Completed multiplication practice sheet, then used this sheet to multiply fractions for. Here are examples 10/1 X 7/13 = 70/13 (I wrote next to his answer 70 divide by 13 and other problems that needed to be turned into mixed fractions, rather than reduced); here is another example 7/1 X 7/10= 49/10 and 49 divide by 10—converting to a mixed fraction.

T.E. & A.I. To **differentiate game time tomorrow**, 4-15-16, these students will use math gaming that increases multiplication skills and fluency.

This group unit will extend into Monday, 4-18-16 where it will end with a post test.

**To Scaffold learning for T.E. & A.I.:**

A. E. & A. I. Completed multiplication practice sheet, then used this sheet to multiply fractions for. Here are examples 10/1 X 7/13 = 70/13 (I wrote next to his answer 70 divide by 13 and other problems that needed to be turned into mixed fractions, rather than reduced); here is another example 7/1 X 7/10= 49/10 and 49 divide by 10—converting to a mixed fraction.

T.E. & A.I. To **differentiate game time tomorrow**, 4-15-16, these students will use math gaming that increases multiplication skills and fluency.

**Thursday, 4-15-16**

Today students went to http://www.sheppardsoftware.com/math.htm and clicked on Math Man. Rather than selecting reducing fractions, they selected mixed operations where they were challenged to work through basic equations using mental math to do so. P. J. and J. W. were challenging themselves to get through the problems quickly. The answers are posted on the Math Man icon, and each time they select a correct answer, they received points and the choices were narrowed down for them for the next problem to solve. M. C. worked on completing a math project for another class, since this was the last day he could finish it.

As the students played, I talked with each of them about what they would like to do next. P. J. and J. W. miss using the Dreambox math computer program. M. C. wants to focus more on the Aleks computer program to help him keep up in his other math class where they use this as a center. P. J. and J. W. want to use both math programs. J. W. showed to me a section he can work on within Aleks that has problems like, round this fraction to the nearest hundredth: 41/13 = 3.15. There is a calculator provided on the program page, so his focus is on the process of dividing 41 by 13 and considering what the nearest hundredth means. In Dreambox, the students used visual tools to see hundreds, tens, ones, as well as tenths and hundredths. I observed J.W. processing what his own error was when he first answered 3.1 . This gave me the confidence that combining programs that individualize for them and my own mini-lessons in the fractions unit are indeed a great combination over the long run.

As I consider where they are with reducing fractions through assessing their progress in a variety of ways, I want to make sure they become automatic in changing unlike denominators to like denominators and then reducing. The computer programs are individualized for each of their needs. I think we can alternate days where we continue the fractions unit through the end of the school year (with Culture week coming up, the end of school is fast approaching—about mid-May for them). We can also have computer program days. This sounds like a good balance for an Response to Instruction/Intervention (RTI) program for then.

After reconsidering, on Monday, 4-18-16, the students will review and then spend some time on Brainpop using the numberline fraction game; an idea I received from Amy after reading her post on 4-16-16 and trying out the game: https://www.brainpop.com/games/battleshipnumberline/ This game will give the students a more focused way to see and ask questions about where a fraction with a smaller denominator number vs. a faction with a larger denominator number falls on a line.

A note on looking forward: When they continue working on reducing fractions beyond this UbD plan, the students will also use worksheets from http://themathworksheetsite.com numberline fraction worksheets to see whole numbers (inches) with fractions of inches. I believe they will start out doing okay in the Brainpop battleship online game, then as it gets more challenging, I will bring out the more visual worksheets to use with them. We will work through these together, as I have a SmartKapp that allows me to present the worksheet on the board, go through a think aloud with them, and then save that lesson in case I need to bring it back up to help them visualize the line on the battleship fractions numberline game.

On Tuesday, 4-19-16, they will take the post test. The process used in the visual radial fractions strategy; like the examples provided above from what was presented on the board for their lessons; will need to be reflected in the post test. Since students actually focused a lot more on the process of converting unlike denominators to like denominators, than on the end goal of reducing fractions, this should become part of the post assessment to reflect this and be clearly distinguished from reducing. Reducing will be derived from the actual answer they get after converting unlike denominators (and adding or subtracting them).

tessiesimAleta, I see so many positive aspect of DI happening in your unit! I love how you state that on-task behavior is one way to see engagement and learning. I agree with this statement 100%, as this is something I normally struggle with in my math group, but I am seeing less behavioral issues currently with the UbD unit. You cite several examples of how you’re differentiating for your students (computerized games at different levels, multiplication facts work, individual teacher assistance with corrections) so that each can be successful. The fact that all are engaged and wanting to continue with the unit speaks to the fact that it is well planned and is meeting their needs. I like how you’re using their worksheets as formative assessments to help you plan the next day’s lesson. Your mention of a student’s grandpa being ill and this affecting his performance at school is an important reminder of how we have to consider students’ social/emotional needs as we plan our academics. It sounds like having a small group is letting you reach each student where they need it with fractions, and I like the way you highlighted specific evidence that shows learning.

aletakmayPost authorAmy,

I so appreciate that you took the time to read through what I wrote and commented specifically! This helps so much. Today, I made a change to my blog post: instead of using Monday for the pretest, we will review, use the Brainpop numberline site you referred to in your post, and I will add the mathworksheetssite.com worksheets to visually help them, as I know they will stumble. I gave you credit in my revision 🙂

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