Understanding by Design (UbD) Fractions Unit Reflection

For EDET 637: Differentiating Instruction through Technology

Instructor: Lee Graham

By Aleta May

Please refer to artifact links in reference section at the end of this paper. Padlet showcases evidence of gaming, next steps after the Brainpop battleship numberline game (numberline worksheet samples from a referenced website) and the math chart used by students for converting and reducing fractions. Also, there is a dropbox link to show pre- and posttest artifacts with work samples between that were scanned to my computer and placed into dropbox. Additionally, I have blogged throughout the course with students regarding learning in this class and specifically giving and receiving feedback for my unit design and progress as the unit was taught.

**Contributing to Individual Paths for Learning**

Students were taught in a small Response to Intervention (RTI) group. Three students in the group were ready for learning how to convert fractions to like denominators and reduce fraction. Three other students in the group were placed on a learning path that allowed them to practice their multiplication tables and applying this understanding to multiplying fractions to give applied practice to using multiplication tables as a reference tool.

Within my UbD Fractions Converting and Reducing Unit, students were given individualized help as needed. Students were given opportunities to correct errors not corrected during the group time-frame on the following day, since the RTI time is shorter than the usual full 90 minute block.

**Planning and Customization**

Planning in the beginning was very through. Daily monitoring of progress allowed me to adjust learning according to specific learning needs. Sometimes students did not complete all the problems in one session. Although a dropbox link is provided in the below to show these worksheet types of artifacts, students completed much more work than shown. This is a sampling of the progress of students, pre- and posttests, and structure of the unit.

There are practice exercises with applied problem solving exercises in Chapter 3 Fractions in my Basic Math Skills book by AGS Publishing (known for age appropriate but lower readability and explanations).

**Student Learning**

Student progress was significant, as can be seen on student pre- and posttests. Much of this is because of monitoring, adjusting and reviewing material as needed. Also, gaming in the class gave them an engaging opportunity to learn skills more fluently and to get a break from worksheets, though the concepts were connected between.

Following is a reflection I wrote on Week 10 where we discussed our units in a weekly Twitter session:

By learning to use TweetDeck for weekly Twitter sessions, I was able to schedule with two colleagues, Amber Novak (from another state location) and Jeff Clay, to host the last week of class. I feel empowered now to communicate with teachers “the modern way.”

One very important point was made: I wanted to figure out how to find time to reflect on student learning throughout the unit. What came to my mind was to use some class time to model writing a reflection on my teaching, while asking students to write a reflection on their learning. Dr. Graham wrote that this is an idea that she has applied and that she learned it from Nancy Atwell. As I think back to my Reading Specialist training, I remember watching DVDs of Donald Graves. He taught that the best way to teach writing is to model writing as an adult; such as using a mini-lesson think-aloud approach. He also spoke about just writing in class while students write. So if I want to teach students to reflect on their learning, I need to model this for them.

We also discussed the value of teaching deeper, rather than wide/broad. We tend to feel the push as teachers to cover the curriculum. It is important to touch on as much of that curriculum that is tied to the standards as is possible, but it is not possible to try to make kids learn faster than they are ready to learn. We can engage, motivate, redesign instruction, and review—all with a forward momentum. But particularly in subject areas, such as the fractions unit my students are learning, it does no good to move on if they do not have the foundations down yet! I commented that we need persistence without frustrating our students.

To demonstrate further Twitter discussion thinking, here are questions I spent much time coming up with for our Week 13 session:

**Differentiated instruction —-Aleta**

#diffimooc How much did available technology affect your customization of standards or curriculum

#diffimooc In what ways did you use technology to modify existing materials to make a better fit for your students? (Matuk, Linn, & Eylon, 2015, p. 231).

#diffimooc How was your students’ thinking made visible to you when using technology

4. **Assistive technology —–Aleta**

#diffimooc Did tech. help any of your students with visual, auditory, being able to perceive and make meaning better than no tech.?

#diffimooc In what ways did you use technology to illustrate content in a way that is more comprehensible to their own lives?

#diffimooc Are there examples of how technology brought the outside world to the students?

#diffimooc Were there certain digital apps that helped your more advanced students explore beyond the norm?

**Problem-based learning —-Aleta**

#diffimooc Why does PBL begin with learning outcomes instead of traditional information transmission?

(It is student-centered instruction, and begins with real questions to real problems. It is self-directed. —Begin planning, thinking about specific learning outcomes students should gain by analyzing and discussing. Rico Ertmet (p. 97)

#diffimooc What various student configurations, were used to inspire students to cooperate? (Examples can be: small group activities, role play, students chatting in online games, and blogging.)

#diffimooc In PBL, how does collaborating affect student engagement?

#diffimooc Since the teacher assumes the role of facilitator in a PBL instruction model, what were some scaffolds you provided.

#diffimooc In PBL, did you notice your students engaging group talk: describing, questioning, elaborating, predicting, explaining?

**Creating, implementing, and evaluating a unit on differentiation –**

#diffimooc Did you use reflective journals as exit tickets? If so, how did this help you evaluate teaching & learning?

#diffimooc How you think having students reflect on their learning helps them take ownership & set personal goals?

As my classmates responded to these questions, I was simply amazed at the level of dissusion we were having regarding applications of technology applied to our well designed UbD units! References for the studies I read just to prepare for this Twitter session reflect the amount of thinking that has gone into planning for this unit.

**3-28-16**

Pre-Test: 20 problems possible– Please refer to artifacts in dropbox link in references at the end of this paper

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

JW: 6/20

PJ: 14/20

MC: 15/20

AI: 6/20

TE: 4/20

4-19-16 **Posttest** for Three Who Participated in UbD Fractions Converting and Reducing Unit—Please refer to artifacts in dropbox link in references at the end of this paper:

JW: 90% correct (missed 2)

MC: 100% correct.

PJ: 90% correct (missed 2)

Students will need to continue practicing this skill with more difficult fractions to convert to like denominators and reduce. They will need more opportunities to apply these skills to real world applications through problem based learning in projects and word problems. I plan to search MobyMax http://www.mobymax.com website for appropriate applied fractions lessons. I still want to explore the use of MineCraft for teaching math concepts, fraction measurement included.

**Overall Unit Plan:**

**ESTABLISHED GOALS **

Instructional Focus: Sixth Grade Standards—

- “Students use the meaning of fractions, the meanings of multiplication and division, and the relationship between multiplication and division to understand and explain why the procedures for dividing fractions make sense. Students use these operations to solve problems.” (Alaska English/Language Arts & Mathematics Standards June 2012, p. 140)

**Transfer**

*Students will be able to independently use their learning to… *

Reduce, calculate and conceptually apply fraction in addition and subtractions.

Recognize concepts and terminology related to reducing, calculating and applying fraction concepts.

Transfer their knowledge to pre-algebra concepts and understanding of how fractions are used in the real world.

**Meaning—**

Students will ** understand** that . . .

Multiplication and division fluency directly impact their ability to calculate addition and subtraction of fractions.

Fluency in recognizing different types of fractions and how fractions relate to a whole helps them understand concepts and terminology.

*ESSENTIAL QUESTIONS *

How can reducing or increasing fractions, using least common multiple or greatest common factor, help me in the real world—at home, on the job? (cooking, sewing, construction, water treatment, computer coding. . .)

What type of math does knowing this prepare me for?

**Acquisition**

Students will know; based on standards

*Students will know… *

Apply and extend previous understandings of multiplication and division to divide fractions by fractions 6.NS.1. Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions (e.g., by using visual fraction models and equations to represent the problem).

Students will be ** skilled **at . . .

According to individual needs: reducing and calculating fractions through addition and subtraction. They will work on multiplication and division fluency to help them complete fraction calculations with 95% or higher accuracy.

**Stage 2- Evidence**

Pre and post test | PERFORMANCE TASK(S): Students will take a pretest and post test to demonstrate their strengths and weaknesses in adding and subtracting fractions, including a few word problems. They will use a paper and pencil test for this. |

Students will use computer games to increase skills in calculations.
Students will use worksheets to practice skills where they can practice their computation accuracy at an instructional skill level. |
OTHER EVIDENCE:
The teacher will observe and track which games they are using to make sure students are working at an appropriate level for their skills as shown on the pretest. Worksheets will be collected as evidence of calculation for accuracy. Students will be observed for engagement, understanding, and motivation. Increases math fact fluency will be noted through timed multiplication / division paper pencil tests. |

**Stage 3 – Learning Plan**

*Summary of Key Learning Events and Instruction*

Coolmath.com for visual support and discuss this concept with the teacher.

Three days per week of paper pencil practice at individualized levels.

Two days per week of game practice. Students will choose a game that will strengthen personal areas of need.

To begin with, students will complete pretest activities using worksheet and pencil. Then they will start using gaming to get started with fluency. When fraction concepts need to be further clarified, students will view and go over mini-lessons that are presented in Coolmath.com for visual support and discuss this concept with the teacher.

Three days per week of paper pencil practice at individualized levels.

Two days per week of game practice. Students will choose a game that will strengthen personal areas of need.

**Aleta May’s Week 10 – Week of March 28, 2016**

Update to Week 1 of my UbD Fractions Unit:

During this week, I have a paper/pencil pre-assessment on paper. The post assessment will replicate the pre-assessment with different problems. As an initial incentive, students used fraction games found on Coolmath.com; it has initially been used as a draw in motivator and fluency for my lowest students.There are other games I want to use. Ideally, I could get MathBlaster to work on our iPads soon.

Student self assessment is through watching their progress in games, and using the visual fraction strategy called Radial Fractions. McMullen, C. Ph.D. (2010). Radial Fractions math workbook (addition and subtraction): A fun & creative visual strategy to practice adding and subtracting fractions. CreateSpace. This can be found on amazon.com The students use this visual that looks like the spokes of a bicycle wheel to add or subtract.

My step-by-step plan is now (after noting their progress) in the visual strategy as follows:

This week they added or subtracted without reducing, using the wheel; since students were sometimes getting adding and subtracting mixed up.

Next week, they will subtract more than they did the first week; and they will begin reducing within this visual strategy.

This is looking more and more like a 3 week (instead of a 2 week unit plan).

I’ll be able to really focus more deeply on all the “embellishments”. . . as there will be less school-wide assessment focus!

Here is a new link I found that will include the more challenging fractions (such as reducing) fractions online (PacMan games):

http://www.sheppardsoftware.com/math.htm

Presently, students are using a visual strategy that even though it is paper based, it is a brightly colored bicycle wheel.

**Week 2 of Fractions Unit**

*Essential question: What are my challenges and successes in implementing my unit? **Students solidifying basic math facts.*

*Looking ahead: This week and next week (through April 15) will be dedicated to teaching your unit as much as possible in your classroom. *

Students will go onto an internet site to practice math skills:

shepherdsoftware.com choose ‘math games’

More specific at this site, students went to Math Man (a branch off of the former Pac Man game) during the end of week one and more so during week two: http://linkis.com/sheppardsoftware.com/vXPu1

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.

Make notes for yourself as you teach your unit this week. How did things go?

**I was surprised to see how fast students caught on to the first step of adding fractions. **

Was it as expected?

**It went better than expected.**

What challenges did you see?

**I found that the students followed the first steps and are ready for the second step: Reducing, which includes dividing the top and bottom numbers by a common denominator. **

Did you see evidence of learning?

**Yes! **** **

What was this evidence?

**Students followed one-step rules in week 1.**

Will you need to change the unit in some way for the second week? **I will only add step two, the reducing fractions this week and see how well they can follow a two-step rule.**

Steps given by EDET 637 rubric are included as I respond, and reflect from week 2 then plan for week 3:

*Reflection of the internship provides evidence that the teacher participated in and contributed to individual paths for learning for students engaged in the experience.*

**During the pretest I gave no help, support, or directions. During the first week of assignments, I demonstrated on the white board a simple method of adding fractions with out asking students to ‘reduce or simplify their answers. **

** **** The teacher summarizes information from observations in the lesson about why students were making choices they did.** – So, you need to make notes of the way that you helped individual students as they pursued their learning path (how your “scaffolded” student learning).

**During actual assignment time, after demonstrating at the white board, I sat with the students looking busy. They would ask, “Is this right? Am I doing it right?”**** **

This is the support that new learners need to become expert in their new knowledge. So if a student asks for assistance – why did this happen? Was it appropriate at the time?

**This is the normal method I use to energize and help students stay on track.**

Is there a way that you could build in supports so that the next time you do this unit this issue is covered?

**I could make a place near the teacher desk where a student could go to check their answers when finished.**

**Week 3**

Students will be assigned web page to continue to practice reducing fractions prior to worksheet assignments:

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

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

I will incorporate gaming that is specifically geared to individual student needs. They will continue to practice skills using both radial and other practice worksheets

**Additional Pieces to Original Plan:**

**Group Composition**

Student Group is made up of one sixth grader, two seventh graders, and two eighth graders. They are sent to me for response to intervention (RTI) each day for extra practice in focus areas of math for them. Two students are on an IEP and are preparing for pre-algebra for next fall. The other three students will likely be in small group basic skills RTI math again next year.

**Technology Resources for practicing terminology and fluency:**

http://www.coolmath-games.com/0-fraction-splat

CoolMath Fraction Splat Instructions:

Click on the types of fractions for each round, (There are three rounds.) Click the finished button once you have found them all.

Round 1 Target: Mixed Numbers

Teaches terminology: improper fraction whole number mixed number

Round 2 Target: Fractions that are greater than or equal to 1

Round 3: Target=Fractions that are less than 1/2

http://www.coolmath-games.com/0-fractone

FractOne – Your goal is to get sums of 1. Get it? FractONE

Click on pairs of squares that add up to 1 and do it as fast as you can!

**Technology Resources through Cool Math using simple explanations and visual representations for mini-lessons that will be used to individualize according to student needs:**

http://www.coolmath.com/prealgebra

- Factors and Primes http://www.coolmath.com/prealgebra/00-factors-primes
- Divisibility Tests
- Factorizations
- Prime and Composite Numbers
- Prime Factorizations

- Intro to Fractions
- Mixed Numbers http://www.coolmath.com/prealgebra/01-fractions/fractions-02-mixed-numbers-01
- Equivalent Fractions Part 1 http://www.coolmath.com/prealgebra/01-fractions/fractions-04-equivalent-01
- The Magic 1 (fluency in matching fractions to make one whole)
- http://www.coolmath.com/prealgebra/01-fractions/fractions-03-magic-one-01

- GCF’s and LCM’s http://www.coolmath.com/prealgebra/01-gcfs-lcms

- Common Factors (Common Divisors)
- Greatest Common Factor (GCF)—Also known as Greatest Common Divisor (GCD)
- Common Multiples
- Least Common Multiple (LCM)

**Game choices**

**Technology Resources for practicing terminology and fluency:**

http://www.coolmath-games.com/0-fraction-splat

CoolMath Fraction Splat Instructions:

Click on the types of fractions for each round, (There are three rounds.) Click the finished button once you have found them all.

Round 1 Target: Mixed Numbers

Teaches terminology: improper fraction whole number mixed number

Round 2 Target: Fractions that are greater than or equal to 1

Round 3: Target=Fractions that are less than 1/2

http://www.coolmath-games.com/0-fractone

FractOne – Your goal is to get sums of 1. Get it? FractONE

Click on pairs of squares that add up to 1 and do it as fast as you can!

Teaches fluency in adding numerators with a variety of denominators to equal one whole. Results produce how many seconds it took the player and what this adds up to in minutes and seconds.

Students will track their progress for fluency in games and paper pencil.

Game: *The Clue Finders Math Adventures Ages 9-12 with multiplication, division, and fractions. *The Learning Company—Windows & Macintosh. With 10 levels of difficulty; auto-leveling, 50 printable activities, personalized workbooks and rewards. Game to practice multiplication and division fluency and fractions: http://www.mathblaster.com

Game: MindTwister Math by Edmark. Increases math fact fluency and strengthens mental math skills.

Game: Math Blaster Hyper Blaster II-HD

Game: Fractions and Smart Pirates In App Store

**Week of 4-11-16**** **

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 timeframe 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 wall with screenshots of their Sheppardsofware.com fractions gaming. 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

JW: 6/20

PJ: 14/20

MC: 15/20

AI: 6/20

TE: 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.

**Monday, 4-11-16**

Lesson–Math Has Problems:

__3__= __1__ __1__ + __1__ = __7+ 3__

6 2 3 7 2

2= 1 __1__+ __1__ = __5 + 2__

4 2 2 5 10

__8 __= __4__ __4__ + __1__ = __5__

10 = 5 8 8 8

**Practice and review**

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

Sheppardsofware.com

- JW. 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%

- PJ. 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%

- MC. 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.

- PJ. 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**

**Lesson–How to subtraction Fractions:**

__4 __ – __3___ = __16 -___________

3 4 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 =__ __7__

12 = 12 Then for reducing ask: Is there number that can fit into both

the numerator and denominator evenly?

Another Problem:

__5__ _ __1__ = __15 – 6___ = __9____ = __1 __

6 3 = 18 18 2 Reduce: The **biggest number** that can fit into

both the numerator and denominator evenly is 9.

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

- PJ.—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.

- TE.—multiply to get ready for fractions. (Serious attendance problems lately.)
- AI.—Came in 20 minutes late; multiply to get ready for fractions.

T.E.—multiplication page

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.

- MC. 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.

- PJ. 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.

- JW. 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.:**

- TE. & 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).

** ****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.

- MC. 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.
- PJ. 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.
- JW. 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.:**

- 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 to Monday, 4-18-16 where it will end with a post test.

** ****4-19-16**

** ****Specific Lesson Taught**

** **Patterns: 3/? = 9/18; 5/? = 10/12; 1/5=?/10

Add or Subtract Top Numbers

Bottom Number Stays The Same

The bottom numbers stay the same

1/12 + 4/12 = 5/12 (be sure to add)

5/8 – 2/8= 3/8 (be sure to subtract)

Reduce= Make Smaller:

5/10 divide by 5/5 ½

**Computer Game Accessed:**

https://www.brainpop.com/games/battleshipnumberline/

**References **

Battleship Fraction Numberline Game:** https://www.brainpop.com/games/battleshipnumberline/**

Aleta May’s Artifact Padlet Wall for Technology Embedded Within the UbD Fractions Unit:** **

**http://padlet.com/aleta_57/tq5v224rfbuk**

Aleta May’s Artifact in Dropbox for Visual and Other Worksheets to Show Students’ Progress Through the UbD Fractions Unit and Differentiation:

MobyMax Retrieved on 4-23-16 at: http://www.mobymax.com

Treff, A. V. and Jacobs, D. H. (2003). *Basic Math Skills*. Circle Pines, MN: AGS Publishing.

The Mathworksheet Site On-line Math Worksheet Generator at: http://themathworksheetsite.com

**Resources Read for UbD Fractions Unit Planning:**

Alaska English/Language Arts and Mathematics Standards pp. 144-162. Retrieved on 3-27-16 from: https://education.alaska.gov/akstandards/standards/akstandards_elaandmath_080812.pdf

Childre, A., Sands, J. R., & Pope, S. T. (2009). Backward design. *Teaching Exceptional Children, *41(5), pp. 6-14.

** ****Twitter Session References:**

Hutchison, A. & Woodward, L. (2014). A planning cycle for integrating digital technology into literacy instruction. *The Reading Teacher, *67(6), pp. 455-464.

Matuk, C. F., Linn, M. C, & Eylon, B. (2015). Technology to support teachers using evidence from student work to customize technology-enhanced inquiry units. *Instructional Science, * 43, pp. 229-257. Springer Science & Business Media B.V.

Meij (van der) , H. (2011). Learning from games: Does collaboration help? *British Journal of Educational Technology, *42(4), pp. 655-664. Wiley-Blackwell.

Rico, R. & Ertmer, P. A. (2015). Examining the role of the instruction in problem-centered instruction. *TechTrends, *59(4), pp. 96-103.

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