Stage 1 Desired Results  
ESTABLISHED GOALS
Instructional Focus: Sixth Grade Standards— 2. “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 prealgebra concepts and understanding of how fractions are used in the real world. 

Meaning  
UNDERSTANDINGS
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…
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  
Evaluative Criteria  Assessment 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
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 minilessons 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.

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 prealgebra 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.coolmathgames.com/0fractionsplat
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.coolmathgames.com/0fractone
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 minilessons that will be used to individualize according to student needs:
http://www.coolmath.com/prealgebra
 Factors and Primes http://www.coolmath.com/prealgebra/00factorsprimes
 Divisibility Tests
 Factorizations
 Prime and Composite Numbers
 Prime Factorizations
 Intro to Fractions
 Mixed Numbers http://www.coolmath.com/prealgebra/01fractions/fractions02mixednumbers01
 Equivalent Fractions Part 1 http://www.coolmath.com/prealgebra/01fractions/fractions04equivalent01
 The Magic 1 (fluency in matching fractions to make one whole)
 http://www.coolmath.com/prealgebra/01fractions/fractions03magicone01
 GCF’s and LCM’s http://www.coolmath.com/prealgebra/01gcfslcms
 Common Factors (Common Divisors)
 Greatest Comon 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.coolmathgames.com/0fractionsplat
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.coolmathgames.com/0fractone
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 912 with multiplication, division, and fractions. The Learning Company—Windows & Macintosh. With 10 levels of difficulty; autoleveling, 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 IIHD
Game: Fractions and Smart Pirates In App Store
Resources Read:
Alaska English/Language Arts and Mathematics Standards pp. 144162. Retrieved on 32716 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. 614.
Donhauser, M., Hersey, H., Stutzman, C., & Zane, M. (2014). From lesson plan to learning plan: An introduction to the inquiry learning plan. School Library Monthly, 31(1).
Keeling, M. (2015). Backwards design considerations for the 21^{st}century school library. School Library Monthly, 21(4), pp. 2224.
Lubiner, G. (2014). Understanding by design: A unit on color theory. Arts & Activities, 156(1), pp. 2044.
Wiggins, G. and McTighe, J. (2011). The understanding by design guide to creating highquality units. Alexandria, VA: ASCD
Aleta,
Since we’re both doing fractions units, I was especially interested to check out your unit. Since it is geared for middle school RTI students, it gives me future ideas for my students, as we’re focusing on third and fourth grade skills right now. I like how you tie your fraction work to realworld activities, like cooking, sewing and coding. This will let your students see that what they’re learning has authentic uses in life and is worth mastering. I feel like this is an area that I will strengthen in my fractions unit and spend more time discussing how we use fractions in real life. Your students should be motivated by the use of online games, and it’s wonderful how you’re able to use the pretest results to differentiate games for each student. That is something that I love about small groups! I like how students will be doing selfassessment in your group so that they see their growth and are motivated to keep working. I’m going to try selfreflection journals in my group to help kids clarify their thinking during the unit, and that might be an idea for you to try also, so that students can ask questions or make connections. One thing I worry about with the journals, though, is the difference in writing ability that my students have, with some able to quickly jot down ideas and others laboring over their words. I will check out the radial fractions activity that you are doing, as it sounds like a good way for students to see their work visually. I like your update after teaching your unit for a few days and how your ideas will continue to grow as you assess your students’ needs. Thanks for sharing your thinking!
Amy,
I think your idea for trying selfreflection journals for asking questions or making connections is perfect! Thank you for your feedback and idea! Maybe this is where I can have them actually take notes and reflect on how fractions are used in real life situations. Although students at every age need to think about real life applications, it seems to become even more important as a way to give older students a reason to invest their time or to engage more deeply and try learning this again–it must be so discouraging to older students who have not learned a concept that many of their peers have already caught on to.