Lesson Plan: Subtracting Fractions

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Unit Goals

The learner will learn to apply knowledge about equivalent fractions, reducing fractions to lowest terms, subtracting fractions with unlike denominators, and borrowing fractions.

Unit Objectives

  • The learner will learn to apply knowledge about equivalent fractions
  • The learner will reduce fractions to lowest terms
  • The learner will subtract fractions with unlike denominators and
  • The learner will borrowing fractions
  • The learner will create a 3-2-1 bridge to demonstrate an understanding of subtracting fractions

Background and Rationale

Learning how to subtract fractions helps to start to build confidence and establish a great foundation to more advanced math and science classes as it leads into multiplying and dividing fractions. Fractions are in everyday life; construction, recipes, and landscaping are just a few things where fractions show up. In this lesson, the student will learn about how to subtract fractions with unlike denominators and borrowing with fractions. The students will review adding fractions, equivalent fractions, improper fractions, mixed numbers, prime numbers, and LCM. The student will have access to lessons that have been taught online, and there will be extra problems provided for students that need more practice. The steps for the process will be given to them in their notes, Anchor Charts will be used, collaboration and conferencing with students and teacher will take place, and the students will be reflecting throughout the unit. At the end of the unit, along with an end-of-the-unit test, the students will be creating a 3-2-1 Bridge about subtracting fractions with unlike denominators. This will allow me to see if they truly understand what they are doing and why.

Lesson Objectives

Objective

Bloom’s Verb

Use the concepts and steps in solving the problems.

Remembering

Brainstorm ideas for a student-chosen topic

Remembering

Develop similes and metaphors as it is applied to fractions and used to develop their 3-2-1 bridge

Analyzing

Use the concepts they have learned to compare to a real world activity, object, person, place, or thing

Creating
Complete teacher’s examples of practice problems Appying

Provide peer feedback from peers and teacher

Applying

Bloom’s Taxonomy

Creating (highest level)

Common Core / State and District Standards

Clear, understandable, and consistent

Based on rigorous content and the application of knowledge through higher-order thinking skills

Built upon the strengths and lessons of current state standards

Technology Integration (ISTE Standards•S)

1. Creativity and innovation Students demonstrate creative thinking, construct knowledge, and develop innovative products and processes using technology.

  • Apply existing knowledge to generate new ideas, products, or processes
  • Create original works as a means of personal or group expression
  • Use models and simulations to explore complex systems and issues
  • Identify trends and forecast possibilities

2. Technology operations and concepts Students demonstrate a sound understanding of technology concepts, systems, and operations.

  • Understand and use technology systems
  • Select and use applications effectively and productively
  • Troubleshoot systems and applications
  • Transfer current knowledge to learning of new technologies

Learning and Innovation Skills (P21.org)

Creativity and innovation                   

      Think Creatively:

  • Use a wide range of idea creation techniques (such as brainstorming)

  • Create new and worthwhile ideas (both incremental and radical concepts)

  • Elaborate, refine, analyze and evaluate their own ideas in order to improve and maximize creative efforts

       Work Creatively with Others:

  • Develop, implement and communicate new ideas to others effectively

  • Be open and responsive to new and diverse perspectives; incorporate group input and feedback into the work

       Reason Effectively:

  • Analyze how parts of a whole interact with each other to produce overall outcomes in complex systems

       Make Judgments and Decisions

  • Effectively analyze and evaluate evidence, arguments, claims and beliefs

  • Analyze and evaluate major alternative points of view

  • Reflect critically on learning experiences and processes

       Communicate Clearly

  • Articulate thoughts and ideas effectively using oral, written and nonverbal communication skills in a variety of forms and contexts

      Collaborate with Others

  • Demonstrate ability to work effectively and respectfully with diverse teams

Life and Career Skills (P21.org)

Flexibility and Adaptability: Be Flexible

  • Incorporate feedback effectively

  • Deal positively with praise, setbacks and criticism

Initiative and Self Direction: Work Independently

  • Monitor, define, prioritize and complete tasks without direct oversight

Productivity and Accountability: Produce Results

  • Multi-task

  • Participate actively, as well as be reliable and punctual

  • Present oneself professionally and with proper etiquette

  • Collaborate and cooperate effectively with teams

  • Respect and appreciate team diversity

  • Be accountable for results

Information, Media, and Technology Skills (P21.org)

Create Media Products

  • Understand and utilize the most appropriate media creation tools, characteristics and conventions

 Apply Technology Effectively

  • Use technology as a tool to research, organize, evaluate and communicate information

  • Use digital technologies (computers, PDAs, media players, GPS,  etc.), communication/networking tools and social networks appropriately to access, manage, integrate, evaluate and create information to successfully function in a knowledge economy

Materials

  1. Learning Management System: I use Haiku, but Google has Google Sites where you can set up a free learning management system.
  2. Recorded Lessons: This can be used for students and parents to go back and review the lesson, more practice problems, and for a flipped classroom. You can use ScreenChomp
  3. Steps and procedures that the student has written down. — he/she can use them as they practice problems.
  4. Daily Assessments: —- Questions (5-10) that cover the topic. The students discuss answers with teacher and their peers. They reflect on how to solve the problem and what they need to continue to work on before the test.
  5. Practice Problems: — Problems that I have created or worksheets. These are problems that are customized to the student and what they need to continue to work on and practice.
  6. Visuals/Drawings: Have students that are having trouble with the concept to draw pictures of what they think the fraction addition problem will look like. You can check for understanding with this activity. As a teacher you can also have drawings on hand to help those that learn better with visuals.
  7. Question of The Day: — http://socrative.com/ — This is the website where I post the question on the day. I use this for the students to evaluate themselves each day after they have had practice and meet with me and worked with their peers. I want my students to have an understanding of where they are with their learning and be able to see their own progress. This also allows them to take ownership of their own learning process. Got the idea from this blog: http://classorganize.blogspot.ca/2013/10/exit-slip-exit-ticket-ticket-out-door.html
  8. Google Docs: This is where the student will put their work for the 3-2-1 Bridge.

Lesson – Introduction

Have the students to think of something that is like a concept we have learned in our unit on Fractions. Then they had to explain to a partner what they had chosen to compare. If it made sense to their partner, they could use it in a 3-2-1 Bridge. I gave them the example below and told them they could not use this example and could not use the word given when writing their 3-2-1 bridge. when the students were approved by me that they had a good 3-2-1 bridge, they got to find a picture that represented it.  

Lesson Activities and Procedures

Day one will consist of 30 minutes for practice. Day two will consist of collaboration with peers and/or the teacher which will be 60 minutes. The student will also be required to work the few new practice problems that are customized to what the student is having trouble with. They will then be required to take a *checking-in (Some students that get a 100 on their *checking in will not be required to work extra problems.) All students will need to watch the teacher-made tutorials of the lesson and take notes on mean, median, and mode. Day three will consist of  the learner watching another teacher-made tutorial and taking notes on the material. They will practice what they have learned through collaboration with their peers and teacher. Day four will consist of collaboration with peers and/or the teacher which will be 60 minutes. The student will also be required to work the few new practice problems that are customized to what the student is having trouble with. They will then be required to take a *checking-in (Some students that get a 100 on their *checking in will not be required to work extra problems.) All students will need to watch the teacher-made tutorials of the lesson and take notes on mean, median, and mode. Day Five will consist of the students applying the thinking routine

Student Procedure

Teacher Procedure

Materials

 Day 1 Day 1  Day 1
The student will watch a teacher-made lesson created by their teacher on adding fractions with unlike denominators, Or the students can watch the teacher demonstrate how to subtract fractions using the steps during fact-to-face instruction. (5 min) The teacher will provide 3 Simple Steps for Subtracting Fractions.Step 1: You need to have a common denominator.
  • Find the LCD (aka LCM)
  • Once you change the denominator you need to change the numerators.
  • Do unto the numerator as you do to the denominator. – (golden rule in Fraction World)

Step 2: Add or subtract the numerators keeping the denominator the same. Step 3: You need to simplify your fraction if needed. You might need to change an improper fraction to a mixed number. This will give you your final answer.

Teacher-made tutorials
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Screencast: teacher-made video for delivering instruction at home for flipped teaching (5 min)

The student will take notes and work some practice problems while watching the lesson.

The teacher will provide practice problems for the students to work. practice problems from AAA math or from IXL (see above links)or
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Day 2 Day 2 Day 2

The student will come in the next day and take a “checking-in” so the teacher and student can see where they are on their understanding of the concept.

The teacher will give a few practice problems either on a sheet of paper or within a technology tool (Quia.com) or Learning Management System (Haiku.com) Learning Management System (LMS):  Google, Edmodo, and/or Haiku for online learning

The student will then reflect on the problems they got wrong by doing the following:

a. They will go over the steps making sure they followed each step. b. Collaborate with a peer to talk about how to work the problems. c. They will meet with the teacher in small groups.   Differentiation: Have students that are having trouble with the concept to draw pictures of what they think the fraction addition problem will look like. You can check for understanding with this activity. As a teacher you can also have drawings on hand to help those that learn better with visuals.

The teacher will have the students to recall the steps for subtracting fractions in small groups or one-on-one with the teacher. The teacher will provide differentiation through drawings for the visual learners.
After making corrections and reflecting the student will work another practice problem following the steps. The teacher will instruct the students who need more practice to complete additional problems.  customized list

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 Day 3  Day 3  Day 3
The student will watch a teacher-made tutorial on subtracting mixed fractions with unlike denominators and adding whole numbers to fractions, or the students can watch the teacher demonstrate this on the board. The teacher will provide the steps for subtracting mixed fractions with unlike denominators and adding whole numbers to fractions. Teacher-made tutorials Screencast: teacher-made video for delivering instruction at home for flipped teaching (5 min)see link above
 The student will take notes and work some practice problems while watching the lesson. The teacher will provide practice problems for the students to work.
Screen Shot 2015-03-31 at 12.28.38 PM

Click on image to access website

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Click to enlarge

Screen Shot 2015-03-31 at 12.26.07 PM

Click on image to access website

 Day 4                  Day 4  Day 4
 The student will come in the next day and take a “checking in” so the teacher and student can see where they are on their understanding of the concept. The teacher will give a few practice problems either on a sheet of paper or within a technology tool  Learning Management System (LMS):  Google, Edmodo, and/or Haiku for online learning

The student will then reflect on the problems they got wrong by doing the following:

a. They will go over the steps making sure they followed each step. b. Collaborate with a peer to talk about how to work the problems. c. They will meet with the teacher in small groups.   Differentiation: Have students that are having trouble with the concept to draw pictures of what they think the fraction addition problem will look like. You can check for understanding with this activity. As a teacher you can also have drawings on hand to help those that learn better with visuals.

The teacher will have the students to recall the steps for subtracting fractions in small groups or one-on-one with the teacher.The teacher will provide differentiation through drawings for the visual learners.  Customized list
 Day 5 Day 5  Day 5
The student will work on their 3-2-1 with a partner and collaborate on what they are going to compare the concept to. The teacher will organize groups for completing a 3-2-1 Bridge using fractions and explain how to apply the thinking routine.   Making Thinking Visible 
The student will present their final 3-2-1 to the class in a Google Doc. The teacher will give feedback to the students. When they have a final product the student can find a picture that will work 3-2-1 bridge

Lesson Closure

Students will share their work with the class on a Google Doc, some will present to the class, and others will display their work in the classroom. The students will also take a test on the concepts they learned in this unit.

Assessment

imagesAs I look over the 3-2-1 Bridges, I look for creativity, and understanding. Does the student understand the concept well enough to pick an out of the box concept to compare to Subtracting fractions with borrowing. When they present the 3-2-1 Bridge are they able

to explain why they wrote what they wrote.

Student Sample

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Click on image to access student sample

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Teacher Reflection

321 bridge

 

Author Profile: 

Windy May

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References:

English Idioms Daily Blog. (2012, January 1). Retrieved August 3, 2014, from

     http://www.english-idioms.com/articles/files/tag-idiom-exercises-for-kids.html

Ritchhart, R., Church, M., & Morrison, K. (2011). Making Thinking Visible: How to Promote Engagement,  Understanding, and

     Independence for All Learners. San Francisco, CA:     Jossey-Bass.