User:Bpolack

Bryan Polack's Portfolio Page

Return to: 2018 ETAP 623 Home Page | Teaching Fractions and Number Sense

About Me

My name is Bryan and I am certified to teach mathematics in NYS for grades 7-12. This is my third year teaching middle school math at a public school. I taught one year of high school math at a private school prior to my current position and long-termed substituted for most of the school year before that. I am married and have five kids-three boys and two girl. The youngest will be two in June and my oldest turned 8 on New Year's Eve. After graduating from Albany, I would like to take physics classes over the next two summers in order to gain a second certification in Physics. I had subbed years ago for two months in a Physics class and loved it!

My Topic and Purpose

Teaching Fractions and Number Sense This mini-course is designed for teachers and students of elementary or middle school math to better understand what fractions are and how to complete problems involving the four operations. The course stresses a focus on number sense and how and why the math works. While knowing an algorithm can be helpful, when truly understanding the math and how it works, students will build a strong number sense and will likely remember and make more connections.This course focuses on an introduction to fractions, finding equivalent fractions and adding, subtracting, multiplying, and dividing fractions using various models and manipulatives, including the standard or modern technique.

Learning Outcomes

Students will create fractions using paper strips.

Students will use manipulative to identify fraction sizes.

Students will understand that fractions are numbers on a number line.

Students will develop a deep number sense that connects with fractions.

Students will examine and reason why common denominators are needed when adding and subtracting fractions.

Students will discover that while there are an infinite number of equivalent fractions, there is only one decimal form of the fractions.

Needs Assessment

Problem Many students are afraid of fractions and do not have a strong fraction sense. Since number sense and fractions are the foundation to mathematics, it is important to make sure that students have a solid foundation before moving onto more difficult problems. When students do not develop this foundation, they tend to struggle and lose interest in math. By this point, it is difficult to re-engage students into loving mathematics

What is to be Learned Students will learn and build a foundation in fractions and operations with fractions. Students will discover ideas of equivalency, number lines, using all four operations with fractions, and building a strong number sense. Students will add, subtract, multiply, and divide fractions using models, manipulatives, and standard algorithms.

Learners This course is intended for both students and new mathematics teachers. The lessons are ideal of grades 4-6, but are also good for students who are in grades 7+ who need interventions due to being below grade level expectations for mathematics. Anyone who has or is struggling with number and fraction sense can benefit from this mini-course.

Instructional Context Student will take this mini-course through the wiki page. Students will need a gmail account in order to link to google classroom. Students will complete video lessons through Edpuzzle, taking formative assessments embedded in the video. Students will take summative assessments through Quizizz. Lastly, students will need paper or online journal in order to reflect on what they learning in their learning journals.

Exploring the Problem and Solution Students will make connections to real world and hands-on learning. Manipulatives and models will be stressed. Students will learn the standard algorithm only after they have completed the previous lessons.

Goal The goal is for students to build a solid foundation in fraction and number sense. Students should be able to add, subtract, multiply, and divide fractions using various methods.

Analysis of the Learner and Context

Students will be proficient at navigating both standard computers and wiki pages. Students should know how to create a gmail account and how to join google classroom. The students will watch teacher made videos and answer either open-ended questions or multiple choice questions. Student will need access to a computing device and have internet accesses. Learner should be a student who needs help with fraction sense or a teacher who is looking for other methods to teach fraction work.

Performance-Based Objectives

When given models or manipulatives, students will be able to create equivalent fractions 90% of the time.

When given addition, subtraction, multiplication, and division fraction problems, students will be able to find the solution 85% of the time using models or manipuatives.

When given addition, subtraction, multiplication, and division fraction problems, students will be able to find the solution 80% of the time using the standard methods.

When given various fractions, students will be able to analyze which fraction is the larger fraction, 80% of the time.

When given fraction problems, students will be able to explain and rationalize the correct mathematical steps to the solution, 80% of the time.

Task Analysis

Part I-Goals:

Terminal Goal:

Students will be able to add, subtract, multiply, and divide fractions with fluency.

Enabling Goal:

Students will find equivalent fractions by modeling or multiplying by one whole.

Students will add, subtract, multiply, and divide fractions using models, manipulatives, and through standard methods.

Students will create their own fraction problems and solve them using various methods.

Part 2: KASI

Knowledge:

Know the multiplication facts

Understand how numbers are plotted on a number line

Typical computer skills, such as email and wikis

Be able to add, subtract, multiply, and divide whole numbers.

Attitudes:

Know that everyone can learn basic mathematics and should not fear the word fractions.

Persevere at solving a fraction problem when having trouble getting a solution.

Attend to precision when drawing models and using manipulatives.

Skills:

Identify what operation to use and what those operations really mean (i.e. Making Groups, etc.)

Be able to do all operations with whole numbers fluently.

Interpersonal Skills:

Be able to work with manipulative and draw models without a strong artistic background.

Be able to compare answers with classmates and not fear being wrong.

Part 3: Pedagogical Approach

Units I and II focus on inquiry and constructing knowledge using models or manipulative, so it should be constructivism.

Unit III is direct instruction on using the standard methods or algorithms

Curriculum Map

References and Resources

Larson, M. B., & Lockee, B. B. (2014). Streamlined ID: a practical guide to instructional design. New York: Routledge.

Google Classroom Connect all of your students in one place to update the entire class on work and upcoming events.

Edpuzzle A website to upload or edit videos and embed formative assessment questions.

Quizizz A website that helps to motivate and engage students by having them assess or compete by answering questions. Data can be taken and used as a score or as formative assessment.

Khan Academy This is a great website that offers videos to teach math and science.

iXL This website is a great resource to have students practice skills that they have already learned but may not have mastered.

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