Final+Project

Unit Plan- ** Fractions **

Introduction:
This unit extends the understanding of fraction equivalence and ordering. Students will use visual representations of fractions and manipulatives to explore how the number and size of the parts differ between two fractions even though they are equivalent. Students will recognize and generate equivalent fractions. Students will compare two fractions with different numerators and different denominators by creating common denominators or numerators, or by comparing them to a benchmark fraction such as it is important for students to understand that the comparison is only valid when the two fractions refer to the same whole or set. Students will use the symbols >, =, or < to record their comparison and use visual fraction models to justify their conclusions.

Understanding Fraction Equivalence and Ordering
 * Part 1. Lesson Topic **

Part 2. Learning Goals
The goal of this unit is understand that fractions are numbers. Students will be able to use manipulatives and visual presentations to model fractions. Students will understand the different parts of a fractions and what they mean. Student will compare, order and justify fractional equivalences with visual representations. Students will use benchmark when working with fractions.

Part 3. Standards
The Common Core Standards include:

4.NF.1: Explain why a fraction a/b is equivalent to a fraction (n x a)/(n x b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.

4.NF.2: Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1⁄2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using visual fraction models.

Part 4. Potential Barriers
Student C- Moderate Visual Challenges || May not be able to fold paper independently || Student B- Fine Motor Challenges Student C- Moderate Visual Challenges || May not be able to form letters accurately or quickly.
 * ** Materials & Methods ** || ** Student Qualities ** || ** Potential Barriers/ Missed Opportunities ** ||
 * Folding Materials || Student B- Fine Motor Challenges
 * Written responses || Student A- Learning Disabled

May not be able to express thoughts through writing (processing) || Student C- Moderate Visual Challenges Students D- Moderate Hearing Challenges || Difficulty processing one direction at a time.
 * Following teachers directions || Student A- Learning Disabled

Difficulty seeing the models.

May not be able to hear directions. ||
 * Collaborative learning || Student A- Learning Disabled

Students D- Moderate Hearing Challenges || May have a completing work in order.

May need activities scaffolded || Student C- Moderate Visual Challenges || May not be able to manipulate the rubber band and geoboard at the same time.
 * Geoboard manipulation || Student B- Fine Motor Challenges

Difficulty seeing the prongs of the geoboard. || Student C- Moderate Visual Challenges || Student has difficulty manipulating objects Difficulty seeing manipulatives due to size or color ||
 * Fraction manipulatives || Student B- Fine motor Chalenges

Part 5. Solutions
High tech: use virtual manipulatives, use kidspiration application ||
 * ** Potential Barriers/ Missed Opportunities **
 * // (from above) //** || ** UDL Solutions ** ||
 * May not be able to fold paper independently || Low tech: Use card stock with pre-folded areas
 * May not be able to form letters accurately or quickly.

May not be able to express thoughts through writing (processing) || Low tech: adult scribe for student High tech: allow students to use a digital recorder for journal entries dictations, allow students have access to a word procesing software ||
 * Difficulty following directions

Difficulty seeing the models.

May not be able to hear directions. || Low tech: Provide a visual picture schedule of tasks for individual students or post for all students to see, provide written instructions, have a peer tutored/ buddy to assist, use enlarged material

High tech: use a document camera to enlarge materials on the smartboard, use a amplification system within the classroom ||
 * May not be able to manipulate the rubber band and geoboard at the same time.

Difficulty seeing the prongs of the geoboard. || Low tech: use adapted goeboard, color prongs with a bright color

High tech: use virtual geoboard with touch screen ||

Part 6. Lesson Descriptions

 * __Lesson #1: Exploring equivalent fractions of a shape__**


 * __Objectives:__**
 * Students will demonstrate and understand that equivalent fractions are two or more ways of describing the same amount by using different size fractional parts.
 * Students will use visual models of the fraction to create equivalent fractions and record their results using symbols.


 * __UDL Components:__**
 * Representation ** is present in the activity through highlighting how complex terms and expressions are composed of simpler words or symbols.
 * Expression ** is present in the activity through the use of options such as folding, cutting, or drawing to demonstrate mathematical understanding.
 * Engagement ** is present in the activity through the use of a task that allows for active participation and exploration.


 * __Warm Up:__**
 * Give each student paper clocks. Ask them to divide the clocks into; one half, one forth and one third.
 * Next ask students if they would like to have 2/8 or ¼ of a pizza and why.


 * __Activity__**
 * Give each student a piece of paper and crayons or markers.
 * Have students fold the paper in half. (Do not specify which way to fold in half.) Have students use a crayon to shade in half of their paper.
 * Have students fold the paper in half again.
 * Have students open their paper.
 * Ask, how many parts are there now in the whole? (Four, which is the denominator) How many of those four parts are shaded? (Two, which is the numerator). What fraction is shaded? ( 1/2 or 2/4) What is the relationship between 1/2 and 2/4?
 * Have students fold the paper back up so that 1/4 is showing.
 * Fold the paper in half again.
 * Have students open their paper.
 * Ask, how many parts are now in the whole? (Eight, which is the denominator) How many of these eight equal parts are shaded? (Four, which is the numerator) What fraction is shaded?
 * Again ask what is the relationship between the fractions (1/2, 2/4 or 4/8 ) is. (Record the fractions)
 * Have students fold the paper back up so that 1/8 is showing.
 * Fold the paper in half again.
 * Ask, how many parts do you think there are now that we folded the paper once again and how many parts do you think are shaded? Record student predictions. Have students open paper and verify their predictions. Ask, “What fraction is now shaded?” (1/2, 2/4, 4/8 or 8/16 )
 * Ask, “What relationships do you notice about the fractions (1/2, 2/4, 4/8 or 8/16 )
 * “What even number denominators are missing between 2 and 16? What would the numerators need to be in order for the fractions to be equivalent to 1/2 ?” Teachers should continue to record student responses on chart paper or the board so that students can reflect upon the discussion.
 * Ask, “If 2/4 is equivalent to 1/2 and 3/6 is equivalent to ½, then what is the relationship between 2/4 and 3/6 ? How could you prove that 2/ 4 is equivalent to 3/6?”
 * Formulate further questions based on student discussions.
 * Ensure students understand that equivalent fractions are two or more ways of describing the same amount but using different size fractional parts.
 * Repeat this activity with Geoboards or with an interactive white board and manipulatives.


 * __Assessment__**__:__
 * Draw shapes on the board and partition the shapes into fractions.
 * Ask students to determine if the fractions or not equivalent, and why.
 * Students should record their responses on an Index card


 * __Lesson #2: Exploring equivalent fractions of a region__**


 * __Objectives:__**
 * Students will demonstrate and understand that equivalent fractions are two or more ways of describing the same amount by using different size fractional parts.
 * Students will use visual models of the fraction to create equivalent fractions and record their results using symbols.


 * __UDL Components:__**


 * Representation** is present in the activity through the use of symbolic representation as well as the use of concrete or virtual manipulatives.


 * Expression** is present in the activity through the use of alternatives for physically responding (coloring, use of Geoboards and/or Geodot paper, use of virtual manipulatives).


 * Engagement** is present in the activity through the use of autonomy in choosing tools to work with and through the use of assessment that provides the opportunity for personal response.


 * __Warm Up:__**
 * Give students a sheet of paper. Ask them to color in 1/3 of the paper. How many equivalent fractions can you create?


 * __Activity__**
 * Students will determine equivalent fractions other than a half by folding paper and recording their fractions as they did yesterday.
 * Have each group of four students break into pairs. Give each student a piece of paper and crayons or markers.
 * Ask one pair to fold a paper into thirds and sixths. Ask the other pair to fold their paper into fourths and eights. (Equal parts) Have students look for relationships among the equivalent fractions.
 * Have each pair share their display with their group. Ask if there are additional equivalent fractions they could create by continuing to fold their paper. Allow time for students to explore folding paper. Some students may wish to use Geoboards to find equivalent fractions.
 * Allow time for students to discuss their findings. Record a list of student’s responses on the board.

__Assessment:__
 * Students will answer the following question in their math journals: “Would you rather have 2/6 or 4/12 of a pizza? Why? Use words, numbers or symbols to explain your answer.


 * //__Lesson # 3: Parts of a Whole__//**


 * __Objectives:__**
 * Students will demonstrate and understand that equivalent fractions are two or more ways of describing the same amount by using different size fractional parts.
 * Students will use visual models of the fraction to create equivalent fractions and record their results using symbols.


 * __UDL Components:__**
 * Representation ** is present in the activity throughhighlighting how complex terms and expressions are composed of simpler words or symbols.
 * Expression ** is present in the activity through the use of options such as folding, cutting, or drawing to demonstrate mathematical understanding.
 * Engagement ** is present in the activity through the use of a task that allows for active participation and exploration.


 * __Warm Up:__**
 * Give students a sheet of paper. Ask them to color in 1/3 of the paper. How many equivalent fractions can you create?


 * __Activity__**
 * Divide the class into groups.
 * Using one of the manipulatives, give each group the same number of wholes (ex. 3 whole rectangles or circles).
 * Each group would receive a different fractional part of the whole to find (1/2, 1/3, 1/4).
 * Each group needs to find how many fractional pieces it takes to equal 3 wholes (6/2, 9/3, 12/4). Students should be encouraged to think-pair-share before beginning. (If students have difficulty working with 3 wholes, modify by starting with simply 1 whole and finding halves, thirds, fourths, etc.).
 * Compare 6/2, 9/3, 12/4 to each other.
 * Locate these fractions on the number lines so students can see that 6/2= 3 and 9/3 = 3. Therefore 6/2 and 9/3 are also equivalent fractions.
 * Have students do the same activity but with different-shaped wholes. Example: if you used circles in the previous activities, now have students find fractional parts of a rectangle

Students will answer the following question in their math journals: Ask students “Which is more, 5/5 or 5/10? Explain your reasoning using words, numbers or symbols to explain your answer.
 * __Assessment__**__:__


 * Reflection**

The lessons presented in my final project are based on the constructivist learning theory and allow student to explore concepts by manipulating objects. Barriers could exist because students are using many manipulatives to build their knowledge. When creating or adapting lessons to meet the needs of all learners, I first have to identify what barriers might exist for each learner. I need to pinpoint the appropriate modifications and accommodations that will help my students meet the learning targets with success. I often fine that the strategies I use with my special education students are good for all learners.

I used the SETT framework as a guide to providing appropriate instruction. The SETT framework is a team approach to meet the needs of students. I first considered the student’s needs, the learning environments, and the tasks the class was expected to complete. Next I identified the tools needed to support the student to not only successfully complete the task but to meet the learning outcomes. These tools could be in the form of high or low-tech assistive technology. The specific AT devices used were derived from the WATI guidelines. I used the AT consideration wheel to reference appropriate technologies to support instruction. These technologies range from low to high tech devices. When choosing appropriate accommodations for student with difficulty writing I referred to the Adapted Pencils to Computers. I was able to identify tools that would be good for students with processing or fine motor challenges. In this project I planned as if I had already used the ATDP cycle. I references AT devices that I felt would benefit specific students. I realize that AT might also help all students; I may want to show them how to use the speech to text software on the computers. However, I would be cautious because these devices would not be used on assessment.