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Unit Plan

FRACTIONS, RATIOS, & DECIMALS ARE AMAZING!

 

NAMES: Meghan Powers, Annmarie McGonagle, Derrick LaBombard

 

CLASS/SEMESTER: EDR 524, Fall 2011

 

GRADE LEVEL: 7th Grade

NUMBER OF STUDENTS IN THE CLASS: Approximately 24 students

 

 

UNIT TITLE: Fractions, Ratios, & Decimals Are Amazing!

RATIONALE: Basic pre-requisite knowledge for higher mathematical learning and thinking, as well as for day-to-day use.

INSTRUCTIONAL GOAL(S):  At the end of the unit, students will be able to understand the relationships between fractions, ratios and decimals.  Students should also be able to apply the basic operations to rational numbers.

STUDENT PERFORMANCE INDICATORS/OUTCOMES:

  1. Common Core Curriculum Standards:

 

Ratios & Proportional Relationships                                     7.RP

Analyze proportional relationships and use them to solve real-world and mathematical problems.

1. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.

2. Recognize and represent proportional relationships between quantities.

a. Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.

b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

c. Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.

 

The Number System                                                        7.NS

Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.

1. Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

2. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

c. Apply properties of operations as strategies to multiply and divide rational numbers.

d. Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.

3. Solve real-world and mathematical problems involving the four operations with rational numbers.1

_________________

1 Computations with rational numbers extend the rules for manipulating fractions to complex fractions.

 

Expressions & Equations                                                  7.EE

Use properties of operations to generate equivalent expressions.

Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

3. Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.

 

IRA/NCTE Standards for the English Language Arts:

 

4. Students adjust their use of spoken, written, and visual language (e.g., conventions, style, vocabulary) to communicate effectively with a variety of audiences and for different purposes.

 

5. Students employ a wide range of strategies as they write and use different writing process elements appropriately to communicate with different audiences for a variety of purposes.

 

11. Students participate as knowledgeable, reflective, creative, and critical members of a variety of literacy communities.

 

Taken from the NCTE/IRA Standards (1996)

 

  1. CONTENT:

 

INTEGRATION/INTERDISCIPLINARY APPROACH/METHODS: 

 

INSTRUCTIONAL PROCEDURES/STRATEGIES:

(a)  Generalities of Lesson Plans

 

(b)  Type(s) of Grouping Patterns (WC, SG and type of SG, P, and I; include description of SG types)

         WC: The whole class will go over the vocabulary words with the teacher.

         I: Students will individually write their own short story about their favorite number, while incorporating the vocabulary words into it.

         No SG, or P.

         P: Students will then work with a partner and share their story, while the other partner draws their own picture representation of that story.

         I: Students will post their pictures that they have created on the board.  Students will finish class with a review worksheet (whatever is left to the worksheet will be assigned for homework).

         WC: Students will have the opportunity to share their story with the class on a volunteer basis.

         No SG.

         P: Students will work with a partner(s) when going over the homework from previous class as well as when using technology in the computer lab.

         I: The students will individually work on examples given by the teacher and start homework due the next class if time allows.

         WC: The whole class will go over basic examples in class.

         No SG.

         P: Students will work with a partner(s) when going over the homework from previous class.

         I: The students will individually work on examples given by the teacher and start homework due the next class if time allows.

         WC: The whole class will go over basic examples in class.

         No SG.

         SG: Students will work together in groups of 3 or 4 while determining which fractions and proportions the food should be cut up into.

         I: Students will individually work on examples given by the teacher and start homework due the next class if time allows.

         WC: The whole class will go over homework together, as well as basic examples in class.

         No P.

 

(c)  Vocabulary Instruction:

         Direct:  I plan to lecture to the students about the vocabulary.  For some of the words I will simply read the definition and use them in sentences to solidify the students’ understanding.  Students will discuss the meanings of some vocabulary words in groups and then the class will come together to have a discussion.  During the discussion I will guide the students to help them with their definitions.

         Indirect:  The students will be divided into groups so that they can discuss the vocabulary terms and try to make sense of them.  These learning stations will help students work together to put the meanings of the terms into their own words.

 

(d)  Meeting the Special Learning Needs of a Student or Group of Students –

 

UNIT SCHEDULE

         Thursday: The Story Behind Your Favorite Number(s) (LP1).

         Friday: Sharing Stories With Friends (LP2).

         Monday: Fractions: Addition, Subtraction (LP3).

         Tuesday: Fractions: Multiplication, Division (LP3).

         Wednesday: Ratios (LP4).

         Thursday: Decimals and Conversion (LP4).

         Friday: Fractions Outside the Classroom (LP5).

         Monday: Overview.

         Tuesday: Long Quiz: Approximately 25 Questions.

 

INTRODUCTION/ MOTIVATION: 

 

CULMINATION/CULMINATING ACTIVITY: 

 

ASSESSMENT and EVALUATION PROCEDURES:

(a)  Student Assessment (methods/techniques and procedures):

               

                1)      Teacher’s assessment of student: I will observe the students during class to make sure they are grasping concepts and skills.  There will also be weekly journal entries kept by the students so that I can read them and gather information.  I will also interview each student individually throughout the unit to determine if they have any problems with material.    

 

                2)      Student self-assessment: During the individual interviews, students will be asked to assess themselves on how they think they are progressing with the mathematical material.

 

   (b) Student Evaluation (methods/techniques and procedures): I will grade worksheets, quizzes, a test at the end of the unit, journal entries (pass/fail), math stories, and math pictures (pass/fail), etc.

(c) Self-assessment/evaluation (methods/techniques and procedures):  I will assess my teaching and make adjustments accordingly based on class discussions and student evaluations and assessments.

MATERIALS & RESOURCES: 

(a)   Types of, Titles of, and Brief Descriptions of Printed Texts:

These trade books will be used throughout the unit to allow students to explore the stories and pull out mathematical ideas.

 

(b)   Types of, Names of, and Brief Descriptions of Audio-Visual Materials:

(c)   Types of, Addresses of or Names of, and Brief Descriptions of at least three Technology Resources:

 

ADDITIONAL NOTES AND COMMENTS: 

1.  ADDITIONAL MATERIALS (Not specifically included in other sections):

 

(a)  Quizzes and/or Tests; Rubrics for grading:

(b)  Homework, newsletter, invitations:

 

(c)  Guest speakers, details of field trips, other out-of-class activities:

 

(d)  Details of Introduction and Culmination of the unit:

         The students will now be able to do the "impossible" problem that was presented to them at the beginning of this Unit.  It will be done individually and handed in to the teacher; after which a confident volunteer will do the problem at the board, explaining each step as they solve it.

         Watch a Mr. Duey video again; "Fractions," or another video related to the next Unit the class will be learning.

         Play a review game.

         For homework one night, students will make/create at least 1 question related to this Unit (on fractions, decimals, and/or ratios), as well as giving the correct answer with their problem.  Little do they know that each of their problems will be mixed into their next quiz or test!

         Quiz or test.

       

 

2.  INFORMATION FOR SUPERVISOR and/or READING SPECIALIST and/or SUBSTITUTE TEACHER:

 

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Rubric

Name:

 

Student Activity: Students are to create a short story about their favorite number (s) using mathematical vocabulary that is provided below. Students must use at least 7 vocabulary words and the rubric below must be followed.

 

Grammar/Spelling             4       3       2       1

Vocabulary use                 4       3       2       1

At least 1 pages            4       3       2       1

Creativity                          4       3       2       1

Readability                        4       3       2       1

 

Total:                                                          Score:

 

Vocabulary list: circle, square, triangle, radius, rational, numerator, linear, area, volume, diameter, perimeter, distance, cube, graph, fraction, denominator, ratios

(We created this rubric ourselves).

 

 

Prepared by:  

Snowden, P. L. (1995). Department of Elementary and Special Education, Southeast Missouri State University, Spring Semester 1995 (revised Summer Semester 1996).

Additional revisions:

Snowden, P. L. (1999). Center of Educational Studies and Services. Plattsburgh State University of New York.

Snowden, P. L. (2005, 2006, 2007, 2009, 2011). Literacy Education. SUNY-Plattsburgh

 






*Please note that this document was created by Meghan A. Powers, Annmarie McGonagle, and Derrick LaBombard.



Website created and maintained by Meghan A. Powers.
Email: mpowe002@mail.plattsburgh.edu.
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Website last updated: 12/11/2011
2011 Meghan A. Powers