Lessons and Activities

Transcription

1 Grade Level: 5 Title: Working with Fractions Essential Question(s): Subject Area(s): Reading, Writing, X Mathematics Science Social Studies How can you rewrite a pair of fractions so that they have a common denominator? How can you use a common denominator to add and subtract fractions with unequal denominators? How can you find the product of a fraction and a whole number without using a model? How can you divide unit fractions by whole numbers and whole numbers by unit fractions? Assessment(s): Pre-Assessment Formative X Summative GT Scope and Sequence Skills: (Aligned with 21 st Century Skills Framework & College and Career Readiness Standards) X Creative Thinking X Critical Thinking X Communication Research Student Learning Styles: Auditory X Visual/Spatial Kinesthetic X Other: Logical/Mathematical GT Differentiated Exemplar Lesson Mathematics TEKS/Student Expectations: Number and operations. The student applies mathematical process standards to develop and use strategies and methods for positive rational number computations in order to solve problems with efficiency and accuracy. The student is expected to: 5.3H represent and solve addition and subtraction of fractions with unequal denominators referring to the same whole using objects and pictorial models and properties of operations; 5.3I represent and solve multiplication of a whole number and a fraction that refers to the same whole using objects and pictorial models, including area models; 5.3J represent division of a unit fraction by a whole number and the division of a whole number by a unit fraction such as 1/3 7 and 7 1/3 using objects and pictorial models, including area models; 5.3K add and subtract positive rational numbers fluently; and 5.3L divide whole numbers by unit fractions and unit fractions by whole numbers Elements of Depth and Complexity: X Language of the Discipline X Details Patterns Trends X Rules Ethical Considerations Unanswered Questions Over Time Different Perspectives Big Ideas X Whole Class Small Group X Independent Activity PART ONE: Whole Class: Lessons and Activities This is a culminating activity to show understanding of working with fractions using the 4 operations addition, subtraction, multiplication, and division. Students should come into this lesson having a full understanding of creating equivalent fractions and finding a common denominator. Resources: Working with Fractions Menus (attached below) Adapted from Westphal, Laurie E. Differentiating Instruction with

2 Introduce students to the available options on the Working with Fractions Menu (see below), explaining that they should choose projects that total between 90 and 100 points. Consider completing one of the projects whole-class to explain and show what your expectations are for the project. Menus: Math. Prufrock Press, Inc. The free choice proposal form is attached below for students to submit if they would like to create their own project. On Grade Level: Students should choose projects from the Working with Fractions menu. They should get approval on the projects they selected before beginning. Projects should be completed in a way that allows for sharing with peers. GT Level Group: Students should choose projects from the Working with Fractions Extensions menu. They should get approval on the projects they selected before beginning. Projects should be completed in a way that allows for sharing with peers. These options are similar to the on Grade Level options, but have extensions for multiple fractions within an equation and using multiple operations in an equation. In addition, there is a new project for creating a jigsaw puzzle with equivalent fraction equations. The jigsaw puzzle should be created with squares that will then connect to complete the puzzle. See the example of a jigsaw puzzle of this format to the right. Whole Class: Share completed projects via a gallery walk, small group presentations, playing of games, etc. Project Proposal Form (attached below) Project Cube Template (attached below) Excerpted from Westphal, Laurie E. Differentiating Instruction with Menus: Math. Prufrock Press, Inc. Project Materials: Grid paper for crossword puzzle (or Netbooks with online access for creating crossword puzzle) Cardstock for cube Poster board or large tag or construction paper for game board Blank notecards for concentration cards Construction paper for foldable and/or jigsaw puzzle Netbooks with PowerPoint as an option for lesson idea

3 Picture of jigsaw puzzle example

4 Working With Fractions Guidelines: 1. You may complete as many of the activities as you would like within the time period given. 2. Your goal is points. You may earn up to 10 points extra credit (for totals over 100). 3. You may be as creative as you like within the guidelines listed below. 4. You must show your plan to your teacher by. 5. All addition and subtraction problems must be with unlike denominators and must include steps for how to create an equivalent fraction before adding and/or subtracting. 6. All answers must be written in simplest form. 7. Activities may be turned in at any time during the working time period. They will be graded and recorded on this sheet as you continue to work, so keep up with this rubric! Plan to Do Activity to Complete Point Value Date Completed Choose your favorite recipe. Your friends have decided to prepare it for a party of 50 people. Create a grocery list for the total amount of items they will 25 need to buy. Make an Understanding Fractions brochure that explains how to add, subtract, multiply, and divide fractions. Include examples. 15 Create a cartoon in which the main character, One Half, has to divide itself. Be creative about why this has to happen and how it takes place. 25 Create a number crossword puzzle for different fraction problems, using addition, subtraction, multiplication, and division. The answers should be the 20 fraction word form and the clues should be the problems. Create a cube with 6 word problems using fractions. Include 2 problems for each operation. Provide a separate answer key showing all work. 20 Make a board game that tests your classmates knowledge of working with fractions and the 4 operations. Have a group play the game to make sure they 25 understand and the rules are clear. Create a set of concentration cards that match multiplication, division, addition, and subtraction problems with their answers. 15 Write a children s story about a fraction that has to keep multiplying. 25 Create a lesson for the class that teaches the addition and subtraction of fractions. Use manipulatives and allow your classmates to practice their skills! 20 Your school librarian has asked your class for some help on the purchase of some new bookcases with 2 shelves each. She has 300 new books she needs to shelve. One half of the books are half an inch thick. One third of them are one fourth of an inch thick, and the rest are three fourths of an inch thick. Her 30 shelves are 30 inches long. How many bookcases should she buy? Show your work in a way that the librarian could understand and know what she should purchase. Free choice: Must be outlined on a proposal form and approved before beginning work. Total number of points you are planning to earn. Total points earned: Points Earned I am planning to complete activities that could earn up to a total of points. Teacher s intials Student s signature

5 Working With Fractions Extension Menu Guidelines: 1. You may complete as many of the activities as you would like within the time period given. 2. Your goal is points. You may earn up to 10 points extra credit (for totals over 100). 3. You may be as creative as you like within the guidelines listed below. 4. You must show your plan to your teacher by. 5. All addition and subtraction problems must be with unlike denominators and must include steps for how to create an equivalent fraction before adding and/or subtracting. 6. All answers must be written in simplest form. 7. Activities may be turned in at any time during the working time period. They will be graded and recorded on this sheet as you continue to work, so keep up with this rubric! Plan to Do Point Value Activity to Complete Choose your favorite recipe. Your friends have decided to prepare it for a party of 50 people. Create a grocery list for the total amount of items they will need 25 to buy. Make an Understanding Fractions brochure that explains how to add, subtract, multiply, and divide fractions. Include examples. 15 Create a cartoon in which the main character, Three Fourths, has to divide itself. Be creative about why this has to happen and how it takes place. He/She 25 must divide at least 4 times. Create a number crossword puzzle for different fraction problems, using addition, subtraction, multiplication, and division. The answers should be the fraction word form and the clues should be the problems. Equations should have more than 2 fractions and at least 2 operations. Ex: 1/2 + 3/8 4/7 Create a cube with 6 multi-step word problems using fractions. Include 2 problems for each operation. Provide a separate answer key showing all work. 20 Make a board game that tests your classmates knowledge of working with fractions and the 4 operations. Have a group play the game to make sure they 25 understand and the rules are clear. Create a set of concentration cards that match multiplication, division, addition, and subtraction problems with their answers. 15 Write a children s story about a fraction that has to keep multiplying. 25 Create a jigsaw puzzle where the sides match up with equivalent fraction equations. Ex: ½ + ¼ matches with 3/6 + 3/12 20 Your school librarian has asked your class for some help on the purchase of some new bookcases with 2 shelves each. She has 300 new books she needs to shelve. One half of the books are half an inch thick. One third of them are one fourth of an inch thick, and the rest are three fourths of an inch thick. Her 30 shelves are 30 inches long. How many bookcases should she buy? Show your work in a way that the librarian could understand and know what she should purchase. 20 Date Completed Free choice: Must be outlined on a proposal form and approved before beginning work. Total number of points you are planning to earn. Total points earned: I am planning to complete activities that could earn up to a total of points. Points Earned Teacher s initials Student s signature

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8 Process Assessment Teacher observes the following: Process Observation - Frequency: Student demonstrates inquiry skills throughout the stages of the tasks. Seldom/Never Occasionally Often Consistently Process Observation Frequency: Student uses language of the discipline during interactions and mathematical work Seldom/Never Occasionally Often Consistently Process Observation Quality: Student ideas are creative and original throughout the task. Typical of Peers Fluent Thinker Flexible Thinker Unique and Original Process Observation Quality: Student uses background information and knowledge to create appropriate work. Typical of Peers Fluent Thinker Flexible Thinker Unique and Original Product Assessment Score Fraction Reasoning Terminology 3 Fraction equation steps are consistently clear and correct throughout the work 2 Fraction equation steps are clear and correct throughout most of the work; 1 Fraction equation steps are not clear and correct shows several errors; division work Uses unusual and highly complex mathematical reasoning. Uses complex and refined mathematical reasoning. Uses effective mathematical reasoning Correct terminology and notations are used creatively and originally. Correct terminology and notations are always used, making it easy to understand what was done. Correct terminology and notations are usually used, making it fairly easy to understand what was done.