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Michigan Department of Education Technology-Enhanced Lesson Plan Lesson Title: Fraction Facts taken from: http://www.shodor.org/interactivate/lessons/multdeci.html Adapted by: Marsha Myles and Carolyn Newkirk Lesson Abstract: The following discussions and activities are designed to introduce students to fractions, including operations with fractions, converting fractions to decimals and percents. The activities provide ample practice opportunities to reinforce the information from the discussions. Subject Area: Mathematics Grade Level: 6 Unit Title: Numbers and Operations Michigan Educational Technology Standards Connection: Technology Productivity Tools 1. apply common software features (e.g., thesaurus, formulas, charts, graphics, sounds) to enhance communication and to support creativity 2. use a variety of technology resources, including the internet, to increase learning and productivity 3. explore basic applications that promote creativity (e.g., graphics, presentation, photo-editing, programming, video-editing) Technology Communication Tools 1. use a variety of telecommunication tools (e.g., e-mail, discussion groups, IM, chat rooms, blogs, video-conferences, web conferences) or other online resources to collaborate interactively with peers, experts, and other audiences aaadc5e4-58a4-46b6-a7b7-8ba9c3307b46.doc - Page 1 Michigan Grade Level Content Expectations Connection: N.MR.06.01 Understand division of fractions as the inverse of multiplication, e.g., ■, then __ x ■ = __ , so ■ = __ • __ = _ __ . N.FL.06.02 Given an applied situation involving dividing fractions, write a mathematical statement to represent the situation. N.MR.06.03 Solve for the unknown in equations such as: ■ ■= _ and __ = 1 • ■. N.FL.06.04 Multiply and divide any two fractions, including mixed numbers, fluently. N.ME.06.05 Order rational numbers and place them on the number line. N.ME.06.06 Represent rational numbers as fractions or terminating decimals when possible, and translate between these representations. N.ME.06.07 Understand that a fraction or a negative fraction is a quotient of two integers, e.g., - __ is -8 divided by 3. N.MR.06.08 Understand integer subtraction as the inverse of integer addition; add and subtract integers using integers from 10 to -10. N.FL.06.09 Add, subtract, multiply, and divide integers between -10 and 10; use number line and strip models for addition and subtraction. N.FL.06.10 Add, subtract, multiply and divide positive rational numbers fluently. Estimated time required to complete lesson or unit: One 45 – 60 minute class period Instructional resources: http://www.shodor.org/interactivate/lessons/multdeci.html http://www.shodor.org/interactivate/activities/sequencer/worksheet1.h tml aaadc5e4-58a4-46b6-a7b7-8ba9c3307b46.doc - Page 2 http://www.shodor.org/interactivate/activities/sequencer/worksheet2.h tml http://www.shodor.org/interactivate/activities/sequencer/index.html Prior required technology skills: o perform basic mouse manipulations such as point, click and drag o use a browser such as Netscape for experimenting with the activities Sequence of Activities: Multiplying Decimals and Mixed Numbers Abstract This lesson is designed to reinforce skills associated with multiplying decimals and mixed numbers and allow students to visualize the effects of multiplying by a decimal or mixed number. Objectives Upon completion of this lesson, students will: have practiced multiplying decimals and/or mixed numbers. have explored the effects of multiplying decimals and mixed numbers. have practiced predicting the effects of multiplying a number by a decimal or mixed number. Standards The activities and discussions in this lesson address the following NCTM Standards: aaadc5e4-58a4-46b6-a7b7-8ba9c3307b46.doc - Page 3 Numbers and Operations Understand numbers, ways of representing numbers, relationships among numbers, and number systems work flexibly with fractions, decimals, and percents to solve problems Understand meanings of operations and how they relate to one another understand the meaning and effects of arithmetic operations with fractions, decimals, and integers understand and use the inverse relationships of addition and subtraction, multiplication and division, and squaring and finding square roots to simplify computations and solve problems Compute fluently and make reasonable estimates select appropriate methods and tools for computing with fractions and decimals from among mental computation, estimation, calculators or computers, and paper and pencil, depending on the situation, and apply the selected methods develop and analyze algorithms for computing with fractions, decimals, and integers and develop fluency in their use Algebra Analyze change in various contexts use graphs to analyze the nature of changes in quantities in linear relationships Links to other standards. Student Prerequisites Arithmetic: Students must be able to: o multiply whole numbers. o recall some knowledge regarding multiplication of mixed numbers and decimals. o It will also prove helpful if students have the skills needed to interpret a line graph. Technological Students must be able to: o perform basic mouse manipulations such as point, click and drag aaadc5e4-58a4-46b6-a7b7-8ba9c3307b46.doc - Page 4 o use a browser such as Netscape for experimenting with the activities Teacher Preparation Students will need: Access to a browser Pencil and paper Access to a calculator (optional) Copies of supplemental materials for the activities: o Multiplying Decimals Worksheet o Multiplying Mixed Numbers Worksheet Lesson Outline 1. Focus and Review Remind students what has been learned in previous lessons that will be pertinent to this lesson and/or have them begin to think about the words and ideas of this lesson: oCan someone tell me what a decimal/mixed number is? o If I multiply the number 1 by a decimal, will the result be larger or smaller than 1? OR If I multiply 1 by a mixed number, will the result be larger or smaller than 1? o Entertain a discussion on decimals and mixed numbers, including how to multiply these types of numbers. 2. Objectives Let the students know what it is they will be doing and learning today. Say something like this: Today, class, we will be talking about multiplying decimals and o mixed numbers. o We are going to use the computers to look at the effect of multiplying a number by a decimal or mixed number, but please do not turn your computers on or go to this page until I ask you to. I want to show you a little about this program first. 3. Teacher Input aaadc5e4-58a4-46b6-a7b7-8ba9c3307b46.doc - Page 5 Explain to the students how to do the assignment. You should model or demonstrate it for the students, especially if they are not familiar with how to use the computer applets on the Project Interactivate site. o Open your browser to The Sequencer in order to demonstrate this activity to the students. o Show the class that there is a box where they may enter a starting number, in other words, the number that will be multiplied by a decimal or mixed number. o Show the class the box where they will enter the multiplier, or the number that our starting number will be multiplied by. o Explain to the class that they should enter a "0" into the add-on box as this lesson is about multiplying decimals, not adding them. Show students where to enter the zero. 4. Guided Practice o After answering all questions that the students might have regarding the use of The Sequencer, pass out the Multiplying Decimals Worksheet. o Walk the students through the worksheet, having all of the students in class use the same numbers, for example: 3 for the whole number and 0.43 for the decimal number. For each question, ask two different students what they think the answer is. Ask the students to settle any disputes on what the answers are. 5. Independent Practice o Allow students to work independently or in groups to complete the worksheet and circulate the room to offer help where necessary. o When the students are finished with the Decimal worksheet, pass out the Multiplyi ng Mixed Numbers Worksheet and have them work through it independently. 6. Closure You may wish to bring the class back together for a discussion of the findings. Allow students to describe what steps are needed and how they differ when numbers are multiplied by a decimal or a mixed number. Alternate Outlines This lesson can be rearranged in several ways. aaadc5e4-58a4-46b6-a7b7-8ba9c3307b46.doc - Page 6 You may choose to allow students to work in cooperative groups to make predictions about the effects of multiplying two particular number together and then check them as a class. You may invent your own way of using this lesson to suit the needs of your students. Suggested Follow-Ups or Extensions This lesson can be followed by: Fraction Facts: A lesson which introduces students to fractions and explores basic mathematical operations with fractions, comparing fractions, and converting fractions into decimals or percents. Ideas that Lead To Probability: which is an introduction to concepts about probability. Assessments: Pre-Assessment: This worksheet could be used as a pre- assessment activity: Multiplying Decimals Worksheet Please answer the following questions, showing your work where appropriate. Good luck! 1. Choose a whole number to be your starting number: _______________ 2. Choose a decimal to multiply the number in #1 by: _______________ 3. Will the product (multiplication) of the numbers you chose be larger or smaller than the starting number? _______________ 4. What is the product when the two are multiplied? _______________ What is the difference between this product and the starting number?_______________ Please show your work. 5. What will happen if you multiply the result in #4 by the decimal you chose in #2? Will the result be larger or smaller than the starting aaadc5e4-58a4-46b6-a7b7-8ba9c3307b46.doc - Page 7 number? than the result in #4? Please explain and show work that supports your conjecture: 6. What is the ratio of the starting number and the result in #4? _______________ What is the ratio of the result in #4 and the result in #5? _______________ How do the two ratios compare? Please show your work: 7. If you continue to multiply each result by the decimal that you chose in #2, what will happen over time? 8. Enter your starting number and multiplier into the computer program. Look at the numbers that were generated. Were your predictions correct? If not, what was different about the result? 9. Try this again with another starting number. Perhaps you would like to try a starting number that is a decimal? What results might that give you? Can you come up with a starting number and a multiplier that give interesting or unexpected results? Post-Assessment: Using different values for the starting numbers, etc., the worksheet can now be utilized as a final assessment. Multiplying Mixed Numbers Worksheet Please answer the following questions, showing your work where appropriate. Good luck! 1. Choose a whole number to be your starting number: _______________ aaadc5e4-58a4-46b6-a7b7-8ba9c3307b46.doc - Page 8 2. Choose a mixed number to multiply the number in #1 by: _______________ 3. Will the product (multiplication) of the numbers you chose be larger or smaller than the starting number? _______________ 4. What is the product when the two are multiplied? _______________ What is the difference between this product and the starting number?_______________ Please show your work. 5. What will happen if you multiply the result in #4 by the mixed number you chose in #2? Will the result be larger or smaller than the starting number? than the result in #4? Please explain and show work that supports your conjecture: 6. What is the ratio of the starting number and the result in #4? _______________ What is the ratio of the result in #4 and the result in #5? _______________ How do the two ratios compare? Please show your work: 7. If you continue to multiply each result by the mixed number that you chose in #2, what will happen over time? 8. Enter your starting number and multiplier into the computer program. Look at the numbers that were generated. Were your predictions correct? If not, what was different about the result? 9. Try this again with another starting number. Perhaps you would like to try a starting number that is also a mixed number? What results might that give you? Can you come up with a starting number and a multiplier that give interesting or unexpected results? aaadc5e4-58a4-46b6-a7b7-8ba9c3307b46.doc - Page 9 Technology (hardware/software): Individual computers for each student, put students in groups of 2 to 3 to a computer, or use teacher computer to work through the activity as a class. Key Vocabulary: fractions percents decimals mixed numbers multiplier inverse relationships square a number square root of a number estimation Application Beyond School: Students will utilize these skills in both higher level mathematics and in real world applications in their personal and professional lives. Teacher Reflection and Notes: aaadc5e4-58a4-46b6-a7b7-8ba9c3307b46.doc - Page 10