ࡱ> g IbjbjVV <r<r<A:::::NNNN,NdARFp> @@@@@@@$ChF A:@"::A{{{::@{@{{6:-=&i;@4A0dA;F|F8-=-=PF:}={@@ ^dAF : Understanding by Design Unit Template Title of UnitDecimalsGrade LevelGrade 6Curriculum AreaNumberTime Frame6 weeksDeveloped BySchoolIdentify Desired Results (Stage 1)Content Standards Curricular OutcomesN6.1-Demonstrate understanding of place value for numbers greater than one million and less than one thousandth with and without technology. N6.4-Extend understanding of multiplication and division to decimals (1-digit whole number multipliers and 1-digit natural number divisors). Essential QuestionsEnduring UnderstandingsOpen-ended questions that stimulate thought and inquiry linked to the content of the enduring understanding.What do you want students to understand & be able to use several years from now?-How does a decimal point affect the value of a number? -How and when is estimating with decimals relevant in real life? When is an exact value important? -How are decimals important to the way society shares money? -Digits to the right of a decimal point represent numbers less than one whole. Digits to the left of a decimal point represent numbers equal to or greater than one whole. -The value of a digit is defined by its placement within the number. -An estimate is not the exact answer. -Both estimation and exact answers are useful at different times when solving problems with decimal products and quotients. Misconceptions(Optional)-Unlike their whole number counterparts a longer decimal number does not necessarily mean that it is also the larger number. A long decimal number can be smaller in value than a short decimal number (ie. 0.22222222 > 0.9). -That multiplication/division of a decimal number that is less than 1 by a whole number should result in a smaller/larger number than the original whole number. (ie. 0.5 x 2 =1; the answer 1 is a number that is less than 2-the original whole number) -Students are often scared of decimal questions have them multiply and divide the number without the decimal first. (ie. Calculate 0.000041/6 by dividing 41/6 first then look at the question and the answer will have the same number of decimal places as the number of decimal places in the question.Knowledge Students will knowSkills Students will be able to-Explain how the repetitive pattern of the place value system (ones, tens, hundreds) helps us to read and write numbers with and without decimals -How to multiply and divide decimals with and without technology. -Where to place the decimal in the solution of a multiplication and division statements. -What happens when we multiply or divide a decimal number by a whole number. -Estimate products and quotients involving decimals.-Estimate and solve real-life situational questions involving operations on quantities larger than one million or smaller than one thousandth. -Determine whether an estimation or and exact value is required given a particular situation. -There are many situations which require the multiplication and division of decimals.Assessment Evidence (Stage 2)Performance Task Description The performance task describes the learning activity in story form. Typically, the P.T. describes a scenario or situation that requires students to apply knowledge and skills to demonstrate their understanding in a real life situation. Describe your performance task scenario below:Helpful tips for writing a performance task.PART ONE: GOAL Calculate profits using decimals to raise money for the year-end class trip. ROAL You are the class president and you need to return a sufficient profit for your trip. AUDIENCE Your class, teacher and your parents SITUATION - Your job is to plan and implement a pizza-sale fundraiser PRODUCT/PERFORMANCE - Determine the COST per piece of each kind of pizza and per each kind of drink that you will sell. You will need to keep at least four decimal places to reduce round-off error. -Determine how much more to charge for a piece of pizza and each drink then calculate the PROFIT from the sale of one piece of pizza and from the sale of one drink. ESTIMATE the total profit from the sale of 150 pieces of pizza and 100 drinks. -Collect the orders from each grade and calculate the number of pieces of pizza ordered and the number of drinks ordered per class. ESTIMATE and then CACLULATE the PROFIT for each class. Additionally, calculate the TOTAL number of pieces of pizza and drinks sold and the TOTAL PROFIT for the TOTAL order. Calculate the total number of each kind of pizza that would need to be ordered and the total number of each kind of drink that would need to be ordered. Finally, calculate the Total Gross Income and Total Gross Expenses, Total Net Profit and the Net Profit for the sale and then the amount of Net Profit for each student in the class. PART TWO: -You won the lottery!! 50 million dollars!!! You have decided to treat as many people as possible to an ice cream cone at McDonalds. How many people would be able to get a cone if the cones cost $1.39 each? PERFORMACE ASSESSMENT RUBRIC See Unit Rubric Below. Goal: What should students accomplish by completing this task?Role: What role (perspective) will your students be taking?Audience: Who is the relevant audience?Situation: The context or challenge provided to the student.Product/Performance: What product/performance will the student create?Standards (Create the rubric for the Performance Task)BLOOMS TAXONOMY: REMEMBERING: Can the students recall or remember the information? UNDERSTANDING: Can the students explain ideas or concepts? APPLYING: Can the students use the information in a new way? ANALYZING: Can the students distinguish between the different parts? EVALUATING: Can the students justify a stand or decision? CREATING: Can the students create new product or point of view?Digital Taxonomy for Bloom: KNOWLEDGE: Highlighting, bookmarking, social networking, searching, googling COMPREHENSION: Advanced searches, blog journaling, twittering, commenting APPLICATION: Running, loading, playing, operating, hacking, uploading, sharing, editing ANALYSIS: Mashing, linking, tagging, validating, cracking, reverse-engineering SYNTHESIS: Programming, filming, animating, blogging, wiki-ing, publishing, podcasting, video casting EVALUATION: Blog commenting, reviewing, posting, moderating, collaborating, networking, posting moderatingStandards Rubric The standards rubric should identify how student understanding will be measured. Please attach rubric to unit plan. UNIT RUBRIC - DECIMALS EXCELLENT 4 ACHIEVING 3 BEGINNING TO ACHIEVE 2 NOT YET ACHIEVING 1 N 6.1 DIVIDES decimals (divisors from 1-9) Divides decimals accurately AND successfully selects and uses appropriate strategies to solve problems in a variety of contexts involving decimals. Divides decimals accurately BUT requires occasional assistance to successfully select and use appropriate strategies to solve problems in a variety of contexts involving decimals. Divides decimals with partial accuracy but makes frequent errors or omissions. Requires frequent assistance to divide decimals. N 6.1 MULTIPLIES decimals (multipliers from 1-9) Multiplies decimals accurately AND successfully selects and uses appropriate strategies to solve problems in a variety of contexts involving decimals. Multiplies decimals accurately BUT requires occasional assistance to successfully select and use appropriate strategies to solve problems in a variety of contexts involving decimals. Multiplies decimals with partial accuracy but makes frequent errors or omissions. Requires frequent assistance to multiply decimals. N 6.4 Understands place value of numbers greater than one million In various contexts; appropriately demonstrates and explains place value. Appropriately demonstrates and explains place value. Partially able to demonstrate and explain place value. Requires some assistance. May be unable to demonstrate or explain place value. Requires frequent assistance. N 6.4 Understands place value of numbers less than one thousandth In various contexts; appropriately demonstrates and explains place value. Appropriately demonstrates and explains place value. Partially able to demonstrate and explain place value. Requires some assistance. May be unable to demonstrate or explain place value. Requires frequent assistance. Other Assessment Evidence: (Formative and summative assessments used throughout the unit to arrive at the outcomes.)ConversationObservationProductCHECKLIST ACNECDOTAL RECORD Hand-In Assignments Sub-Unit Quiz Mulitplying Decimals Sub-Unit Quiz Dividing Decimals Final Unit QuizLearning Plan (Stage 3)Where are your students headed? Where have they been? How will you make sure the students know where they are going?UNIT RUBRIC DECIMALS PERFORMANCE TASK FUNDRAISER AND LOTTERYHow will you hook students at the beginning of the unit? (motivational set)BRAIN-POP VIDEO CLIP:  HYPERLINK "http://www.brainpop.com/math/numbersandoperations/decimals/" http://www.brainpop.com/math/numbersandoperations/decimals/ With rulers: measure the length, width, and depth of their textbook so that we can make new covers for them. Is it accurate enough to just use whole numbers to provide these measurements? What about detemining the length of 5 different mosquito?What events will help students experience and explore the enduring understandings and essential questions in the unit? How will you equip them with needed skills and knowledge? How will you organize and sequence the learning activities to optimize the engagement and achievement of all students?RESOURCE: Math Makes Sense 6 Student Text LESSON 1: Use a place value chart to investigate numbers with decimal places beyond thousandths. (N6.1) -Provide students with a place value chart (Sample for SMART Notebook at HYPERLINK "C:\\Documents and Settings\\ldryka\\Local Settings\\Temporary Internet Files\\Content.Outlook\\B56XMUW5\\Place Value Chart.notebook"H:/Math 6/UNIT 3/Place Value Chart and an Excel spreadsheet at HYPERLINK "C:\\Documents and Settings\\ldryka\\Local Settings\\Temporary Internet Files\\Content.Outlook\\B56XMUW5\\Place Values Spreadsheet.xls"H:/Math 6/UNIT 3/Place Value Spreadsheet). Work through several examples include numbers with zeroes like 0050 and 5.007800000. Compare numbers to determine which is larger? Compare numbers like 0.005 and 0.0050000000. Talk about why we dont need zeroes to the left of a number nor to the right of a decimal number). -Extra Practice SMART Notebook Ordering Decimals Practice -Read Text Pages 88-90. Assign Page 90: Practice LESSON 2: Estimate products and quotients with decimals. (N6.4) -Review estimation and that we need to be able to round-off numbers to estimate. -Read Text Pages 92-93. Assign Page 94: Practice LESSON 3: Multiply decimals (greater than 1) by a whole number (1-9). (N6.4) -Review multiplication of whole numbers by a whole number (1-9). -Read Page 95-96. Assign Page 97: Practice. -Correct answers to number 1 by using a calculator and comparing the real answer to the estimate. LESSON 4: Multiply decimals (less than 1) by a whole number (1-9). (N6.4) -Read Page 99. Handout Easy Multiplication Statements Chart - Complete and note how to answer these types of questions simply in our head. Available on the Excel spreadsheet identified in Lesson 1 above. Use the link above to access the spreadsheet. -Read Page 100-101. Assign Page 101: Practice. HYPERLINK "C:\\Documents and Settings\\ldryka\\Local Settings\\Temporary Internet Files\\Content.Outlook\\B56XMUW5\\Page 101.notebook"Answer Key SMART Notebook -Investigate Handout (Available on the Excel spreadsheet identified in Lesson 1 above. A quicksheet with 10 multiplication questions leading to the discovery that when you multiply a whole number by a decimal less-than-one the answer is smaller than the whole number. Ex. 2 x 0.001 = 0.002 (the answer, 0.002 is smaller than the whole number, 2). LESSON 5: Dividing decimals (greater than 1) by a whole number (1-9). (N6.4) -Review division of whole numbers by a whole number (1-9). -Show the long method and practice 3 examples. Show the short method ONLY for those who find math easy. Pick your favorite method to complete an additional 2 examples. -Extend your examples to include decimals and note that the number of decimal places in the question is the same as the number of decimals in the answer. --Read Page 103 and 105. Assign Page 106: Practice. Question #1 do not use Base 10 blocks, just divide on paper using either the long or short method as above. HYPERLINK "C:\\Documents and Settings\\ldryka\\Local Settings\\Temporary Internet Files\\Content.Outlook\\B56XMUW5\\Page 106.notebook"Answer Key SMART Notebook LESSON 6: Write zeroes in the dividend to get an exact or approximate quotient. (N6.4) -Read Page 109 and 110. -Sample and review long division. Introduce adding zeroes to divide decimals on the SMART Notebook: HYPERLINK "C:\\Documents and Settings\\ldryka\\Local Settings\\Temporary Internet Files\\Content.Outlook\\B56XMUW5\\Long Division Its Scary.notebook"H:\Math 6/UNIT 3/Long Division Its Scary -Assign Page 111: Practice LESSON 7: Dividing decimals (less than 1) by a whole number (1-9). (N6.4) -Read Page 112. -Investigate Handout Decimals - Available on the Excel spreadsheet identified in Lesson 1 above. Use the link above to access the spreadsheet. A quicksheet with 10 division questions leading to the discovery that when you divide a decimal less-than-one by a whole number the answer has the same number of decimal places as the question and that the answer is smaller than both the whole number and the decimal in the question. Ex. 0.001 2 = 0.0005 (the answer, 0.0005 has 4 decimal places and we used 0.0010 to divide which also has 4 decimal places and also the answer, 0.0005 is smaller than both the whole number, 2 and the decimal 0.001). -Read Page 113. Assign Page 114: Practice. LESSON 8: Strategies for Solving Problems (N6.1) -Read Page 116. Assign Page 117: Practice UNIT REVIEW: Assign Page 118 PERFORMANCE TASK Assign Page 120-121 FINAL TEST Time Frame 90 minutes 90 minutes 90 minutes 90 minutes 90 minutes 90 minutes 90 minutes 90 minutes 45 minutes 90 minutes 45 minutes (20 classes)How will you cause students to reflect and rethink? How will you guide them in rehearsing, revising, and refining their work based on your essential questions and enduring understandings? Questioning to disprove inaccurate assumptions regarding decimals. How will you help students to exhibit and self-evaluate their growing skills, knowledge, and understanding throughout the unit?Attach the rubric at the end of the FINAL TEST for them to self-evaluate themselves. How will you tailor and otherwise personalize the learning plan to optimize the engagement and effectiveness of ALL students, without compromising the goals of the unit? What resources will you use in the learning experiences to meet the outcomes?Math Makes Sense 6 Student Textbook Calculator Click on the links to access the documents identified in the Learning Plan above.Assess and Reflect (Stage 4)Required Areas of Study: Is there alignment between outcomes, performance assessment and learning experiences?BALs: Does my unit promote life long learning, encourage the development of self and community, and engage students?CELS & CCCs: Do the learning experiences allow learners to use multiple literacies while constructing knowledge, demonstrating social responsibility, and acting autonomously in their world?Adaptive Dimension: Have I made purposeful adjustments to the curriculum content (not outcomes), instructional practices, and/or the learning environment to meet the learning needs of all my students?Instructional Approaches: Do I use a variety of teacher directed and student centered instructional approaches?Student Evaluation: Have I included formative and summative assessments reflective of student needs and interests based on curricular outcomes?Resource Based Learning: Do the students have access to various resources on an ongoing basis?FNM/I Content and Perspectives/Gender Equity/Multicultural Education: Have I nurtured and promoted diversity while honoring each childs identity? Blueprint for Life: Have I planned learning experiences in the unit that prepare students for a balanced life and/or work career?Adapted from: Wiggins, Grant and J. McTighe. (1998). 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