DOCSLIB.ORG

5/4- 5/8 Day 28: Fractions and Mixed Numbers As Quotients Standard: 5NF.3 Interpret a Fraction As a Division of the Numerator by the Denominator Problem

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
5/4- 5/8 Day 28: Fractions and Mixed Numbers As Quotients Standard: 5NF.3 Interpret a Fraction As a Division of the Numerator by the Denominator Problem Grade 5 Math Weeks: 5/4- 5/8 Day 28: Fractions and Mixed Numbers as Quotients Standard: 5NF.3 Interpret a fraction as a division of the numerator by the denominator problem. Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers. Objective: Students will demonstrate how a fraction or mixed number can represent the quotient of two whole numbers. Instructional learning videos to support the review objective: https://www.khanacademy.org/math/arithmetic-home/arith-review-fractions/fractions-as- division/v/fractions-division-mixed-numbers 1. Practice Worksheet: TOPIC 9-2 Guided Practice ( 2 pages to be copied) 2. Problem of the Day: (POD): Debbie has a 5 pound bag of flour. She divides the flour evenly into 3 flour jars. How much flour is in each jar? Solve 2 ways. (Hint: You may make a drawing or use the algorithm). 3. *NEW!! Fun Online Practice: Go on ST Math 30 minutes a day (access through Clever) 4. Amazing Race: Write down 10 ways you can show the number (pictures, numbers words): 1/3 Additional Support: https://www.youtube.com/watch?v=Qf_Qvi4RZxU Additional Online Resources: • EnVisions (through CLEVER) • Imagine Math Name Practice Tools Assessment Buddy * Do You Understand? Do You Know How? 10 1. How can you write 3 as a division 3. Find 11 , 10 and 10 , 11. Write expression and as a mixed number? each quotient as a fraction or mixed number. 2. MP.2 Reasoning Suppose 3 friends want to share 16 posters equally. For In 4 and 5, tell how much each this situation, why does the quotient person gets when they share 5 R1 make more sense than the equally. 1 quotient 53? 4. 2 friends share 3 apples. 5. 3 students share 5 breakfast bars. In 6–13, find each quotient. Write each answer as either a fraction or mixed number. 6. 11 , 6 7. 1 , 5 8. 18 , 4 9. 5 , 9 10. 9 , 8 11. 23 , 10 12. 12 , 17 13. 28 , 20 In 14–17, tell how much each person gets when they share equally. 14. 2 girls share 7 yards of ribbon. 15. 4 friends share 7 bagels. 16. 4 cousins share 3 pies. 17. 8 soccer players share 12 oranges. *For another example, see Set A on page 577. Topic 9 Lesson 9-2 535 18. Daniella made gift bows from 8 yards of 19. MP.6 Be Precise Tammi has 4 pounds 1 ribbon. The bows are all the same size. If of gala apples and 32 pounds of red 3 she made 16 bows, how much ribbon did delicious apples. If she uses 14 pounds she use for each one? Give the answer as of gala apples in a recipe, how many a fraction or mixed number. pounds of apples does she have left? 20. Casey bought a 100-pound bag of dog 21. Higher Order Thinking Write a word food. He gave his dogs the same amount problem that can be solved by dividing of dog food each week. The dog food 6 by 5. lasted 8 weeks. How much dog food did Casey give his dogs each week? Give the answer as a fraction or mixed number. 22. The amount of fabric needed for an adult SCARECROW and a baby scarecrow costume is shown COSTUME PATTERN at the right. The amount of fabric for an adult scarecrow costume is how many times the amount of fabric for a baby scarecrow costume? Give the answer as a fraction or mixed number. Baby: 2 yards Adult: 7 yards Common Core Assessment 23. Which is the quotient 37 , 6? 24. Lindsay divides 40 by 9. Between what 6 two whole numbers is her answer? 햠 37 햠 2 and 3 햡 61 6 햡 3 and 4 5 햢 66 햢 4 and 5 1 햣 637 햣 5 and 6 536 Topic 9 Lesson 9-2 © Pearson Education, Inc. 5 .
Load more

Recommended publications
  • Elementary Number Theory and Methods of Proof
    CHAPTER 4 ELEMENTARY NUMBER THEORY AND METHODS OF PROOF Copyright © Cengage Learning. All rights reserved. SECTION 4.4 Direct Proof and Counterexample IV: Division into Cases and the Quotient-Remainder Theorem Copyright © Cengage Learning. All rights reserved. Direct Proof and Counterexample IV: Division into Cases and the Quotient-Remainder Theorem The quotient-remainder theorem says that when any integer n is divided by any positive integer d, the result is a quotient q and a nonnegative remainder r that is smaller than d. 3 Example 1 – The Quotient-Remainder Theorem For each of the following values of n and d, find integers q and r such that and a. n = 54, d = 4 b. n = –54, d = 4 c. n = 54, d = 70 Solution: a. b. c. 4 div and mod 5 div and mod A number of computer languages have built-in functions that enable you to compute many values of q and r for the quotient-remainder theorem. These functions are called div and mod in Pascal, are called / and % in C and C++, are called / and % in Java, and are called / (or \) and mod in .NET. The functions give the values that satisfy the quotient-remainder theorem when a nonnegative integer n is divided by a positive integer d and the result is assigned to an integer variable. 6 div and mod However, they do not give the values that satisfy the quotient-remainder theorem when a negative integer n is divided by a positive integer d. 7 div and mod For instance, to compute n div d for a nonnegative integer n and a positive integer d, you just divide n by d and ignore the part of the answer to the right of the decimal point.
    [Show full text]
  • Introduction to Uncertainties (Prepared for Physics 15 and 17)
    Introduction to Uncertainties (prepared for physics 15 and 17) Average deviation. When you have repeated the same measurement several times, common sense suggests that your “best” result is the average value of the numbers. We still need to know how “good” this average value is. One measure is called the average deviation. The average deviation or “RMS deviation” of a data set is the average value of the absolute value of the differences between the individual data numbers and the average of the data set. For example if the average is 23.5cm/s, and the average deviation is 0.7cm/s, then the number can be expressed as (23.5 ± 0.7) cm/sec. Rule 0. Numerical and fractional uncertainties. The uncertainty in a quantity can be expressed in numerical or fractional forms. Thus in the above example, ± 0.7 cm/sec is a numerical uncertainty, but we could also express it as ± 2.98% , which is a fraction or %. (Remember, %’s are hundredths.) Rule 1. Addition and subtraction. If you are adding or subtracting two uncertain numbers, then the numerical uncertainty of the sum or difference is the sum of the numerical uncertainties of the two numbers. For example, if A = 3.4± .5 m and B = 6.3± .2 m, then A+B = 9.7± .7 m , and A- B = - 2.9± .7 m. Notice that the numerical uncertainty is the same in these two cases, but the fractional uncertainty is very different. Rule2. Multiplication and division. If you are multiplying or dividing two uncertain numbers, then the fractional uncertainty of the product or quotient is the sum of the fractional uncertainties of the two numbers.
    [Show full text]
  • Unit 6: Multiply & Divide Fractions Key Words to Know
    Unit 6: Multiply & Divide Fractions Learning Targets: LT 1: Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b) LT 2: Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g. by using visual fraction models or equations to represent the problem. LT 3: Apply and extend previous understanding of multiplication to multiply a fraction or whole number by a fraction. LT 4: Interpret the product (a/b) q ÷ b. LT 5: Use a visual fraction model. Conversation Starters: Key Words § How are fractions like division problems? (for to Know example: If 9 people want to shar a 50-lb *Fraction sack of rice equally by *Numerator weight, how many pounds *Denominator of rice should each *Mixed number *Improper fraction person get?) *Product § 3 pizzas at 10 slices each *Equation need to be divided by 14 *Division friends. How many pieces would each friend receive? § How can a model help us make sense of a problem? Fractions as Division Students will interpret a fraction as division of the numerator by the { denominator. } What does a fraction as division look like? How can I support this Important Steps strategy at home? - Frac&ons are another way to Practice show division. https://www.khanacademy.org/math/cc- - Fractions are equal size pieces of a fifth-grade-math/cc-5th-fractions-topic/ whole. tcc-5th-fractions-as-division/v/fractions- - The numerator becomes the as-division dividend and the denominator becomes the divisor. Quotient as a Fraction Students will solve real world problems by dividing whole numbers that have a quotient resulting in a fraction.
    [Show full text]
  • Background Document for Revisions to Fine Fraction Ratios Used for AP-42 Fugitive Dust Emission Factors
    Background Document for Revisions to Fine Fraction Ratios Used for AP-42 Fugitive Dust Emission Factors Prepared by Midwest Research Institute (Chatten Cowherd, MRI Project Leader) For Western Governors’ Association Western Regional Air Partnership (WRAP) 1515 Cleveland Place, Suite 200 Denver, Colorado 80202 Attn: Richard Halvey MRI Project No. 110397 February 1, 2006 Finalized November 1, 2006 Responses to Comments Received on Proposed AP-42 Revisions Commenter Source Comment Response and Date Category John Hayden, Unpaved NSSGA- This comment reference a test report prepared National Stone, Roads sponsored tests by Air Control Techniques for the National Sand and Gravel (report dated Oct. Stone, Sand & Gravel Association, dated Association 15, 2004) at October 4, 2004. The report gives the results of (NSSGA); June California tests to determine unpaved road emissions 14, 2006 aggregate factors for controlled (wet suppression only) producing plants haul roads at two aggregate processing plants. support the A variation of the plume profiling method using proposed fine TEOM continuous monitors with PM-2.5 and fractions. PM-10 inlets was employed. Tests with road surface moisture content below 1.5 percent were considered to be uncontrolled. Based on the example PM-10 concentration profiles presented in the report, the maximum roadside PM-10 dust concentrations in the subject study were in the range of 300 micrograms per cubic meter. This is an order of magnitude lower than the concentrations typically found in other unpaved road emission factor studies. For the range of plume concentrations measured in the NSSGA-sponsored test program, an average fine fraction (PM-2.5/PM- 10 ratio) of 0.15 was reported.
    [Show full text]
  • Solve by Rewriting the Expression in Fraction Form. After Solving, Rewrite the Complete Number Sentence in Decimal Form
    GRADE 4 | MODULE 6 | TOPIC D | LESSONS 12–14 KEY CONCEPT OVERVIEW In Lessons 12 through 14, students add decimals by converting decimal numbers to fraction form before adding and then converting the sum back to a decimal number. (See Sample Problem.) It is important to note that, in these lessons, students do NOT learn to add decimals by lining up the decimal points. You can expect to see homework that asks your child to do the following: ▪ Express tenths and hundredths as hundredths (e.g., 3 tenths + 4 hundredths = 34 hundredths). ▪ Add tenths and hundredths by converting tenths to hundredths before finding the sum. ▪ Add mixed numbers with units of ones, tenths, and hundredths. ▪ Solve word problems requiring the addition of numbers written in decimal form, converting to fraction form before solving. SAMPLE PROBLEM (From Lesson 13) Solve by rewriting the expression in fraction form. After solving, rewrite the complete number sentence in decimal form. 5.9 + 4.94 9 94 90 94 184 84 59..++=4945=++=4 =+5 +=4 ==9 = 10 10 100 100 100 100 100 5.9 + 4.94 = 10.84 Additional sample problems with detailed answer steps are found in the Eureka Math Homework Helpers books. Learn more at GreatMinds.org. For more resources, visit » Eureka.support GRADE 4 | MODULE 6 | TOPIC D | LESSONS 12–14 HOW YOU CAN HELP AT HOME ▪ Although it may be tempting to show your child how to add numbers in decimal form by lining up the decimals, it will be more helpful to support the current lesson of adding decimals by converting to fractions.
    [Show full text]
  • Fractions: Teacher's Manual
    Fractions: Teacher’s Manual A Guide to Teaching and Learning Fractions in Irish Primary Schools This manual has been designed by members of the Professional Development Service for Teachers. Its sole purpose is to enhance teaching and learning in Irish primary schools and will be mediated to practising teachers in the professional development setting. Thereafter it will be available as a free downloadable resource on www.pdst.ie for use in the classroom. This resource is strictly the intellectual property of PDST and it is not intended that it be made commercially available through publishers. All ideas, suggestions and activities remain the intellectual property of the authors (all ideas and activities that were sourced elsewhere and are not those of the authors are acknowledged throughout the manual). It is not permitted to use this manual for any purpose other than as a resource to enhance teaching and learning. Any queries related to its usage should be sent in writing to: Professional Development Service for Teachers, 14, Joyce Way, Park West Business Park, Nangor Road, Dublin 12. 2 Contents Aim of the Guide Page 4 Resources Page 4 Differentiation Page 5 Linkage Page 5 Instructional Framework Page 9 Fractions: Background Knowledge for Teachers Page 12 Fundamental Facts about Fractions Possible Pupil Misconceptions involving Fractions Teaching Notes Learning Trajectory for Fractions Page 21 Teaching and Learning Experiences Level A Page 30 Level B Page 40 Level C Page 54 Level D Page 65 Level E Page 86 Reference List Page 91 Appendices Page 92 3 Aim of the Guide The aim of this resource is to assist teachers in teaching the strand unit of Fractions (1st to 6th class).
    [Show full text]
  • Operations with Fractions, Decimals and Percent Chapter 1: Introduction to Algebra
    Section 1.8: Operations with Fractions, Decimals and Percent Chapter 1: Introduction to Algebra Multiply decimals Step 1. Determine the sign of the product. Step 2. Write in vertical format, lining up the numbers on the right. Multiply the numbers as if they were whole numbers, temporarily ignoring the decimal points. Step 3. Place the decimal point. The number of decimal places in the product is the sum of the number of decimal places in the factors. Step 4. Write the product with the appropriate sign. For Example: Section 1.8: Operations with Fractions, Decimals and Percent Chapter 1: Introduction to Algebra Multiplication by powers of 10 Section 1.8: Operations with Fractions, Decimals and Percent Chapter 1: Introduction to Algebra Divide decimals Step 1. Determine the sign of the quotient. Step 2. Make the divisor a whole number by “moving” the decimal point all the way to the right. “Move” the decimal point in the dividend the same number of places—adding zeros as needed. Step 3. Divide. Place the decimal point in the quotient above the decimal point in the dividend. Step 4. Write the quotient with the appropriate sign. Remember these terms for division: For Example: Section 1.8: Operations with Fractions, Decimals and Percent Chapter 1: Introduction to Algebra A percent is a ratio whose denominator is 100. Percent means per hundred. We use the percent symbol, %, to show percent. Since a percent is a ratio, it can easily be expressed as a fraction. Convert percent to decimal Convert decimal to percent Section 1.8: Operations with Fractions, Decimals and Percent Chapter 1: Introduction to Algebra Convert decimal to a fraction Convert fraction to a decimal • Convert the fraction to a long division problem and perform the division.
    [Show full text]
  • Division Into Cases and the Quotient-Remainder Theorem
    4.4 Direct Proof and Counterexample IV: Division into Cases and the Quotient-Remainder Theorem 4.4 Quotient-Remainder Theorem 1 / 4 1 n = 34 and d = 6. 2 n = −34 and d = 6. Examples For each of the following values of n and d, find integers q and r such that n = dq + r and 0 ≤ r < d. The Quotient-Remainder Theorem Theorem Given any integer n and positive integer d, there exist unique integers q and r such that n = dq + r and 0 ≤ r < d: 4.4 Quotient-Remainder Theorem 2 / 4 2 n = −34 and d = 6. The Quotient-Remainder Theorem Theorem Given any integer n and positive integer d, there exist unique integers q and r such that n = dq + r and 0 ≤ r < d: Examples For each of the following values of n and d, find integers q and r such that n = dq + r and 0 ≤ r < d. 1 n = 34 and d = 6. 4.4 Quotient-Remainder Theorem 2 / 4 The Quotient-Remainder Theorem Theorem Given any integer n and positive integer d, there exist unique integers q and r such that n = dq + r and 0 ≤ r < d: Examples For each of the following values of n and d, find integers q and r such that n = dq + r and 0 ≤ r < d. 1 n = 34 and d = 6. 2 n = −34 and d = 6. 4.4 Quotient-Remainder Theorem 2 / 4 1 Compute 33 div 9 and 33 mod 9 (by hand and Python). 2 Keeping in mind which years are leap years, what day of the week will be 1 year from today? 3 Suppose that m is an integer.
    [Show full text]
  • Quantile® Resource Overview
    Quantile® Resource Overview Resource Title: Finding the Least Common Denominator Quantile Skill • Compare and order fractions using renaming and Concept: strategies (QSC155) • Find multiples, common multiples, and the least common multiple numbers; explain. (QSC221) Quantile Measure: 710 Q Excerpted from: The Math Learning Center PO Box 12929, Salem, Oregon 97309-0929 www.mathlearningcenter.org ©Math Learning Center For access to other free resources, visit www.Quantiles.com. The Quantile® Framework for Mathematics, developed by educational measurement and research organization MetaMetrics®, comprises more than 500 Quantile Skills and Concepts taught from kindergarten through high school. The Quantile Framework depicts the developmental nature of mathematics and the connections between mathematics content. By matching a student's Quantile measure with the Quantile measure of a mathematical skill or concept, you can determine if the student is ready to learn that skill, needs reinforcement in supporting concepts first, or whether enrichment would be appropriate. For more information and to use free Quantile utilities, visit www.Quantiles.com. 1000 Park Forty Plaza Drive, Suite 120, Durham, North Carolina 27713 METAMETRICS®, the METAMETRICS® logo and tagline, QUANTILE®, QUANTILE FRAMEWORK® and the QUANTILE® logo are trademarks of MetaMetrics, Inc., and are registered in the United States and abroad. The names of other companies and products mentioned herein may be the trademarks of their respective owners. set a6 numbers & Operations: Fraction Concepts Blackline Use anytime after Set A6, Activity 2. Run a class set. name date set a6 H Independent Worksheet 2 independent Worksheet Finding the least Common denominator 2 4 Which is greater, 3 or 5 ? Exactly how much difference is there between these two fractions? If you want to compare, add, or subtract two fractions, it is easier if you rewrite them so they both have the same denominator.
    [Show full text]
  • Teaching Fractions for Understanding: Addressing Interrelated Concepts
    Getenet & Callingham Teaching Fractions for Understanding: Addressing Interrelated Concepts Seyum Getenet Rosemary Callingham University of Southern Queensland University of Tasmania <[email protected]> <[email protected]> The concept of fractions is perceived as one of the most difficult areas in school mathematics to learn and teach. The most frequently mentioned factors contributing to the complexity is fractions having five interrelated constructs: part-whole, ratio, operator, quotient, and measure. In this study, we used this framework to investigate the practices in a New Zealand Year 7 classroom. Video recordings and transcribed audio-recordings were analysed through the lenses of the five integrated concepts of fraction. The findings showed that students often initiated unexpected uses of fractions as quotient and as operator, drawing on part-whole understanding when solving fraction problems. Fractions are notoriously difficult for students to learn and present ongoing pedagogical challenges to mathematics teachers (e.g., Behr, Lesh, Post, & Silver, 1983; Siemon et al., 2015). They are crucial, however, to students’ future understanding of concepts such as proportional reasoning that are necessary not only for deeper mathematical understanding but also to support daily activities. These difficulties are often observed across all levels of education beginning from early primary years (e.g., Charalambous & Pitta-Pantazi, 2006; Empson & Levi, 2011; Gupta & Wilkerson, 2015). Different reasons have been identified for these difficulties, particularly in primary school. For example, fraction understanding is underpinned by larger mathematics cognitive processes including proportional reasoning and spatial reasoning (Moss & Case, 1999). In relation to having different notions of fractions, Hackenberg and Lee (2015) showed that limited understanding of particular aspects of the different meanings of fractions affects the ability of students to generalise and to work with fraction concepts.
    [Show full text]
  • Eureka Math™ Tips for Parents Module 2
    Grade 6 Eureka Math™ Tips for Parents Module 2 The chart below shows the relationships between various fractions and may be a great Key Words tool for your child throughout this module. Greatest Common Factor In this 19-lesson module, students complete The greatest common factor of two whole numbers (not both zero) is the their understanding of the four operations as they study division of whole numbers, division greatest whole number that is a by a fraction, division of decimals and factor of each number. For operations on multi-digit decimals. This example, the GCF of 24 and 36 is 12 expanded understanding serves to complete because when all of the factors of their study of the four operations with positive 24 and 36 are listed, the largest rational numbers, preparing students for factor they share is 12. understanding, locating, and ordering negative rational numbers and working with algebraic Least Common Multiple expressions. The least common multiple of two whole numbers is the least whole number greater than zero that is a What Came Before this Module: multiple of each number. For Below is an example of how a fraction bar model can be used to represent the Students added, subtracted, and example, the LCM of 4 and 6 is 12 quotient in a division problem. multiplied fractions and decimals (to because when the multiples of 4 and the hundredths place). They divided a 6 are listed, the smallest or first unit fraction by a non-zero whole multiple they share is 12. number as well as divided a whole number by a unit fraction.
    [Show full text]
  • Reflecting on Fraction Addition
    fractionReflecting on fraction addition addition: Margaret Marshman University of Sunshine Coast, QLD <[email protected]> Using the mirror formula to visualise unit fraction addition Damien Igoe Nicholas Boucher Iain Clark University of Southern Queensland Esperance Anglican Esperance Anglican <[email protected]> Community School, WA Community School, WA <[email protected]> <[email protected]> Alfio Parisi Nathan Downs University of Southern Queensland University of Southern Queensland <[email protected]> <[email protected]> This article proposes a practical method of teaching the addition of unit fractions using a series of mirror equation experiments. Introduction Mathematical knowledge and skills are crucial for success in many of today’s endeavours. Mathematical modelling prepares students to develop a working knowledge of dynamic information systems (Shahbari and Peled, 2017). Addition of unit fractions is one of the important, yet more difficult, concepts for students to master initially. Our experience is that these concepts are often taught through repetitious textbook examples, often with very little or no real-life application, making them abstract in nature. Visual and manip- ulative models of the relationships between fractions provide a crucial tool for developing student understanding (Scaptura et al. 2007; Suh et al. 2005) and obtaining proficiency with fractions (Tsai and Li, 2017). Fractions can be challenging to teach and learn (Shahbari and Peled, 2017) and their real-life relevancy is often difficult to articulate (Suh et al. 2005). Research suggests that fractions, particularly unit fractions, are more effectively understood by students when taught in an immediate context (Ganor-Stern et al.
    [Show full text]