Presentation on theme: "Essential Understanding:"— Presentation transcript:
1 Essential Understanding: Fractions NFEssential Questions:How do we add or subtract with unlike denominators?How can we use visual models to solve problems using fractions?How can we use an estimation to check our answer?How are fractions related to division?How are multiplying whole numbers and multiplying fractions related?Does size of fractions matter? How does the thinking about resizing a number help to interpret possible products for a multiplication problem?How can you write a number sentence for a word problem and how can you determine the reasonable answers involving fractions?How does the context of a problem relate to the models or equations?Essential Understanding:Students will apply their understanding of fractions and fraction models to represent the addition and subtraction of fractions with unlike denominators as equivalent calculations with like denominators. They develop fluency in calculating sums and differences of fractions, and make reasonable estimates of them. Students also use the meaning of fractions, of multiplication and division, and relationship between them to understand and explain why the procedures for multiplying and dividing fractions make sense.(Limited to the case of dividing unit fractions by whole numbers and whole numbers by unit fractions.Vocabulary:fraction, equivalent, addition, sum, subtract, difference, unlike denominator, numerator, benchmark fraction, estimate, reasonableness, mixed numbers, denominator, common denominator, multiple, factor, fraction models-area, tape, number line, etc., partition, product, quotient, array, square unit, unit fraction, resizing, scaling, improper and proper fractions, length and widthGuiding questions:How do you find quick common denominators?What strategies do you use to find the common denominator and/or simplest form?Why is it important to have more than one method for finding equivalent fractions?How is adding with unlike denominators different from adding with like denominators?Why do we use number models to represent problems?Which representation of fraction multiplication helps you most? Why?How could it help you to know different methods for solving the same problems?How do visual models help you in math?AssessmentSummative: Assessment for each of the four operations with fractions (x,/,+,-) will consist of procedural problems along with real world problems that will require students to use their knowledge of fractional relationships to be solved. Answers will require justification using representations and explanations.Formative:We will be using a skills checklist as we progress through the lessons of this unit.
2 Lesson Math Concept Standard Skills Problems to Pose Anticipated Errors1Part to wholeand decomposing fractionsBenchmark fractions5.NF.A2Represent a fractionDecompose a fraction, add/subtract with like denominators, use benchmark fractionsCloser to 0, ½, or wholeBreak down 4/6 into sixths1/3+2/3=?4 2/3- 3/3Vocabulary difficultiesBenchmark fractions used incorrectlyNumerator vs. denominator roles2Equivalent fractions5.NF.A1Identify and create equivalent fractionsUse several strategies and justify answers½ is equivalent to ?Show why 2/3 is equivalent to ? Using a modelNot multiplying the numerator and denominator by the same amountCalculation errors3Comparing fractions with like and unlike denominatorsUse benchmark fractions correctlyFind common multiples and create equivalent fractionsGreater than less than with fractions, sequenced from like to unlike denominatorsOrder fractionsIncorrect multiples, not ordering correctly because of trouble finding common denominators4Adding fractions with unlike denominators5.NF.A.1Finding common denominatorsAdding fractions2/3+1/2 with numbers getting more difficultAdding the denominatorIncorrect common denominators5Subtracting fractions with unlike denominatorsSubtracting fractions2/3-1/2 with numbers getting more difficultSubtracting the denominator6Add/subtract fractions with mixed numbers and whole numbersConverting mixed numbers and adding and subtracting fractions6-2/33 ½ +3/4Converting mixed numbers improperlyForgetting the whole numbers7Solve word problems add/subtract fractions with unlike denominators5.NF.A.2Interpret problem, find correct number sentence, justify reasonableness of answerIncorrect equations to be fixedWord problemsNot understanding what the fractions refer to, incorrect number sentences
3 Lesson Math Concept Standard Skills Problems to Pose Anticipated Errors8Multiplying fractions5.NF.B.45.NF.B.5Multiplying fractions including whole numbers and mixed numbersUsing area arrays and modelsScaling to check reasonableness6 x ¾61/2 x ¾2 ½ x 3 1/4Converting mixed numbersMay try to use common denominatorsRepresentations9Word problems requiring multiplication of fractions and mixed numbers5.NF.B.65.NF.5Interpret the problem to determine the correct number sentenceUsing models to justify reasonableness of answerReal world problemsInterpreting the problem correctlyCalculation errors10Interpret a fraction as division5.NF.B.3a/b=a divided by bInterpreting this relationship correctly using story problemsSee NCSS standardsInterpreting the relationship between terms correctly. What happens with remainders?11Dividing fractions5.NF.B.7-7A-7BRelationship between multiplication and division, dividing fractionsCreating models6 divided by ½Or½ divided by 6Mixing up divisors and dividendsIncorrect modelsNot understanding relationship12Word problems with division of fractions5.NF.B.7CInterpreting the relationship between terms, justifying reasonableness of answers using modelsStory problemsInterpreting the terms correctly (do not divide up the cats)