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Fractions 5.NF Essential Questions: Essential Understanding: 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? 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: Assessment 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 width Summative: 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. Guiding 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? Formative: We will be using a skills checklist as we progress through the lessons of this unit. Lesson Math Concept Standard Skills Problems to Pose Anticipated Errors 1 Part to whole and decomposing fractions Benchmark fractions 5.NF.A2 Represent a fraction Decompose a fraction, add/subtract with like denominators, use benchmark fractions Closer to 0, ½, or whole Break down 4/6 into sixths 1/3+2/3=? 4 2/3- 3/3 Vocabulary difficulties Benchmark fractions used incorrectly Numerator vs. denominator roles 2 Equivalent fractions 5.NF.A1 Identify and create equivalent fractions Use several strategies and justify answers ½ is equivalent to ? Show why 2/3 is equivalent to ? Using a model Not multiplying the numerator and denominator by the same amount Calculation errors 3 Comparing fractions with like and unlike denominators 5.NF.A1 5.NF.A2 Use benchmark fractions correctly Find common multiples and create equivalent fractions Greater than less than with fractions, sequenced from like to unlike denominators Order fractions Incorrect multiples, not 4 Adding fractions with unlike denominators 5.NF.A.1 Finding common denominators Adding fractions 2/3+1/2 with numbers getting more difficult Adding the denominator Incorrect common denominators 5 Subtracting fractions with unlike denominators 5.NF.A.1 Finding common denominators Subtracting fractions 2/3-1/2 with numbers getting more difficult Subtracting the denominator Incorrect common denominators 6 Add/subtract fractions with mixed numbers and whole numbers 5.NF.A.1 Converting mixed numbers and adding and subtracting fractions 6-2/3 3 ½ +3/4 Converting mixed numbers improperly Calculation errors Forgetting the whole numbers 7 Solve word problems add/subtract fractions with unlike denominators 5.NF.A.2 Interpret problem, find correct number sentence, justify reasonableness of answer Incorrect equations to be fixed Word problems Not understanding what the fractions refer to, incorrect number sentences ordering correctly because of trouble finding common denominators Lesson Math Concept Standard Skills Problems to Pose Anticipated Errors 8 Multiplying fractions 5.NF.B.4 5.NF.B.5 Multiplying fractions including whole numbers and mixed numbers Using area arrays and models Scaling to check reasonableness 6x¾ 61/2 x ¾ Converting mixed numbers May try to use common denominators Representations 2 ½ x 3 1/4 9 Word problems requiring multiplication of fractions and mixed numbers 5.NF.B.6 5.NF.5 Interpret the problem to determine the correct number sentence Using models to justify reasonableness of answer Real world problems Interpreting the problem correctly Calculation errors May try to use common denominators 10 Interpret a fraction as division 5.NF.B.3 a/b=a divided by b See NCSS standards Interpreting the relationship between terms correctly. What happens with remainders? Interpreting this relationship correctly using story problems 11 Dividing fractions 5.NF.B.7-7A-7B Relationship between multiplication and division, dividing fractions Creating models 6 divided by ½ Or ½ divided by 6 Mixing up divisors and dividends Incorrect models Not understanding relationship 12 Word problems with division of fractions 5.NF.B.7C Interpreting the relationship between terms, justifying reasonableness of answers using models Story problems Interpreting the terms correctly (do not divide up the cats)