Essential 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.

Fractions 5.NF

Lesson Math Concept Standard Skills Problems to Pose

Anticipated Errors

1 Part to wholeand decomposing fractionsBenchmark fractions

5.NF.A2 Represent a fractionDecompose a fraction, add/subtract with like denominators, use benchmark fractions

Closer to 0, ½, or wholeBreak down 4/6 into sixths1/3+2/3=?4 2/3- 3/3

Vocabulary difficultiesBenchmark fractions used incorrectlyNumerator vs. denominator roles

2 Equivalent fractions 5.NF.A1 Identify and create equivalent fractionsUse 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 amountCalculation errors

3 Comparing fractions with like and unlike denominators

5.NF.A15.NF.A2

Use benchmark fractions correctlyFind common multiples and create equivalent fractions

Greater than less than with fractions, sequenced from like to unlike denominatorsOrder fractions

Incorrect multiples, not ordering correctly because of trouble finding common denominators

4 Adding fractions with unlike denominators

5.NF.A.1 Finding common denominatorsAdding fractions

2/3+1/2 with numbers getting more difficult

Adding the denominatorIncorrect common denominators

5 Subtracting fractions with unlike denominators

5.NF.A.1 Finding common denominatorsSubtracting fractions

2/3-1/2 with numbers getting more difficult

Subtracting the denominatorIncorrect common denominators

6 Add/subtract fractions with mixed numbers and whole numbers

5.NF.A.1 Converting mixed numbers and adding and subtracting fractions

6-2/33 ½ +3/4

Converting mixed numbers improperlyCalculation errorsForgetting 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 fixedWord problems

Not understanding what the fractions refer to, incorrect number sentences

Lesson Math Concept Standard Skills Problems to Pose

Anticipated Errors

8 Multiplying fractions 5.NF.B.45.NF.B.5

Multiplying fractions including whole numbers and mixed numbersUsing area arrays and models Scaling to check reasonableness

6 x ¾61/2 x ¾

2 ½ x 3 1/4

Converting mixed numbers May try to use common denominatorsRepresentations

9 Word problems requiring multiplication of fractions and mixed numbers

5.NF.B.65.NF.5

Interpret the problem to determine the correct number sentenceUsing models to justify reasonableness of answer

Real world problems Interpreting the problem correctlyCalculation errorsMay try to use common denominators

10 Interpret a fraction as division

5.NF.B.3 a/b=a divided by b

Interpreting this relationship correctly using story problems

See NCSS standards Interpreting the relationship between terms correctly. What happens with remainders?

11 Dividing fractions 5.NF.B.7-7A-7B Relationship between multiplication and division, dividing fractions Creating models

6 divided by ½Or½ divided by 6

Mixing up divisors and dividendsIncorrect modelsNot 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)