5 th Grade Shenandoah Kolbe Maxine Weiss Ana Sanchez Heather Tinker Amy Horn Dan Scurlock

1. 5th Grade Shenandoah Kolbe Maxine Weiss Ana Sanchez Heather Tinker Amy Horn Dan Scurlock

2. Vocabulary frac·tion ˈfrakSHən/ noun noun: fraction; plural noun: fractions; noun: Fraction; noun: the Fraction 1. a numerical quantity that is not a whole number (e.g., 1/2, 0.5).

4. Importance of Math Vocabulary • The language of mathematics uses three linguistic tools that are each a form of text: • words • symbols • diagrams • ELA is needed in addition to symbols and diagrams. • Language in mathematics is important because it is necessary for: • communication • mathematics reasoning • Precision • Words are not just for story problems; math uses words with specific applications that have very different meanings in other settings (odd, even, radical, obtuse, circle, rational). • Words, symbols, and diagrams must map onto each other. www.doe.virginia.gov

5. Word Walls

6. Concept Mapping

7. Interactive Math Journals

12. ADDING AND SUBTRACTING FRACTIONS - 5.NF.A.1 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. 

13. Misconceptions-5.NF.1 & 2 • Students often mix models when adding, subtracting, or comparing fractions • Students tend to want to add the denominators

14. ADDING AND SUBTRACTING FRACTIONS - 5.NF.A.2 Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. 

15. INTERPRETING FRACTIONS AS AN IMPLIED DIVISION – 5.NF.3 Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). 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. 

16. MULTIPLYING FRACTIONS 5.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. a. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently as the result of a sequence of operations a × q ÷ b.  b. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.

17. MULTIPLYING FRACTIONS 5.NF.5 Interpret multiplication as scaling (resizing), by: a. Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. b. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1.

18. MULTIPLYING FRACTIONS 5.NF.6 Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

19. DIVIDING WITH FRACTIONS 5.NF.7 Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. a. Interpret division of a unit fraction by a non- zero whole number and compute such quotients.  b. Interpret division of a whole number by a unit fraction, and compute such quotients.  c. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem.

20. Misconceptions-5.NF.3-7 • Students may believe that multiplication results in a larger number and that division always results in a smaller number

21. Larry has ½ of a fruit bar and wants to give half of it to his brother. How much of the whole fruit bar will Larry give to his brother?This problem can be solved by thinking of ½ of ½.http://www.learner.org/courses/learningmath/number/session9/part_a/try.html

22. Ava has ½ of a pizza. She eats 2/3 of the pizza she has. How much of the whole pizza did she eat?To solve this problem, think of 2/3 times ½.http://www.learner.org/courses/learningmath/number/session9/part_a/try.html

23. Assessing Fraction Knowledge One informal assessment on: CCSS.Math.Content.5.NF.A.1 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. CCSS.Math.Content.5.MD.B.2 Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). The outcome about five different levels on the learning trajectory.

24. 4,3,2,1 based on:1. Understanding the problem2.Strategies3. Accuracy

25. Self Assessmentchecklistbased on Polya’s problem solving method

26. 1. The student was able to partition the number line into eighths, but do not consider the range of the data or plot the data.2. The student added up all the data, regardless of the denominator.3. The student attempted a fraction bar strategy, but failed to realize that the 2 15/52 would not match.

27. 1. The student was able to partition the number line and included equivalent fractions, but failed to plot the data.2. The student may have the misconception that ¼ is smaller than 1/8. 3. The student was able to compare the most frequent term with mode. 4. The student was able to combine fractions with like denominators, but then added different denominators across.

28. 1. The student partition the number line according to the range of the data, failed to attend to precision 2. Evidence is clear that the student was able to convert all fractions to eighths and was able to recognize the improper fractions and simplified

29. 1. There is evidence of partitioning of eighths with equivalent fractions, and some of the data is plotted correctly.2. There may be vocabulary issues with least and most frequent3. The student was able to add unlike denominators4. Evidence of algorithm strategy with multiples and concept of wholes5. Teacher guided to review final answer since there was an improper fraction

30. 1. The student was able to create a line plot, with a minor precision issue with labeling2. The student used mental strategies to create whole numbers

31. Fraction Checklist

32. Resources • EngageNewYork.org • O'Malley, . (n.d.). Authentic Assessment for English Language Learners. N.p.: Addison-Wesley. • Howard County (No URL, search) • http://www.learner.org/courses/learningmath/number/session9/part_a/try.html