Day 49: Unlike Denominators & Borrowing

6th Grade Math Standards: 3.NF.3 Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. a. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. b. Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3. Explain why the fractions are equivalent, e.g., by using a visual fraction model. c. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram. d. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

4.NF.2 Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model

5.NF.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. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12 . (In general, a/b + c/d = (ad + bc) /bd.)

Objective: Add fractions with like and unlike denominators; Find the difference in a mixed number problem such that the fractional part of the number being subtracted by is smaller than the fractional part that is subtracting from the bigger number

Agenda:

1. Open Middle Equivalent Fractions 
2. Quote, Star Student, Question
3. Study Guide in Partners
4. Review of Study Guide
5. 5 Minutes of Pepper
6. Independent Study Guide

Assessment: I was circumventing the room throughout the study guide. As students struggled with borrowing, I would continue to provide them with borrowing types of questions until they had successfully met the objective.

Glass Half-Full: For being a 4th grade open middle question, the warm up problem definitely made us sweat. That being said, all of my students were able to access the problem and try it. They just did not immediately come to a conclusion about its solution. In one class, a few of the students that did answer it were students that have had their share of struggles in math this year. Meanwhile students that are typically asking to be challenged or need to be challenged were still working it out. It was kind of a nice self-esteem boost for these students.

Regrets: Not having computer access hurt this lesson a little. If students could check their answer themselves or at least plug their answers into a computer in which I could oversee everything it would have been more efficient for giving feedback.

Link: I think Twitter makes sense too.