Day 43: Division of Fractions Practice

6th Grade Math Standards: 6.NS.1 Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc .) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?

The Learning Objective: Divide fractions to find a quotient

Quote of the Day: "Born into poverty, Lincoln was faced with defeat throughout his life. He lost eight elections, twice failed in business and suffered a nervous breakdown. He could have quit many times - but he didn't and because he didn't quit, he became one of the greatest presidents in the history of our country.

Here is a sketch of Lincoln's road to the White House:

• 1816 His family was forced out of their home. He had to work to support them
• 1818 His mother died.
• 1831 Failed in business.
• 1832 Ran for state legislature - lost.
• l832 Also lost his job - wanted to go to law school but couldn't get in.
• 1833 Borrowed some money from a friend to begin a business and by the end of the year he was bankrupt. He spent the next 17 years of his life paying off this debt.
• 1834 Ran for state legislature again - won.
• 1835 Was engaged to be married, sweetheart died and his heart was broken.
• 1836 Had a total nervous breakdown and was in bed for six months.
• 1838 Sought to become speaker of the state legislature - defeated.
• 1840 Sought to become elector - defeated.
• 1843 Ran for Congress - lost.
• 1846 Ran for Congress again - this time he won - went to Washington and did a good job.
• 1848 Ran for re-election to Congress - lost.
• 1849 Sought the job of land officer in his home state - rejected.
• 1854 Ran for Senate of the United States - lost.
• 1856 Sought the Vice-Presidential nomination at his party's national convention - got less than 100 votes.
• 1858 Ran for U.S. Senate again - again he lost.
• 1860 Elected president of the United States.

Agenda:

1. Return weekly quizzes and distribute weekly quizzes as students do 4 word problems on dividing fractions
2. Review the jumpstart and make corrections to Weekly Quiz #7 
3. Do this 3-act math activity of dividing fractions with my nieces. The key point is getting students to recognize the milk needs to be divided by two
4. Distribute homework on dividing fractions and let students do it in class. Most students finished more than half of the assignment and a few students were able to finish.

The Assessment: I let two of the classes work in partners and one class I had work independently (they were too fussy when I told them what partner they were with - I have to set limits and they got the message). As they worked I would call back partners to the back of the classroom to work with me on the homework. As soon as I saw they had the concepts, I let them go back to their seats. I differentiated within this assessment. Some students I gave the basic steps (keep the first fraction the same, change division to multiplication and take the reciprocal of the second fraction) and had them go back and give the basic steps back to me in a different problem. For other students I asked them to find out if I ate 3/4 cups of ice cream and they ate 1/2 cups of ice cream how many times more cups of ice cream I ate than them. Almost all students guessed that we did 3/4 divided by 1/2 or 1/2 divided by 3/4 but it was difficult for these students to explain why it was one and not the other. We discussed how the answer should come to more than one since I ate more than they had. We also discussed using analogous numbers in lieu of the fractions that I had chosen to understand what is divided by what. For some students, they were fine with fractions divided by fractions, but were struggling with mixed numbers because they took the reciprocal too soon so we worked on that. For other students I wanted them not just to memorize a process (they were getting that already) but to understand why the answer was coming out the way it was. We discussed estimation and using common denominators as alternative strategies to make sense of problems.

In addition to this assessment, I did have students weekly quizzes graded from the prior week.

Homework: Division of fractions worksheet

My Glass Half-Full Take: I really enjoyed hearing the logic students were applying to the problem where I ran out of Bisquick. I followed up and asked them why I didn't subtract one of every ingredient (since I used one less cup of Bisquick than the recipe required). It was clear to students that we would then not use any eggs or vegetable oil. It was a great example of why equivalent ratios need to be divided or multiplied by the same number - not added or subtracted.

One Thing to Do Differently: I should have pre-warned students that the word problems were significantly more difficult than the problems that did not involve word problems. They always get more motivated by forewarning of challenges and increase focus. Two of the word problems were very difficult.

Link of the Day: Is this a future warm up problem? Almost certainly. Whinnie the Pooh stay home.