Day 46: Fraction & Decimal Conversion

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?

6.NS.6c Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.

The Learning Objective: Convert numbers fluently from fractions to decimals and decimals to fractions.

Quote of the Day: “Perseverance doesn’t really come into play until you are tired. When you’re fresh, excited, and energetic, you approach a task with vigor. Work is fun. Only when you become tired do you need perseverance.” - John Maxwell

Agenda:

1. Review the Fractions Test
2. My favorite no converting fractions to decimals
3. Place value review
4. Fraction & Decimal Conversion Packet

Here a student somehow figured that 3/8 is equivalent to 2 and 2/8. We were trying to convert to a decimal and we ended up with not only a fraction, but a mixed fraction. It's hard to criticize though as this was something the student admitted he had no clue. I'm happy the student tried - at least they were curious in going over it. 

In this instance, a student recognizes the need to divide, but makes the most common mistake of making the 8 a dividend and the 3 a divisor. I told students that a fraction is part of a whole - the key word being part. It's less than one. 

The student did everything right and to celebrate he slid the decimal, and suddenly it all became wrong. 

This will not be the last time I see this. 

Or this...

The Assessment: After I did My Favorite No, I handed back the index cards to students and asked them again to try a problem. They were much more successful the second time - although as a couple pictures below indicate they were not all set by any means.

Homework: None

My Glass Half-Full Take: I like the amount of times I asked students whether or not a fraction which was being converted to a decimal was going to be greater than or less than one. I think this is the biggest obstacle for students in converting fractions to decimals - the decision of what number is the divisor and which is the dividend. If students have a strong understanding of what a proper and improper fraction is though, it is not an issue. I also used "the trick" of put the numerator in the house because it is getting rained on, but I am increasingly trying to show students why mathematically because a trick will only take them so far.

One Thing to Do Differently: I spent almost a full block going over the quiz. I wonder how much learning took place in that time. Sure I gave students a self-assessment checklist but that would take a responsible student a minute to complete. I wonder if I could have given students similar problems instead of just going over the test exclusively. I think that would have made the students take ownership of what we were reviewing and increased the overall focus of the class.

Link of the Day: Granted time is needed to get the best out of this site from the Arizona Department of Education, but the standards are unpacked really well here for middle school mathematics from what I saw taking a quick glance. The site is unique because it offers deeper examples than the way that the common core standards are presented.