Parts, Parts, and More Parts

Hello!

Our fraction ideas are continuing to develop in fourth grade.  Last week, we looked at a context of sharing sandwiches and we were grappling with whether or not the distribution was fair.

Take a look at the posters students created:

As we were discussing our findings, some really interesting mathematical ideas emerged.  One noticing was about the relationship between division and fractions.  In the first situation in the problem, there were 3 sandwiches being divided by 4 students and we discovered that 3 divided by 4 gave us 3/4.  When we had 7 sandwiches being divided by 8 students, the result was that each student got 7/8 of a sandwich.  This phenomenon seems to keep occurring which led to a discussion about division and fractions.

Students also shared ideas of how they decided which group got the most amount of food and which got the least.  They realized that making accurate drawings to represent the situations was really hard (especially when comparing 3/4 and 4/5).  One group remedied this by using a ruler to be sure they had equal parts, but still grappled with how to break up the measurements.  Some other partnerships realized that we can decide which is the biggest by looking at the missing part.  If one student gets 7/8 of a sandwich and another gets 4/5 of the same sized sandwich, the first student is getting all but 1/8 while the second student is getting all but 1/5.  Since 1/8 is less than 1/5, the first student is missing less of a sandwich which results in getting a larger portion.

We will be continuing to use contexts to develop fraction understanding in the next few weeks.

Fifth graders have just wrapped up their decimal unit.  As we explored decimal multiplication and division, a number of big ideas emerged, such as what happens to the quotient when the divisor is less than one? What happens to the product when one of the factors is less than one?  We will revisit this idea again as we begin our fraction unit.

We also used our understandings of whole number division to help us with decimal division.  In 4th grade, students learned  that when we multiply both the dividend and divisor by the same number, we create an equivalent expression.  This is a big help when working with decimals.  We can use this understanding to create an easier problem.  If we have 5.42 divided by 0.35, we can multiply both the dividend and divisor by 100 to get 542 divided by 35, which will have the same quotient as the original problem.  This is the reason we can use the trick of moving the decimal point.

Later in the week, we will begin to explore fraction concepts though a number of context problems.