Fourth Grade Math- Fractions: Redistributing and Comparing

In fourth grade, we wrapped up our sub sandwich investigation.  In our final exploration, we discussed that the only fair way to share all the sandwiches was to share the 17 sandwiches among the 22 students, giving each student 17/22 of a sandwich.  Since it would be really hard to cut each sandwich into 22 pieces, we explored landmarks. If we only wanted to make one cut, would 17/22 be closest to ½, 2/3 or ¾?  Below is some student work that displays their thinking.  It was great to see so many students using number lines and think about what halves, thirds, and fourths would be in relation to 22nds.

We have also been looking at equivalence a little more formally.  We have used pictures, number lines, and using multiplication to create equivalent fractions.  I have been  impressed with the students’ developing reasoning skills.  Today we looked at comparing ⅖ and ⅜.  I chose these fractions since they are so close together and are difficult to reason about.  However, many students were able to reason through it!  They all realized both fractions were less than a half.  They also could say that ⅜ was ⅛ away from a half and ⅖ is a half of a fifth away.  However, which is smaller distance?  An eight or a half of a fifth?  Using what they know about equivalence, some students were able to say that half of a fifth is equivalent to a tenth.  Since 1/10 is less than ⅛, ⅖ is closer to ½ and therefore greater.   We then went on to explore how we could find common denominators if we weren’t comfortable reasoning through such close fractions.  In doing so, we found that the two fractions are only 1/40 apart!