Make Math Moments Academy › Forums › MiniCourse Reflections › The Concept Holding Your Students Back › Lesson 62: Unpacking Ratios – Discussion › Reply To: Lesson 62: Unpacking Ratios – Discussion

Multiplicative comparison: A zipper snack bag measures 6.5 in x 3.25 in and a sandwich bag measures 6 1/2 x 5 7/8 in. How much taller is the sandwich bag to the snack bag? Honestly I was at my kitchen table looking for a comparison and saw these boxes. I find it interesting that the same company wrote one set of dimensions as decimals and the other as fractions. I wondered why? What a great question to ask students as we go to actually do the comparison. Even the real world switches between fractions and decimals not just school math problems. I think I would use the fractional amounts first as it can be modeled more easily as I have seen you do with the relational rods.
Snack bag length is 3 1/4 or 13/4 or 26/8
Sandwich bag is 5 7/8 or 47/8
Sandwich bag is 47/26 times bigger than the snack bag or 1 21/26 times bigger.
Snack bag is 26/47 times smaller than the sandwich bag
Wow! I think I got there and I see multiplying by the reciprocal but this was a complex problem because of the numbers. The models that you have been doing through the lessons helped me visualize what I was doing with the algorithm. That’s a powerful testimony about why we need visual for learners.
Composed unit: A snack bag hold 3 Oreos. How many bags would I need to bag 15 Oreos?
This seems so much easier if 1 snack bag holds 3 Oreos, 2 snack bags hold 6 Oreos, and I can jump in thinking that 5 snack bags hold 15 Oreos.
So I didn’t get this from a textbook. Am I on the right track? This real world problem seemed great and interesting until it got way complex. However, I could see my students engaging like I did, after a moment of wanting to give up. But I could see some students dealing out because we haven’t done enough visual and concrete work in class. I need to work on this.