Reply To: Lesson 6-1: Question

[Marion Mulgrew]

I went back and forth with the idea of using the Evergreen task or the Snack Time task for early in our number sense – operations with rational numbers unit. I know we are supposed to focus on connections with positive and negative numbers, but I want to shore up their number sense around fractions and decimals first, then be able to connect that to the concept of making 0 and then to positive and negatives due to opposites. In the end, I decided to start with the Snack time task as fair sharing is intuitive to most by 7th grade. It also lends itself to representations of the same amounts in a variety of partitions and connects the idea of fractions to division. I can see using Piggy Bank as a continuation.

Attention – Food! Also, without more context, it raises many questions. I think students will be surprised that they aren’t being given more information, so that will get their attention too.

Generation – Students will need to find a way to generate fair sharing of the given amount of cheese and not be sure of the number of crackers. Once they find out the number of crackers and move to breaking up the 3 pieces into 4 each, they will be able to have generated that breaking thirds into 4 pieces each is 12 small bits, or 1/3 divided by 4 gives 1/12 of the original amount. We can contemplate why it isn’t 1/3 x 4 or why 1/4 of 1/3 is 1/12.

Emotion – Not sure beyond the social connection and fun in solving a puzzle, while overcoming a reasonable level of frustration. There may be students who are masters at fractions already and can feel great as leaders, or others who were able to know they needed to break each 1/3 stick into 4 pieces, but will have a hard time internalizing that the algorithm isn’t 1/3 divided by 1/4 but 1/3 divided by 4 because of each stick being broken up into 4 pieces.

I could also bring in some food that they are able to actually consume at the conclusion.

Spacing – This task so far, allows students to mostly work at their own pace, as I can nudge or grant more time for them to explore this one concept. We can then move to fair sharing other things or looking at things in parts and find ways to describe them, including with the Piggy Bank Task.

I am looking forward to working with these tasks and more, but yet not rushing my summer. 🙂