Numberless 3-acts

On Wednesday I posted a 3-act task that I planned to use in my class the next day.

Here’s how it went…

Act 1 asked students to watch a video and record what they noticed and what they wondered. As a usual modification for my students I had them make a T-chart graphic organizer in their math notebooks to record their observations. We watched the 1 minute video 4 times, twice for noticing and twice for wondering.

IMG_0784

One student’s math notebook

Students noticed:

  • The plastic bag was being filled
  • There were some cheerios
  • There were some chex
  • There were some M&Ms
  • There was 1 raisin

Students wondered:

  • How many trail mix pieces altogether?
  • Why didn’t I add more cereal?
  • Why the whole bag on M&Ms was being put in the trial mix?
  • Why only 1 raisin?
  • How many cheerios, chex, and M&Ms?

After addressing which of our questions we couldn’t answer with the information provided (essentially eliminating all the “why?” questions), I introduced the picture from Act 2 (100 total pieces). This reveal answered one of our wonderings (how many altogether?) I then introduced another step where we collected all the information we knew. This collective list is located in the bottom right of the student notebook pictured above.

We know:

  • 4 ingredients
  • 1 raisin
  • some cheerios
  • some chex
  • some M&Ms
  • 100 total pieces

As a group we decided to subtract the one raisin from the 100 total pieces, which left us with 99 total pieces. Students then used various problem solving strategies such as guessing and checking with addition (33+33+33=99, and 49+25+25=99 pictured above) and making a mathematical model by using division (99÷3=33). Students were able to make conjectures and use mathematical reasoning to justify the reasonableness of their solutions. In this 3-act task students were able to utilize at least six of the Standards for Mathematical Practice.

One thing that stood out to me was the language the students used, “some cheerios, some chex, some M&Ms.” Some. This made me think of a wonderful post by Brian Bushart on numberless word problems. (If you haven’t been to his blog, please go there, look around, but remember to come back here!) Kristin Gray has also been experimenting with using numberless word problems in her school as well. Using numberless word problems allows students to make sense of problems and construct reasonable solutions. Bushart says about using numberless word problems, “I do think this is a great way to prompt rich discussion and get students to notice and grapple with the relationships in problem situations and to observe how the language helps us understand those relationships.” Since Dan Meyer first introduced the idea of creating 3-act tasks to make “solving word problems” more like doing real math, isn’t it time we integrated Brian’s numberless idea also?

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