NWP & 3-Act Tasks

7. Try numberless word problems or 3-act tasks.

We know the key word strategy is out when teaching practical problems, but what's in? These two routines, numberless word problems and 3-act tasks, provide a structure that helps students make sense of the operations. If you want to have students learn through problem solving, this is a great place to start. Both routines are engaging for students and begin with the context, not the computation.

Numberless Word Problems

In this routine, students are initially presented a word problem without any numbers nor question. The teacher leads students in a discussion about what they already know about the situation. Gradually, additional pieces of information are added into the problem, each time stopping for students to talk about the problem situation and what they know. Often times students are able to solve the problem, even before the question has been revealed, thanks to the rich discussion that results from slowing down to digest the situation together.

Brian Bushart, a math educator from Texas, has written extensively about the use of numberless word problems. Through this landing page, you will find an explanation of how to use a NWP, instructions for writing your own, problem banks for each operation, and links to other teachers who have written about this strategy. There's so much to explore here!

3-Act Tasks

3-Act Tasks present real-world, engaging problems to students in the following structure:

Act 1: Students usually watch a video or see an interesting image in which at least one quantity is unknown. They are prompted to notice and wonder about what they see. The teacher has a pre-selected question in mind, and usually at least one student also asks this question as they are wondering. Students then quickly estimate the answer to the selected question, and also record an estimate that is definitely too low and one that is definitely too high. This process helps them establish a reasonable range.
- In Krispy Kreme Me, a 3-act task by Graham Fletcher, students see this giant box of doughnuts, and many will wonder how many are in the box. The teacher establishes that this is the question they will investigate. A student might estimate that there are 500 doughnuts in the box, and they know there are more than 100 and less than 2,000.

Act 2: Students are now asked, "What do you know, and what do you need to know?" This question, "What do you need to know?" starts students in the direction of thinking about possible operations they might use to solve this problem. Teacher reveal just enough information in Act 2, after they are asked for it, in order for students to solve the problem. Students typically then work on their own for a few minutes on the problem, and then join up in small groups to compare strategies. The teacher supports students through productive struggle in this step; this does not mean showing or telling them how to solve it! Instead she provides tools, manipulatives, or guiding questions as needed. During Act 2, the teacher circulates throughout the room, taking note of students' problem solving strategies. During this time she selects student strategies that she wants highlighted during Act 3.
- In Krispy Kreme Me, students might ask "How many doughnuts are in each row and column?" At this point the teacher could reveal the picture to the right, as well as an email from the company explaining that there are 3 layers. Students might work for 5-10 minutes individually, then group into teams of 3 to compare strategies. Students might have access to base 10 blocks and graph paper as supports for the necessary computation. If a student is stuck, the teacher might ask, "How can you model a layer of this box with one of the tools we have?"

Act 3: After the majority of teams are finished, selected students share their strategies and solutions in an order chosen by the teacher. The teacher guides students in making connections between different strategies and representations. The teacher will then "reveal" the answer, often with another video or image. If the actual answer is different than the calculated answer, a discussion should be had about the possible causes for the discrepancy.

In Krispy Kreme Me, a teacher might first ask a team to share who built a model of the box with base 10 blocks. This could be followed by a team who outlined the size of the box on graph paper. Connections could then be drawn between those two representations and a student who already knew how to use the area model algorithm. The "reveal" comes in the form of an email and news report.