Thursday, November 28, 2013

Math problem of the week: Oregon Turkey Math

Courtesy the Oregon Department of Education via the North West Regional Education Laboratory:

“Cooking the Turkey” 

A third grade class is beginning to work with multiplication. The purpose of this lesson is to use an open-ended investigation to develop students’ ideas, strategies, and models for multiplication through a problem that is based in a familiar context.

Background: On the previous day, the teacher had posed a real-life problem to the class for which she requested their assistance. The teacher told the students that she had invited a large group of people over to her house for Thanksgiving dinner. The problem she posed was to find out how much it would cost to buy a large turkey (24 pounds) if it costs $1.25 per pound. The students discussed and solved this problem in pairs and then reported out their solutions and solutions methods to the whole group.

Launching the problem: ...The teacher again gathers the class together on the rug and poses a second, related turkey problem. The teacher wants to make sure her dinner is cooked properly. According to her favorite cookbook, a turkey of this size should cook for 15 minutes per pound. She again sends the students off to work in pairs or threes to solve this problem. Students may use any strategy or approach they choose and must record their solution and their method on a large sheet of poster paper that will later be shared with the class.

Students at work: Four groups of students are seen working on the problem.
1. Hannah M. and Julia: They split 15 into 10 and 5 and add groups of 10 and groups of 5 separately.
2. Kenneth, Marlon, and Sam: They keep track of the number of pounds each fifteen minutes represents and skip count by 15s in a list that resembles a table when they include their labels.
3. May and Rafe: They use a doubling and halving strategy (15 + 15 = 30 and 24 ÷ 2 = 12)
4. Nate and Nellie: They put two fifteens together to make thirty minutes and count by that group. They count by 30s (minutes) while simultaneously counting by 2s (pounds).

Students discuss solutions: After students have solved the problem and created posters showing their solutions and strategies, the teacher brings the group back together on the rug and asks some groups to share with the class. This portion of the class is called the Math Congress.

We see Amber and Vicky present their poster. After they share, the teacher promotes discussion of their method by asking other students to explain Amber and Vicky’s method. Next the teacher chooses Marlon, Kenneth, and Sam to present because she sees a connection between their method and the method used by Amber and Vicky. Finally, she asks May and Rafe to share because their method used a “shortcut” that included an important mathematical idea: the inverse relationship between doubling and halving. Since other students had not used this thinking and were somewhat confused by it, the teacher allowed this discussion to go longer than the others until many students indicated that they understood the strategy.

Evidence of engaging students with the mathematics content

The teacher chose a scenario from a real (or at least believable) context to frame the problem. The need to buy and cook food for a large group is a situation that students have likely encountered and/or can relate to. The use of a real cookbook increases student engagement as does the notion that she is personally seeking students’ help to solve her real-life problem.

Evidence that the students are engaged can be seen in their conversations both during the work time and during the math congress. During the math congress the teacher says, “There is something similar between yours and Amber and Victoria’s [method]” but she does not tell them what the similarity is. Instead she engages them in the process of identifying the connection.

Evidence of creating an environment conducive to learning

Students work in pairs or small groups assigned by the teacher to solve the problem. Purposeful partner selection minimizes the likelihood that any students will be excluded from the process. By gathering students together on the rug for the posing of the problem as well as the subsequent discussion, the teacher creates a friendly atmosphere that is inclusive and engaging. During the student sharing, the teacher sits on the floor as a member of the classroom community. This increases the student-to-student interaction and diminishes the tendency for the conversation to be teacher-dominated. She offers encouragement that is authentic and based on students’ work and conversations. For example, after listening to and then restating Hannah M. and Julia’s approach she said, “You guys have a really good idea here.”

Evidence of ensuring access for all students

Because the problem is posed in a context that students can relate to, there are many access points for students. The teacher does not specify a solution strategy nor does she put a time-limit on students. In her conversations with individual groups and during the math congress, she very often orchestrates the discussion in a way that ensures all students stay engaged. For example when working with Nate and Nellie, she asks Nellie about what Nate had said, “Do you understand what he’s doing?”

During the math congress she offers multiple opportunities for different students to restate or rephrase the explanations that others have given. She also allows and encourages student-student questions, particularly when students are sharing with the class. The classroom climate appears to be one in which questions are welcomed and students are expected to interact respectfully.

Evidence of use questioning to monitor and promote understanding

The classroom interactions that the teacher has with students are characterized by her listening and asking questions. She rarely makes a statement, and when she does it is often to paraphrase or restate the idea that a student has shared.

Evidence of helping students make sense of the mathematics content

The teacher uses the context of the problem to make sure students understand the results their mathematical methods produce. For example, after Vicky and Amber share their solution, the teacher asks, “And what is the 360?” The teacher returns to the context of the problem to make sure the students understand the relationship of the numerical answer they have found and the situation of the problem.

During the whole class sharing, the teacher purposefully chooses the students who will share and the order in which they will share to encourage connections between methods. For example, she has Marlon, Kenneth, and Sam present after Amber and Vicky because she wants to reinforce the connection between jumps on the number line and a skip counting strategy.

Since one pair of students used a strategy that involves a deeper level of mathematical content knowledge (doubling and halving) the teacher makes a point to have that group share. She introduces their approach by saying, “And I would like May and Rafe to come up. And May and Rafe came up with an interesting shortcut, and I’d like you to explain.” The discussion that follows their presentation causes the rest of the class to interact with and explain this strategy and the mathematics that underlie it.
Presumably this discussion does not cause anyone to wish that Thanksgiving break would begin as soon as possible.


Anonymous said...

It sure made me wish that! I think it's useful to elicit and/or demonstrate alternative ways of multiplying. But this lesson could take all morning, and if this type of lesson is done at all frequently, it will gobble up most of the time available for math (pun intended). It also depends on the groups coming up with different alternative strategies, or any strategy at all; and being able to explain them. Not a safe assumption.

Auntie Ann said...

What an unbelievable waste of time!!! In the time it took to break apart, please the teacher by playing dumb (which you just know some kids were doing--while thinking: just multiply the two numbers! No, we can't do that! We're not supposed to know the traditional algorithm, how it works, or when to apply it. Just shut up and make up some convoluted hand waving instead! Yeah, I suppose. You know she'll really get thrilled by that!), make a stupid poster, regroup for the congress, and discuss the results, every kid in the class could have been doing about 20 similar word problems.

GoogleMaster said...

So, none of the groups actually just sat down and multiplied the numbers? Ugh.

Anonymous said...

I've seen no sign that either the ed world or the practitioners therein (at the ES-MS levels and in many HS) have any awareness of the concept of efficiency, let alone any appreciation of it. Teach the algorithms directly, and give kids lots of practice. This class could have done something real-world and practical in far less time. Teach the algorithm and give the kids a menu for a family dinner for 16 people. Post/pass out recipes, which vary between 4 and 8 servings each, for all items and have the kids calculate the amounts needed. Given a list of usual sizes for the grocery items, they could also create s shopping list. Work individually, of course.

lgm said...

Oh, a POD discussion. Probably took 20 minutes at the most. My son's third grade had Friday POD time and it was quite informative, rather like a math club meeting.

I notice the classroom in the article though, is not fully included -- no input from those well below grade level --, so I doubt this was actually done at a public school.

Cynthia812 said...

They could actually cook a turkey in the time it would take to do this lesson. And I don't believe for a minute this is an actual description from an actual event.