SWBAT use a model to show the solution to demonstrate the relationship between multiplication and division.

You're hungry; figure out who you would rather have make your sandwich! Someone gives away extra!

5 minutes

Some students don't go to the grocery store with their parents, so they might not know that you can buy turkey at a deli. (They're used to buying the precut, packaged, version.) We don't have any independent delis in our community, but we have two local grocery stores. There is a deli in each of these stores, but we wouldn't typically go there to order a sandwich.

In Wilmington though, our closest city, there are many delis. Most of my students visit Wilmington pretty often, and know about some of the delis there; we have some great ones! I bring in menus from Jason's and McAlisters delis to hook students' appetites for learning and good food. Bringing the menus in helps to give the students who haven't been to a deli a better frame of reference.

You may want to do this right before lunch, as some of the pictures in the menus are quite appealing. I give students a few minutes to look at these with their table partners; this is a really simple thing that will pull students into this lesson. My students notice the prices right off the bat, and think that between $6-$8 is too much money to pay for a sandwich. We talk about all of the other delicious stuff that's on the sandwich, which makes it cost more. In this lesson we'll talk about cost, weight, and value.

20 minutes

We're on to My Deli Dilemma Problem!

(a) Uses MP4 (Model with mathematics), and is a Level 1 DOK; here students draw a model of a problem situation and explain how the model shows the solution. Students experiment with representing problem situations in multiple ways including numbers, words (mathematical language), drawing pictures, using objects, making a chart, list, or graph, creating equations, etc. Students have to have opportunities to connect the different representations & also to explain the connections. Students have to evaluate their results to determine whether the results make sense. I suggest that students think about how many pounds of turkey there are and how much is needed for each sandwich.

(b) Uses MP4 as well, and is a Level 2 DOK; here students write an equation that matches the model from item 5a. I have students study their model to help them determine the equation.

(c) Uses MP6 (Attend to Precision), and is a Level 3 DOK; here students use the relationship between multiplication and division to show the equation is correct. In this challenge, students continue to refine their skills by using clear & precise language in their discussions with others and even in their own reasoning, including use approrpriate content vocabulary. Also important, is that students are accurate with measurements. It's important to remind students that the relationship between multiplication and division does not change because they are working with fractions.

(d) uses MP2 (Reason abstractly & quantitatively), and is a Level 3 DOK; here students write a problem situation to match the expression. At this level, students should be able to recognize that a number represents a specific quantity. Students connect quantities to written symbols, & create a logical representation of the problem at hand, considering both the appropriate units involved and the meaning of quantities which includes fractions & decimals. Students write simple expressions that record calculations with numbers & represent or round numbers using place value concepts. I suggest to students now to look at (a) to help them think of a situation.

15 minutes

In the Paired Practice, students work on My Other Deli Dilemma Problem. I'm looking for students to:

- Draw an accurate model and give a clear explanation.
- Write a correct equation.
- Provide complete reasoning.
- Interpret a correct situation.

In Student Work Sample 1, you'll notice that the answer to the last question is very vague. Knowing this, I know I need to extend this student's thinking. I ask her what else she can write about. I purposely left this question somewhat open-ended to see how students would respond, and if they could challenge themselves. You can see in the video in the closure section that some students did just that---connecting giving away product to being fired----a real life situation.

20 minutes

At the end of the independent practice, I extend learning by asking the students to hypothesize who they would rather have make their sandwich. In this clip you'll see students who extend their response and carefully consider the consequence of giving away product (meat) in a deli situation. This is something that I didn't expect, but you have to use those teachable moments, so I quickly add to their response and threw in a few review questions, and made the problem go full-circle to have them making meaning of the task.