Today’s lesson focuses on students solving real world problems involving double-digit division. Students work in groups to complete the task and then present their findings at the end of the lesson.
I open today’s lesson by posing the Old Mother Hubbard story problem to the students. I allow students time to think the problem with their neighbor and I have them show any work needed on their whiteboards. After giving the students about five minutes I bring them back to the group to discuss their solutions. The students must determine that the type of operation needed is division, and that answer is $27 each.
Students are given a task today that they will solve with their groups. The task involves a parent group trying to purchase sod for the football field of the school. The sod comes in four different sizes and prices. The students must decide which size piece of sod would be the least expensive to purchase based on the price per unit and quantity needed. I found the idea for this task on the Georgia Department of Education website and modified it for reuse.
The task to students in this lesson is somewhat complex. Students have to apply their knowledge of multi-digit multiplication and double-digit division. They also have to use some spatial reasoning first in order to determine the area of the field.
I start this task out by giving students a copy of the task and read over with them. I do not provide too many directions. I want the students to self-discover what parts and pieces they need to complete in order to solve this task. I tell students to work with their group to solve this task which includes creation of a short presentation to be given to the parent committee to offer their suggestion and rationale. I place students in groups of three or four and let them begin working.
Before assigning this task I thought that the students would be able to easily navigate through it. I was wrong. Including determining area in this task made it difficult for students to figure out where to start. I let them struggle for about ten to fifteen minutes and then bring them back to the whole group to discuss strategies.
I focus the group discussion on the first step of the problem, which is determining the area of the football field. I also did a little explanation as to what sod is. My students really had no concept of sod and what it was used for. After explaining that the sod was sold in pieces, I send my students back to work. They work for another 15 minutes and then I decide we have to wrap up our work for today. What I thought was going to be a one day task turned into a two day task. The spatial reasoning concept was starting to come into focus in the minds of my students but they are going to need some more time.
The next day I bring students back into the problem by showing them a quick video of how sod is replaced on an actual football field. This video is a time-elapsed version of the process. It is a good visual for students to reason out that each piece of sod is put in one by one.
Before releasing students to work in their groups we reread the task and get focused on what they need to accomplish today. Students need to determine which piece of sod will be the least expensive for the parent committee to purchase for the football field. I allow the students the remaining time to work on their solution and prepare their presentation.
For groups that begin to finish early and are prepared for their presentation I extend the activity for them. I tell them that now they need to determine how much tax will be associated with the cost of sod. Students really don’t have a good grasp on what tax is or how it is calculated but only know that it is something that is added to the price of things they purchase. I provide them a little background information and have them calculate the cost of the sod including the tax.
To wrap up this lesson I have students present their findings on the task. I have each group come up to the document camera and present their solution and rationale for which type they are suggesting, what the quantity needed is, and what the total cost of the product will be.