Area Word Problems - Days 1 & 2

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SWBAT solve word problems to find the area.

Big Idea

Area word problems using a real world context pose new mathematical challenges for students to negotiate.

Warm Up

10 minutes

To begin this lesson on word problems, I decide to present a short story (word problem) to the students.  I say, "I will be telling you a story today, and you will need to listen carefully for important information."  I have purposely chose to use the same numbers and concept from the lesson of the previous day, Area Within An Area, because I wanted to students to focus on the finding the key information within a word problem.  

Our story begins with school, a teacher, a class, and a principal who wants to help the school.  The principal has been given the opportunity to make the school bigger for one of the classrooms, but he does not want to choose a classroom.  He has decided to have the students solve different problems to help him make his decision.  Every classroom has been given a different problem to solve, and ours is based on area.  

There is extra space available to build a new classroom.  It is 11 yards by 9 yards.  There are extra bookcases, tables, and cabinets that will be used around the room that will take away 3 yards from the length of 11 yards leaving 8 yards.  Another 2 yards from the width of 9 yards leaves 7 yards.  How much space will be available for students to use when the space is taken out for all of the extra tables and bookcases?

After presenting the problem to the students, I repeat it.  Following this, the students use their whiteboards to create a diagram for the problem. 

Because this problem used the same information from the lesson on the previous day, it did not take long for the students to solve this problem.  They did focus on finding the information within the word problem, and it created a level of self confidence for the students to be successful with solving word problems.  

The students used their whiteboards to solve the problem for review

11 x 9 = 99 yards

8 x 7 = 56 yards

99 - 56 = 43 yards

Group Practice - Day 1

10 minutes

During the group practice, I present two of the problems the students will be working on the first day.  I have chosen to have the students complete two problems each day, because I want them to focus on looking for key information and coming up with a strategy to solve each problem rather than rushing through a number of problems. 

Today, I work through the problems alongside the students, because I know it will help their success with this multi-day lesson.  Also, I am using their work in this lesson as an observational assessment rather than a formative assessment.  I am analyzing their skills and strategies for solving word problems as this will impact how I will approach our lesson tomorrow.

One of the strategies I focus student attention on when working with word problems is to have them underline important words and information within each problem.  

The first problem is about finding, drawing, and labeling two rectangles with the same area.  These drawings are not to scale, but I am looking for the labels to represent actual dimensions (MP6 Attend to precision).  This problem requires students to use their knowledge of multiplication facts with a product of 48.  Within the problem, the key idea (and word) is different.  I model for the students underlining the words two different rectangles and 48 square inches. While this word problem does not include a context for what is required, it is only asking them to construct rectangles to a given area.  This skill of drawing rectangles to a given area will be connected in later questions in this lesson. 

For the second problem, the students determine the words 8 feet by 12 feet, divide, and four equal sections as the key words to underline. 

Before the students begin to solve, I ask them to write in their math journal why we are underlining words within each problem.  The reason I do this is so that students focus on why this step is important to their success with word problems. This step of self reflection helps the students develop a routine to apply whenever they are working with word problems. 

Solving Problems - Day 2

20 minutes

Using the same problem set from the previous day, the students create models and solve the word problems.  I review the steps for identifying the key information for solving word problems. I want them to make sure they are identifying the question being asked, determining the operation that will be needed, and isolating the key numerical information that is required to solve the problem.

Having the students work slowly through the problems to really think about the steps of problem solving is the key point of this lesson.  Their solutions may not always be correct, but establishing a routine and procedure for word problems will support their success.  

Problem 3:  The problem is asking the students to create an area of 18 square acres.  This is related to the problem from day one when the students were asked to create an area to a specific total.  In creating this area, the students will need to know factors for 18.  The students could create an area that is 9 acres by 2 acres, or 6 acres by 3 acres.   

My focus for this problem is their explanation for how they solved the problem.  I want them to describe how they use their knowledge of math facts to design the area, and then section the 18 acres into smaller sections for the house and the barn.  The second step of the problem requires them to subtract to find the area of the grass.  



Presentations Gallery Walk

15 minutes

After students have solved the problems, I ask them to create a small poster of one of the problems using a piece of copy paper.  Their poster is to include a title for the problem, a diagram, and their solution written out for other students to view.  They will be having a Gallery Walk where they will describe their poster to two of their classmates or to me.  Including myself as one of the viewers, increases the focus of the students on their plan and creates accountability.  This also allows me to complete some observational assessments through a performance task.  

I like to use a gallery walk format because the students are only presenting to one or two people at a time, and it lessens their anxiety and shyness when presenting to a large group.