Design A Space Using Area Models - Day 1 and Day 2

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SWBAT design an area using area models.

Big Idea

Students use area models to find the total area of a store, home, or other real world space.

Warm Up

10 minutes

To begin the warm up for this lesson, the students practice math fact fluency by writing different math sentences for a given product.  If I give them the number 24, they write on their whiteboards as many different facts to total 24.  This is a fast paced warm up, and I mix the easy products with challenging products to meet the needs of all students.  

Mini Lesson

10 minutes

During the mini lesson I draw a square, filling most of the space on a piece of white paper.  This square or rectangle will be used to create the size of space that will be designed.  The square is cut out and placed on the grid paper to fit to the nearest centimeter to create a rectangle or square.  I chose to do this because I do not want the students to create a space that is easily determined or counted out.

I explain to the students that they will create designs of a space of their choosing, and determine small interior areas.  They also calculate the whole area by adding the small areas.  To make the real world connection to their design I offer some different ideas including a grocery store, a house, or a bookstore. The Common Core Standards emphasize using non-overlapping rectangles with a real world connection.

I explain to the students all spaces must be included in the design such as hallways or walkways, door entrances, and cashier areas for stores.  The assignment includes writing the number sentence for the array inside of each area.  They are required to have at least 12 different sections to their design. 

These calculations will be necessary on the second day of the lesson when the students determine the total area of their space.  

Design The Space

20 minutes

Once students create their planned spaces, they begin sectioning off the diagram to fit in these spaces as rectangles or squares.  Each of these areas is also colored a different color to differentiate these spaces and create a clear visual of how the space is divided. 

Day 2 - Determine The Total Area

20 minutes

This section of the lesson can be combined with the first day if you have a flexible daily schedule and can extend your math period.  Separating it focuses the students on different tasks each day with first day emphasizing design and smaller areas.  The second day is focused on multiplication and addition skills to find the total area of the designed space. 

When the students have their space designed, they create a list of the areas and write the number sentences.  The students add their individual area measurements to determine the whole area.  Next, they calculate the area of the outer square/rectangle.  This is compared to the total they added to see if it matches.  

This challenge for students may result in frustration, and it may be necessary to provide support or extra pieces of grid paper to help determine the measurement of the entire area. 

Once students have created their designs and area measurements, posters are created for display. 


10 minutes

Students share and present their designs to two other students in the classroom.  I want them to explain their design and for the other students to ask questions about why they included certain spaces.  Their interest in other students' designs allows them to compare to their own spaces, and different options that could be included.