Build A Rectangle With A Given Area

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SWBAT create a rectangle to model a given area.

Big Idea

This lesson moves students from whole to part/part thinking, using area as the whole and finding ways to work backwards to determine the parts.

Warm Up

5 minutes

This lesson is an introductory lesson to the Build A Nest Box Lessons for students to practice skills in creating rectangles to a specific area.

During the warm up section of the lesson, the students were seated on the carpet using whiteboards and determining the area of rectangles using the distributive property.  It was important to practice the application of this knowledge because it helps the students use known facts to find larger areas.  Using the distributive property was applied to both their number sentences and their diagrams.  For example, students write and draw diagrams for

(9 x 10) + (9 x 4) rather than the more complex 9 x 14.

Next, I ask the students to begin drawing a rectangle showing 36 square units, explaining there is more than one way to do this.  Students draw rectangles, and mark the dimensions of their diagrams. One of the reasons I selected 36 is because it allows for a diverse response. Students showed area drawings with the dimensions of 4 x 9, 3 x 12, and 6 x 6.  

The students continue their practice, creating diagrams to show different possible rectangles for the  the areas of 48 and 96.  

Mini Lesson

15 minutes

During this portion of the lesson, I switch from having the students find the total area to finding the dimensions that can create the specified total area.  I want the students to move from viewing problems as part, part, whole to seeing a problem in reverse - whole, part, part. 

I start with a product the is accessible for students to determine how to make a model of the area. I chose the product of 24, because it also allows the students many different factors to create this area.  The students draw on whiteboards as I draw on the document camera.  As the different solutions are presented, the only one I provide for them is 1 x 24.  The students are focusing on the other combinations and never considered this alternative.  Once it is presented, their following models include 1 x n to reach the product. 

This quick lesson provides the opportunity to practice another Common Core Standard, using the identity property  of 1 in multiplication.

I repeat this process of providing a product, this time selecting a problem with increased complexity to have the students draw the rectangle model for area, using 36, 42, 48, and products for doubles including 64, 81, 49.

Partner Work

15 minutes

During the partner work of the lesson, students are asked to find the length of the sides of rectangles with areas above 100 square units.  This requires them to use knowledge of place value in looking at a product and multiples of tens, twos, and fives.  Using centimeter grid paper to create these larger rectangles, the students work in partners to create rectangles with areas of 120, 150, 144, 200, and 225.  

I choose to have the students work together in partners, because it supports students by providing different entry points into this concept the support.  Some of my students choose to use whiteboards to develop their thinking, before recording on the centimeter grid paper because it provides an easy way to make corrections when necessary. 

Strategies students use include repeated addition, demonstrated in this video.


Wrap Up

5 minutes

To end the lesson, students record in their journal one total area, and draw three rectangles with different dimensions but the same area.  Because this lesson is preparation for the lesson/task of creating a nest box for birds, I ask students to identify three different real world items or places their rectangles could represent such as a playground, a table, or a hallway.  

To grab student interest, I challenge them to think of something that only they would think of, and to write their idea in their journal.  Their responses include a swimming pool, a ruler, a coffin.  The students compare their work with the other students within their group.