Shady Figures Stations Activity

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SWBAT find the area of shaded regions using formulas and grids.

Big Idea

Students will reinforcing the concept of finding the area of shaded regions using technology, independent work, and small groups.


10 minutes

I’m going to have the students create a memory box on how to find the area of shaded regions. Students can use words, pictures or examples in their box.  Begin by giving the students think time.  Have them think about how to find the area of shaded regions.  Then, have them write for a minute or two about everything they remember.  Once the time is up, give them another minute to review their notes.  Then have them write for a moment more.  Students can share their memory box with a partner or you can do an “I have that”.  Students stand up and read something out of their box.  If the students have it, they respond “I have that” and then mark it off.  If they don’t have it, they can add it to their list. This activity stops when all items from their boxes have been read.

Memory box supports:

SMP1: Sense-making, thinking deeply about a concept

SMP3: Arguing, using assumptions and previously established results

SMP7: Structure, discerning patterns and structure.

Tools:  paper and pencil. 


60 minutes

The students will be working in stations to reinforce the concept of finding the area of shaded regions. Students will rotate through 3 stations: independent, computers, and teacher work stations. 

The students working in the computer station will be using the brainpop website to help reinforce finding the area of polygons.  They can watch a video on how to do and then practice problems on their own.  There is a quiz on brain pop that will give the students immediate feedback to the result of their solution.  Students should bring whiteboards or paper to use to solve the problems.

Tools: Brainpop website or other computer site that works with area, white board or paper and pencil.

The students working in the independent station will be working on a real world problem that requires them to find the area of the shaded region.  Once the students find the area of the shaded region, they will then need to explain in words what they did and why they did it.(SMP3: justifying their solution)  Writing in math helps support ELA.  Students will write informative/explanatory texts to examine a topic and convey ideas, concepts, and information through the selection, organization, and analysis of relevant content.

This exercise can be used as an assessment.

Tools:  Independent workstation problem, pencil

The students working in the teacher station will be looking at shaded regions on a grid.  Students will need to devise strategies to find the area of the irregular shapes.  The can use triangles, rectangles, and trapezoids to help them. (SMP7: making use of structure by using familiar shapes) As the students work, you can work with each one and have them do a think aloud.  This will help with questioning.  For example, if students start making the first shape into a familiar shape, you could ask them if there is a simpler way to solve? (they could just count the squares.)  Then you could ask them if this would work for the other shapes (no, because the first example has straight lines and it is easy to count the squares.  The other shapes have rounded edges or squares that are cut off). This, too, would be a good assessment piece for evidence of student learning.

Tool: Teacher workstation problem, pencil


10 minutes

 I’m going to have students create a problem using Geometric shapes and a shaded region.  They should give their shape the side lengths needed to solve.  Then they should solve their own problem.  As an extension, students can create a word problem that includes their shape. I will be looking for students to use shapes they are familiar with.  I will also be looking for them to place one of the shapes inside of the other and then shade part of it to find the area. As students are placing numbers within their shape, it may be a good idea to watch to see that their numbers make sense.  For example, if they label the long side of the rectangle 5 inches and the short side 10 inches.  Be sure to ask the students about those measurements and if they make sense. (SMP6: Precision).  If time permits, students can share their shapes with a partner or let the partner solve for the area of the shaded region.

Tools:  Closure Problem