This whole lesson is about how to find the area of abstract shapes. Students would work on breaking the shapes down into simpler ones that they know and then find the area from there. They would start out with finding the area of simple polygon shapes to refresh their memory on how to find the area. Then as the lesson continues, the shapes would get bigger and look more abstract to continue with the idea of finding the area by breaking it down into other shapes.
The main problem the students would be working to solve is: The neighborhood playground is in need of new wood chips to cover the ground beneath the playground. One bag of wood chips covers approximately 25 square feet. How many bags of wood chips will be needed to cover the area the playground sits upon? After determining the answer to this problem, students would have the opportunity to try and find something that was abstract in the classroom and then find the area of that shape. The students would then be asked to write down an explanation for how they found their answer when looking at the abstract shape.
In the classroom, I would use this picture and problem to show students how to find the area of strangely shaped objects. It would also be used to show that even though something may seem like it is going to be hard to accomplish at first, there is always some way to make it easier, which in this case is by breaking the huge shape into smaller shapes.
CCSS.MATH.CONTENT.6.G.A.1
Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.
CCSS.ELA-LITERACY.W.6.2
Write informative/explanatory texts to examine a topic and convey ideas, concepts, and information through the selection, organization, and analysis of relevant content.
CCSS.MATH.PRACTICE.MP1: Make sense of problems and persevere in solving them.
CCSS.MATH.PRACTICE.MP4: Model with mathematics.
CSS.MATH.PRACTICE.MP6: Attend to precision.
Student Handouts: Handout
Great picture problem! I love how you related the pictures shape to student’s playground rather than it just being some strange shape they can’t relate to. An alternate or extension to this idea could be ratios and proportions for seventh graders or some sixth graders who need a challenge during this activity. In your activity, you mentioned, “One bag of wood chips covers approximately 25 square feet. How many bags of wood chips will be needed to cover the area the playground sits upon?” Students could create the unit rate (for every bag of wood chips, there needs to be 25 square feet-1 to 25) and proportions to see how many wood chips are needed to cover the whole playground. Students would have to explore whether the two quantities are in a proportional relationship by using tables or graphs.
CCSS.7.RP.2-Recognize and represent proportional relationships between quantities.