With the implementation of CCSS, there is a shift towards applied math concepts and skills taught through the use of authentic, real-life problems than through a sequence of procedures. Students are expected to work cooperatively, think critically, and solve problems – all while understanding that there are many ways to solve the problem (with no one particular right way) and sometimes more than one answer. Hence, the reason for the Standards of Mathematical Practice.
While to some degree I have always been doing this in my classroom with other area and perimeter activities, I felt it meant that I needed some activities that were a bit more in depth – you know, the ones that require deeper thinking … and more time. I decided to really tackle this during my area and perimeter unit. We dug in deep using a real life example.
I secretly enjoy moving furniture around in my house (although now that I have children, it’s more work than it’s worth sometimes). I use to love just rearranging the furniture and seeing all the unique ways it made the room look after changing it around. So that’s when I got the idea that I would create an activity such as this to have my students practice area and perimeter through applied math in context.
First, I modeled for students using a pre-designed house. I showed students how to find the area by counting squares and partial squares, estimating, and even shortcut methods such as using arrays. I demonstrated breaking up rooms, finding their areas, and later adding them together to get a total area. I also demonstrated finding the area of furniture when you can’t actually see the grid lines. After modeling it, I then had students try out to find the area of a room or two on the house blueprint plans that I was modeling on. (I strongly believe in the gradual release method. You can read about how I teach using the I do, We do, and You do Method.) Finally, I provide students with their own house design to try finding the area on. Of course, I differentiate it based on my students’ needs. Some students work with smaller rooms and furniture, while other students work with furniture that is angled and more advanced. They also answered questions related to their house.
Once I felt students were ready to move on, I provided them with the materials to create their own house! They were given a blank grid graph and the furniture pieces. I gave them specific requirements, such as they had to have at least one bedroom, one bathroom, a kitchen, and a living room. They also had to have a couch, a large bed, two tables (of any size), chair, desk, table & chair set, bathroom furniture (toilet, sink, and tub) and kitchen furniture (sink, stove, fridge, counters). We discussed thinking logically – for instance, you would never stack a tv on top of your bed to save room, nor would you block your bedroom door. We also talked about how we had to create walls and not put furniture through it.
The students had first arranged things where they thought they wanted it, and then sketched their lines. They would glue their parts down and then find the area and perimeter of each room and piece of furniture.
We discussed how we could rearrange the furniture to create more area (and I challenged some students who finished early to try it!) Then students answered questions related to their house design when they were done – basically using applied math!
Of course this activity could easily be done in any classroom. All you would need is graphing paper and students could draw their own furniture with color pencils on the paper or you can provide students with construction paper to create them. However, if you are looking to save some time, you can read about and purchase my Design My House Area Applied Math Activity in Teachers Pay Teachers store.
What is really great about the product I created, is I provided two different direction sheets for teachers – one with requirements (as described above) and one that is more open-ended. I have also provided many opportunities for differentiation, including allowing for completing this activity as a whole group or small groups instead of individually. There is also an extra enrichment activity that allows for further critical thinking.
Regardless of which route you choose to take, the benefits are tremendous! Students find the activity engaging and it’s one of those applied math activities that really help you assess what your students understand about area and perimeter!