I was noticing yesterday that many of you were counting the unit squares of figures to find the area. Did anyone come across all challenges when doing this?
Yesterday I observed many students who lost count when determining the number of unit squares for area because - as the lesson intended - they were counting by ones. Today, I want to have a discussion around this to point out that we often need additional math problem solving tools in order to make problem solving more efficient. (BTW - If you need graph paper for this lesson, there are some terrific free downloadable resources online. One that provides a great deal of variety of grid types is Incompetec.)
Who can tell me what they know about the sides of a square? And a rectangle? In our multiplication unit, we used area models to determine product. My lesson objective is to make the connection between multiplication and determining area, as stated in the Common Core Standards, 3rd Grade Critical Area 3:
Students understand that rectangular arrays can be decomposed into identical rows or into identical columns. By decomposing rectangles into rectangular arrays of squares, students connect area to multiplication, and justify using multiplication to determine the area of a rectangle.
Well we can use that knowledge when we look at figures to help us solve for their area (MP5). We can multiple their length by their width to find their area! Let’s try it out!
Together we solve a few problems that involve squares and rectangles, which students are able to do quickly by relying on their understanding of multiplication. I do these examples first before I introduce sectioning off more irregular shapes.
Now what do you guys notice about this figure? Can you see any shapes within this shape? Who has an idea for what we can do?
I want students to arrive at the conclusion of sectioning figures off, so I lead them directly to it without actually saying it.
Today I want you guys to try using your new tool for solving for area. If you notice any shapes within your shapes, section them off and see if you can solve by multiplying the length of each one by the area. Don’t forget that when we section them off, we much add the area of each section to find the total area of the figure!
Today we were able to use our understanding of 2 math concepts, multiplication and area, to make problem solving easier!