Here is how I teach Area to my kindergartners--lots of hands-on exploration and discussion, of course!
All of the blackline masters I use are available to download free here:
K.10) Measurement. The student directly compares the attributes of length, area,
weight/mass, capacity, and/or relative temperature. The student uses comparative
language to solve problems and answer questions. The student is expected to:
(B) compare the areas of two flat surfaces of two-dimensional figures (covers more, covers less, or covers the same).
- K.MD.1. Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object.
- K.MD.2. Directly compare two objects with a measurable attribute in common, to see which object has “more of”/“less of” the attribute, and describe the difference. For example, directly compare the heights of two children and describe one child as taller/shorter.
To introduce area, I present a simple problem to the kids...
Make sure to choose sticky notes that are easily comparable (fit completely inside each other). Have the kids discuss--which sticky note would be best for writing a long note, and why? When they answer that one note is "bigger," press them for more...Bigger how? Is it longer? Is it taller? Keep pressing them until you get someone to say something close to "The inside part of this note is bigger, or has more room than this one." Let them demonstrate by actually placing one note on top of the other. Then introduce the word area and explain that it is the space inside a region.
Now let the kids do some exploration on their own:
Have the kids look at the pictures of the windows below. Ask them which window has the bigger surface area? How can you be sure?
Have the kids cut out and physically compare the windows.
Is Emma's window bigger? It definitely looks taller...
But wait...this way, Andrew's window looks taller. So which is it? Ask the kids if they can think of a way to find out for sure. Someone will probably suggest measuring it. But how? Measure what? Measure how long a side is? Measure it "this way"? Or "that way"? Remind them that if they really want to know who has the bigger window, they need to figure out which window has the bigger area (the inside part).
Then ask the kids what math tools they could use to measure the area. Don't be afraid to let them experiment. If someone chooses round counters, and there is space left over, discuss whether or not that is the best option.
I made these windows to be measured with 1" square color tiles, but any tool will work, as long as you use the same tool to measure both windows (discuss that with the kids!)
Here I've measured with 1" paper squares. It takes 12 tiles to cover Andrew's window and...
So now it's time for a discussion. How can they be the same size when they are not the same shape? This is a very hard concept for primary learners to grasp--"rearranging areas into different shapes does not affect the amount of area." (Van de Walle, Teaching Student-Centered Mathematics K-3)
And it's not a concept that they are going to grasp after one lesson. But, once again, we are providing the kids with concrete, hands-on experiences to build their schema.
Allow the kids to do some more hands-on exploration today. Have them choose different objects from around the room and measure their areas with different non-standard units. I like to have them estimate how many units it will take to cover their objects first.
Good things to measure...anything flat! Games, books, puzzles, journals, notebooks, rugs, mats, etc.
Good things to measure with...tiles, cubes, playing, cards, dominoes and sticky notes (make sure you re-use the sticky notes--they aren't cheap!).
Good questions to ask while the kids are working:
- Which is a better choice to measure a game--these little tiles or the bigger sticky notes? Why?
- If you run out of dominoes, can you finish measuring with tiles? Why or why not?
- If Alex measured his book with cards and Drew measured his with sticky notes, can you compare the measurements? Why or why not?
More hands-on exploration!
Here's a chance to practice measuring "those hard-to-compare" objects. I encourage the kids to choose 2 objects that you cannot just stack on top of each other to compare their sizes. They love the challenge!
I also make them predict which has the larger surface area before they measure. It makes them start really thinking about how long or short or fat or skinny objects are--and how that affects their area.
Here's a problem that challenges children to apply what they've learned through their hands-on exploration. Here's the catch--I do not give them tiles! They have to figure out that there will be five tiles across and 4 down for the whole rectangle. Some kids will draw the tiles to fill it in, some will draw grid lines, some might even cut out little scraps of paper to fill it in. But do you see where this is going? It's a very early exploration of how height and width relate to total area!
Give the children 14 tiles (or paper squares). The grid paper is just to help the kids organize their arrangements. Tell the kids to make a shape. It will either be a square or a rectangle (an excellent opportunity to review the attributes of squares and rectangles).
It's not this one...
Or this one...
This one works!
But is it a square or a rectangle? (It's a rectangle because 2 sides are long and 2 are short).
You can have your kids glue paper squares in their notebooks...
Or draw the shape on grid paper...
But the most important part, as always, is the discussion!
As an extension, I give the kids a predetermined number of tiles and see how many different shapes they can make. (Numbers with multiple factors work the best... like 12 and 24). Again, the kids start to understand that shapes can look different and still have the same area).
Warning: Teaching kids about measurement definitely exposes you to the If You Give a Mouse a Cookie Syndrome. Before you know it, you will probably be measuring your windows with sticky notes and your carpet with pieces of construction paper.
Have fun with that!