I put a set of ten frames on each student's desk. Each student has 4 blank frames and 8 frames that are filled in with ten dots. Students also have chips to work with. I ask them to use the tens frames to show the numbers I say. (I know that this is a review for many students but I want to remind students of how this visual can be of use for comparing numbers and finding differences.)
I ask them to build 24. Now I ask them to leave that on one side of their desk and build 36 on the other side. How much bigger is 36 than 24? I remind students that they can count the difference on the 2 sets of frames.
I repeat this with the numbers 49 and 25, and then add hundred grids as hundred frames and ask them to build 136 and 187. Again I ask them to find the difference.
I repeat the process with 205 and 171.
I draw a polygon on the board and have a student come up and measure the figure in inches. I draw a rectangle for this first demonstration. I ask students how I would find the perimeter of the shape? I ask them to do that at their desks on scrap paper.
Next I ask how I might find the area of the shape? (In second grade the goal is for students to be able to partition off a figure and count the squares 2GA.2). I help students come up with the way to mark the shape and then I put little tic marks at the inch places. I ask for a volunteer to come up and partition off the figure. When they are done I ask for a student to come up and find the area of the figure.
Now I tell students that they will have 10 minutes to draw a polygon monster on a piece of grid paper. They must use the squares as the edges of the monster (no half squares or diagonal lines or curvy lines, but tracing the lines on the paper. They should not color in the monster.
At the end of 10 minutes I tell students to connect their last line and now find the area of their monster (by counting the squares inside).
When everyone has finished creating the monster, I tell them that they will be placed in small groups to find who has the biggest monster and how much bigger it is than everyone else's.
They will need to write a number sentence to show how they made the comparisons, and organize the area of the monsters from largest to smallest. They will mount their monsters on construction paper in order from largest to smallest and attach their number model comparisons.
I remind them that they might want to use expanded notation, or ten frames to make their comparisons. Everyone should solve the problems that the group creates.
I demonstrate by drawing 2 monsters on the board and writing Area = 88 on the first and Area = 69 on the second. Now I ask students how I might compare the two areas in a math sentence? (69 + ___ = 88, or 88 - 69 = ___). It would also be possible and acceptable for students to create a series of greater than, less than number sentences.
I write the subtraction problem vertically, breaking each number into its expanded form: 88 = 80 + 8 on top, minus 69 = 60 + 9 on the bottom. I solve the problem out loud reminding myself of the no flipping rule* so the problem becomes 70 + 18 up top, minus 60 + 9 on the bottom. Subtracting tens from tens and ones from ones gives me 10 + 9 or 19.
* In the past I have shown students a picture of a gymnast flipping with an X across it. We talked about how you can't turn the problem over when you subtract - i.e. 41 - 26, we can't flip it and make 46 - 21.
I count students off into groups of 4 and ask them to compare the areas of all 4 of their monsters. I provide a paper for writing the number sentences and for solving the problems. I want students to identify the problems they need to solve and then persevere in solving them (MP1).
I have students return to their seats. I ask for one group to show us their monsters and to tell us their number sentences (without the answer). I ask for students at their seats to solve the problems. I tell students that we will share the other group's problems during warm ups tomorrow.