I begin today by reviewing place value with ones, tens and hundreds. I want students to attend to precision(MP6) as they count. Students have been counting by ones, tens and hundreds in previous lessons. This lesson expands that counting as we continue to count across decades and centuries. I ask students if they think they can count by tens from 30 to 130. The students count out loud in unison to 130. I ask students for a thumbs up if they think this is easy. I expect here that most students give me a thumbs up as this is review.
I ask students if they can count from 165 to 265 by tens. I point to students one at a time and ask each one what comes next if I start at 165. As students say the numbers, I write them on the board. This provides a visual reference for each child in addition to the auditory cues. When we are done I ask if students can tell me which place changed as we counted from 165 to 195 (the tens). Then what happened? (it goes to 205). I ask what we count by now (tens still but now in the 200s. I want to reinforce the change here across centuries. I ask students if they remember that 9 was a cue in changing tens when we made our rivers and our canoes in a previous lesson. Now the 9 in the tens place will be our cue. It says "get ready, we are about to cross into a new hundred. You are in the 90s so next will be a new group of hundreds. Ready, set, change! We counted 195 (there is our cue so get ready to change from 100 to 200, and keep that 5 in the ones place just like before so 195, 205! We did it!
I put 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 300 on the board and ask if this would be correct. ( I know that students often make this mistake, forgetting to change the tens place and I want to know if students can see this mistake.) Some children see right away what I have done, but others think that what I did was correct. I ask a volunteer to use base ten blocks to build 199. Now I have a student change that to 200 (what do we add, what can we trade in now). I continue this up to 209, and then ask what would we change if we added one more. We add and count and find we have 210. I ask students to count out loud with me starting at 1 and going to 11. I write the counts on the board under the numbers I just wrote ( 199, 200..) . I ask students to notice what is similar and different about the counts (notice the ones place and the ones I just wrote) and they explain what they see. Many students are able to see and point out the pattern. Those that don't see what has happened, are able to visualize when a peer comes up and points out the ones digits 1 - 9 and then the 10, 11, and the same in the 200s by covering the 2. Finally we clarify why my original count is a mistake. That 9 was in the ones place so it is saying cross into the tens not the hundreds, so what would be correct after 209? (210).
The students have looked at research on planets . In a previous project they found the distance from the sun for each planet. Today they have the average temperatures for each planet. I ask each group to tell me what they found. As students tell me their temperature, I write them on the board. I tell them I am going to put a zero in the ones place to make this a little easier for us. I ask students which planets have only 2 digit numbers meaning they are in the tens (earth and mars). What place do all the rest go to? (hundreds). Notice that the temperatures go from 2 to 3 digit numbers and some have a negative sign in front of them.(I have written them below for reference in order but on the board I did not put them in order.)
Mercury 870 F
Neptune - 330F
I purposely do not call on the planets in order, but put them up in random order. Next I ask students if they know what the little - sign means in front of a number? Several students know this means less than zero. We talk about what less than zero might mean. I often discuss less than zero with money. It is hard to conceptualize less than 0 with temperature because it is still a temperature, but with money I say, "if you have 10 cents and want a toy for 25 cents and your dad lends you the difference of 15 cents then when you get your allowance next week, you would have to give the first 15 cents to your dad. For the time in between you had less than 0 money.
I also talk about the cold and temperatures they are familiar with, (a cold winter day of 20) above zero. A very cold day might be zero, or slightly below zero, but in Alaska, it is common to have days that are less than zero. I also say that 0 celsius is when water freezes so below zero is below freezing.
I reference the large number line at the top of the room that goes from -20 to 120. Next, I point to the zero and show how there are numbers larger than 0 (the ones we usually count with) and numbers less than zero that have a negative sign in front to them to show they are less than zero.
Next I draw an open number line on the board to show students where zero might be, and how we can keep going down below zero. If we go further away from zero, we are getting more and more cold so the numbers get bigger. I use my arms to show a little cold at zero and keep making them further and further apart showing how the numbers are getting more and more "bigger" because there is more and more cold. It is a tricky concept, so modeling (MP4) with your arms and with the number line by showing 1 away from zero (-1), then 2 away from zero (-2) helps to show that the numbers are getting bigger meaning further and further from zero.
Finally I ask each student to try to order the planets from hottest to coldest using an open number line. I help them decide where earth might be as a starting point. I circulate around and help students who may be having some trouble placing the planets on the number line.
I realize that second grade CC standards do not address negative numbers, but students see these numbers in many nonfiction things that they read. I have decided to introduce what the negative numbers mean to help students when they are reading nonfiction.
After students have written the order of the planet temperatures on their paper, we share their ordering of the larger numbers for the planets. We post the order of the planets on the board on the open number line that I created at the beginning of the lesson. The number line presents a visual much like the hanging planets that show the distance from the sun. I ask students if they notice anything about the order of temperatures and the order of the distance of the planets from the sun. We notice that the order is the same and talk about why that might be (students should realize that the closer to the sun the hotter the planet and the further away from the sun, the colder the planet).
To finish the lesson today, I ask students to try to create a word problem (or more than one) comparing the temperatures of 2 planets that are above zero, Earth is 60 degrees and Mercury is 870 degrees. How much hotter is Mercury than Earth? I ask if anyone can give me a number sentence for my question. Students may suggest 60 + ___ = 870, or 870 - 60 = ____ . I ask students how they might solve this problem. (Here we are making sense of the problem and trying to solve it (MP1). I expect that students may try to solve the tens first on their number grid, or in their head, figuring out that 70 - 60 = 10, and then keeping the 800 so the answer is 810. Students may write the problem out and use the tens and ones, or their number line to solve the problem as well.
I give students about 10 minutes to write out and solve their problem. When everyone has at least 1 problem written, I bring students to the rug with their papers.
As an extension for those who quickly write out problems for planets above 0 degrees, I suggest they try to compare 2 planets whose temperatures are less than zero. I tell them that they can drop off the negative sign to do this because they want to compare the two temperatures and how much higher one is than the other. This would mean we could find the difference in degrees from 1 negative number to another rather so because we are only figuring out the difference, the negative sign is not important here. (This is well beyond second grade expectations but for students needing a challenge, it is a good extension of their thinking.)
I ask one student to read us his/her problem. I ask a volunteer to write a number sentence that matches the problem on the easel. Next I ask for volunteers to come up and solve the problem for us. We work through several problems in this manner.