I begin today with the review of partners of 10 and 100. I call out a number and ask students to write the partner of 10 or 100 in their math journals. I say 9, they write 1, I say 6, they write 4. I say 30, they write 70, I say 80, they write 20. I ask students what we call all of these pairs of numbers? (partners of 10 or partners of 100). I ask how can they help us to solve problems? (I let students suggest how knowing these can help us solve math problems.)
I say, "Now I have a challenge for you. Can there be partners of 1,000? What if I have 500? Raise your hand and tell me what 500's partner of 1,000 would be? (500). I tell students I am impressed that they could apply their partners of 10 and 100, to partners of 1,000. "Would you like to try a few more? What would 800's partner be?" "What about 600's partner?" I ask students to tell me how they are figuring these out.
I tell students that today we will be working with all numbers, but we are going to be detectives and try to find partners of 10, 100 or 1,000 in our work. We are going to record all those partners that we can find.
I purposely went from partners of 10 to partners of 100, but then stretched it to include partners of 1,000. Students get excited when they think they are adding or subtracting larger numbers. I challenged them to figure out the partners of 1,000. Students were more invested in figuring these out than they were with the partners of 10 which they have been doing since the beginning of the year.
I had students explain how they knew the partners of 1,000 so quickly and they said things like, "well, its just like partners of 10 but I put on the zeros," or "I knew 5 + 5 so this was easy, its just 500 + 500."
If larger numbers excite students, then it is worthwhile to bring them in to the discussion. The goal is for students to feel good about themselves as mathematicians, and for them to want to try new and harder things.
Students have been reading at home and keeping track of how many minutes they read each week. We are adding up the minutes and pretending they are miles. We are flying from Maine to Japan with the miles we read. I tell students that today we will try to add up the minutes. (Up until this point, I have added the minutes and turned them into hours so students have only had to add up small numbers such as 1+1+1+2+2+2+2+2+3+5+7=). Today we will try to add the larger numbers.
For this lesson you can gather your own data to use (or use the attached copy of our data). It should contain numbers less than 100 with some ending in zero and some not. For this first work with larger numbers I present the numbers in sets of 4. I purposely grouped partners of 10 and 100 next to each other so students would easily identify them. I want students to develop the idea of looking for partners on their own, but for this first experience, I am providing some visual assistance.
I say to students, "today we will add up our reading miles and minutes. I know you are all used to adding up the miles, but today we will also add up the minutes. This will be a little harder, but I know you can do it! Are you ready? I will give you a paper with 4 sets of numbers. Eventually we will add all the numbers together, but to begin, I want you to try to get a total for each set of numbers. What strategies might you use? (Students may suggest number grids, counting on, number lines, etc. I will bring up partners of 10 and 100 if no one else does. )"
I pass out the papers for individual work.
As students work on solving the multi-number problems I circulate around the room asking students to explain what they are doing to get the answers. I assist students who may be struggling by suggesting that they look for partners of 10 or 100. I have a word problem page for enrichment for students who finish more quickly. (You can find lots of resources for problem solving math by searching for second grade math word problems on the web.)
When most of the students are done, I bring students together on the rug with their papers, pencils and clipboards for a closing.
Students are gathered on the rug. We begin by sharing the totals we found for each set of numbers. I record the several answers students may have found. Then we share strategies for how they might have solved the problems. We try a strategy together and decide which answer is right. I remind students that even if they didn't get the correct number, if they were close with both digits, they should be proud of themselves. A lot of math is trying to solve the problem and using a strategy that might work. If we didn't count as carefully and came up off by 10 or by 3, we know we at least had a good strategy and should be glad of that. I want students to know that working at a problem is even more important than a perfect answer every time.
After we have agreed on a total for each set I ask students how we will know how many minutes in all? (We need to add all the answers.) I write a new problem on the board using all of the answers together. I ask for a student to tell me how he/she might start to solve the problem. We follow that step. I ask for another volunteer to tell me what to do next. We continue on until we have a total of minutes read.
I ask how many minutes in an hour? (60) How can we turn this into hours? I say that we want each 60 minutes in our answer to be 1 hour so we can add it to the hours we have. I take suggestions and then we talk about breaking the answer into equal groups of 60 (dividing). We can do this by subtracting on our calculator, or by using the division key. (Students have not been introduced to division yet, so this is merely an introductory discussion that we will finish by using our calculator to find how many hours the minutes equal so we can add them to the hours we read.