Today I begin with a warm up. I ask students to take out their math journals. While they are doing this I put two problems on the board and ask students to figure out if they are right or wrong and if they are wrong, what is the correct answer. (I write the problems vertically to help students visualize how they might need to manipulate the ones and tens if there are more than 9 ones in the answer when adding, or not enough ones when subtracting.)
136 + 207 = 3313 346 - 118 = 132
I ask students what strategies they might use to solve the problems? (columns, expanded form, mountains which are another form of expanded notation where students put the whole number at the top of the mountain and write the hundreds, tens and ones at the bottom of the mountain, tens frames or number lines can help solve the problems).
I have purposefully made common mistakes in these problems. In the addition problem I added the 6 ones and the 7 ones and got 13 ones so I wrote 13. Then I added the 3 tens and 0 tens to get 30 and 1 hundre plus 2 hundreds to get 300. I put them together, dropping out the zeros and got 3313.
For the subtraction problem I flipped the 6 and the 8 ones and did 8 - 6 = 2. This is a very common mistake in second grade and one that we have worked on in several ways during the year.
I give students time to solve the problems and then ask for a show of hands to see how I did today. Is this one right? (point to first) How about this one? (point to second) Can someone come up and show me how they figured out the problem. Call on a volunteer and let them explain their thinking. (You can ask for a second volunteer for each problem who might have solved it differently). Remind students that there is more than 1 way to solve a problem.
It is also possible that students will estimate the answer by rounding to the nearest ten and then adding or subtracting. If a child shows this strategy I say, yes that is the ballpark number and lets compare it with our other answers as a way of checking if our exact answer is in the ballpark of the right answer.
For the next part of the lesson I tell students that they are going to play a game in pairs ( I remind students not to grab a partner because they will be working with the person at their table whom I assign. Sometimes I let students choose partners, but for today I would like to pair a more competent student with a less competent peer to allow for peer teaching). I begin by modeling the game using one of the students for a partner.
For this game, you need a deck of cards with the ace through 9 cards only. Students will draw 4 cards and record them in any order as a money amount on their papers. (ie if I draw a 4,1,8, and 6 I could write $41.86, $84.61, etc.) I remind them that the zero is very important in this game. Do they remember talking about the big role that zero plays in cents? I ask for a volunteer to remind us what would happen if I left out the zero (for instance, if we wrote $41.06 as $41.6). After the first student writes his amount, his partner also draws 4 cards and writes her own money amount. I remind students not to forget the decimal point - the dot between the dollars and the cents. After the second student has written her amount next to the first student's amount, they must work together to draw an alligator mouth (I also say greater than and less than sign to reinforce the mathematical language here) < > = that shows who has the most money. They will need lined paper to write their money amounts and record the < > = signs. Students should play for about 15 minutes.
I want students to practice writing and reading money amounts and this game gives them a fun way to do that. The Common Core Standards include using dollar and cents amounts when solving word problems, so a familiarity with reading the amounts is an important foundation for using money.
After the game, I ring the bell and ask students to clean up and return to their seats. I have a short paper for students to do. These are word problems involving dollars and cents. Common Core standard 2MD.C.8 expects that students will be able to solve word problems involving dollars and cents. MP1 says that students should make sense of problems and persevere in solving them. Both of these standards are part of the independent practice today.
I ask students to also use the estimated (ballpark) amounts to solve the problems. I tell them that they can do the ballpark estimates first and find the answers. This use of the ballpark estimate gives an opportunity for success to students who may be struggling with the larger numbers involved in money amounts less than $99.99. They will be able to manipulate the whole dollar amounts, even if they are still struggling with adding and subtracting exact amounts.
I circulate around to support those students who may be able to do the ballpark estimate, but are not comfortable with the exact amounts. I help them find dollars and coins so they may work out the problems with manipulatives.
I give students time to work on their problems. If several students finish early I ask them to correct each other's papers together and to rework any problem they disagree on to determine the correct answer.