We open by solving 8 + 2, in math journals. I start with partners of ten and doubles because these are familiar and good for warm up. Working with making ten (partners of ten) is important practice for 2nd grade students, because decomposing and composing develops a flexible understanding of numbers.
9 + 1 = _______.
Now let's try something a little harder. Do you remember doing doubles? Compute 8 + 8 = ____.
6 + 6 = ___.
What about subtraction? Can you figure out 10 - 3 = ____? 10 - 8 = ____.
We check our answers together so I can do a quick check for understanding. I decide to continue with a few more.
14 - 7 = ____. 18 - 9 = ____. Again, I stop so we check our answers.
My goal is to build success, not to stump my students.
You all did those pretty quickly. I am proud of how quick you are becoming with partners of ten and doubles. Thumbs up if you feel confident with adding and subtracting partners of ten and doubles!
Ok I have a problem for you. What if the number sentence looked like this? I write 7 + __ = 14. What would you do?
I ask a student to explain how they might solve that problem. Some will recognize immediately that it is a double and say, I know 7 + 7 = 14, so the missing number is 14. I give another example using a partner of 20. Can you figure out 16 + ___ = 20? Again, I ask a student how they solved the problem.
Today we are going to be detectives and see if we can find the missing numbers, no matter where they are in a number sentence. It will be our job to figure out what is missing and see if we can solve for the missing number.
I bring students to the rug where I have number cards to 50, a +, a - and a = sign card as well as a clear card with a magnifying glass on it (the detective idea). The cards are as follows: 1,2,3,4,5,…50, + - = and the clear magnifying glass. These cards should be made in advance so you can use them to create a wide variety of math sentences by rearranging the cards.
I set up the number sentence: "magnifying glass" - 8 = 12. I ask if anyone can find a card that would go under the magnifying glass? (Make sense of the problem and persevere in solving it MP1)
I wait for most of the students to have their hands up. If I call on someone too quickly, those who are slower to process their thinking don’t even bother to try, because they know someone else will answer for them. To reinforce the expectation that all students participate, I indicate I'm (patiently) waiting by saying, "It looks like six people have it. We'll wait a few minutes for others to figure it out". This reminds all students that their answer is important. When that time comes, I call on someone to come up and show their thinking by filling in the magnifying glass with one of the cards from the pile. We talk about how they know what to put there. Is the sentence true now? Were we good detectives?
We model the number sentence with blocks to check its accuracy.
I continue with the thinking through start with an unknown equations for 15 minutes. We talk about always seeing if the new equation makes sense, whether it is "true" or not, and the importance of checking the accuracy of our mathematical computations. We also talk about how manipulatives can help us check our work if we are unsure of an answer. Checking for accuracy: this is helping students to reason abstractly and quantitatively (MP2)
As we work, I talk about how equations can go in any order as long as one side is equal to the other. We create number sentences horizontally and vertically, as well as using the inverse property, to demonstrate equality (the balance scale was how we've done it previously, and it is the symbolism I use now) and how an equal (=) symbol means that the quantity on each side must be the same.
I check for understanding during this time by calling on each child and carefully listening to how they are solving the problems. It is important that I don't "speak for them" or finish sentences. I want my students to do the work themselves.
I want students to continue to work with the idea of making sense of equations, even if they are not presented in the A+ B = C format. I hope that by moving the magnifying glass to different parts of the equation, students will begin to connect part part whole relationships.
I invite students to sit at their desks. I give them snap blocks. I ask them to look at the equation I have written on the board. Magnifying glass + 3 = 9. I ask them to take 9 blocks and make a tower. I tell them that is the total. Now I say, how many do you already have in your matching tower? (3) How many more do you need to finish the tower? (6) Would 6 + 3 = 9 be a true sentence?
Great, let's try that again. Make a tower of 12 while I write on the board 5 + magnifying glass = 12. How many is in our total tower? (12) How many in our matching tower? (5). How many more do we need to get to 12? (7).
I repeat this process putting the magnifying glass in both the beginning and middle of the addition sentences for 4 more examples.
When I feel that students are secure in this process, I stop for the day. I will repeat the process at another point using subtraction with the blocks. I hope that by modeling with math blocks, students will begin to see the part part total relationship. (MP4)
I put a word problem on the board. I try to keep it similar to the math sentences we have used today. I write:
I have 16 marbles in a bag. How many did I get at the store if I had 13 before I went to the store?
I ask students to build the total number of marbles with their blocks. Now I ask them to build the second matching tower and see if they can figure out the mystery number. I also ask them to write the number sentence for the problem. I am interested to see if they will write 16 - mag.glass = 13, or whether they will write 13 + mg = 16, or 13 + 3 = 16 or 16 = 13 = 3. All of these are acceptable, and give me some insight into how they are making sense of the problem and solving it. MP1.
This problem reflects a number sentence not in traditional order and, as a word problem, creates a context using language which needs close reading for correct interpretation. I review their math journals and block towers to check for understanding.