Students have been researching animal facts during non-fiction reading lessons. They have recorded some facts that they found interesting. I have taken those facts and written them up as a list of interesting animal facts entitled, "Did you know?"Did You Know.docx
Today we will use the "Did you know?" to determine what information is missing and to solve comparison problems.
I begin today by asking students what do you need to do to solve a math problem? (They will probably say, add, subtract, etc.). I ask what would happen if the problem was mostly in words? How would I know what to do? I put the following problem on the Smart Board as an example:
There were 16 ducks in the pond. There were 28 ducks in all. How many ducks are not in the pond?
I ask for volunteers to share with me what I should do to solve the problem and how do they know that?
Students at second grade often assume that they should add everything, or they ask, "do I add?" I want them to go beyond that to looking for what they know and what they need to know.
After a volunteer has shared their solution, I ask students what did I know? (16 ducks in pond and 28 in all) I put up a blank bar model (also known as a tape diagram) with two parts and a whole (see example part total example.docx). Which boxes can we fill in? Do we know a total or whole? I wait for a response. Ok we know that 28 is the "in all" number or total so lets put the 28 into the biggest box. Do we know another number? 16. That quantity makes up part of our total, so lets put in one of the smaller boxes at the beginning of the equation and call it a part. Will we need to add another part or subtract it to get to 28? (add) I write "16 +" on the board. Now do we know the other part? (No) OK lets put a ? (16 + ? = 28). Remember when we looked for mystery numbers. Now we have that mystery number to find.
Use your math suitcase to find a tool (such as number grids, number lines, blocks, addition/subtraction houses, calculators, rulers, templates, columns, graph paper, hands to represent counting up or down, etc.) that could help you find the missing number. When you have it fill it in.
I check here to see if students can solve the problem 16 + ___ = 28. They may be using drawings or other tools here to solve the problem. Students may suggest that this is a subtraction problem. I can help them see this by asking, "Do I have a total? (28) Ok where does a total (or biggest number) go in a subtraction problem? (first) ok lets put it first? Now do I have part of the problem? (16) Ok lets put that next. Do we want to add or subtract these two? (subtract). Great! Now you can again use your tools to subtract and get the answer.
"Some of you may see an addition problem with a missing number and some may see a subtraction problem with a missing answer. Both are correct. Remember our fact families?
3 + 4 = 7
4 + 3 = 7
7 - 3 = 4
7 - 4 = 3
"When we solve problems with either addition or subtraction, we are really creating a fact family. We were all using the same three numbers when we tried to solve this problem its just that some of us chose adding and some chose subtracting."
This is a complex thought. It is one you can keep returning to throughout this lesson and subsequent lessons.
I repeat this portion of the lesson with a variety of other problems with the missing number in a variety of positions. We work together for this part of the lesson so that I can make sure that students are understanding how to take what they know, plug it into a blank equation, find the missing piece and then solve for that.
I close this section of the lesson by discussing that there are 2 steps to a word problem, first I have to figure out what I know and don't know, and then I have to use one of my math tools to actually find the answer based on what I have decided I need. In other words I need to figure out what I don't know or make sense of the problem, choose an operation to help me find that out and then model with mathematics to use the operation correctly to obtain my answer (MP1, MP4). I post a chart asking:
1. What do I know? 2 parts; a part and a total; A bigger and a smaller part; a change from beginning to end?
What do I need to know? The total; a part; how much bigger or smaller something is; how much something changed
How can I figure that out? add, subtract, compare by counting up or down (other strategies the class suggests here or uses regularly).
CCSS 2.OA.A1 says that students will be able to complete comparison problems with unknowns in all positions using drawings and equations.
For the independent practice, I hand out word problems based on our "Did you know?" facts.What Do I Need Problems.pdf I remind students that they will fill in the equation form below each problem, and then use a tool from their math suitcase to solve the problem. They need to tell which tool they used. (Today we are not using calculators, so they will need to choose a different tool)
I tell students that I would like them to finish today by creating their own comparison problem using the "Did you know?" facts.
I circulate around the room to talk to students about their work, to check to see if students are using the equation form and sharing how they solved the problem. I note understandings and misunderstandings as a formative assessment for future lessons.
We close today's lesson by checking the equations we created for the problems, and looking at how they form fact families. We share solutions. I want students to check their own work so they have an idea of what they understood, the strategies they used, and what they might want to work on next time.
If we have time, I ask for a volunteer to share their problem. I ask 2 students to write the equation on the board, and to solve the problem. We look to see if they used the same equations and strategies.
If there is no time left, I begin the next lesson by doing this.