I begin today with some fluency practice. I give students the following equations to solve. They write the answers in their math journals. They do not need to write the whole problem, but some students choose to.
Problems: 40 + 40 = 70 + 30 = 90 - 20 = 100 - 50 = 60 + 60 = 140 - 70 =
I tell students that I will be only giving them a short time to solve each problem. They should go on to the next one even if they have not finished the one before it. I tell them that today we are working on figuring things out quickly. They might want to think about math facts they have been working on for homework, partners of 10 and partners of 100 as they work. I say each problem aloud, count to 10 silently and then give the next problem.
I stop and ask students to check their work. I say the problem again and allow the class to call out the answer. I repeat the correct answer and students check their work.
I ask students what did they notice about these problems? (They all ended in 0, some were partners of 100, some were math facts with zeros on the end, etc.)
Today I invite students to the rug to hear a story. I want them to get the idea that there is more than one way to solve a problem. We have talked about this before, but I still see students often relying on a single, inefficient strategy.
I tell the following story:
Once upon a time there was a carpenter's apprentice. (Do you know what an apprentice is? Someone who learns a trade from an expert). The carpenter's apprentice was very excited about his new job. He really wanted to learn how to build things from wood. He came to work on his first day with a new hammer, some nails and a screw driver. He was ready to work.
The carpenter said to him, today we will be building a cupboard. We will measure the wood, cut it with a saw, and hammer it together. The carpenter showed the boy how to measure the wood with a measuring stick, how to mark the wood with a pencil, how to cut the wood with a saw, and then how to set one piece against the other and hammer the nails from the back of one piece, through the wood and into the other. The boy did as he was told.
The next day the carpenter said, "today we will be building part of a house that I have started. You will help me to build the frame." The carpenter went to fetch his tools. Meanwhile, the boy was sure he knew what to do because he had learned yesterday. He measured a piece of wood the same size as the day before. He cut it, and he held it against the first piece and nailed it. He smiled at his work.
The carpenter returned and looked at what the boy had done. "What are you doing?" he demanded.
"Building the way you taught me," said the boy.
"That was for a cupboard," explained the carpenter. "Today we are building a wall and it is not done the same way."
The boy shook his head confused. "You mean that all building is not done the same way?"
"Of course not," said the carpenter. "Each project has a best way to do it."
"I will never be able to do that,"said the apprentice. "That is too much to learn."
"Nonsense," replied the carpenter, "with a little practice, you will know what tools to use and what way to do each new project."
I stop and ask the students what they think the apprentice learned about building? (That there is more than 1 way to do things, that there are different tools for different jobs, etc.)
I agree with the students and tell them that math is a lot like building. There are different tools, and different methods for solving problems. We don't always have to pick just one way to do things. We need to look at the problem, think about what we want to find out, and then find a way to solve the problem that works best for us.
I tell students that today they will have the chance to do just that. They will look at the problems, figure out the best way to solve them, and then work to find an answer. They will be working alone today, but we will check our answers at the end of class when we come back to the rug.
Before they leave the rug, I do a sample problem that I bring up on the Smart Board: The reason for doing a sample problem is to help children think about what is needed. I want them to see that I think about the problem, and try to make sense of what it is asking (MP1) and then model my thinking with mathematics as I try to solve the problem (MP4).
I have 36 balloons in a bag. I need 19 balloons for the class. How many will I have left over? Do I have enough to give everyone a second balloon?
I talk through the problem as I solve it: "Hmm, 36 balloons in a bag." (I draw a bag with a picture of a balloon on the outside and write 36 on it.) "Hmm, and I need to take 19 out of the bag. That means there will be less in the bag so I must subtract 19" (I write - 19 next to the bag.) "Now I know that I need to figure out 36 - 19. Let me see, I could draw base 10 blocks, or maybe ten frames, or I could write it in a tens and ones house. I think I will draw ten frames for 36 and then take 19 out of the frames. (I draw 3 full tens frames and 1 with 6 in it.) I need to take away 19 so I am going to take away 9 out of this frame (I cross out 9) One is left so I will put it with the 6, now I have 7 in that frame and I need to take away 1 frame because 19 has 1 ten in it. I cross out 1 frame. Lets see, now I have 1 full ten and 7 so I have 17 left. So to answer the first question, I have 17 left over. Do I have enough to give everyone a second balloon? (I let students say NO).
If I feel that students may need additional explanation at this point, I may give students a choice and say, if you are ready to do this on your own, you may go back to your seat with your paper. If you are still a little confused, stay here and we will work on these together. I often invite several students to stay if I know they are struggling.
I have students help me work through the problems on the board. We try different strategies as we work. Students fill in their own papers at the same time.
I invite students to come back together. We look at some of the problems we have solved. I ask for volunteers to show us different ways that they solved the same problem. We talk about how there are different strategies for solving a problem and that knowing which which one works for us and which one is the most efficient, is the key to liking and doing math. (I could always use tally marks to get an answer, but if I am adding 325 + 499, that would be a lot of tally marks to make on my paper, so I look for another strategy that might be more efficient such as adding the ones and getting 14 and the tens and getting 110, and the hundreds and getting 700, and then putting them together to get 824 is a lot more efficient than drawing all those tally marks.