Students used temperature data to write comparison problems in a previous lesson. They also employed subtraction strategies to solve those problems. Today we will begin by sharing a few of the problems written by students.
I choose 3 problems that were written previously. I read the first problem to the class and ask them to solve the problem in their math journals. When most of the class has an answer, I ask the writer of the problem to call on someone to share his/her answer and solution. I ask the writer if they agree with the solver. If they do, we move on to the next problem. If they disagree, I ask the writer to show us his/her solution. As a class we discuss what is the same or different about the two solutions, and which one makes more sense.
We repeat this for the other 2 problems and then put away our journals and get ready for the next part of our lesson.
Today I want students to make a connection between the writing they have been doing, the science of motion and balance, and model with math (MP 4)to draw conclusions. I begin today by showing students some balance materials that they have seen in the past. I show them cardboard cutouts of triangles, semicircles, lobsters and a hand holding a pencil. In the past we have tried to balance the lobster shape on a popsicle stick using clothes pins as counterweights. I tell students that I would like them to think about what shapes they might like to use to see how long different things balance.
I remind them that we have been writing science journals. I ask, "What do we need in a science journal?" Students should recall that we start with a question and a hypothesis. I tell them that is correct and then ask if they can think of a question they might ask about the shapes and balance. They suggest several things. (If none of the questions are measurable, I may direct the questions. I want students to use a question like how long something balances, or does a larger object balance longer than a smaller object, etc. so they can collect some data for use in math.
I hand each student a printout of the science journal page and ask them to each write a question. I next ask them to write a hypothesis. I ask if anyone remembers what that means? If no one can tell me, I would remind them that a hypothesis is what we think will happen. I ask students to predict what will happen and to write it in a clear sentence with a correct beginning and ending.
Once they have a question and a hypothesis (remember how to write a question and what it begins and ends with), they need to write down which shapes they will use. Then I ask students to bring up their questions for me to see so I can make sure the answer will be measurable with time, size, etc (i.e. numbers), and to pick up the materials they need which include various shapes of several sizes, rulers, popsicle sticks, and tape. I tell each student they will need to tape a popsicle stick out over the end of their desk so they can balance on the popsicle stick.
Once everyone has their materials, I point out the table on their paper. I explain that a table is a place to record data. I tell students to test their shapes 5 times each and that we will use what they find to create math problems that will help us make conclusions and see if our hypothesis was right. I remind students that if they balance and object and count to 60 seconds which is? (a minute), they should record the 60 seconds on their paper and then turn to a new object.
Students test their hypotheses 5 times and record data on their tables.
My goal for the first part of this math for this lesson is to encourage students to develop strategies for adding multiple 2-digit numbers (2NBT.B.7). Students will have numbers ranging from 0 to 60 for their balance times.
I put a sample table up on the board. I tell students that we will use our findings for how long our shapes balanced to get a total balance time for each object we tested.
I put some numbers in the first column of the table and refer to them as my balance times. I ask students how I might find out how long my shape balanced in all. I let students make suggestions for how we might add the set of numbers. Together we add the numbers and get an answer, which I record below the column.
I tell students that they will do the same with their numbers. I give them about 5 minutes to add their numbers. I allow students to help each other as they finish.
For this second part of the lesson I am going to ask students to compare 2 of their totals. I am asking students to create a problem and then persevere in solving it (MP 1). Now I ask students to write a word problem to compare two of the columns. I write a sample question for my data. "How much longer did the triangle balance than the semicircle?
I give students a few minutes to write their question. Now I turn mine into a number sentence and record it on the board. I ask students if we are adding this time if we want to figure out how much longer one balanced than the other? (No). What are we doing? (counting up, counting back, subtracting.) I use their idea of counting up on the number grid to solve my problem of how much longer one balanced than the other. I ask students to do the same for their question.
Finally I ask students to solve their own question and to show the strategy they used to solve the problem.
Having students compare their math question and hypothesis is the final step of this process. I have students look at their hypothesis, and what they found out when they look at their totals, and modeled it with math problem (MP4). Did the math problem help to answer the original question and support the hypothesis? (Supporting the hypothesis, I tell students, is to see if the question, such as "How much longer did the triangle stay balanced?", help to support my hypothesis that the triangle will balance better? I show that I have an answer of 30 seconds for the triangle and 20 seconds for the semicircle, the numbers show me that my hypothesis was right.
I ask them to look at whether their own hypothesis is supported by the numbers they got, or not? We talk about how the numbers helped us, and that we could now write a conclusion just like a scientist does.
We think about what a good conclusion would be, such as "the triangle balanced longer than the circle because I balanced it on the long side and the circle didn't have any sides," and then each student writes a final conclusion based on their results.