Adding and Subtracting with Lengths

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SWBAT measure the distance 2 objects travel off a ramp and compare using addition and subtraction strategies.

Big Idea

Students will use their addition and subtraction strategies to measure and compare distances, solving using centimeter units.

Warm Up

10 minutes

I begin today with a review of repeated addition strategies. This will provide support for students measuring a length of more than 12 inches using a ruler.

I put the problem 7 + 7 + 7 on the board vertically (to reinforce the idea of vertical addition and subtraction). I ask students to solve the problem in their math notebook, asking for a volunteer to come up and show how they solved the problem. When they are done, I ask if anyone solved using a different way and would like to share. I take a second volunteer.

Next, I put the problem 12 + 12 on the board vertically. Again, I ask students to solve the problem in their books and then I ask for volunteers to share their solutions. 

I hand out a ruler to each student, as well as a piece of clay (I use 5 colors so I can form teams of 4, by color, for part 2). I ask students to use the clay to make a ball no bigger than an inch high, and a log no longer than 4 inches long. I tell students they will have 5 minutes to make these 2 objects, which we will be rolling today on a ramp, similar to the rolling of cars during writing last week. 

At the end of 5 minutes I ask students to put away their math journals and to leave the clay ball and log, and the ruler on their desk. (I use the reminder of "hands and eyes" to proactively cue students not to play with the things while I am explaining our activity.)

Collecting Data

10 minutes

I tell students that we will take 10 minutes to roll both the ball and the log down a ramp, and to measure the distances they each travel. I ask them to predict which will roll further, and why, and to write that prediction at the top of their papers. I have the students build the ramps with a 12 X 24 inch piece of cardboard set up on 3 second grade dictionaries that are about 1 1/2 inches wide each.

Now I organize students in groups of 4, which is determined by the color of their clay, and each student should record all 4 rolls of the ball and all 4 rolls of the log on their recording sheet. I circulate as students are working, keeping a particular eye for those students who might struggle with the motor skills needed, who might become so excited by the activity that they fail to record data, and as always as an enthused facilitator. Any feedback I give is deliberately not directive. Students may productively struggle at times, but developing a habit of perseverance is an important part of becoming a successful student. I also give students an idea of elapsed time, and time remaining essful student. I also give students an idea of elapsed time, and time remaining (both 3rd grade measurement standards so why not begin to help them think about time in these ways), so that they aren't "surprised" when I call the activity to a close.

At the end of 10 minutes, students to return to their seats with their clay and their recording sheets. They should have 8 measurements to use for creating and solving math problems. Students should be careful while measuring in centimeters (MP6) to attend to precision so their measurements can be compared. They may choose to use a meter stick, or centimeter ruler to record distance (MP5). This helps students to think about choosing the appropriate tool for the job. The person who owns the clay gets to decide the total distance if there is a disagreement. 

Creating Math Problems

20 minutes

Students now create comparison problems using the data they have just collected. I ask students what types of things we might be able to figure out about the balls and logs in our experiments? (Students may suggest which one rolled further, how much did they roll together, did all the balls roll the same distance, etc.)

I model how we set up the problem, using actual data. I ask a student how far their log and ball rolled, writing on the board, "The ball rolled 38 centimeters (cm) and the log rolled 22 cm. How much further did the ball roll?"

I ask for a volunteer to come up and show the number sentence they might write for the problem. Now, I ask for a volunteer to come up and try to solve the problem. I support students through this process as needed.

If I feel that students are not clear on what I am doing, I do another problem. If they understand how we set up the comparison problem (which is dependent on distance, not object), I ask students to write at least 2 comparison problems using the information on their papers. They might compare red balls to blue balls, or logs to balls, or yellow logs to red logs, etc. 

I circulate around as students are working and provide support as needed. 

I give students the time they need to write the problems.


10 minutes

Our closing today is the sharing of the math problems. 

When I can see that everyone has at least 2 problems completed, I ring the bell. I ask for a volunteer to read out a problem and I tell the other students that they will try to solve the problems in their math notebooks.

I let the reader call on someone to share their solution. Sharing, at 2nd grade, often includes showing. If students struggle to explain their thinking, they are encouraged to also show it on the board. However, once a problem has been shown, it is important to help these students to learn how to explain their thinking. So, using facilitating questions, I guide these students through describing what they have shown.

If a student makes an error in their problem, it is particularly critical that this is managed in a way that doesn't defeat the learner. I prefer to help the student, through questions, to see the error. Another way is to ask other students if they have a different solution, and ask them to show and explain their thinking.

We share several more problems, depending on the time available. I save those problems we haven't time to share today for warm ups on another day.