I begin this lesson by asking the students what it means to compare. Students consider this question in a turn and talk with a group or partner and then discuss, as a class, their ideas about comparing.
A student is then asked to see how many of certain classroom objects they can grab with one hand. I use glue sticks. Then see how many you, as the teacher, can pick up with one hand. At this point the students discuss how the teacher and the student volunteer could compare the glue sticks. How are they the same? How are they different?
As we discuss this, the use and purpose of a balance scale may come up. If not, I introduce this as a possible tool by asking, "Can we use a balance scale to help us compare the two amounts of glue sticks? How would it help us? What information could it give us? What won’t it tell us?"
We discuss how we can use comparing to help us solve comparison word problems.
I read aloud, and write on the board, a comparison word problem. I think it is important to engage a number of learning modalities for students, as comparison thinking is going to be cognitively demanding.
I have the students use their connecting cubes to create both groups of objects from the word problem. Then instruct the students to place the cube “trains” one on top of the other.
Compare the two trains of cubes.
What do they have that is the same?
What is different?
Remove the cubes that they do not have in common.
This is the difference.
Then we discuss what subtraction problem we could use to solve this comparison problem.
It is important to practice this several times because for many students, this is a different way of reasoning. We practice together with several more word problems. Each time I have the students build the two groups of objects with cubes and compare them, removing the cubes that the trains do not have in common.
My students use a visual resource to help them practice building, comparing, and determining the subtraction number sentence for the word problem.
I close this lesson with a whole group discussion. Students first turn and talk with a neighbor or group about what they know about comparing in math.
I ask them to share, "How you can tell the difference between a separating subtraction word problem and a comparison subtraction problem?" Finding the words to explain their thinking may be difficult, and students are always encouraged to use examples to illustrate their thinking. These examples are often written on the board, either by the student or by me at their direction. This gives all of us a good starting point for a discussion and provides me with insight into their understanding as well as an opportunity to guide them in using math vocabulary in context.
During the math share, I am deliberately developing the students' mathematical thinking, described in MP3 as the practice of constructing arguments and critiquing the reasoning of others.