I begin this lesson by asking for about five student volunteers. I have those volunteers stand in a line, one behind the other, in the front of the room. Then I choose one student in the line. I ask the remaining class to turn and talk with their neighbor about how they could describe that student's place in line.
I am looking for the students to be using language that describes linear relationships but I realize that they needed some help to understand the context of what I'd asked them to do. Tell me, who is our volunteer next to? Are they before or after our volunteer? What else can you tell me? What about other people in the line? Where are they compared to our volunteer? Is that the same as ________?
I hear how the volunteer is in line after so-and-so, before so-and-so. Students also notice how each student could be third, fourth, last, or first in line.
I then have the students take out their hundred chart. I ask the students to turn and talk about what they notice about the way a hundred chart is set up. I am looking for the students to be discussing the patterns across the rows, as well as the patterns down the columns. I then ask one student to choose a number (preferably one near the middle of the hundred chart). I ask the rest of the class to put their chip (or some kind of counter or bead) on that number. I like to use colored, transparent Bingo chips because it helps the students visually track where they are on the hundred chart. I tell the students that I would like them to turn and talk about what numbers come before and what numbers come after the number they have their chip on.
We complete several examples of this concept (before and after). It is important for the students to be able to identify the numbers that come before and after, but also to be able to use the language of before and after. For each example that I have the students complete in this section, they must use their hundred chart to identify the numbers before and after, as well as tell me a sentence for the relationship of the numbers. For example, if the student is to put their chip on the number 34 on the hundred chart, then they would have to say the sentences "33 is one before 34," and "35 is one after 34." I want them to understand and use the language for this idea.
Some students may struggle with moving outside of a number row. This lesson can also be done with number lines.
For this section of the lesson I have the students play the Before and After I Have Who Has Game. For this game, each student receives a card (or a few students could have more than one card, depending on the size of your class). I allow my students to sit on their desktops, just because it's fun!
Have one student read the "Who Has" section of their card aloud. It doesn't really matter which card you begin with, as long as you remember which student began. Each student must listen to the cards being read carefully to see if they have the answer to the question. Continue to go through the game until you get back to the first student.
I play the game several times. The first round I have the students just get used to the game. Then I have the students play the game again, this round I time it. Then they play a third round to see if they can beat their previous time.
To wrap up this lesson, I show the students the following riddle:
"I'm thinking of a number. It is one before 44. It is one after 42. What number am I thinking of?"
I have the students turn and talk about what number it could be and how they could tell. I look for those students who still need to use their hundred chart and those that can complete it mentally.
Then, students write their own riddle in their math journal, to have a friend solve. By asking my students to create a problem of their own, based upon what they have learned today, students are modeling a real-life (at least for them) mathematical story and checking to make sure their work, and their neighbor’s work, is accurate (MP4).