I begin this first math lesson of the year by gathering the children together on the rug. I hold up a cell phone and a rock, asking if either of these objects has anything to do with math. I encourage the children to turn to the person beside them and share what they think about the two objects. Next I tell the students that we are going to do a thumb vote.
As it is the beginning of the year, I explain that a thumb up means yes, a thumb down means no and a thumb in the middle means they are not sure. I remind them that I will hold up each object, one at a time, and if they think the object has to do with math they will give a thumbs up, if not a thumbs down, or if they are unsure they can put a thumb in the middle.
I hold up the rock and tally the results on the chart. I repeat it with the cellphone. Using tally marks gives me a chance to see if they remember this skill from first grade. Once I have the results, I ask several students to justify why they said each object did or did not have to do with math. I encourage students to accept that there may be several points of view for both objects.
The process of asking students to explain their thinking is at the core of the Common Core Standards for Mathematical Practices. Students in this lesson are critiquing viable arguments and critiquing the reasoning of others (MP3). As the lesson progresses, students continue to present their own arguments for why something is or isn't math and they also listen and consider the reasoning of others.
At this point, after about six to ten minutes of listening, thinking, and speaking, it is a great time for a 3 minute stretch before the kids sit at the Smart Board or other video projection for the next part of the lesson. I might count jumping jacks by 2's because its a a great way to include math into the stretch.
Today I begin by introducing the SmartBoard (this is something new to many students at the beginning of the year). I explain how the SmartBoard is a tool like an iPad or computer or iPhone, but one that everyone can use at the same time.
If you do not have a SmartBoard, or similar device you can do this lesson by printing and cutting out the pictures and asking students to move the pictures around. I've provided some ready made images that can be printed here, as a resource. You may want to consider the "landscape" of your students' home cultures, and develop picture or realia resources that provide opportunities, particularly for ELL students, to name and share objects that are common to them.
I bring up the picture lesson on the SmartBoard. I have to teach children how to drag pictures on the SmartBoard before they can sort them into Math Activities and Not Math Activities. Next, I call on individual children to come up to choose a picture to sort. I always have them explain why they chose to put the activity where they did. I ask for feedback from the class after each picture. "Do you agree or not?" Again, I ask why or why not. I am encouraging students to use math reasoning and to apply it to the objects they see. I want them to be begin to use viable arguments and to critique the reasoning of others (MP3).
I tell students that there is no one correct answer. Sometimes math has a right answer, but at other times, answers can be different depending on how an individual figured out the problem. Students will begin to stretch their concept of what is and is not math as they discuss the objects. Reasoning is a critical math skill recognized and emphasized by the Common Core as essential to the development of mathematical understanding.
I give each group of students a large piece of paper and ask them to draw or write about all the things that they think have to do with math. I have desks in my classroom, but I keep the desks in clusters to encourage this type of student interaction.
After about 10 minutes I gather students together to share out what they made. I let each student share at least one thing that they thought of that no one else has mentioned. I keep the papers to refer to at the beginning of the next lesson.
I've attached three examples of student work, and explain in each case the child's reasons for why the object(s) drawn represent math. Open-ended student work gives me deeper understanding of student thinking. Because there is no one "set" correct answer students feel "safe" to share their thoughts.