To see this part of the lesson unfold, watch: Classroom Video: Flexibility
I will start the class with the Quick Flash activity using cube images. I will have the students sit down at their tables or on the floor. I will flash card I first. In order to do this, I use the document camera, I flash the card for 2 seconds and then remove it. The students should try to recreate the image using the tiles on their table. After a few seconds , I will flash the image again to allow kids to check their work. I will then cover it and wait a few more seconds. Finally, I will display the card permanently and slow students to check their work.
"We are going to do more Quick Flash cards today. I want you to use the tiles that are on your table or in front of you. I will flash the image once, then again, and finally leave it up for you to check your thinking."
I then proceed with the routine using card I, then J, and finally M.
"Who can tell me how they saw the first card?"
Students will offer a variety of answers: "I just knew it was three," "I counted each of them," and/or "I saw it as groups of numbers." I will allow students to come up and model their thinking (pointing to the displayed image on the Smart Board. It is the expectation that mathematically proficient students "make sense of quantities and their relationships in problem situations. That they can bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically (CCSS.Math.Practice.MP2)." This activity is one way of developing this ability with first graders.
NOTE: These cards are taken from the Investigations Math Program. I have included all three sheets for you to see. You will need to create your own set if you don't have permission to copy the Investigations materials.
To see this part of the lesson unfold, watch: Classroom Video: Developing a Conceptual Understanding
I will have all of the students gather in a spot on the carpet area and face the white board easel.
"Today, we are going to count and write down our counts on a special type of paper. We are going to start with one and get to the highest number that we can. How high do you think we can count?"
I will take a several responses from them. Their responses will give me an idea of what they think a large number is.
"Let's start counting together as a class. I would like us all to stay together as we count. We wills tart with 1."
I will continue the count until most of the students have faded or we go past 100.
I will then direct their attention to the easel and model how to set up and use a counting tape.
"When you start your strip, I want you to put your name on the top." Then you can start writing your numbers one under the other." Let's try this, What comes after 1?"
I will quickly write the first 10 numbers. Then I will continue and ask them how to write numbers along the way (For example, How do I write 21? Is it 12 or 21?). I will stop once I get to 32. I will then ask them: "Do you notice any patterns on my counting tape?"
Some students will notice the pattern int he 1's column and some might notice the pattern in the 10's column.
"You will now each make your own tape. First you will write your name and then begin with the number 1. I want you to write as high as you can count. I would like the numbers to be neat and clear. If you run out of room, you can tape more paper onto your number tape." It is expected that first grade students can "count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral (CCSS.Math.Content.1.NBT.A.1)." This activity allows for continued development and growth toward this expectation.
**I am going to have all but two of my students do this. The other two students are going to start at different spots. The one student will start at 90 and the other student will start at 990. In previous assessments, these two students have demonstrated that they are secure with writing one and two digit numbers. The one boy is also secure in writing three digit numbers, so I will quickly push him to thousands. I will dismiss these two form the carpet last, so that I can privately talk to them about the accommodations that I am making.
As students are working, I will be circulating looking for the following:
*How far in the counting sequence are students able to write numbers? Are they reversing any digits?
*How are the decade transitions going?
*Are any patterns being recognized by students?
I have added a picture of a student's tape int he resource section.
To see this part of the lesson unfold, watch: Classroom Video: Debate
Advanced preparation: I will make a poster with different examples of number tapes with errors. This poster will be used to lead a discussion about errors. The important idea from this conversation is not what the write answer should be but rather why the mistake might have been made. There is an picture of the poster in the section resource. It is the expectation that mathematically proficient students "make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose (CCSS.Math.Practice.MP3)." You will see that students are suing mathematical reasoning to justify their thoughts in these examples.
"I've been walking around and looking at your number tapes. I have created a poster with some common mistakes that 1st graders make. Let's take a look at each example. What do you notice about the first one (there is one number missing)?" I ask them to turn to someone and tell them what they think. "Why might this mistake happen? Who can come up and fix this for us?" Call on a student to come up and fix the tape.
I then repeat the process for the second and third example.
"I also noticed that some people have gotten past 99 on their strip. I would like to talk a little about this. I will break you up into groups of 3." I quickly break them up and am doing this based loosely on ability (the reason being that I want students to be able to represent their thinking and not just follow the lead of student who is at a more developed understanding of writing the numbers). I give each group an index card. "I am going to ask you to write a number on the card. You should decide as a group how to write this number." I then dictate the numbers 105. I ask each group to write the number. I will then post them onto the board. "We had 105 written different ways. Which way is correct?" I will then let a few students discuss there thinking. Someone will surely say you write 100 and then 5, so it is 1005. I will then pose the following: "Let's stop and think about a smaller number. I write the number 20 not he board and ask what the name of the number is. Then I write the number 26 on the board, If your thinking is correct, I would write 20 and then 6, so it would be 206. Is this correct? Let's try another number. I want each group to write the number 116." I then post their examples and ask which one(s) are correct? I want to focus on the connection that 105 had three numbers, so 116 will need three numbers and that the 1 represents 100.
This is an initial discussion with this concept and mastery is certainly no expected. Learning to write numbers correctly and in sequence takes time and I will allow for more practice in future lessons. I just want to give the students an opportunity to look for and make use of structure. "Mathematically proficient students look closely to discern a pattern or structure (CCSS.Math.Practice.MP7)."
To see this part of the lesson unfold, watch: Classroom Video: Performance Tasks
I will end the class with Center Time today. Students will continue working on their own number tapes that they started earlier in the lesson.
1. Number Tapes: Remind students of the resources that are available in the room, if they get stuck on a number. This can include the number line, number grids, or asking a partner. The expectation is that mathematically proficient students "use appropriate tools strategically (CCSS.Math.Practice.MP5)." In this case the students can sue number lines, the calendar, and/or 100 grids. I want to make sure that they know the tools are available but not tell them which to use. I want them to choose a toll that they know how to use and can be independent with the sue of it.
Mathematically proficient students consider the available tools when solving a mathematical problem.
2. Assessment of Counting 40-50 Objects: I will continue to call students over (started in a previous lesson) and assess their ability to count 40-50 objects. I will use the check sheet provided. Please see the linked lesson above to print out the check sheet. *Note: This will only happen if I didn't get through everyone in the previous lesson.