Counting By 2s

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SWBAT count and find the total of items that come in groups of two. SWBAT rote count by 2. SWBAT record their thinking.

Big Idea

Eyes, shoulders, knees, hands, and feet are the many things that come in twos. Today your students will learn to count groups of eyes as they find the total number of eyes for a given number of students.

Warm Up

10 minutes

The students gather on the carpet and face the Smart Board.  They will need a piece of blank paper and a pencil.  Using the Quick Flash Dot Cards, I will flash three sets of three dots for two seconds.  I will ask them to figure out how many dots there are and then share their strategy.  

"I am going to flash a set of dots for a few seconds.  Your job is to figure out how many dots there are in total.  I will then ask people to come up and explain their thinking to the class.  While students are sharing, I want you to compare it to your strategy and decide if it is the same or different."

I then repeat this process with three fours and then three fives.

As students explain their thinking to the class, they are trying to communicate precisely to others. They are using clear definitions in discussion with others and in their own reasoning. They are stating how they found the total and their rationale for how they saw it (CCSS.MATH.PRACTICE.MP6)

Introducing Groups of Two

15 minutes

I start with a blank chart labeled, Things That Come In Twos.  

"Who can tell me things that come in twos?"  

I will write down their ideas.  I want to make sure that body parts are mentioned. 

"I want to focus on eyes.  Our eyes come in twos.  We have a left one and a right one.  Suppose we wanted to find out how many eyes were in a group of three children.  How could we figure that out?"

I then ask students for suggestions and chart each idea on the chart.  At first I drew 3 heads and out 2 eyes on each one.  Then I took other suggestions from the students and recorded them on the chart (Ways to Represent Six Eyes.png).

It is important to understand that some students may still need to count by 1s.  This is ok and their reliance on this strategy will become less as their understanding of this concept develops.

In this case and in the task in the next section, the students are working on an activity that relates counting to addition and subtraction (e.g., by counting on 2 to add 2).  They are also using repeated addition to find the total number of eyes (CCSS.MATH.CONTENT.1.OA.C.5 & CCSS.MATH.PRACTICE.MP8).

How Many Eyes?

30 minutes

Advanced Preparation:  You will need to make enough copies of Counting Eyes.  

"Now you are going to work on some problems that ask you to find the total eyes for a group of 7 students. Once you finish that, you will solve a few other problems with a different number of students.  I want you to find a spot to work on these problems by yourself.  You can look at the chart we created to see different ways that you can represent your thinking."

As students are working, you will want to circulate and see:

  • How are they modeling their thinking? Are they using pictures, their fingers, counting out loud, or are they using mental facts?  An example of this is Using Pictures To Represent
  • How are they counting? By 1s or 2s? Or are they seeing it as a repeated addition problem or a doubles fact?

I have also included another problem involving tricycles, How Many Tricycles?.  This can be used as a challenge and/or second task.

Lesson Wrap Up

10 minutes

After the students have had ample time to work on this task, I gather the students in from of the Smart Board, so examples of their work can be presented.  As they are working, you will want to identify the types of solutions that will be shared.  In this case, I had students solve the task one of three ways.  So I am having each example presented to the class.  There is a video of each presentation as well as a copy of each presenters work.  

"As you were working today, I noticed a variety of ways that students were working to solve each problem.  Some of you drew pictures, some of you counted by groups of two, and some of you used known facts and/or double facts.  I will ask a few of you to come up and share your strategy. Once an approach is shared, I will ask you to compare it your approach to see if it is similar."

I will ask the students to present in the order that I have them listed in the section resource.  I want the presentations to be in order of efficiency and depth of understanding.  However, it is important to emphasize that each approach is a correct one and yields the right answer.  

The order is:

  1. Representing With Pictures.pdf/Presenting Picture Strategy
  2. Representing With Numbers.pdf/Representing With Numbers
  3. Using Known Facts.pdf/Representing With Known Facts

I have also included a photo, CK's Correct Responses, that demonstrates the student who presented using the picture strategy to solve the task.  You will notice that her answer (for the second part of the task) looks different then the one she presented.  During the work time, I took a picture of her approach because it was clear and organized.  However, she was confused on the third task and tried to use her thinking form the second task to solve it.  This led her to some confusion and her combining her thinking for both problems into one.  I felt this needed to be in here to support what you saw.

Fact Fluency

5 minutes

I will ask the students to meet me on the carpet and hand out their sheet for today's Mad Minute exercise.  This routine was introduced in a previous lesson.  Please check out the link to get a full overview of this routine.

I want to really focus on fact fluency and build upon the students ability to solve within ten fluently (CCSS.MATH.CONTENT.1.OA.C.6).  I am going to use the Mad Minute Routine.  This is a very "old school" routine, but I truly feel students need practice in performing task for fluency in a timed fashion.  Students need to obtain fact fluency in order to have success with multiplicative reasoning.  Students who don't gain this addition fact fluency by the end of 2nd grade tend to struggle with the multiplicative reasoning in third.  Having this fluency also allows them to work on more complex tasks because the have the fact recall to focus on the higher level concepts.

Continued Practice

5 minutes

One of the 1st Grade CCSS is that students can determine if an equation is true or false (CCSS.MATH.CONTENT.1.OA.D.8).  This is a skill that we have been working on throughout the year.  I wanted to use Adapting True False For Understanding sheet to check in and see how students were doing with this concept.  

I have included a copy of a students work with this task. She is a student who needs a lot of differentiation to complete her work.  She has the ability to do this task successfully but needed me to sit and walk he through it.  In this case, I put a box around each part of each equation (for the bottom part of the page) and this allowed her to see each side as its own entity.