Eye, Knees and Feet Problems

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SWBAT identify the 2:1 relationship involved in counting students eyes, knees and feet.

Big Idea

Today students will continue to explore the relationship between the number of students and the total number of eyes.

Warm Up

10 minutes

Explain to the students that they are going to play another round of Popcorn.  Remember, it is a counting game where you start with a number (pre-determined) and you count up until you get to the last number (pre-determined).  Ask them to stand up in a circle.  Tell the students that they are each a kernel of popcorn and ask them what happens when you heat up a kernel of popcorn?  That's right, it POPS!  Explain that today we will count back.  We will start with the number 2 and count by 2s to 20.  I will say 2 first.  Then the person next to me will say 4, and then the next person 6 . . . until 20.  After 20, you say POP and then sit down.  The game will continue with the very next person starting the count all over again.  The game continues until there is only one person left standing.  That person finishes the game by repeating the entire count sequence.

Patterns in Students and Eyes

15 minutes

I start this part of the lesson by displaying this 2s Chart.  I created it as a Smart Board.  It is loaded here as a pdf so that anyone can open it.  I will fill out the chart as the following conversation occurs.

"I want you to think about the work we did with groups of eyes in yesterday's lesson.  What if we had just one person. How many eyes would there be?  How many eyes for two people?  How do you know?"

I continue to gather and record the information through 5 people.  "After each number, I will use cubes to model your strategies and to help them connect two different ways of conceptualizing the problem: counting by 2s and doubling the number of people to find out how many eyes."

Once we have completed the chart, I will ask them about the number of eyes for 8 people, 10 people, and 11 people.  This way I can see if the students can extend the pattern.  

In this discussion the students are making sense of quantities and their relationships in problem situations by seeing the growing pattern that occurs when 2 is added each time.  Thee students are also relating the addition to doubles facts by looking at the left and right eye totals (CCSS.MATH.PRACTICE.MP2).

Problems About Eyes, Knees and Elbows

30 minutes

Advanced Preparation: You will need to make enough copies of the Eyes, Knees, and Feet resource. There is also an adapted set of Eyes, Knees and Feet problems.  This packet is for those students who can use a challenge and generalize counting by 2s to solve problems with larger numbers.

"You will now solve several problems about eyes, knees and feet.  I want you to solve each problem and to make sure that you show your thinking."

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

  • How students approach and model each task.
  • How do they solve each task.
  • How do they record their thinking.

I have included several examples of student work and a couple of videos that have student describe how they were solving the tasks: 

In this situation, 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).

Lesson Wrap Up

15 minutes

For this discussion, I will post the chart, titled End of Lesson Discussion Chart (dragged), on the Smart Board.  

"When we started today's lesson, we filled out a chart about eyes and how many for different number of students.  Would a chart for hands look any different?  What about knees or feet?  Why would they not look different?"  

There is a video, Closing Discussion, in the section resource that captures a student clearly explaining why the numbers won't be different.

"Let's start to fill in some of these numbers together."  

 I then ask students a variety of questions, from each category, and work with them to fill out the discussion chart.

Continued Practice

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.