Representations of Data

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SWBAT make representations to communicate results of a survey.

Big Idea

Stop! It's Data Time. Every time your read me from the left or the right. It's the numbers on the board, that make the data right. Students take part in a quick survey to start the lesson and then continue to work on their data representations.

Warm Up

5 minutes

I place the 31-60 number cards (section resource) in an envelope.  "I would like someone to come up and pull two cards out of the envelope."  I then call on a student and write their numbers on the whiteboard.  "I would like you to each write an expression with the < or > sign.  When you are down hold up your board so I can see it."  I write sown different expressions that are shown and check each one with the class.  I continue to do this as time allows.

During this unit, I want to revisit the use of the < and > signs because they will be using them to wrote I notice statements from their surveys.

First grade students are expected to compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and < (CCSS.Math.Content.1.NBT.B.3).

Reviewing Tally Marks With A Survey

10 minutes

"Who remembers how to use tally marks?  Who could who us the correct way to write 5 tally marks? I call on a student to come up and explain who to draw 4 vertically and then one across them horizontally. When mathematicians are conducting surveys, they sometimes will use tally marks to record their counts.  Why do you think they cross the 5th one?  By making group soy 5, it makes it easier to count."  

Then draw out 13 tally marks on the board and model who to count by 5's and 1's.  

"Today we are going to answer a survey question and you will record your answer by placing a tally mark on the chart."  The chart is in the section resource.

"Do you have light hair or dark hair?"

I call up each student to mark their response. Before the student records their mark, I will ask them how he/she will write the mark.  This way we can talk as a group about when each horizontal mark will be made.  There are two videos in the resources section.  One shows a student using a tally mark to record their response and the other is the discussion about the 5th tally mark.

After the survey is complete, I ask the following questions:

  • What did we learn about our class?
  • How many people had eight hair?  How many have dark hair?  Which one is greater?
  • How many people answered the survey?
  • Can you think of an equation or expression that would show what we found out? ... Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. It is expected that 1st grade students can look at a set of data and write a mathematical representation of that data (CCSS.Math.Practice.MP4).

By the end of 1st grade students are expected to be able to organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another (CCSS.Math.Content.1.MD.C.4). This activity is helping the students develop the conceptual understanding.  

There is a video (interpreting the data) that demonstrates a student writing an expression to represent what he saw with the data.

Work on Representations

20 minutes

Students finish working on their Skier/Boarder? data representations form the previous lesson.  As students finish they can pair up and work on their doubles facts flash cards.  This was also introduced at the end of the above linked lesson.  It is expected that mathematically proficient students consider the available tools when solving a mathematical problem and use the efficiently (CCSS.Math.Practice.MP5). In this case students are creating and using charts to represent data.

As students finish, I will have them work on their doubles facts. I want to continue to work on building fluency with these.  Once students get these down, they can start working on doubles +/- 1 and +/- 2 facts.  I like having an activity like this, so that students can work at their own pace and as they finish, work on something that is purposeful and a good use of time. This fact fluency development builds upon the knowledge for students to be able to add within 20, demonstrating fluency for addition by creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) (CCSS.Math.Content.1.OA.C.6).   

Lesson Wrap Up

20 minutes

As students finish their representations, I hang them up around the room (see video in section resource).  I want to arrange them so that students can do a "gallery walk" and observe the different ways that the data was organized and represented.  

I gather the students together and have the following discussion:

"I have displayed all of your representations about our skiers and boarders.  When I give the signal, I want you to walk around and look at the different representations.  I want you to notice what do you notice that is the same or different in the representations?  How do they differ from the representation that you made?  After a few minutes, I will call you all back to the carpet and we will discuss what we found."


I want to focus on a couple of things during this discussion.  As for similarities, do they notice that every representation has the same data and is about the same categories?  As for differences, do they notice a variety of ways that the data can be represented (i.e. pictures, numbers, letters, etc.)?  

To focus on the similarities, I will ask: What does each survey tell us (and point out that the numbers are the same in each one)?  I will also ask what are the categories for each representation?

To focus on the differences, I will ask:  How are these two (pick to different representations) different from each other? 

There is a photo of one of the students representations and a video of the students participating on the "gallery walk."

A New Example

10 minutes

I will end today's lesson with a whole class discussion and modeling of representing data with a list of names.  I will use the same question about boarding or skiing that we have been working with all along.  

I want to show you another way of representing and collecting data.  We are going to use the same question about skiing or snowboarding and I want you to answer the question the same way you did yesterday.  However, instead of using cubes, pictures, letters, or numbers, you will write your name under the correct category.  I am going to create a t-chart not he easel, when I call your name I want you to come up and put your name under your choice.  There is a video of this process and a picture of the completed chart in the section resource.  

There is a video of the students participating in this activity and a photo of the finished chart.