## Analyzing student representations - Section 2: Small Group Practice

*Analyzing student representations*

*Analyzing student representations*

# Using Class Data

Lesson 4 of 4

## Objective: SWBAT use data to compare types of jobs in their community.

#### Connecting to Social Studies

*15 min*

It is always beneficial when subjects can be integrated with one another. Currently my class is studying their community. This includes the jobs that parents do. Most second grade social studies units include some connection to the child's world and this lesson could be tied into that theme. The Common Core Math standards for second grade include students being able to create a graph using a data set, and then being able to solve add on and take apart problems based on the data. I use this standard today as a base for integrating math and social studies in a meaningful way.

While I could create the graph or just use random data, by using what is meaningful to the students (the jobs that mom and dad do) I am providing incentive for creating the graph. The graph in and of itself is meaningless so the Common Core Standards expect students to begin to analyze the data by creating add on or take apart problems. I ask students to write a problem as a first step to analyzing data on a graph. I don't create the problems because I want them to look at the data and see what they are learning from it.

Today I ask students to begin today by sharing their homework from the previous night. The homework entailed asking an adult in their world (parent, friend, grandparent, etc.) *what they do for work*, if it is a *job that produces a good*, or *performs a service*, as well as *how the person gets to work* and *how they use math at work*.

I ask students to think of how we might display our findings in a way that can be hung up for others to see. Children make suggestions. If no one suggests a graph, I may follow the lead they have suggested (depending on how appropriate it is for the task) or introduce the concept of a graph. I may ask That’s a good idea, but I wonder if someone else might want to build upon ____'s idea; or I noticed that you want to turn the tally marks into pictures and that made me wonder if there is a way to display those pictures so we can see them clearly?; or I can see you are really working hard to find a way to share all that we know, have we ever tried to share data before? Does anyone remember how we did it?

I let students suggest ways of collecting the data from other classmates and hopefully find a type of tally mark system to post on the board. I ask each child to tell me whether their parent does a job that makes goods, or a service job, how they get to work and any ways they use math. We set up a table with their answers.

We post our data in a table form, and then I ask students how they might graph the information we have gathered. Next I ask students how we will know what to include in our graph/representation and if we should make more than one representation because we have several different types of questions.

After we post the results on the board using tally marks, I assign each group one of the questions to create a graph from. I provide large blank paper for the task. I tell students that they will use the data to figure out the types of jobs, transportation and math applications that are common to our classroom and our community.

I give them about 10 minutes to complete the graph.

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#### Small Group Practice

*30 min*

I want students to create add on and take away problems using the data from the graphs. I start by posing a problem based on the data that is being displayed.

Some people identify such word problems as "problem solving"; However, many of these word problems are nothing more than computation practice, just like the pages of numerical problems. When the central focus in the mathematics classroom is on using a prescribed procedure to find the correct answer, we find that students ignore the context in such word problems. They extract the numbers from the problem and use some operation on them -- not necessarily the correct one. We have seen 8- and 9-year-olds who, rather than reading the problem, simply try every possible operation with the numbers in the problem until they get an answer they think is reasonable. Rather than making sense of the problem by drawing a picture or making a model, they look for key words (such as altogether in the problem above) which seem to indicate which operation is correct. Perhaps this is because they recognize that the problem is not a real-life application as it claims to be, but simply slightly disguised computation practice. (TERC)

I want students to go beyond just taking 2 numbers and automatically adding them, which many second graders will try, often especially the brighter children who feel that they don't need to bother reading the problem. I want student to begin to use the words as clues that will help in figuring out what to do with the numbers.

Here is the problem I pose:

*How many more people drive to work than walk to work?*

While the question appears to be a simple computational one, which has within it signal words (how many more), the task is rigorous for 2nd graders. It is my expectation that students decontextualize their data into numbers and symbols, which is an analysis task (MP2).

Students record their problem and solution in their math journals. I circulate around the room to look at how students are solving the problem, to offer suggestions and to listen to solutions. I have several students share their responses with the class.

Next, I ask students to use their graphs to write and answer questions about the types of jobs and the ways adults in the community get to work. They each record just one math problem in their journal based on the information we have graphed. I give them 5 minutes to create a problem. I ask them to read their problem to their seat mates and to let the rest of the group suggest an answer. Here the problems are different based on what the child notices in the data. By sharing the problems with seat mates, the students are then able to see other connections between different parts of the data.

#### Resources

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#### Comparing Conclusions

*10 min*

I close the lesson by asking each child to fill in a personal graph of the data. I will use this to assess student understanding of graphing a set of data. I use the problems they created in their math journals to assess using the data to create and solve add on and take away problems.

These two curriculum embedded assessments allow me to assess student understanding of the Common Core Standard for graphing (2.MD.10) which expects students to pose a question, collect data and represent it on a graph to interpret the results. Second graders are expected to analyze the data to solve simple problems using the information found in the graph (MP4).

#### Resources

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- UNIT 1: What and Where is Math?
- UNIT 2: Adding and Subtracting the Basics
- UNIT 3: Sensible Numbers
- UNIT 4: Sensible Numbers
- UNIT 5: Everything In Its Place
- UNIT 6: Everything in Its Place
- UNIT 7: Place Value
- UNIT 8: Numbers Have Patterns
- UNIT 9: Fractions
- UNIT 10: Money
- UNIT 11: The Numbers Are Getting Bigger
- UNIT 12: More Complex Numbers and Operations
- UNIT 13: Area, Perimeter and More Measurement
- UNIT 14: Length
- UNIT 15: Geometry
- UNIT 16: Getting Ready to Multiply
- UNIT 17: Getting Better at Addition and Subtraction
- UNIT 18: Strategies That Work