# Using Data Representations to Make Substantiated Claims in Historical and Literary Contexts

## Lesson Focus and Instructional Purpose

### Cross Disciplinary Themes Addressed

Statistics are often a powerful tool used to identify disparity when it occurs. However, the quality of statistics used, in addition to the information obtained from statistical analysis, depends heavily on students’ ability to scrutinize these mathematical representations. Disparity as a concept transcended many aspects of daily life including housing opportunities, employment opportunities, education, and conforming or defying social boundaries. To truly apply these skills in an English and History context, students will need to gauge the quality of such representations in a mathematics context.

### Unifying Essential Question(s)

How can I use statistical representations to improve my understanding of historical and literary themes?

### Collaborative Learning Objective(s)

In order to truly make sense of historical and literary themes of disparate prosperity, students will be able to break down any statistical representation according to a comprehensive protocol

### Subject Area Learning Objectives

Subject | Learning Objective |
---|---|

Algebra | Students will be able to learn about the different types of existing data representations. |

Students will be able to interpolate, extrapolate and isolate trends from data sets | |

Students will be able to break down any statistical representation according to a comprehensive protocol. | |

Students will be be able to distinguish between mathematical analysis statements and social science analysis statements made about given graphs. | |

English | Students can analyze the motif and significance of home through the perspective of the character, Ezekiel “Easy” Rawlins in the fictional novel, Devil in a Blue Dress, by Walter Mosley |

History | Students can define restrictive covenant. Students can explain the effects of restrictive covenants on housing segregation. |

### Standards Addressed

Mathematics | ELA/Literacy | Social Studies |

CCSS.MATH.PRACTICE.MP3 | CCSS.ELA-LITERACY.CCRA.R.1 | Determine a theme or central idea of a text and analyze in detail its development over the course of the text, including how it emerges and is shaped and refined by specific details; provide an objective summary of the text. |

Understand statistics as a process for making inferences about population parameters based on a random sample from that population.* |
Cite strong and thorough textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text. | |

Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. | Determine the meaning of words and phrases as they are used in the text, including figurative and connotative meanings; analyze the cumulative impact of specific word choices on meaning and tone |

## Close Reading Text Set

### Anchor Text

Average Happiness as a Function of Age

### Supporting Texts

Subject | Title of Supporting Text | URL of Supporting Text |

Algebra | Usain Bolt v. 116 years of Olympic Sprinters | http://www.nytimes.com/interactive/2012/08/05/sports/olympics/the-100-meter-dash-one-race-every-medalist-ever.html |

Algebra | Bad Graphs | http://www.tc3.edu/instruct/sbrown/swt/chap02.htm |

Algebra | Bar and Pie Graphs | http://room9balmac2014.weebly.com/emma/bar-and-pie-graphs |

### Organized Text Set

Text Title | Learning Objective |

1. Bad Graphs | be able to learn about the different types of existing data representations. |

2. Bar and Pie Graphs | be able to learn about the different types of existing data representations. |

3. Average Happiness as a Function of Age | be able to interpolate, extrapolate and isolate trends from data sets |

4. Average Happiness as a Function of Age | be able to break down any statistical representation according to a comprehensive protocol |

5. Usain Bolt v. 116 years of Olympic Sprinters | be able to distinguish between mathematical analysis statements and social science analysis statements made about given graphs |

## Student Activities and Tasks

### Text-Dependent Questions

**Day 1:**

Students are completing warm-ups individually, recording vocabulary individually, discussing concepts with their groups, answering questions whole-class, and are exploring different graphs within their groups. Students are completing exit slip assessments individually.**Day 2:**

Students are completing warm-ups individually, sharing out vocabulary individually to the entire class, receiving notes about how to follow a protocol with graph analysis, and are exploring different graphs within their groups. Students are completing exit slip assessments individually.**Day 3:**

Students continue with analyzing a sample group during their warm-ups, will share out vocabulary individually, and will practice analyzing a graph with their teams. **Day 4: **

Students will be assessed on their ability to distinguish between mathematical statements and social science analysis statements made about specific graphs. Students must highlight the difference between these statements and justify their purpose for using specific statements.

### Formative Assessment Strategies and Tasks

Students will participate in a "participation quiz" in which groups will have to explain their decision-making strategy for sorting analyses of graphs in a specific way. Students will be assessed on their explanation strategies, their ability to work in groups, as well as their critical observation of vocabulary that may distinguish analytical statements.

## Culminating Assessment

__Summative Assessment (on homework assignment):__

Individually, examine this graph and analyze it fully.

What kind of graph is this?

What is this graph measuring? (What are on the x and y axes?)

What is the scale used for the y axis? X-axis?

What kind of trends do we see? (Increasing, decreasing, linear, non-linear?

What are limitations of this kind of graph? What are its unique benefits?

Is it possible to draw a line of best fit through this graph? Why or why not?__Group Summative Assessment:__

*Card Sort #1:*

Group the cards by:

Which cards are descriptions?

Which ones make claims?

Pick one example from each to discuss as a group. Why did you place it in this pile?

Don’t rush this part! When everyone has contributed to the discussion and you have nothing left to say, move on to the next Card Sort.*Card Sort #2: *

Group the cards by:

Which cards use specific details?

Which ones could include more detail?

Are there any that include too much?

Pick one example from each to discuss as a group. Why did you place it in this pile?

When everyone has contributed to the discussion and you have nothing left to say, move on to the next Card Sort.*Card Sort #3: *

Group the cards by:

Which cards have statements you would include in a math analysis?

Which cards have statements you would include in a social sciences essay?

Are any that would fit in both?

## Background Knowledge and Prerequisite Skills

### Pre-requisite Learning

Students will be required to recall basic skills when analyzing any graph or data set. These skills will involve understanding the independent and dependent variables involved, understanding the type of representation used, as well generating questions about a given data set.

### Pre-assessment of Readiness for Learning

Students will be given the opportunity to think individually, discuss in small groups, and share out with the entire class when asked questions about their exposure to different data representations. Students will also be given opportunities to distinguish between "high-quality" and "low-quality" data representations that may have value depending on their degree of detail. Students will be observed for their recognition of these significant details.

## Organization of Instructional Activities

**Day 1: Introduction to Data Analysis**

(Homework from previous night: Students complete a KWL about data representations.)

Warm-Up: Students answer a series of questions about a given data representation. (Questions are revisited later.)

Vocabulary/Concept Acquisition

Conduct frayer model forms of vocabulary (histogram, scatterplot, box and whisker plot, bar graph)

Look at useful data versus commercial infographics

Present series of data sets (comparing multiple “useful” sources with more commercial types.) Students discuss the data samples they see and decide which one is more “powerful” in groups. Students should also identify the type of graph used (see vocabulary shared above.) Share out from the entire class; scribe general trends on the board.

Protocol Introduction

Gauging the “power” of information from a data representation. Review the warm-up question students saw earlier.

What kind of graph is this?

What is this graph measuring? (What are on the x and y axes?)

What is the scale used for the y axis? X-axis?

What kind of trends do we see? (Increasing, decreasing, linear, non-linear?

What are limitations of this kind of graph? What are its unique benefits?

Practice

Distribute other graph sources and ask students to explore these questions about other representations.

Return as a class and revisit the following questions for class discussion:

What were questions you/your group had about this graph?

What do you feel is missing from this graph, if anything?

What kind of conclusions do you think you can draw from this graph at this moment, if anything? Why?

Closing (Exit Slip/Making Connections)

Students answer the following question as an exit slip: “What’s the purpose of being able to read a graph or data set completely?”

HW: Students complete “Learned” section of KWL**Day 2: Data Table Breakdown: Creating useful representations**

Warm-Up: Students answer a series of questions about a given data representation. (Questions are revisited later.)

Vocabulary

Students will share out Frayer Model vocabulary tables for the following terms: Interpolate, Extrapolate, Trend

Strategies to break down a graph

(Preliminary protocol learned the day prior)

Is it possible to draw a line of best fit through this graph? Why or why not?

What questions do you have about the validity of this graph? (Source, reliability of source?)

What is missing from this graph, if anything?

Interpolate, extrapolate, gauge the trend

Present a scatterplot that presents with a strongly linear relationship as well as one with a non-linear relationship

Draw in a line of best fit on the board. (Which one has a linear/non-linear trend? Is it increasing/decreasing? How do you know?)

Ask students to predict values within the present data (interpolate) and then to predict values outside the bounds (extrapolate) with their groups

Summarize: which situations present for “easier” interpolation/ extrapolation versus others.

Students share out with the whole class about these findings.

Exit Slip

Present a situation non-linear situation and ask students to

Analyze the growth of the pattern (linear? non-linear?)

Interpolate a value

Extrapolate a value

HW: Looking at graphical representation, answer the following questions

Is it possible to draw a line of best fit through this graph? Why or why not?

What questions do you have about the validity of this graph? (Source, reliability of source?)

What is missing from this graph, if anything?

What conclusions can you draw about this graph, if any?**Day 3: Application of Data Analysis to Representations**

Warm-Up: Present another graph and ask students to apply vocabulary to the features of the graph/ answer questions about the graph

Independent Variable

Graph type (histogram, scatter plot, table, box and whisker plot, bar graph)

Line of best fit

Trend ?

Interpolated value ?

Extrapolated value ?

Analysis strategies/protocols

Review homework from the previous night

Assessment

Individually, examine this graph and analyze it fully. (Put these up on a poster for students to consider as they complete the assessment)

What kind of graph is this?

What is this graph measuring? (What are on the x and y axes?)

What is the scale used for the y axis? X-axis?

What kind of trends do we see? (Increasing, decreasing, linear, non-linear?

What are limitations of this kind of graph? What are its unique benefits?

Is it possible to draw a line of best fit through this graph? Why or why not?

Make any conclusions you can about the relationships presented, if possible. Is this a quality data representation? What is it missing, if anything?

**Day 4: Valid and Convincing Claims in Math and Social Science**

Warm-up: Individually, analyze a graph and decide if a statement given is more of a description or a claim.

Discussion: Distinguishing between descriptive statements and claims

Analyze a graph further as a class and highlight the subtle differences

Prompt students to think about uses for descriptions for mathematical analyses and claims for application in social science analyses

Assessment/Practice

Students will be asked to explain with their groups how they organized specific statements about graphs according to specific prompts

Distinguish between descriptions and claims about these graphs

Distinguish between too little detail versus too much detail

Distinguish between application of statements to math contexts or social sciences contexts