# Analyzing and Making Mathematical and Historical Claims from (Linear) Data Representations

## Lesson Focus and Instructional Purpose

A team of high school teachers developed a series of lessons that are connected by theme and skills through math, English, and History. The themes include segregation, symbolism, and the making of valid claims based on interpretations of data.

### Unifying Essential Question(s)

What was the experience of Californians during the post-war period? What changes did they experience, and were they ultimately beneficial or harmful?

### Collaborative Learning Objective(s)

Students understand literary and historical themes of disparate prosperity.
Students can make a claim supported by evidence.

### Anchor Text

California Department of Finance, “A Modern Economy is Born,” Bar chart titled: "Enrollment in California Colleges and Universities

### Text-Dependent Questions

1. What information could we predict from this data?
2. Could we use this information to make a prediction about the number of students enrolled in the 30s? What about today? How accurate would our predictions be? What if we were missing data for an intervening year?
3. How could we use this information to predict the missing data?
4. What does this information tell us about the changes in California during the post-war era?
5. How could we use this to argue that prosperity was increasing?
6.  What information might be missing?

### Formative Assessment Strategies and Tasks

Students will discuss their ideas in pairs, groups of four, and as a whole class as well as record their work on a worksheet each day. The teacher can listen in on student conversations in groups and collect student work at the end of each day to see which ideas and questions are surfacing, the ways they are describing and defending their observations, how they annotate their graphs, and how students created and used their line of best fit.

## Culminating Assessment

The overall summative task for the unit will ask students to choose from several different sources to build an argument for Californians' prosperity or decline in the post-war years. Students may choose not to use the mathematical representation.
Math-specific summative task: students write and interpret a linear equation for a different set of approximately linear data.

## Background Knowledge and Prerequisite Skills

### Pre-requisite Learning

1. Know how to write the equation of a line given a slope and y-intercept.
2. Find the change in two different variables and use them to find slope.
3. Identify slope as rate of change and y-intercept as starting value.
4. Read individual data points from a bar chart.

### Pre-assessment of Readiness for Learning

Possible ways to pre-assess students' understanding:
"Entry lesson" in which students describe everything they can about the data representation.
A homework asking students to generate linear equations from various pieces of information (situation to equation, graph to equation, table to equation, given slope and y-intercept to equation).

## Organization of Instructional Activities

Day 1:
Objective: Carefully observe, describe, and interpret the features of a data representation
Apply: (30 min) Jigsaw with representations: describing and making claims from the representations
Exit Ticket: (5 min) Make two claims about this graph. Try to use at least 2 terms from the word bank.

Day 2:

Objective: Analyze increasing and decreasing trends in more detail, improve descriptions and claims from data, distinguish when it is appropriate to use equations, etc. and how to use data representations to support a larger thesis.
Interpet slope of a linear trend, and use it to write equations
Interpolation vs extrapolation
Launch (5-7 min): Describe the trend in a scatterplot. How much has it increased/decreased? In how much time?
Apply (40 min): Quantify the increasing trend in the bar chart. Find a slope and write a linear equation. Use the equation to interpolate and extrapolate data points.
Exit Ticket: (5 min) Write down two things you learned to do today and one question.

Day 3:
Objective: Distinguish when it is appropriate to use equations, etc. and how to use data representations to support a larger thesis.
Warm Up (5 min): Write linear equations from a graph with a labeled y-intercept and one other point.
Launch (2 min): How can we use our mathematical analysis in other settings? Introduce the idea of description vs. claim, specific detail vs. too general or vague, appropriate for a mathematical context and appropriate for a history context.
Apply (30 min):
(5 min) Students examine description cards in groups.
(7 min) Card sort #1: Which descriptions of data are descriptions and which make claims?
(7 min) Card sort #2: Which cards have too many details, which have enough specific details, which don’t have enough?
(7 min) Card sort #3: Which cards have more mathematical analysis and which could you use in a history context? What overall thesis could we use this to support?
Exit Ticket (10 min): Write more detailed claims for cards OR write a description, a claim, a mathematical argument, and a social sciences argument (responding to the prompt “Did California prosper or decline in the post-war period?”) for our original central source graph.