Documents: Charts in Math Class

Throughout the math curriculum students are expected to study, read, interpret and analyze data in the form of charts and graphs. The following charts and graphs have been selected to model applications of primary sources that focus on a concept, time period or interest to which students can relate.

The questions provided are meant to give a sample and scope of the mathematical curricula and activities that can be applied.

Terms used on this page represent the terms in the original documents.

Index:

Statistical atlas of the United States, based upon the results of the eleventh census by Henry Gannett.

1)Pie charts of the composition of the foreign-born population in 1890

2)Pie charts of church membership by state and territory from the 1890 census.

3)Pie chart of leading religious sects in the United States from the 1890 census.

4)Distribution graph of occupations by color and nationality from the 1890 census.

5)Bar graphs of population by state and territory from the 1890 census.

6)Bar graphs of population by individual state and territory from 1790 to 1890.

7)Line graph of the urban population by state and cities from the 1890 census.

8)Distribution graphs and pie charts of population

(#)From 1790 – 1840 by color

(#)From 1790 – 1840 by foreign and native born

(#)From 1850 – 1890 by nationality of foreign born

(#)In 1890 by state and territory

(#)In 1890 by great cities

Iraq's petroleum and gas infrastructure.

9)Pie chart of Distribution of Iraq’s Main Ethnoreligious Groups in 2002

10) Pie chart of the Types of Iraqi Oil

11) Line graph of Crude Oil Production and Projection 2001 – 2020

12) Distribution graph of Crude Oil Production and Projections 1980 – 2004

13) Bar graph of Iraqi Oil Exports Under Phases 9,10,11 and 12

14) Pie chart of the Estimated Share of World Oil Production by country/region in 2000 and 2010

1)Pie charts of the composition of the foreign-born population in 1890

Basic interpretation

Which state had the greatest percentage of immigrants from Ireland? Which had the least?
Which state had the fewest countries represented by immigrants? Which had the most?
In which state(s) was there more than 50% immigration from one country?

Calculations

Which state(s) had a Methodist population closest to ¼ of the population?
Which state(s) had more than 50% of its population belong to 1 religious sect?
Look at Iowa, can you identify a country that had ½ the immigrants that Germany had? Can you identify a country that had ½ the immigrants of the new country?

Analysis

Group the states by its dominant immigrant country. Can you find a relationship to the region of the country where the states are located? Can you think of a reason for this?
What countries are missing that would be included in current data? Why was this so?

Extensions:

Conduct a survey of your own class and have your students make their own pie graph of student’s immigrant countries, or the countries of their ancestors. (blank graphs are provided in the back of the folder)

Find the data and have your students make a pie chart for their state currently. Is the class pie chart representative of the state? How do the current state statistics compare to those in 1890?

2)Pie charts of church membership by state and territory from the 1890 census.

Basic interpretation

Which state had the greatest percentage of Catholic church population? Which had the least?
Which state had the fewest religious sects represented? Which had the most?
In which state(s) was the Baptist sect a greater percentage than the Catholic?

Calculations

Which state(s) had a Methodist population closest to ¼ of the population?
Which state(s) had more than 50% of its population belong to 1 religious sect?
Look at the bar graph of the populations. Pick one state and approximate the percentages of each sect. Approximate the total population and find the estimated number of people who belonged to each religious sect.
Repeat the directions above for the Methodist population of New York and Pennsylvania.
Use the pie chart for your state and the population bar graph of the state to make a religious sect bar graph for your state.

Analysis

Group the states by its dominant religious sect. Can you find a relationship to the region of the country where the states are located? Can you think of a reason for this?
Look at the graphs of Nevada and New York. What would be a common misunderstanding that happens from interpreting only a pie chart without the population statistics as well?

Extensions:

Conduct a survey of your own class and have your students make their own pie graph of student’s religions. Compare the results to those from 1890. (blank graphs are provided in the back of the folder)

Find the data and have your students make a pie chart for their state currently. Is the class pie chart representative of the state? How do the current state statistics compare to those in 1890?

The pictures are printed on two pages and go in the folder one on each page so that it looks just like this again

3)Pie chart of leading religious sects in the United States from the 1890 census.

Basic interpretation

Which was the largest religious sect? Which was the least?
Rank the religious sects in order of from highest to lowest of the percentage of the population.

Calculations

Estimate the percentages for each sect.
Can you identify a sect that appears to have half the number of members that the Catholic sect has? Can you repeat this for all of the other sects?
Can you find any sects that together would be equal to the number of Baptists?
Compare your state pie chart to the this pie chart of the whole United States. Was your state representative of the country? Why or why not?

Analysis

What was the ancestry of most of the inhabitants of the United States in 1890? Does the give any insight into the dominant percentages of religious sects in the country?

Extensions:

Conduct a survey of your own class and have your students make their own pie graph of student’s religions. Compare the results to those from 1890. (blank graphs are provided in the back of the folder)

Find the data and have your students make a pie chart for the country currently. Is the class pie chart representative of the state? Is the class pie chart representative of the country? How do the current state statistics compare to those in 1890?

4)Distribution graph of occupations by color and nationality from the 1890 census.

Basic interpretation

Which occupations had the highest percentage of native white, native parents? Which had the lowest?
Which occupations had the highest percentage of colored ? Which had the lowest?
In which occupations were there the most German workers?

Calculations

Estimate the percentage of foreign parent workers in the dressmakers field.
Estimate the number of non-foreign parent workers in the dressmakers field.

Analysis

What occupations had higher than average foreign participants? Which had lower?
Rank the occupations by skill/expertise required. Which colors and nationalities worked the most in those occupations?
Think about the timeframe, what events since this time would make you believe that subsequent reports on this data would show different results?

Extensions:

Conduct a survey of your own class and have your students make their own bar charts and compare them with those from 1890. (blank graphs are provided in the back of the folder)

Hypothesize about the statistics before and after a specific world event (emancipation, woman’s movement, immigration trends). Use the data to verify the students’ hypotheses.

Have the students choose a profession and see whether they would be an average or extraordinary participant in the timeframe of the data. Would they be average or extraordinary in this age? Find the data to back up this claim.

5)Bar graphs of population by state and territory from the 1890 census.

Read the 2 bar graphs on the page. This page will refer to them by their diagram numbers on the original document - #6 and #8. The numbers are located next to the title of each diagam.

Consider the following questions using graph #6:

Basic interpretation

Which states had the highest population or inhabitants? Which had the lowest?
Estimate the population or inhabitants of Mississippi.
Estimate the difference between the highest and lowest populations or inhabitants.

Calculations

What is the range of the populations?
Estimate the mean of the populations.
Estimate the mode of the populations.

Repeat using graph #8.

Use both graphs together for analysis :

Analysis

What does the graph mean?
What can you deduce about the populations in the different regions of the country based on this data?
Read the population of your state and then the number of inhabitants per square mile. Based on those two, can you figure out the square mileage of the state at that time?
Why do you think the graphs were displayed as they are on the page?

6)Bar graphs of population by individual state and territory from 1790 to 1890.

Basic interpretation

Which states had the highest population or inhabitants? Which had the lowest?
Which state had the highest population at the 1850 entry?
Are there any states whose population decreased at all between 10 year periods?

Calculations

What is the approximate percentage of growth from 1790 – 1890 for your state?
What is the highest approximate percentage of growth? The least?

Analysis

Which state’s population was growing at the highest rate during this time?

Extensions:

Look up the current statistics and have your students make their own bar charts and compare them with those from 1890. (blank graphs are provided in the back of the folder)
Hypothesize about the statistics before and after a specific world event (world war, plague, end of world war and population booms). Use the data to verify the students’ hypotheses.

This pages go one next to the other so both can be seen at the same time

7) Line graph of the urban population by state and cities from the 1890 census.

Line graph of the increase of population of the “great cities” of the United States from the 1800 to 1890.

Basic interpretation

Which city had the largest increase between 1800 and 1890? Which had the least?
Which cities had an ending population of over 1 million people? Which had an ending population less than 250,000?
Why do some cities line graphs start in different places than others?

Calculations

Which cities had steep periods of growth?
Did any cities have a decline in population?
Which cities had a population that doubled within a 10 year period? Identify the years in which the population doubled.
Did any cities have a population that tripled within a 10 year period? Identify the years in which the population tripled.
Which cities had a population equal to or greater than Chicago’s in 1870? Which cities population in 1890 was greater than or equal to Chicago’s in 1870?
Determine how much bigger New York was than Washington at each 10 year time period.
Determine the percent change in the population of New York between 1800 and 1860. Repeat between 1860 and 1870. Repeat between 1870 and 1890. What was the percent change in Omaha between 1880 and 1890?

Analysis

Can you think of a reason for the sudden growth in 1850 of Chicago, Philadelphia and Brooklyn?

Extensions:

Find the data for the size of the classes in your school and have your students make a line graph for the school.

Bar graph of the total and urban populations by state and territory and Proportion of urban to total

population chart

Basic interpretation

Which states had a total population over 2 million? Which were under 1 million?
Which states had more urban population than rural? Which had ½ it’s population urban?
Which state had a total population equal to the urban population of Massachuesetts?

Calculations

Estimate the percentage of the total population that was urban for a given state.

Analysis

Which state(s) had a ratio of urban to total that was closest to the entire United States’ ratio?

8)Distribution graphs and pie charts of population

Pie Charts

#34 From 1790 – 1840 by color

From 1790 – 1840 by foreign and native born

#39 From 1850 – 1890 by nationality of foreign born

Basic interpretation

(#34) Was there much change between the years in the total percent of the population that was colored?
(#34) Estimate the percentage of colored population in 1840.
(#34 & #39) Estimate the percentage of each group in 1890.

Calculations

(#34) Estimate the change in foreign white population between 1850 and 1890.
(#39) Estimate the change in the Scandinavian population between 1850 and 1890.

Analysis

(#34) Why would the native population born of native parents be included in the 1870 graph and beyond and not before 1870?

Extensions:

(#39) Conduct a survey of your own class and have your students make their own pie charts for the nationalities of student’s parents. Compare the results to those from 1890. (blank graphs are provided in the back of the folder)

Distribution Graphs

#35 In 1890 by state and territory

#36 In 1890 by great cities

Basic interpretation

(#35) Which state had the greatest percent of foreign white population?
(#36) Which city’s colored population was the larger than it’s foreign white population?

Calculations

(#36) Pick a city and estimate the how many times larger the white population was than the colored, native white of foreign parents, or foreign white population.

Analysis

(#35 & #36) Compare the cities New York, Buffalo and Brooklyn. Which of these cities population best models the population distribution of the entire state in #35?

Extensions:

Conduct a survey of your own class and have your students make their own distribution graph of student’s races. Compare the results to those from 1890. (blank graphs are provided in the back of the folder)

Iraq’s petroleum and gas infrastructure

9)Pie chart of Distribution of Iraq’s Main Ethnoreligious Groups in 2002

Identify the percentages of each group.
Use the information to determine the actual number of people in each group.

10) Pie chart of the Types of Iraqi Oil

Identify the percentages of each type of oil.
What percentage more is the Heavy oil than the Light oil?

11) Line graph of Crude Oil Production and Projection 1980 – 2004

What was the lowest production and in what year?
What was the production for 1988?
What was the percent change between 1990 and 1991?
What was the projected rate of change between 2003 and 2004?

12) Bar graph of Oil Ministry Production Goals2001 – 2020

What was the amount of improved production in 2001? Projected in 2010?
What percent of the total production was estimated to come from undeveloped discovered fields in 2004? What were the percents of improved production and unimproved production during the same year?
What was the percent change in the production from 2001 to estimated production in 2008?

13) Bar graph of Iraqi Oil Exports Under Phases 9,10,11 and 12

What was the amount of exports during the first week of July in phase 10?
Why is the average of the each phase the same as the initial amount of export?
Look at the drops in exports during phase 9. Estimate the drop in exports between the 3rd and 4th weeks in December. Estimate the drop in the average during the same time. Repeat for the drop in January and in May. Why is the rate of change in the average so much different than the changes in the actual export amounts?

14) Pie chart of the Estimated Share of World Oil Production by country/region in 2000 and 2010

What percent of the total oil was produced in the Americas in 2000? In 2010?
Determine the percentage of oil that was produced by continent for 2000 and 2010.
Use the information for 2010 to determine the estimated number of barrels Iraq will produce. How much is it estimated the U.S. will produce?

Extensions:

Find the current data and compare it to the estimated projections for oil production.
Using the current price per barrel for oil, estimate Iraq’s possible income from oil base on the production projects for the current year.

The Iraq poster should be in the pocket of the folder.

4 pages go here at the end to finish up.….they are the sample pie charts and bar graphs. See the separate word documents.