Lesson developed by: Hina Siddiqui
Age group: Algebra I
Length of Lesson: 2 Class Periods
TEKS addressed
§111.32. Algebra I (One Credit)
(b) Knowledge and skills.
(A.1) Foundations for functions. The student is expected to:
(A) describe independent and dependent quantities in functional relationships;
(B) gather and record data and use data sets to determine functional relationships between quantities;
(D) represent relationships among quantities using concrete models, tables, graphs, diagrams, verbal descriptions, equations, and inequalities; and
(E) interpret and make decisions, predictions, and critical judgments from functional relationships.
(A.2) Foundations for functions. The student is expected to:
C) interpret situations in terms of given graphs or creates situations that fit given graphs; and
(D) collect and organize data, make and interpret scatterplots (including recognizing positive, negative, or no correlation for data approximating linear situations), and model, predict, and make decisions and critical judgments in problem situations.
(A.5) Linear functions. The student is expected to:
(A) determine whether or not given situations can be represented by linear functions;
(A.6) Linear functions. The student is expected to:
(A) develop the concept of slope as rate of change and determine slopes from graphs, tables, and algebraic representations;
(B) interpret the meaning of slope and intercepts in situations using data, symbolic representations, or graphs;
Objectives:
Overview:
Students will use a website program called ClimProb to research average temperatures and precipitation ranges over 5 assigned years, in quarterly periods. The class as a whole will collect data over the period between 1879 and 2007. Students will graph their data and make comparisons from quarter to quarter. Students will also be reminded of the concepts of correlation and slope and determine whether the slope in each five year period is increasing, and overall is it increasing at a steeper rate now than it was 100 years ago.
Resources:
Five-E-Organization
Engage:
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Teacher does: Teacher
shows students a picture of Teacher leads students into a discussion about change in elevations.
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Student does: Students are engaged and bewildered at being asked to climb such an enormous mountain. |
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Questions: Is
it more difficult to go up or come down? Describe
the change in elevations you exhibit while climbing up and down. Is the change in elevation constant or always changing? What term can we use to label this change? |
Expected Student Response: More difficult to go up the Mt. When
you are going up, the elevations are increasing, coming down the elevations
are decreasing. Changing. Slope |
Explore:
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Teacher does: Students work in assigned groups of two. Each group is given a 5 year time period (dating from 1879-2007) to find the average temperature of each year by quarters. Example Jan-Mar=1st quarter, Apr-Jun=2nd quarter, and so on. Teacher asks students to graph their data by quarters. Thus, for Jan-Mar, students will graph the average temperatures over the 5 assigned years. |
Student Does: Students
use the ClimProb program and locate Students make a graph of their data using graph paper. Each team will have 4 graphs, one for each quarter, over the 5 year period |
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Questions: Why
are we looking at average temperatures? Why
are we looking at quarterly temperatures and not yearly temperatures? Do
you notice anything about the average temperatures? |
Expected Student answers: If we look at daily temperatures, we will have too many data points. Also, temperature varies so much, it is difficult to compare day to day. There are different seasons in the year, so it is not correct to compare temperatures from the winter to those in the summer. This way we can compare what is happening from one season to the next. Temperatures in general seem to be increasing. |
Explain:
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Teacher does: Teacher asks students to look at the graphs they have made. She enters the class into a discussion about the comparisons from year to year. Teacher explains, the idea is to compare the average temperature of one quarter to the next. We are looking for trends. Teacher asks students to think carefully about their graphs and draw a line depicting either a positive or negative correlation of their points. Teacher asks students to define slope and relate this to their graphs. |
Student does: Students are able to interpret and discuss their graphs intelligently. Students realize that comparing temperatures in each quarter is only meaningful if looked at over a period of many different years. Students are able to see the overall trend that is happening from year to year. Students look at their graphs and are able to determine if there is a positive or negative correlation. Students define slope as a measure of steepness or a gradient. It is the change in height over distance. They are able to determine whether or not their graphs have a positive or negative slope. |
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Questions: Looking
at your own graphs, would you say the temperatures are getting hotter,
colder, or staying the same? Is
there a positive or a negative correlation in the points you have graphed? Is
the slope positive or negative? What might be the reason for this? |
Expected Student Responses: Students will find that sometimes the
temperatures got hotter, sometimes they got colder. In
general, there will be a positive correlation. Positive
slope. For
some reason, the climate is just getting hotter year to year. Students might
have some ideas on why. |
Extend/Elaborate:
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Teacher does: Once students have collected and graphed the temperature data, they will be asked to do the same for average precipitation for the same years. Teacher asks students to collect and graph the precipitation data on the same graphs in a different color. Again, teacher asks students to find the correlation and slope of their precipitation data. |
Student does: Students go back to the ClimProb program and change the variable from temperature to precipitation and record the average quarterly precipitation for each of their given years. Students graph the precipitation data in a different color onto their previous graphs. Students find the slopes of their new graphs. |
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Questions: Again, why are we using average quarterly values? What
do you notice about the average precipitation?Is it increasing, decreasing, or remaining the
same? What
might be the reason for this? |
Expected
Student Response: Average
because we cannot compare day to day and quarterly because some months there
is more precipitation versus others. It
is increasing for some months, remaining the same for others. There are more hurricanes and natural disasters occurring now. |
Evaluate:
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Teacher does: Teacher asks each group to present their findings to the rest of the class. Afterwards, students are asked to compile the class data into one big graph for each quarter. |
Student does: Students get up in teams and informally present their data tables and graphs. Students discuss whether or not the temperatures and amount of precipitation in their time periods were increasing, decreasing, or remaining constant. Students work together to combine all of their data into 4 sets of graphs, including all of the years from 1879-2007. |
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Questions: From
the data you have collected and analyzed, what are the overall trends you
notice? Is
Global Warming happening in What
about the slope, we know it is increasing in each 5 year period, but overall,
is it increasing at a faster or slower rate? |
Expected
Student Response: Students review the class data and discuss
that overall the temperatures are rising and
precipitation is increasing. Over a period of 128 years, we noticed a
warmer climate with increasing natural disasters, so it seems like yes there
is global warming in Austin At a faster slope, the temperatures have
always been increasing, but the steepness is much greater now than it was
before, hence the temperatures are rising at a much quicker pace. |