|
Creating Scatter Plots
 Subject:
Mathematics
Grade Level: Sixth through Eighth Grade
Materials: TI-73 graphing calculators
About: Students learn how to use a graphing calculator and explore the powers of a scatter plot. They draw a line of best fit around the given data, which simulates the beginning of regression analysis.
Students create a scatter plot and find a line of best fit. This enables them to project a future event.
Underprivileged students use technology in the form of a mini-computer/calculator to utilize the power of mathematics as a forcasting tool. Information is graphed in the form of a Scatter plot so that a line of best fit is draw. They are introduced to regression analysis.
Students are eager to learn with new tools. Students who experience difficulty in numerical computation are assisted by the calculator. Scatter plots are created from raw data in a short time that might otherwise take all day. For some students, frustration is eliminated because of the calculator.
teacher created material.org
| Students learn about the calculator and how it can assist them. |
| Students operate the calculator and understand that the answers still have to be checked. |
| Students work with data and understand that extraneous data needs to eliminated. |
| Students learn fine points on operating the TI-73 or any other graphic calculator. |
| Students learn how using a line of best fit to write an equation will enable them to make a prediction. |
| Students understand that future predictions are based on past experiences or trends.
|
| Students review the possibility of other factors affecting their predictions. |
|
|
|
| Students know the difference bewteen relevant and irrelevant information when solving problems. |
| 6th - PS1 |
| Mathematics |
| Students understand that some ways of representing a problem are more effecient that others. |
| 6th - PS2 |
| Mathematics |
| Students model problems with pictures/diagrams or physical objects. |
| 6th- PS13 |
| Mathematics |
| Students analyze problems by observing patterns. |
| 6th- PS14 |
| Mathematics |
| Students use physical objects drawings, charts, tables, graphs, symbols, equations, or objects created using technology as representations. |
| 6th- R1 |
| Mathematics |
| Students read, interpret, and extend external models. |
| 6th- R2 |
| Mathematics |
| Students investigate the relationship between diferent representations and their impact on a given problem. |
| 6th- R5 |
| Mathematics |
| Students evaluate formulas for given input values (circumference, area, volume, distance,temperature,interest,etc.). |
| 6th- A6 |
| Mathematics |
| Students determine and justify the most appropriate graph to display a given set of data (pictograph, bar graph, line graph, histogram, or circle graph). |
| 6th- S4 |
| Mathematics |
| Students read and interpret graphs. |
| 6th- S7 |
| Mathematics |
|
|
|
|
|
|
|
| Day 1:
How Much Blood Do You Have? |
| How much blood do you have in your body? |
| What is blood type? |
| Students learn how to enter data on the TI-73. |
|
|
|
| Access to the Internet to review the life cycle of a blood cell:
http://www.tcmpub.com/urlupdates/ |
| Data collection sheet |
| Calculator to organize data and find the line of best fit |
|
|
| Students are introduced to blood cells and think about what they do. |
| Students create a brochure about the amount of blood in the body. |
| Students are instructed on how to use the calculator to represent their data.
|
| Students answer questions on work sheet based on data obtained. |
| Students create a brochure. |
|
|
|
|
|
|
| How did we use the calculator to predict the amount of blood in our bodies?
Complete brochure. |
|
| Students graph the relationship between weight and the amount of blood in the body. Most begin the creation of a sample brochure. |
|
| Day 2:
Let's Go to the Movies |
| How much would a night at the movies cost for your entire family in 2198? |
| Students read data from a table and create a scatter plot of a set of data. |
| Students find the line of best fit for a given set of data. |
|
|
|
| Data collection sheet |
| TI-73 calculators |
|
|
|
| Students are asked to think about the cost of going to the movies?
Will people still be going to the movies in 2189? |
| Students transfer information about the past to the calculator. |
| Students discuss trends and the line of best fit (regression analyses). |
| Students use the line of best fit and the equation generated. |
| Students share there results and how they arrived at their conclusions. |
|
|
|
|
|
|
| Student worksheet - function table of inputs and outputs to arrive at the equation |
|
| Students arrive at a reasonably close estimate, if not the exact answer, since they will all be using the same data. |
|
| Day 3:
The Tortoise or the Sloth? |
| Introduce students to a real-world situation that can be modeled by parametric functions. |
| Students become more familiar with the other functions on the calculator. |
| Students understand the effects of parameter changes on functions and their graphs.
|
| Students write the equation of a line in parametric form. |
|
|
| TI-73 calculator |
| Data collection sheet |
|
|
|
| Can students recall the story about the tortoise and the hare? What was the main idea of the story?
What is the equation of a line? (y=mx + b) |
| Students determine the winner of a race between a tortoise and a sloth, who start from different points and move in different paths. |
| Students graph the two lines using the calculator in the simultaneous mode. The relative motion of the two lines and when they will reach the point of intersection will be discussed. |
| Slope is the change in Y relative to the change in x. |
| Students are taught how to create a stat plot marking each animals position in relation to the time.
|
| The calculator is reset to the Parametric mode. Students re-enter the sloth's formula and the tortoise's formula. |
| Review how to toggle between functions and the scoring process based on the rubric. |
|
|
|
|
| Students are asked to verify mathematically why the results are as they were. What parameter changes would have changed the outcome of the race? |
|
| Students share their scatter plots on the overhead projector. They discuss the various ways they entered data and arrived at their conclusions. |
|
| Day 4:
Area Formulas Application |
| The calculator has the area formulas available for parallelograms, triangles, trapezoids, and circles. Students learn how to access this information.
|
| The calculator has a short tutoral on how formulas is derived. Students learn how to access this imformation.
|
| What is area and how do we measure it? |
|
|
|
| Review with students the various geometric shapes they will be exploring. |
| Students explore the concept of area and how we measure it--in terms of squares. |
| Model for students how to access the definitions and formulas on the calculator. |
| Students quiz themselves at Level 1 to be followed by Level 2. Students receive immediate feedback and the calculator scores the quiz. |
|
|
|
|
|
|
|
| Students take home a worksheet to review the area formulas and review the concepts. |
|
| Student scores from the calculator will assess their knowledge. |
|
|
Larry Kapuvari
ldkapuvari@optonline.net
Leonardo di Vinci Intermediate School
98-50 50th Avenue
Corona, NY 11368
Larry is a sixth-year Mathematics teacher who has demonstrated a passion for teaching young adults the joy of working with numbers. He believes that teaching is all about the enthusiasm and passion you can bring to the classroom every day.
Important documents for this lesson plan.
|
Creating Scatter Plots
Subject:
Mathematics
Grade Level: Sixth through Eighth Grade
Materials: TI-73 graphing calculators
About: Students learn how to use a graphing calculator and explore the powers of a scatter plot. They draw a line of best fit around the given data, which simulates the beginning of regression analysis.
Students create a scatter plot and find a line of best fit. This enables them to project a future event.
Underprivileged students use technology in the form of a mini-computer/calculator to utilize the power of mathematics as a forcasting tool. Information is graphed in the form of a Scatter plot so that a line of best fit is draw. They are introduced to regression analysis.
Students are eager to learn with new tools. Students who experience difficulty in numerical computation are assisted by the calculator. Scatter plots are created from raw data in a short time that might otherwise take all day. For some students, frustration is eliminated because of the calculator.
teacher created material.org
| Students learn about the calculator and how it can assist them. |
| Students operate the calculator and understand that the answers still have to be checked. |
| Students work with data and understand that extraneous data needs to eliminated. |
| Students learn fine points on operating the TI-73 or any other graphic calculator. |
| Students learn how using a line of best fit to write an equation will enable them to make a prediction. |
| Students understand that future predictions are based on past experiences or trends.
|
| Students review the possibility of other factors affecting their predictions. |
|
|
|
| Students know the difference bewteen relevant and irrelevant information when solving problems. |
| 6th - PS1 |
| Mathematics |
| Students understand that some ways of representing a problem are more effecient that others. |
| 6th - PS2 |
| Mathematics |
| Students model problems with pictures/diagrams or physical objects. |
| 6th- PS13 |
| Mathematics |
| Students analyze problems by observing patterns. |
| 6th- PS14 |
| Mathematics |
| Students use physical objects drawings, charts, tables, graphs, symbols, equations, or objects created using technology as representations. |
| 6th- R1 |
| Mathematics |
| Students read, interpret, and extend external models. |
| 6th- R2 |
| Mathematics |
| Students investigate the relationship between diferent representations and their impact on a given problem. |
| 6th- R5 |
| Mathematics |
| Students evaluate formulas for given input values (circumference, area, volume, distance,temperature,interest,etc.). |
| 6th- A6 |
| Mathematics |
| Students determine and justify the most appropriate graph to display a given set of data (pictograph, bar graph, line graph, histogram, or circle graph). |
| 6th- S4 |
| Mathematics |
| Students read and interpret graphs. |
| 6th- S7 |
| Mathematics |
|
|
|
|
|
|
|
| Day 1:
How Much Blood Do You Have? |
| How much blood do you have in your body? |
| What is blood type? |
| Students learn how to enter data on the TI-73. |
|
|
|
| Access to the Internet to review the life cycle of a blood cell:
http://www.tcmpub.com/urlupdates/ |
| Data collection sheet |
| Calculator to organize data and find the line of best fit |
|
|
| Students are introduced to blood cells and think about what they do. |
| Students create a brochure about the amount of blood in the body. |
| Students are instructed on how to use the calculator to represent their data.
|
| Students answer questions on work sheet based on data obtained. |
| Students create a brochure. |
|
|
|
|
|
|
| How did we use the calculator to predict the amount of blood in our bodies?
Complete brochure. |
|
| Students graph the relationship between weight and the amount of blood in the body. Most begin the creation of a sample brochure. |
|
| Day 2:
Let's Go to the Movies |
| How much would a night at the movies cost for your entire family in 2198? |
| Students read data from a table and create a scatter plot of a set of data. |
| Students find the line of best fit for a given set of data. |
|
|
|
| Data collection sheet |
| TI-73 calculators |
|
|
|
| Students are asked to think about the cost of going to the movies?
Will people still be going to the movies in 2189? |
| Students transfer information about the past to the calculator. |
| Students discuss trends and the line of best fit (regression analyses). |
| Students use the line of best fit and the equation generated. |
| Students share there results and how they arrived at their conclusions. |
|
|
|
|
|
|
| Student worksheet - function table of inputs and outputs to arrive at the equation |
|
| Students arrive at a reasonably close estimate, if not the exact answer, since they will all be using the same data. |
|
| Day 3:
The Tortoise or the Sloth? |
| Introduce students to a real-world situation that can be modeled by parametric functions. |
| Students become more familiar with the other functions on the calculator. |
| Students understand the effects of parameter changes on functions and their graphs.
|
| Students write the equation of a line in parametric form. |
|
|
| TI-73 calculator |
| Data collection sheet |
|
|
|
| Can students recall the story about the tortoise and the hare? What was the main idea of the story?
What is the equation of a line? (y=mx + b) |
| Students determine the winner of a race between a tortoise and a sloth, who start from different points and move in different paths. |
| Students graph the two lines using the calculator in the simultaneous mode. The relative motion of the two lines and when they will reach the point of intersection will be discussed. |
| Slope is the change in Y relative to the change in x. |
| Students are taught how to create a stat plot marking each animals position in relation to the time.
|
| The calculator is reset to the Parametric mode. Students re-enter the sloth's formula and the tortoise's formula. |
| Review how to toggle between functions and the scoring process based on the rubric. |
|
|
|
|
| Students are asked to verify mathematically why the results are as they were. What parameter changes would have changed the outcome of the race? |
|
| Students share their scatter plots on the overhead projector. They discuss the various ways they entered data and arrived at their conclusions. |
|
| Day 4:
Area Formulas Application |
| The calculator has the area formulas available for parallelograms, triangles, trapezoids, and circles. Students learn how to access this information.
|
| The calculator has a short tutoral on how formulas is derived. Students learn how to access this imformation.
|
| What is area and how do we measure it? |
|
|
|
| Review with students the various geometric shapes they will be exploring. |
| Students explore the concept of area and how we measure it--in terms of squares. |
| Model for students how to access the definitions and formulas on the calculator. |
| Students quiz themselves at Level 1 to be followed by Level 2. Students receive immediate feedback and the calculator scores the quiz. |
|
|
|
|
|
|
|
| Students take home a worksheet to review the area formulas and review the concepts. |
|
| Student scores from the calculator will assess their knowledge. |
|
|
Larry Kapuvari
ldkapuvari@optonline.net
Leonardo di Vinci Intermediate School
98-50 50th Avenue
Corona, NY 11368
Larry is a sixth-year Mathematics teacher who has demonstrated a passion for teaching young adults the joy of working with numbers. He believes that teaching is all about the enthusiasm and passion you can bring to the classroom every day.
Important documents for this lesson plan.
|
|
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