Unit 1, Lesson 9
Technological Graphing
Algebra 1
9.1
Warm-up
Standards Alignment
Building On
HSS-ID.A.2
Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.
Addressing
Building Toward
Instructional Routines
NoneMaterials
Activity Narrative
The mathematical purpose of this activity is to gain familiarity with entering data into a spreadsheet and to prepare students for finding statistics using technology.
Launch
Arrange students in groups of 2. If students are using the digital version of the materials, show them how to open the GeoGebra spreadsheet app in the math tools. If students are using the print version of the materials, they can access the GeoGebra spreadsheet app at www.geogebra.org/spreadsheet. If students will be using statistical technology other than GeoGebra for this activity, prepare alternate instructions.
Make sure students input the data in one column, even though the data are represented in two columns in the task statement.
Activity
NoneOpen a spreadsheet window and enter the data so that each value is in its own cell in column A.
- How many values are in the spreadsheet? Explain your reasoning.
- If you entered the data in the order that the values are listed, the number 7 is in the cell at position A1 and the number 5 is in cell A5. List all of the cells that contain the number 13.
- In cell C1 type the word “Sum,” in C2 type “Mean,” and in C3 type “Median.” You may wish to double-click or drag the vertical line between columns C and D to allow the entire words to be seen.
| A | |
|---|---|
| 1 | 7 |
| 2 | 8 |
| 3 | 4 |
| 4 | 13 |
| 5 | 5 |
| 6 | 15 |
| 7 | 14 |
| 8 | 8 |
| 9 | 12 |
| 10 | 2 |
| A | |
|---|---|
| 11 | 8 |
| 12 | 13 |
| 13 | 12 |
| 14 | 13 |
| 15 | 6 |
| 16 | 1 |
| 17 | 9 |
| 18 | 4 |
| 19 | 9 |
| 20 | 15 |
Student Response
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Building on Student Thinking
Activity Synthesis
The goal is to make sure that students know how to type data into a spreadsheet and to locate values in the spreadsheet by row and column. The locations will be referred to with spreadsheet functions in upcoming activities. Here are some questions for discussion.
- “What value is in cell A7?” (14)
- “What was interesting or challenging about this activity?” (I never knew that you could describe each cell in a spreadsheet using the row and column labels.)
Math Community
After the Warm-up, display the Math Community Chart with the “Doing Math” actions added to the teacher section for all to see. Give students 1 minute to review. Then share 2–3 key points from the teacher section and your reasoning for adding them. For example,
- If “questioning vs. telling,” a shared reason could focus on your belief that students are capable mathematical thinkers and your desire to understand how students are making meaning of the mathematics.
- If “listening,” a shared reason could be that sometimes you want to sit quietly with a group just to listen and hear student thinking and not because you think the group needs help or is off-track.
After sharing, tell students that they will have the opportunity to suggest additions to the teacher section during the Cool-down.
9.2
Activity
Instructional Routines
NoneMaterials
To Gather
Statistical technologyActivity Narrative
The mathematical purpose of this activity is to calculate statistics, create data displays, and to investigate how those change when values are added or removed from the data set. Monitor for students discussing the relationship between outliers and the measure of center.
Launch
Keep students in the same groups. They will continue working using the spreadsheet they started in the previous activity.
Tell students that statistics are values that are calculated from data, such as the mean, median, or interquartile range.
Tell students that after they change the value in A1 to change the mean in the first set of questions, they should continue to use the changed values for the second set of questions rather than reset them to the values from the warm-up.
Note that GeoGebra is like any other computer program. It needs directions written in a specific way for it to execute a command. For example, if students forget to type the “=” symbol or don’t capitalize “Sum,” the formula won’t work. Ask students to pause after typing the formulas and to ensure that cells D1, D2, and D3 display numbers for each statistic. If not, ask students to delete the contents of the cell and retype the formula, ensuring that they start with an “=” symbol and capitalize “Sum,” “Mean,” and “Median.” If students will be using statistical technology other than GeoGebra for this activity, prepare alternate instructions.
Action and Expression: Internalize Executive Functions. To support development of organizational skills in problem-solving, chunk this task into more manageable parts. For example, present one set of questions at a time.
Supports accessibility for: Organization, Attention
Supports accessibility for: Organization, Attention
9.3
Activity
Materials
NoneActivity Narrative
The mathematical purpose of this activity is for students to create data displays and calculate statistics using technology. Students plot the survey data that they collected from a statistical question in a previous lesson.
If students are using GeoGebra or the Spreadsheet tool in Math Tools to create a histogram, there is an issue when the maximum value is on the boundary of the greatest interval. In this case, GeoGebra includes the maximum value with the previous interval rather than following the convention of creating a new bar for the next interval. Address this issue during the Launch.
This activity uses the Collect and Display math language routine to support students as they develop their mathematical language.
Launch
Arrange students in groups of 2. Tell them that they will be using technology to create data displays and to calculate statistics for data that they collected from a survey question in a previous lesson.
If students are using GeoGebra or the Spreadsheet tool in Math Tools to create a histogram for the data set in the Student Task Statement, draw their attention to the last interval in the created histogram. Tell students that GeoGebra has an issue when the maximum value of the data set is on the boundary of an interval. In that case, it includes the maximum value in the count for the previous bar rather than creating a new bar for that value, which is the convention it uses for other data. Demonstrate using the sample data set to show that this happens with the value “12”.. They should check the maximum value, and adjust (either by hand or by redrawing—or just mentally) their histogram based on this issue when using GeoGebra or the Spreadsheet tool from Math Tools. If students will be using statistical technology other than GeoGebra for this activity, prepare alternate instructions.
Use Collect and Display to create a shared reference that captures students’ developing mathematical language. Collect the language that students use to talk about technology and data representations. Display words and phrases such as “data set,” “skewed distribution,” “median,” or “the IQR on the box plot.”
Engagement: Develop Effort and Persistence. Provide prompts, reminders, guides, rubrics, or checklists that focus on increasing the length of on-task orientation in the face of distractions. For example, create an exemplar dot plot highlighting specific features, such as the scale and labels, as well as calculations for the mean and median.
Supports accessibility for: Attention, Social-Emotional Functioning
Supports accessibility for: Attention, Social-Emotional Functioning
Lesson Synthesis
The goal of this lesson is for students to display and investigate data using technology. Here are some questions for discussion.
- “How do you create data displays using technology?” (You type the data into the spreadsheet and then click the appropriate buttons.)
- “What are some advantages of using technology to display data and calculate statistics?” (You can easily switch between different data displays and you can change the intervals on histograms without having to sort through the data again. The advantage of having the technology calculate the statistics is that I can see how the statistics change as I enter or make changes to the data.)
- “When do you think it is appropriate to use technology to display data or to calculate statistics?” (Graphing technology makes it easier to determine the shape of a distribution. I might use it to determine the most appropriate measure of center for a data set. Using technology to calculate statistics makes sense in most situations because statistics are calculated using algorithms that can get complicated when there are many values in the data set. The chance of making a mistake while calculating statistics by hand makes using technology a good choice.)
Student Lesson Summary
Data displays (like histograms or box plots) are very useful for quickly understanding a large amount of information, but often take a long time to construct accurately using pencil and paper. Technology can help create these displays as well as calculate useful statistics much faster than doing the same tasks by hand. Especially with very large data sets (in some experiments, millions of pieces of data are collected), technology is essential for putting the information into forms that are more easily understood.
A statistic is a quantity that is calculated from sample data as a measure of a distribution. Mean and median are examples of statistics that are measures of center. Mean absolute deviation (MAD) and interquartile range (IQR) are examples of statistics that are measures of variability. Although the interpretation must still be done by people, using the tools available can improve the accuracy and speed of doing computations and creating graphs.