TAMUCT-KISD Professional development session April 6th 2018

TEKS

Probability:

Grade 4+5:

Students organize data, choose an appropriate method to display the data, and interpret the data to make decisions and predictions and solve problems.

Probability and statistics. The student solves problems by collecting, organizing, displaying, and interpreting sets of data. The student is expected to:

1. list all possible outcomes of a probability experiment such as tossing a coin;

2. use a pair of numbers to compare favorable outcomes to all possible outcomes such as four heads out of six tosses of a coin; and

3. interpret bar graphs.

Probability and statistics. The student describes and predicts the results of a probability experiment. The student is expected to:

1. use fractions to describe the results of an experiment; and

2. use experimental results to make predictions.

13. Probability and statistics. The student solves problems by collecting, organizing, displaying, and interpreting sets of data. The student is expected to:

1. use tables of related number pairs to make line graphs;

2. describe characteristics of data presented in tables and graphs including the shape and spread of the data and the middle number; and

3. graph a given set of data using an appropriate graphical representation such as a picture or line.

Grade 6:

Probability and statistics. The student uses experimental and theoretical probability to make predictions. The student is expected to:

1. construct sample spaces using lists, tree diagrams, and combinations; and

2. find the probabilities of a simple event and its complement and describe the relationship between the two.

Probability and statistics. The student uses statistical representations to analyze data. The student is expected to:

1. draw and compare different graphical representations of the same data;

2. use median, mode, and range to describe data;

3. sketch circle graphs to display data; and

4. solve problems by collecting, organizing, displaying, and interpreting data.

Grade 7:

Probability and statistics. The student recognizes that a physical or mathematical model can be used to describe the probability of real-life events. The student is expected to:

1. construct sample spaces for compound events (dependent and independent); and

2. find the approximate probability of a compound event through experimentation.

11. Probability and statistics. The student understands that the way a set of data is displayed influences its interpretation. The student is expected to:

1. select and use an appropriate representation for presenting collected data and justify the selection; and

2. make inferences and convincing arguments based on an analysis of given or collected data.

12. Probability and statistics. The student uses measures of central tendency and range to describe a set of data. The student is expected to:

1. describe a set of data using mean, median, mode, and range; and

2. choose among mean, median, mode, or range to describe a set of data and justify the choice for a particular situation.

Grade 8:

11. Probability and statistics. The student applies concepts of theoretical and experimental probability to make predictions. The student is expected to:

1. find the probabilities of compound events (dependent and independent);

2. use theoretical probabilities and experimental results to make predictions and decisions; and

3. select and use different models to simulate an event.

12. Probability and statistics. The student uses statistical procedures to describe data. The student is expected to:

1. select the appropriate measure of central tendency to describe a set of data for a particular purpose;

2. draw conclusions and make predictions by analyzing trends in scatterplots; and

3. construct circle graphs, bar graphs, and histograms, with and without technology.

13. Probability and statistics. The student evaluates predictions and conclusions based on statistical data. The student is expected to:

1. evaluate methods of sampling to determine validity of an inference made from a set of data; and

2. recognize misuses of graphical or numerical information and evaluate predictions and conclusions based on data analysis.

Navigate to:

https://www.geogebra.org

Select “GeoGebra Classic” and then “Spreadsheet”.

Task 1.1:

1. Enter the number 10 into cell A1. Hint: Always confirm your input by pressing the Enter key.

2. Enter the coordinates \((-2, 2)\) into cell B1. Note: The point \(B1 = (-2, 2)\) is automatically shown in the Graphics View.

3. Select the Move tool and drag point B1 in the Graphics View. Note: The Spreadsheet View shows the current position of point B1 in cell B1

Task 1.2

1. Change the number in cell A1 to 1.5 and confirm your input.

2. Enter the formula = 2 * into cell B1 and then select cell A1 in order to insert its name into the formula. Confirm your input.

Note: GeoGebra calculates 2 * 1.5 and displays the solution 3 in cell B1.

3. Change the content of cell A1 to 3. Note: The content of cell B1 automatically adapts to your changes.

Task 1.3:

Enter the coordinates \((A1, B1)\) into cell C1 and confirm your input.

Hint: Cell C1 now shows the coordinates \((3, 6)\). The corresponding Point C1 is automatically displayed in the Graphics View. 2. Change the value of cell A1 to 2. Note: The coordinates in cell C1 and the corresponding point automatically adapt to your changes.

Relative and Absolute Copy of Cell Content

Relative copy

Using relative copy, you can easily create number sequences or apply formulas to a series of numbers. Note: If you relative copy formulas to other cells, by default all references are changed according to the target position.

Task 2.1

Create a number sequence in column A.

1. Enter 1 into cell A1 and 2 into cell A2.

2. Highlight both cells A1 and A2 and drag the little square in the lower right corner of the highlighted area down to cell A10.

Note: You just used relative copy in order to create the integers from 1 to 10 in cells A1 to A10.

3. A2 Change the number in cell A2 to 3.
4. Highlight both cells A1 and A2 again and relative copy the new values to the other cells in order to update the number sequence.

Task 3.1

Calculate the sum of a series of numbers using the Sum tool.

1. Use the Move tool to highlight all cells of column B that contain numbers.

2. Select the Sum tool from the Spreadsheet View Toolbar.

Note: The sum of the numbers in the highlighted cells is displayed in the next empty cell of column B.

Task 3.2 Create a list of points based on the numbers provided in the spreadsheet.

1. Use the Move tool to highlight all cells of columns B and C down to row 6.
2. Select the List of Points tool from the Spreadsheet View Toolbar. In the appearing dialog window, press Create in order to create points from your data set.

Note: The values in column B determine the x-coordinates and the values in column C specify the y-coordinates of the plotted points.

Example 3.1

There have been claims that you can tell how tall a person will be by just looking at their sho size. On average, a tall person is figured to have bigger feet than a shorter person. The height of a person is measured from the top of the head to the bottom of the feet. Depending on a person’s nationality, height can vary due to different environmental and genetic factors. The shoe size is measured from the tip of the longest toe to the ankle.

Task:

The main purpose of this investigation is to determine whether there is a correlation between the height of a person and their shoe size.

Plan:

Collect data from students and see if their height correlates with their shoe size. The independent variable is the shoe size and the dependent variable is the height.

Collect the data and input into the spreadsheet in GeoGebra.

Data analysis:

1. Create a scatterplot.
2. Create a linear regression model.
3. What is the equation of the line of best fit?
   
4. Is there a correlation between the height of a person and their shoe size?

Probability and relative frequency

Example 1:

Flip a coin. What is your sample space?

Example 2:

Let’s start with dice. Take a die (make sure it’s fair, not weighted or “funny” in any way). What are the odds (the probability) of rolling a 3 if you roll the die one time? Hopefully you figured out that it is one in six because there are six sides to the die, and one of those sides has three dots.

Let’s try it. Take the die and roll it 100 times, recording your results below. Calculate the percentage of each result (for example, if you rolled a 2 17 times, that would be 17/100, or 17 percent).

Fig. 5.2

We would expect that the percentages for each number would hover around 16 or 17, which is 1/6 or .1666. This is probability in a nutshell.

Now guess what the percentage would be if you added up the percentages of the rolls of only the oddnumbered sides. When you add up those roles, does the percentage come close to your guess?

Probability is the ratio of the times an event is likely to occur divided by the total possible events.

In the case of our die, there are six possible events, and there is one likely event for each number with each roll, or 1/6. If there were no dots on any of the sides, the probability of rolling a 3 would be zero because there would be no 3 and no other dots either, giving us this ratio: 0/0. If every side had three dots, the probability of rolling a 3 would be 1 because it would be 6/6, or 1. So, probability is expressed as a number somewhere between 0 (not gonna happen) and 1 (definitely going to happen), with ratios closer to 1 being most likely.

Example:

2. If you go to school Monday through Friday and you know the cafeteria is going to serve pizza two days that week, what is the probability that pizza will be served on any given day? It would be 2/5, because there are two desired outcomes (pizza!) and five possible outcomes (days of the school week).