# K12MATH007: Math Grade 7

Unit 5: Probability and Statistics   Imagine that you would like to open a new business, but you need data on what the local people would think and whether the business would be successful. Your work on probability and statistics will help you build an appropriate sample for surveying and show you how to use your data to analyze the results and make predictions.

In this unit, you will begin by finding the probability of single events. This will lead to the probability of compound events. You will draw inferences based on random sampling, compare multiple samples, and build representations of events using tables and tree diagrams. From the models, you will make predictions and calculate the measure of center and variability.

Unit 5 Time Advisory
Completing this unit should take approximately 11 hours and 30 minutes.

☐    Subunit 5.1: 5 hours and 30 minutes

☐    Subunit 5.2: 2 hours and 15 minutes

☐    Subunit 5.3: 3 hours and 45 minutes

Unit5 Learning Outcomes
Upon successful completion of this course, you will be able to: - Solve problems involving basic and compound probabilities.
- Make predictions about an event based on theoretical and experimental probabilities.
- Use data from random samples to make inferences about a population.
- Calculate the measures of center and variability.
- Create tree diagrams and organized lists to represent sample spaces.
- Develop models to represent the probability of different events occurring.

5.1 Probability   “There is a 30% chance of rain for Friday.” The chance of something happening is the probability of an event occurring. Probabilities are used to help make decisions. A 30% chance of rain is a fairly low probability of occurring. A 90% chance of rain tells us that it is most likely going to rain. We may need to cancel plans or at least remember to bring an umbrella. In this subunit, you will take a look at how to compute probabilities and how some events can affect the probability of other events.

5.1.1 Basic Probability   - Explanation: Khan Academy’s “Basic Probability” Link: Khan Academy’s “Basic Probability” (YouTube)

Instructions: Watch the video to see the notation that is used when writing probabilities and the three different forms that can be used to write the probabilities.

Viewing this video should take approximately 15 minutes.

Standards Addressed (Common Core):

``````-   [CCSS.Math.Content.7.SP.C.5](http://www.corestandards.org/Math/Content/7/SP/C/5)

attributed to Khan Academy.
``````
• Activity: XP Math: “Plinko Probability - The Probability is Right” Link: XP Math: “Plinko Probability - The Probability is Right” (Flash)

Instructions: In this game, you will answer probability questions about the amounts you are able to win. You will place your answer in the maroon box at the bottom right. The game will tell you whether your answer is correct. If the sound is on when you play the game, you will hear a noise for a wrong answer and you will not be given a chip. If you are correct, you will be given a chip to drop down the plinko board. The hint button places a triangle under each of the given values you need to answer the question. This way, you can count up the total to get the probability.

Playing this game should take approximately 15 minutes.

Standards Addressed (Common Core):

• Did I Get This? Activity: orgLib: “Preview Questions for Test: 7.SP.5 - Worksheet” Link: orgLib: “Preview Questions for Test: 7.SP.5 - Worksheet” (HTML)

Instructions: Scroll down to the five questions and click on “Consume” beneath them. You will be brought to a new screen where you can type in your answers. After each question you will need to click on “Submit Answer.” When you have all five questions done, you will click on “Submit Test.” At this point, you will be brought to a screen that will show whether your answers are correct.

Completing this activity should take approximately 15 minutes.

Standards Addressed (Common Core):

5.1.2 Compound Events   - Explanation: CK-12: “Probability of Compound Events” Link: CK-12: “Probability of Compound Events” (PDF)

Instructions: Read the section entitled “Guidance” to find the difference between independent and dependent events. Be sure to take note of how calculating the probability for a dependent event is different from calculating the probability of an independent event. Then solve the 17 practice questions at the bottom of the page.

Completing this activity should take approximately 45 minutes.

Standards Addressed (Common Core):

``````-   [CCSS.Math.Content.7.SP.C.8](http://www.corestandards.org/Math/Content/7/SP/C/8)

attributed to CK-12 Foundation. The original version can be found
[here](http://www.ck12.org/probability/Probability-of-Compound-Events/lesson/Probability-of-Compound-Events/).
``````

5.1.2.1 Tree Diagrams, Organized Lists and Tables   - Explanation: Dr. Carol Fisher Burns’s “Probability Tree Diagrams” Link: Dr. Carol Fisher Burns’s “Probability Tree Diagrams” (HTML)

Explanation: Read through the examples of probability questions and take a look at the tree diagrams formed to answer the questions. Then go back up to the top of the page and click on “Jump right to the exercises!” This will bring you to a new screen where you can practice making your own tree diagrams.

Making tree diagrams should take approximately 15 minutes.

Standards Addressed (Common Core):

``````-   [CCSS.Math.Content.7.SP.C.8](http://www.corestandards.org/Math/Content/7/SP/C/8)

``````
• Did I Get This? Activity: orgLib: “Preview Questions for Test: 7.SP.8 - Worksheet” Link: orgLib: “Preview Questions for Test: 7.SP.8 - Worksheet” (HTML)

Instructions: Scroll down to the four questions and click on “Consume” beneath them. You will be brought to a new screen where you can type in your answers. After each question you will need to click on “Submit Answer.” When you have all four questions done, you will click on “Submit Test.” At this point, you will be brought to a screen that will show whether your answers are correct.

Completing this activity should take approximately 15 minutes.

Standards Addressed (Common Core):

5.1.3 Experimental Probability   - Explanation: CK-12: “Experimental Probability” Link: CK-12: “Experimental Probability” (HTML)

Instructions: Read through the entire lesson on experimental probability. Focus on the differences and similarities between your hypothesis (theoretical probability) and the actual results (experimental probability). You do not need to watch the video clip after the reading. Instead, work through the questions in the “Time to Practice” section.

Completing this activity should take approximately 1 hour and 15 minutes.

Standards Addressed (Common Core):

``````-   [CCSS.Math.Content.7.SP.C.6](http://www.corestandards.org/Math/Content/7/SP/C/6)

``````
• Activity: Shodor: “Experimental Probability” Link: Shodor: “Experimental Probability” (HTML)

Instructions: Now is your chance to try out your own experiments. On this site there are several different interactive spinners. For three of the spinners, do the following:

• 1. Calculate the theoretical probability of the spinner landing on red.
• 2. Complete 20 spins and keep track of the results.
• 3. Use the results to calculate the experimental probability of landing on red.
• 4. Compare the theoretical to the experimental probability.
• 5. Make a prediction: If you were to continue spinning the spinner 1,000 times, how many times would you expect the spinner to land on red?

Completing this activity should take approximately 45 minutes.

Standards Addressed (Common Core): - CCSS.Math.Content.7.SP.C.6

• Activity: Dan Meyer’s Three-Act Math Tasks: “Yellow Starbursts” Link: Dan Meyer’s Three-Act Math Tasks: “Yellow Starbursts” (HTML)

Instructions: Follow the directions for the activity. There are videos and images to help you answer the questions. In Act 3, the answer will be provided and you will be given a chance to reflect on your work.

Completing this activity should take approximately 30 minutes.

Standards Addressed (Common Core):

• Did I Get This? Activity: orgLib: “Preview Questions for Test: 7.SP.6 - Worksheet” Link: orgLib: “Preview Questions for Test: 7.SP.6 - Worksheet” (HTML)

Instructions: Scroll down to the five questions and click on “Consume” beneath them. You will be brought to a new screen where you can type in your answers. After each question you will need to click on “Submit Answer.” When you have all five questions done, you will click on “Submit Test.” At this point, you will be brought to a screen that will show whether your answers are correct.

Completing this activity should take approximately 15 minutes.

Standards Addressed (Common Core):

5.1.4 Geometric Probability   - Activity: GeoGebra: “A Look at Geometric Probability” Link: GeoGebra: “A Look at Geometric Probability” (HTML)

Instructions: The probability of landing in the inside shape can be calculated by finding the area of the inside shape and the area of the outside shape and writing the results as a fraction. This activity allows you to manipulate the lengths of the sides and therefore change the areas. Follow the directions given in the activity. Use the dots below to change the values of the lengths. Then, on separate paper, calculate the probability to see if you get the same answer as the program. Practice with five different lengths.

Completing this activity should take approximately 30 minutes.

Standards Addressed (Common Core):

``````-   [CCSS.Math.Content.7.SP.C.7](http://www.corestandards.org/Math/Content/7/SP/C/7)
-   [CCSS.ELA-Literacy.RST.6-8.3](http://www.corestandards.org/ELA-Literacy/RST/6-8/3)
-   [CCSS.ELA-Literacy.RST.6-8.7](http://www.corestandards.org/ELA-Literacy/RST/6-8/7)
-   [CCSS.ELA-Literacy.WHST.6-8.1b](http://www.corestandards.org/ELA-Literacy/WHST/6-8/1/b)
-   [CCSS.ELA-Literacy.WHST.6-8.4](http://www.corestandards.org/ELA-Literacy/WHST/6-8/4)

``````
• Did I Get This? Activity: orgLib: “Preview Questions for Test: 7.SP.7 - Worksheet” Link: orgLib: “Preview Questions for Test: 7.SP.7 - Worksheet” (HTML)

Instructions: Scroll down to the four questions and click on “Consume” beneath them. You will be brought to a new screen where you can type in your answers. After each question you will need to click on “Submit Answer.” When you have all four questions done, you will click on “Submit Test.” At this point, you will be brought to a screen that will show whether your answers are correct.

Completing this activity should take approximately 15 minutes.

Standards Addressed (Common Core):

5.2 Samples   Have you ever heard a commercial claim “9 out of 10 dentists recommend this toothpaste”? The claim that 9 out of 10 dentists like the toothpaste isn’t very meaningful if 9 of the 10 dentists also work for that toothpaste company. In that case, the sample that was questioned does not truly represent the entire population of dentists. In this subunit, we will take a look at samples and see how a well-chosen sample can represent the population and help make informed decisions.

5.3 Compare Data Sets   Oftentimes we look at one set of data in a graph or table. However, there are times when we might want to compare two different sets of data. Maybe Mr. Smith’s math class is in a competition with Ms. Sanchez’s class. Both classes have a set of data that will need to be compared to see who wins the competition. This subunit looks at different ways of comparing multiple sets of data. It starts by looking at different types of graphs and measures of center and variability. Then it continues on to discuss multiple sets of data.

5.3.1 Mean Deviation   - Interactive Lab: GeoGebra: “Calculate Mean Absolute Deviation (M.A.D.)” Link: GeoGebra: “Calculate Mean Absolute Deviation (M.A.D.)” (HTML)

Instructions: There is a detailed list of the steps that need to be taken to get the MAD at the bottom of the worksheet. Follow them to calculate the MAD. Then use the option to show the steps in #1 to check your work.

Completing this activity should take approximately 15 minutes.

Standards Addressed (Common Core):

``````-   [CCSS.Math.Content.7.SP.B.3](http://www.corestandards.org/Math/Content/7/SP/B/3)
-   [CCSS.Math.Content.7.SP.B.4](http://www.corestandards.org/Math/Content/7/SP/B/4)

``````

5.3.2 Box and Whisker Plots   - Explanation: CK-12: “Box-and-Whisker Plots” Link: CK-12: “Box-and-Whisker Plots” (PDF)

Instructions: Read the lesson on creating a box-and-whisker plot until you reach the videos from Khan Academy. While reading, take note of what the following terms mean and where they appear in a box-and-whisker plot: median, upper quartile, and lower quartile.

Completing this activity should take approximately 15 minutes.

Standards Addressed (Common Core):

``````-   [CCSS.Math.Content.7.SP.B.3](http://www.corestandards.org/Math/Content/7/SP/B/3)
-   [CCSS.Math.Content.7.SP.B.4](http://www.corestandards.org/Math/Content/7/SP/B/4)
-   [CCSS.ELA-Literacy.RST.6-8.4](http://www.corestandards.org/ELA-Literacy/RST/6-8/4)

text is attributed to CK-12 and the video is attributed to Khan
Academy. The original version can be found
[here](http://www.ck12.org/user%3AbXN0b2RlcmxAcGVyaGFtLmsxMi5tbi51cw../book/Mrs.-Stoderl%2527s-Pre-Algebra-book/r20/section/13.4/).
``````

5.3.3 Stem and Leaf Plots   - Explanation: CK-12: “Stem-and-Leaf Plots” Link: CK-12: “Stem-and-Leaf Plots” (PDF)

Instructions: Start by reading the example of using data from the Iditarod in Alaska. Continue reading until you reach the videos. Take note of the following while reading.

``````-   1. How is the stem different than a leaf?
-   2. How can I write a three-digit number as a stem and leaf?
-   3. What does the key for a stem and leaf plot look like?
-   4. How can I get the mean, median, and mode from the stem and
leaf plot?

Next, watch the video from Khan Academy in order to see a stem and
leaf plot made and why it is important. Finally, using the
information in the reading and the video, answer the questions in
the “Time to Practice” section.

Completing these activities should take approximately 1 hour.

Standards Addressed (*Common Core*):
-   [CCSS.Math.Content.7.SP.B.3](http://www.corestandards.org/Math/Content/7/SP/B/3)
-   [CCSS.Math.Content.7.SP.B.4](http://www.corestandards.org/Math/Content/7/SP/B/4)
-   [CCSS.ELA-Literacy.RST.6-8.2](http://www.corestandards.org/ELA-Literacy/RST/6-8/2)

text is attributed to CK-12 and the video is attributed to Khan
Academy. The original version can be found
[here](http://www.ck12.org/user%3AbXN0b2RlcmxAcGVyaGFtLmsxMi5tbi51cw../book/Mrs.-Stoderl%2527s-Pre-Algebra-book/r20/section/13.3/).
``````

5.3.4 Comparing Multiple Sets of Data   - Explanation: CK-12: “Data Analysis Using Dot Plots, Measures of Central Tendency, and Interquartile Range” Link: CK-12: “Data Analysis Using Dot Plots, Measures of Central Tendency, and Interquartile Range” (PDF)

Instructions: Read through the lesson, taking note of how measures of center (mean, median, mode) and measures of variability (MAD, interquartile range, range) can be used to compare two sets of data.

Reading this lesson should take approximately 30 minutes.

Standards Addressed (Common Core):

``````-   [CCSS.Math.Content.7.SP.B.3](http://www.corestandards.org/Math/Content/7/SP/B/3)
-   [CCSS.Math.Content.7.SP.B.4](http://www.corestandards.org/Math/Content/7/SP/B/4)

attributed to CK-12 Foundation. The original version can be found
[here](http://www.ck12.org/na/Data-Analysis-Using-Dot-Plots,-Measures-of-Central-Tendency,-and-Interquartile-Range---7.SP.3,4-1/lesson/user:c2ZveDJAb3N3ZWdvLm9yZw../Data-Analysis-Using-Dot-Plots%252C-Measures-of-Central-Tendency%252C-and-Interquartile-Range---7.SP.3%252C4/).
``````
• Did I Get This? Activity: orgLib: “Preview Questions for Test: 7.SP.3 - Worksheet” Link: orgLib: “Preview Questions for Test: 7.SP.3 - Worksheet” (HTML)

Instructions: Scroll down to the four questions and click on “Consume” beneath them. You will be brought to a new screen where you can type in your answers. After each question you will need to click on “Submit Answer.” When you have all four questions done, you will click on “Submit Test.” At this point, you will be brought to a screen that will show whether your answers are correct.

Completing this activity should take approximately 15 minutes.

Standards Addressed (Common Core):

• Did I Get This? Activity: orgLib: “Preview Questions for Test: 7.SP.4 - Worksheet” Link: orgLib: “Preview Questions for Test: 7.SP.4 - Worksheet” (HTML)

Instructions: Scroll down to the four questions and click on “Consume” beneath them. You will be brought to a new screen where you can type in your answers. After each question you will need to click on “Submit Answer.” When you have all four questions done, you will click on “Submit Test.” At this point, you will be brought to a screen that will show whether your answers are correct.

Completing this activity should take approximately 15 minutes.

Standards Addressed (Common Core):

• Checkpoint: Illustrative Mathematics: “College Athletes” Link: Illustrative Mathematics: “College Athletes” (PDF)

Instructions: Complete parts a though e. You may use a calculator when completing this checkpoint. Then check your work on page 3.

Completing this checkpoint and checking your work should take approximately 1 hour.

Standards Addressed (Common Core):

• Checkpoint: Illustrative Mathematics: “Waiting Times” Link: Illustrative Mathematics: “Waiting Times” (PDF)

Instructions: Determine the number of boxes of cereal that would need to be purchased in parts A and B. Then scroll to page 2 to check your work.

Completing this checkpoint and checking your work should take approximately 15 minutes.

Standards Addressed (Common Core):

`````` Instructions: Complete this exam.