7th Grade Unit 6: Probability/Sampling

Unit Driving Question 

What is the relationship between rational numbers and proportionality?

Essential Questions 

1. How do you predict future probability based on data?

2. How can we gather, organize and display data to communicate and justify results in the real world?

3. What is the best way to display data for a given real-world situation?

4. How is proportionality used in probability?

Big Ideas 

1. Data can be displayed, analyzed and applied in a variety of ways. 
2. Proportional reasoning can be used to determine probability. 
3. Probability can be expressed as a rational number. 

Technology Resources

• 7th Grade Technology Resources

Launch Task 

1 Lesson 

This is a fun game where students are given a bag of colored blocks to collect data to make decisions based on their sampling to introduce them to probability.

Playing the Block Game (Open Up)

Playing the Block Game Student Sheet

Big Ideas for Development Lessons 

3Weeks (approximately 1 week per big idea) 

Big Idea 1: Data can be displayed, analyzed and applied in a variety of ways.

Key Resources

• Warm-Up- Notice and Wonder Comparing Heights Warm- Up and Student Recording Sheet (Open Up)- This initial activity helps students review and begin communicating their observations regarding measures of central tendency. 

1. Family Heights and Family Heights Student Sheet (Open Up)- Students begin analyzing the mean of the heights of men vs. women and look at how adding more babies would affect the mean.
2. Prices of Homes and  Price of Homes Student Sheet (Open Up)- This is an activity comparing housing prices of two different neighborhoods. Students find the mean, median, mode and range of the neighborhoods to make comparisons.
3. Describing the Center and Describing the Center Student Sheet (Open Up)- Students are presented with whether they need to use the mean or median as the best representation of the data in various scenarios. 
4. Three Different TV Shows and Three Different TV Shows Student Sheet (Open Up)- Students are given data to analyze and match up which mean represents each of the different TV shows. It demonstrates how measures of central tendency can be used to drive decision- making.
5. Quartiles and Interquartile Range (Open Up): In Activity 1, students learn how to partition a data set into four sets by finding the five-number summary (minimum, first quartile, median, third quartile, maximum) that will be used to make a box and whisker plot in later a lesson.  In Activity 2, students find the range and the interquartile range (IQR) of data sets which are measures of variability.  The Cool Down asks students to compare data using median and IQR.
6.  Box Plots (Open Up): The Warm Up asks students what they notice and wonder about a data set using what they know about measures of central tendency and distributions of data sets.  In Activity 1, students use their class data from The Median of a Data Set (Open Up) to find the five-number summary of the data set in order to create a human box plot.  Open Up resources use the term box plot in the place of box and whisker plot. Activity 2 asks students to create a dot plot and box plot for a data set collected from a study about blinking.  Students then analyze the results using the two plots.  In the Cool Down, students compare data given in the form of two box plots and then match the box plots to the correct dot plots.
7.  Using Box Plots to Make Comparisons (Open Up): The Warm Up asks students to find the value in the middle of two given numbers.  In Activity 1, students are given three sets of data about the flight distances of paper airplanes and asked to create box plots for each data set on one number line in order to compare them.  Activity 2 has students compare heights of professional athletes using four box plots.  The Cool Down has student compare the lengths of humpback whales using box plots created for male and female humpback whales.

Bootstrap Computer Science Integration (for Bootstrap trained teachers)

• Introduction to Computational Data Science 

Big Idea Probe 

1. Unit 6 - Big Idea 1 Probe 
2. Box and Whisker Plot Probe 

Evidence of Understanding

Students can:

• Calculate measures of central tendency including range.

• Determine which measure of central tendency is most useful for a given situation.

• Choose the best way to graphically represent a data set.

• Graphically represent a data set.

• Design experiments and collect data.

• Identify how outliers affect a data set.

• Identify relationships in a set of data.

• Use technology to create graphical representations of data.

• Explain how removing a number or adding a number to a data set can affect the measures of central tendency.

• Use Technology to create box and whisker plots for real-world data.

• Identify the five numbers (minimum, first quartile, median, third quartile, and maximum) needed to construct a box and whisker plot for a given data set.

• Analyze real-world data sets using box and whisker plots.

• Describe the range and interquartile range as it relates to the associated data set.

• Describe the meaning of each quartile of a box and whisker plot as it relates to the associated data set.

• Compare data sets using box and whisker plots.

• Discuss the advantages and disadvantages of using box and whisker plots to analyze a data set (Ex. What information about a data set is gained from a box-and-whisker plot?  What information is lost?). 

Big Idea 2: Proportional reasoning can be used to determine probability.

Key Resources  

1. Reaction Times, Reaction Times Student Sheet, Reaction Times Cards (Open Up)- In this activity students apply their estimation skills to estimate the proportion of a population that matches certain characteristics.
2. A New Comic Book Hero, A New Comic Book Hero Student Sheet (Open Up) - In this activity, students use proportions to make conclusions and predictions based on their samples.
3. SKUNK - A fun game where students their knowledge of probability in a game setting.

Big Idea Formative Assessment

• Unit 6- Big Idea 2 Probe

Evidence of Understanding 

Students can:

• Use proportional reasoning to draw conclusions and predict relative frequencies outcomes based on probability.

• Identify the sample space and express it as a rational number.

• Use theoretical probability to determine how an event might occur if it is increased or decreased proportionally.

• Utilize probability to draw conclusions and make predictions about data using proportional reasoning.

Big Idea 3: Probability can be expressed as a rational number.

Key Resources 

• Which is More Likely?  Warm-Up, Which is More Likely?  Student Sheet (Open Up)- Students discuss and determine whether events are likely, unlikely, impossible, certain to happen.
• Which One Doesn’t Belong: Spinners (Open Up)- This is an interesting discussion activity comparing different spinners.
• Which Game Would You Choose? (Open Up)- Students are challenged with two different events with different outcomes and choose what they think would be the best outcome to win the game.
• Probability with Marbles - Can you determine which marbles are in the bag to make the probability of drawing a red marble the same in each bag?
• The Probability of Spinning B (Open Up)- Three students are spinning a spinner with different size sections. Based on each of the 3 results, students have to determine which student is correct.
• Designing Experiments, Designing Experiments Student Sheet (Open Up)- In this activity students design their own experiments to represent the probability of real-life events.

Big Idea Formative Assessment

• Unit 6 - Big Idea 3 Probe    

Evidence of Understanding

Students can:

• Find the theoretical probability of an event and express it as a rational number.

• Calculate probability as a fraction of a sample space or as a fraction of an area.

• Express probability as a fraction, decimal and percent.

• Explain the relationship between probability and sample spaces.

• Identify the number of desirable outcomes and sample space from various representations.

Unit Closure

1 Week (includes time for probes, re-engagement, and assessment) 

• Unit 6 Assessment 
• Designing a Spinner Performance Assessment (covers 7.D.1.2, 7.D.2.1, 7.D.2.2, 7.D.2.3): For access to scoring rubric and student samples, complete the NextThought PLC Common Assessment Discussion, Implementation, and Analysis training module.