Lesson Plan Template: General Lesson Plan
Learning Objectives: What will students know and be able to do as a result of this lesson?
- Students will be able to estimate population percentages of a normal distribution using the mean and standard deviation of a data set.
- Students will be able to estimate the area under the normal curve using calculators and the empirical rule.
Prior Knowledge: What prior knowledge should students have for this lesson?
- Students will not be required to calculate the standard deviation during this lesson, however they should come into the lesson familiar with the process and the definition of standard deviation as a method of measuring spread from the mean.
- Students should be familiar with quartiles from working with box plots and be able to transfer this knowledge and process to the normal distribution.
- Even though students will not be calculating the mean, students should have a working understanding of mean as a measure of center and how to determine the mean from a set of values.
Guiding Questions: What are the guiding questions for this lesson?
- What is Cinderella's shoe size?
Engage: What object, event, or questions will the teacher use to trigger the students' curiosity and engage them in the concepts?
Estimated Time: (2 – 3 minutes)
Distribute the Engage, Explore, Elaborate worksheet, the bags of pre-cut normal distribution manipulative, and the exit slip at the beginning of the period to each student. Students should not open the bags until told to do so during the explore phase.
Read the following adaptation of the Cinderella story to them as they follow along on their worksheet.
In the story of Cinderella, her fairy godmother creates a set of glass slippers and a beautiful dress for her to wear to the ball. While at the ball, Cinderella meets the Prince and they fall madly in love with each other. Unfortunately the fairy godmother's spell only works until the last stroke of 12 at midnight. Cinderella is having such a wonderful time at the ball that she loses track of time until the bells start tolling. Knowing that the spell will soon end, Cinderella rushes from the ball, and in her haste, she loses one of her glass slippers. The Prince, desperate to find his lost love, searches the kingdom for the one woman whose foot will fit into the shoe perfectly.
If there are 1000 women in the kingdom with a mean shoe size of 9 and a standard deviation of 1, and if we know that Cinderella's step-sisters' feet are too big for the shoe, what is Cinderella's shoe size?
Write your prediction on the worksheet. We will come back to this question at the end of the lesson and you will be able to revise your answer if you choose.
You should collect all the initial prediction data at this time using a quick tally and construct a histogram for the data. It will be useful to see the change in the data from the beginning of the lesson to the end and to see which data set is more symmetrical.
Explore: What will the students do to explore the concepts and skills being developed through the lesson?
Estimated Time: (5 – 8 minutes)
Students should now open their bag of the pre-cut normal distribution manipulative (see attachment "Normal Distribution Puzzle"). Students will take the pieces from the bag and assemble them using the standard deviations as guides.
Students will answer the Explore questions on their worksheet. This process should take the students about 5 minutes to complete. You should be circulating around the classroom to ensure that students have the normal distribution constructed correctly and they are working to answer the Explore questions.
Students should also write their Explore phase prediction on the exit slip.
After 5 minutes, or when the students have completed the Explore questions, they should compare their answers with another student or group and discuss any differences in their answers.
Explain: What will the students and teacher do so students have opportunities to clarify their ideas, reach a conclusion or generalization, and communicate what they know to others?
Estimated Time: (10 – 15 minutes)
Open the "Cinderella Explain PPT" and follow through the notes section to ensure that students have at least a basic understanding of how the normal distribution curve is set-up and what the different standard deviation changes signify with respect to the percent of values in each area.
Slide 1 Title slide
The next phase of the 5E model is the Explain phase where we will discuss the parts of the normal curve and how we will use those parts to determine the area under the normal curve.
Slide 2 Blank Normal Curve
The graph of a normal distribution depends on two factors – the mean and the standard deviation. The mean of the distribution determines the center of the graph and the standard deviation determines the height of the graph. When the standard deviation is large the graph is short and wide, when the standard deviation is small the graph is tall and narrow. All normal distributions look like a symmetric, bell-shaped curve.
- Question 1: Is every distribution a "normal" distribution?
No, it must have one mode and be symmetric about the mean, median, and mode
- Question 2: Where is the mean/median located on this slide?
In the middle
Slide 3 Normal Curve with Mean/Median
- Question 1: What percent of values are above the mean?
- Question 2: What percent of values are below the mean?
Slide 4 Normal Curve with Standard Deviation Breaks above and below
Standard deviation is a measure of how spread out the values are in the data set. On the normal curve we show changes in standard deviations below the mean with negative numbers and changes in standard deviations above the mean with positive numbers.
Slide 5 Normal Curve with Percentages Between Each Standard Deviation
One of the things that makes the normal distribution curve so special is that we can predict the percent of values between each standard deviation.
- Question 1: What percent of the data is between 1 standard deviation above and 2 standard deviations above the mean?
- Question 2: What percent of the data is between the mean and 1 standard deviation below the mean?
Slide 6 Normal Curve with Empirical Rule
Using a method known as the "empirical rule" or the "68-95-99.7 rule" we can roughly predict the grouping of data points about the mean. All normal distributions follow this pattern and this allows us to make some predictions about the data if we know that it is normally distributed.
- Question 1: What percent of the data is within 1 standard deviation of the mean?
- Question 2: What percent of the data is within 2 standard deviations of the mean?
- Question 3: What percent of the data is within 3 standard deviations of the mean?
Slide 7 Normal Curve Final
Bringing all this information together we are able to make predictions about the data as long as we know the mean and the standard deviation.
For the following questions we are going to use a mean of 50 and a standard deviation of 10. Write mean = 50, standard deviation = 10; on the board so students may reference the values when answering the questions.
- Question 1: How many standard deviations from the mean is a value of 40?
1 standard deviation below
- Question 2: How many standard deviations from the mean is value of 60?
1 standard deviation above
- Question 3: What percent of the values fall between 40 and 60?
68% (two pink areas on the chart)
- Question 4: How many standard deviations from the mean is a value of 30?
2 standard deviations below
- Question 5: How many standard deviations from the mean is a value of 80?
3 standard deviations above
- Question 6: What percent of the values fall between 30 and 80?
97.35% (the two orange areas, the two pink areas, and the upper blue area)
After addressing any student questions from the PowerPoint you should model the process to solve #1 in the Explain phase then allow the students to answer #2. After checking #2 you should model the process to solve #3 in the Explain phase, then allow the students to answer #4. After addressing any questions on #4 students should continue on to the Elaborate questions.
Elaborate: What will the students do to apply their conceptual understanding and skills to solve a problem, make a decision, perform a task, or make sense of new knowledge?
Estimated Time: (10 – 15 minutes)
After answering questions from the Explain phase students should be able to apply their knowledge on the Elaborate phase questions. These questions require them to extend their thinking to more real-world situations and also revisits their prediction from the Explore phase.
Using their normal distribution manipulative students should be able to work through the Elaborate questions in about 10 minutes. After students have completed the Elaborate questions they should complete the Exit Slip with their final prediction and mathematical reasoning process that they used to come up with that value. If you have time to allow students to discuss their answers please allow them to do so. If you have time to collect data from every student on their second prediction and organize it into a histogram it would be an interesting extension to see which data predictions are more symmetric. If you are running short on time you may have to forgo the discussion to allow time for the students to return the manipulative puzzle to the bag, complete the 5E worksheet, and exit slip. You can also get the data for the second student prediction from the exit slip and construct a histogram to discuss at a later time.
You Must: make sure each student has all eight pieces in the bag and collect the 5E worksheet and exit slip from each student before the end of the period.
The questions on the Elaborate phase are still formative but they should be checked for accuracy and discussed as a class prior to assigning the Evaluate summative assessment. The summative assessment questions could be administered the following day or may be included as part of a unit assessment at a later date.
The summative assessment for this lesson will take place during another class period. Students should be able to work through four of the five E's in the model (Engage, Explore, Explain, Elaborate) during one 45 minute class period, while the fifth E (Evaluate) will take place on a separate day using the summative assessment included ("Cinderella Summative"). Students should be able to complete the summative assessment within 20 minutes, however more time may be given to those students who require accommodations.
- There is an exit slip where the students will record their prediction for Cinderella's shoe size before, during, and after the lesson ("Cinderella Exit Slip"). This exit slip should be collected at the end of the lesson and can be used as data during a lesson on bivariate data correlation.
- The questions on the 5E worksheet ("Cinderella 5E Worksheet") should guide student learning during the lesson. The student responses to the Explore phase questions will also serve as a formative assessment to judge their basic understanding of the material after working with the manipulative. Any questions from this phase should be used to drive the direct instruction during the Explain phase.
During the Explain phase you should follow the PowerPoint ("Cinderella Explain PPT") and questioning strategies provided to ensure that the students have a good understanding of mean and standard deviation as they relate to a normal distribution curve, before moving to the Elaborate phase. The Elaborate questions require students to relate their understanding of the normal curve to real-world questions. These questions are still formative in nature and should be reviewed for understanding before the end of the lesson.
Feedback to Students
- Students will receive feedback from their peers at the end of the Explore phase and during the Explain phase. Students will receive feedback from the teacher during each phase, but will receive specific direct instruction during the Explain phase.
- Students will then use this feedback immediately to complete the Elaborate and Evaluate phases.