## Opener - Section 1: Launch

# Random Sampling - How do you make sure your sample is random?

Lesson 6 of 10

## Objective: Students will be able to conduct a random sampling simuation.

#### Launch

*10 min*

**Opener: **As students enter the room, they will immediately begin working on the opener. The opener is a mixture of previously learned questions, and students should work individually, and then as table groups to discuss the methods for solving the questions. After approximately 5 minutes, I will call on students to go to the board and solve the opener questions. As with all openers, I will take volunteers to go to the board – the volunteer is expected to explain their reasoning, and other students are expected to follow along with the work and ask questions/make suggestions as necessary. By having a student explain their reasoning while others listen and provide feedback, **mathematical practice 3** – construct viable arguments and critique the reasoning of others – becomes a natural part of class.

**Learning Target: **After completion of the opener, I will address the day’s learning targets to the students. In today’s lesson, the intended target is, “I can make a conclusion based on a simulation of random sampling.” Students will jot the learning targets down in their agendas (our version of a student planner, there is a place to write the learning target for every day).

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#### Explore

*40 min*

Random Sampling Inquiry and Notes: In this lesson, students will begin to explore the concept of random sampling through inquiry. Using a map of a gardener’s tomato crop (I make a poster out of the Tomato Crop Map), students will drop paperclips onto the map to develop a random sample. Students will then calculate the average of the tomatoes on the ten plants that they chose. Next, students will use an alternate method of sampling, which is to just choose the first ten plants on the map – and the students are asked to calculate the mean of the tomatoes on those plants. Then, they compare the two means. After finding the means of the two different samples, students are asked to calculate the mean of the entire crop – there are 100 numbers, so I ask that each person at the table calculates the mean because it would be easy to make a mistake, perhaps they can sum each row, then find the sum of all rows, then find the mean. After finding the mean of the entire population, students are asked to make comparisons from the means of their samples to the mean of the actual population. Finally, students are asked to discuss why they think the mean of their first sample was closer to the actual mean than the second sample. Points to discuss are that the first sample was truly random, but the second sample only looked at the first row – what if that row got more sun, more rain, was attacked by an animal, etc.

By conducting an actual sampling experiment that could be used to solve a real world problem, students are truly modeling the mathematics, and then abstracting information from their model to draw conclusions and make predictions, **mathematical practices 2 and 4.** Given that it would not be feasible to use an actual 10 by 10 crop of tomato plants, the students use the tools that they do have, map of crop, paperclips, calculator strategically in an effort to model a real crop - **mathematical practice 5.**

We will discuss the questions as a class, and then move onto to notes – introducing the idea of biased and unbiased samples. This is the topic of tomorrow’s class, so today will just be a brief intro to the idea.

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#### Summarize

*10 min*

To summarize this lesson, after we discuss the concept and relate it to the experiment, students will be given three scenarios and asked as a table to determine which of the three would be considered a true random (unbiased) sample. I will have students stand for 1, 2, or 3 depending on which scenario they believe is truly random. This activity will help me to gauge their understanding of the day’s lesson.

#### Resources

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Hi Heather,

I'm Looking forward to using this lesson next week after days of standardized testing. Thank you.

| 11 months ago | Reply

Hi Heather,

I have used several of your lessons this year. I Love all of them!!! Thank You.

Mary

| 11 months ago | Reply

Lynne - This is my favorite lesson of the entire year :) The kids really get into it!

| one year ago | Reply

Tomato plot calculations looks like a great hands on teaching tool. THANK YOU@

| one year ago | Reply

After this lesson my students told me that math is their favorite class. Thanks!

| 2 years ago | Reply

Traci -

I think once your students get used to the constant spiral review, the opener time will be shorter and shorter :)

| 2 years ago | Reply*Responding to Traci Gornick*

Lesson went well. I started doing your openers, and my students are taking a long time with them. While I'm glad they are talking and perservering with these, I have a whole lesson to get through. I am hoping that since I just switched my routine, they will get quicker. I love their presentations though.

| 3 years ago | Reply

Hi Heather,

I agree with your philosophy on homework. I use it for basic facts and further thought, and they usually finish in class. I allow my students to correct EVERYTHING the next day on any homework I give before I collect it. I tell them I don't care if you learn it the day I teach it, at home, or the next day when I correct it, as long as you learn it. They have to explain their mistakes, which is often even more beneficial to them.

I'm trying the tomato crop lesson tomorrow, we'll see how it goes!

| 3 years ago | Reply*expand comments*

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- UNIT 1: Introduction to Mathematical Practices
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- LESSON 1: Interpreting Measures of Center - What does the mean, mean?
- LESSON 2: Mean Absolute Deviation - Why be MAD?
- LESSON 3: Comparing Populations - What are center, shape and spread?
- LESSON 4: Measures of Center and Variability Fluency Practice
- LESSON 5: Measures of Center and Variability Test
- LESSON 6: Random Sampling - How do you make sure your sample is random?
- LESSON 7: Biased versus Unbiased Samples - What does your sample represent?
- LESSON 8: Making Predictions - What do you do with the data from a random sampling activity?
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