Elementary Pull-Out: Statistics: Sampling

The Elementary Mathematician, COMAP's award-winning K-6 newsletter is available for the first time in electronic format. Each issue contains a collection of K-6 mathematic lessons that are fun to teach and exciting to learn.

Each issue of The Elementary Mathematician contains a Pull-Out section which includes thematic lessons based on the national census, wildlife, other cultures, technology, and provides a practical way to bring the concepts and pedagogy of the NCTM Standards into your classroom. 

Note: The information below was created with the assistance of AI.

Level of Mathematics
This lesson is designed for upper elementary or early middle school students, generally Grades 5–7.

Mathematical Complexity: Moderate to High for this level
It introduces core statistical reasoning skills, including sampling, data analysis, proportional reasoning, and inference-making—key components of inferential statistics.

Prerequisite Skills
Students should have prior experience with:

Basic arithmetic operations (addition, multiplication, division)

Understanding of fractions and percentages

Graphing skills (bar graphs, circle graphs)

Using calculators and optionally computer graphing software

Constructing and interpreting data tables

Application Areas

1. Statistics and Data Science
Core focus is on sampling techniques and inferential statistics: drawing conclusions about an unknown population based on data from a sample.

Students calculate proportions, fractions, and percentages to make generalizations about the full population.

2. Consumer Science and Manufacturing
Explores real-world context (M&M color distributions) to discuss quality control and production standards (i.e., how Mars, Inc. might intentionally distribute colors).

3. Probability and Predictive Reasoning
Builds foundational skills for making predictions from data, interpreting distributions, and assessing variation across samples.

4. Technology Integration
Encourages the use of calculators and optionally graphing software, emphasizing how technology supports data analysis.

Subject Matter Overview
Key Mathematical Concepts:

Sampling and Population: Understanding the role of a sample as a representation of a larger group.

Descriptive statistics: Mode, median, frequency.

Proportions and Percentages: Used to compare sample values with population expectations.

Graphical Representations:

Bar graphs (frequency by color)

Circle graphs (percent composition)

Stem-and-leaf plots and number lines (to represent total counts)

Predictive Modeling: Using data from one sample to estimate results for a second bag or full population.

Activities:

Counting and sorting M&M colors in sample bags.

Graphing individual and class data.

Discussing sampling variability and expected outcomes.

Making and testing predictions across multiple sample trials.

Comparing class-wide data to manufacturer expectations.

Correlation to Mathematics Standards
Common Core State Standards (CCSS):

CCSS.MATH.CONTENT.5.MD.B.2: Make a line plot to display a data set and use operations to solve problems involving fractions.

CCSS.MATH.CONTENT.6.SP.A.1: Recognize a statistical question and understand data distributions.

CCSS.MATH.CONTENT.6.SP.B.4: Display numerical data in plots, including dot plots, histograms, and box plots.

CCSS.MATH.CONTENT.6.RP.A.3: Use ratio and rate reasoning to solve real-world problems, including percent and fractional reasoning.

CCSS.MATH.PRACTICE.MP2: Reason abstractly and quantitatively.

CCSS.MATH.PRACTICE.MP4: Model with mathematics.

CCSS.MATH.PRACTICE.MP5: Use appropriate tools strategically (calculators and graphing tools).

NCTM Process and Content Standards:

Data Analysis and Probability: Pose questions and collect, organize, and display data to answer them.

Number and Operations: Work flexibly with fractions and percents.

Communication: Use mathematical language to explain and defend predictions and conclusions.

Reasoning and Proof: Analyze mathematical situations and construct logical arguments.

Connections: Connect mathematics to real-world issues such as product packaging and market trends.