Benchmark Instructional Guide
Connecting Benchmarks/Horizontal Alignment
Terms from the K-12 Glossary
- Random Sampling
Purpose and Instructional Strategies
In grade 7, students solved real-world problems involving percentages and they calculated means of numerical data sets. In grades 7 and 8, students explored the relationship between theoretical probabilities and experimental probabilities. In Algebra I, students use means and percentages from data obtained from statistical experiments to make predictions about actual means and percentages in populations and they relate the experimental data to actual values through margins of error. In later courses, students will work more formally with margins of error and use the normal distribution to estimate population percentages.
- In Algebra I, students are not expected to master the skill of estimating a margin of error using simulation. But instruction may include such an activity, to allow students to experience the need for a margin of error whenever a mean or population percentage is estimated using data.
- Instruction includes introducing examples from the media of reports of population means and percentages that include margins of error.
- Instruction includes the understanding that an actual population mean or percentage is not necessarily within the margin of error of the estimated mean or percentage. Even if the data has been carefully collected, these estimated quantities are only within the margin of error with a “high degree of confidence.” If the data has not been carefully collected, or if the situation has changed significantly since the data were collected (as is often the case with election polls), the margin of error may not be very meaningful.
Common Misconceptions or Errors
- When asked for population totals, students may forget to complete the final calculation with the margin of error and only report the mean or percentage as their final answer.
- Students may confuse three percentages: the estimated population percentage, the margin of error expressed as a percentage and the actual population percentage. Students can use a number line to visualize how the first two quantities determine an interval that is likely to contain the third quantity.
Strategies to Support Tiered Instruction
- Teacher provides a list of definitions to students to eliminate misunderstandings that may be caused by the key terms. Because it is important that students understand the meanings of the terms when interpreting sample surveys, this should be an entry in a math journal.
- Instruction includes providing multiple scenarios and asking for identification of the key terms associated with the percentages given in the context.
- Teacher models the use of a number line to visualize how the estimated population percentage and the margin of error determine an interval that is likely to contain the actual population percentage.
Instructional Task 1 (MTR.7.1)
- A packaging company prints 100,000 boxes per day. They determine that their printing machines are making a mistake on an average of 0.11% of boxes per day with a margin of error of ±0.01%. How many boxes will need to be recycled due to a printing error in one week?
Instructional Item 1
- Based on a survey of 150 students at Long Lake High School, the average number of hours spent on social media per week is 30.5 with a margin of error of 3.25.
- Part A. Give a range of values, based on this data, for the actual mean numbers of hours spent on social media.
- Part B. If there are a total of 723 students at the high school, give a range of values for the total number of weekly hours spent by all students.
*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.