﻿ Gr. HS Inferences and Conclusions from Data ~ Math Units of Study ~ Instruction ~ School Improvement in Maryland

# Gr. HS Unit: Inferences and Conclusions from Data

##### Unit Overview

In this unit, students see how the visual displays and summary statistics learned in earlier grades relate to different types of data and to probability distributions. Students identify different ways of collecting data—including sample surveys, experiments, and simulations—and the role that randomness and careful design play in the conclusions that can be drawn. Students will be introduced to standard deviation as a measure of variability and use the mean and standard deviation of a normal distribution to estimate population percentages.

Essential Questions:

• Mathematics can be used to solve real world problems and can be used to communicate solutions to stakeholders.
• It is important to be well-informed on the correct ways to gather data, interpret data, and make sound decisions.
• Use data analysis tools to compare two independent groups.
• Relationships between quantities can be represented symbolically, numerically, graphically, and verbally in the exploration of real world situations
• The context of a question will provide insight on the best method for collecting and analyzing the data.
• Recognize when to apply simulations to model real world situations.
• Conduct simulations to represent a variety of real world situations.
• The results of statistical analysis must be interpreted and analyzed to determine if there is a significant evidence to justify conclusions about real world situations.
• Statistics need to be applied to make inferences and justify conclusions
• Recognize possible sources and types of error in context of the real world.

A question is essential when it stimulates multi-layered inquiry, provokes deep thought and lively discussion, requires students to consider alternatives and justify their reasoning, encourges re-thinking of big ideas, makes meaningful connections with prior learning, and provides students with opportunities to apply problem-solving skills to authentic situations.

##### Unit Lesson

Additional information such as Teachers Notes, Enduring Understandings,Content Emphasis by Cluster, Focus Standards, Possible Student Outcomes, Essential Skills and Knowledge Statements and Clarifications, and Interdisciplinary Connections can be found in this Lesson Unit.

##### Available Model Lesson Plans

The lesson plan(s) have been written with specific standards in mind. Each model lesson plan is only a MODEL - one way the lesson could be developed. We have NOT included any references to the timing associated with delivering this model. Each teacher will need to make decisions related ot the timing of the lesson plan based on the learning needs of students in the class. The model lesson plans are designed to generate evidence of student understanding.

This chart indicates one or more lesson plans which have been developed for this unit. Lesson plans are being written and posted on the Curriculum Management System as they are completed. Please check back periodically for additional postings.

CCSC Alignment: S.ID.4

The student will find the mean and standard deviation of a data set; find and interpret the standardized score for an observation in a data set; determine if a data set fits an approximately Normal distribution; estimate population percentages using the mean and standard deviation of a Normal distribution and estimate the areas under a Normal curve.

##### Available Model Lesson Seeds

The lesson seed(s) have been written with specific standards in mind. These suggested activity/activities are not intended to be prescriptive, exhaustive, or sequential; they simply demonstrate how specific content can be used to help students learn the skills described in the standards. Seeds are designed to give teachers ideas for developing their own activities in order to generate evidence of student understanding.

This chart indicates one or more lesson seeds which have been developed for this unit. Lesson seeds are being written and posted on the Curriculum Management System as they are completed. Please check back periodically for additional postings.

CCSC Alignnment: S-ID-4

Reinforcement: The activity in this lesson seed could be used as a follow up to a lesson on the Empirical Rule. Students will demonstrate their understanding of the Empirical Rule as it relates to a normal curve.

CCSC Alignnment: S-ID-4

Reinforcement: The activity in this lesson seed could be used in lesson normality

CCSC Alignnment: S-ID-4

Developmental: This lesson seed describe a data generating process that will engage students. By being part of the data generating process students should be more engaged in the development of the concepts.

CCSC Alignnment: S-ID-4

Developmental: The intent of the activity in this lesson seed is to have students calculate the standard deviation of a set of data by hand. The thought is that seeing where the statistic comes from will increase understanding of what the standard deviation reveals about the data.

CCSC Alignnment: S-ID-4

Reinforcement: To complete the activity in this lesson seed students must first understand how to compute and analyze z-scores. This activity is intended to help students strengthen their understanding of how to compute and interpret z-scores.

CCSC Alignnment: S.IC.3

Application: Students will work with partners to develop a research question that could be answered using a sample survey, experiment or observational study. Students will justify and defend their data collection method as the most appropriate. Students will create a step-by-step procedure for their data collection method.

CCSC Alignnment: S.IC.3, S.IC.5

Developmental: Students will generate data using random assignment in order to describe the difference between two treatments. Students will help design the randomization procedure for an experiment. Students will participate in a randomized experiment. Students will calculate and compare means from the two treatments. Students will discuss the concept of significance and Law of Large Numbers.

CCSC Alignnment: S.IC.5

Developmental: Students will conduct a simulation that allows them to generate data and then make inferences about the generated data.