Mathematics
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 Elementary Mathematics Curriculum 20172018 SY
 Elementary Mathematics Curriculum 2015  2016 SY
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 Erie's Public Schools
 Middle School Mathematics Curriculum
 Grade 7
 Samples and Populations

Middle School Mathematics Grade 7
Subject: MathematicsGrade: 7Timeline: 6 daysUnit Title: Samples and PopulationsUnit Overview:Statistics is a tool for representing and analyzing data that may then be used to describe a population. Probability is a tool for understanding sampling issues in statistics. The problems in Samples and Populations Investigation 2 help students make connections between probability and statistics. Students explore what samples are, how they are related to populations, and ways to select samples, including random samples. In this investigation, data is provided. It is assumed that students have had prior experience collecting data as part of statistical investigations. If they have not, it is recommended to have the students collect their own data as time and situations permit. The problems can be explored using either the data provided or data collected by students (Samples and Populations, pg. 3).Unit Objectives:At the end of this unit, all students must: Use the process of statistical investigation to explore problems
 Use information from samples to draw conclusions about populations
 Explore the influence of sample size on the variability of the distribution of sample means or medians
 Evaluate sampling plans
 Use probability to select random samples from populations
 Compare sample distributions using measures of center (mean and median), measures of variability (range, minimum, and maximum data values, percentiles) and data displays that group data (line plots and boxandwhisker plots)
Focus Standards:PA.CCSS.Math Content.CC.2.4.7.B.1 Draw inferences about populations based on random sampling concepts. (7.SP.1, 7.SP.2)PA.CCSS.Math Content.CC.2.4.7.B.2 Draw informal comparative inferences about two populations. (7.SP.3, 7.SP.4)Mathematical Practice Standards:#1 Make sense of problems and persevere in solving them.Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends.#3 Construct viable arguments and critique the reasoning of others.Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.#5 Use appropriate tools strategically.Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, or a calculator. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts.#7 Look for and make use of structure.Mathematically proficient students look closely to discern a pattern or structure. Midlevel students will see 7 × 8 equals the wellremembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. Structure can be found in tables, lists, area models and other diagrams.Concepts  Students will know: The difference between a sample and a population
 How to use samples to make predictions about a population
 The various ways to develop a sampling plan
 How to select a random sample from a population
 How to use sampling distributions, measures of center, and measures of variability to describe and compare samples
 How to apply elementary probability with spinners or calculators to choose from random samples
 How to use data from a sample to estimate a characteristic of a population
Competencies Students will be able to: Identify populations, samples and method of sample collection from a given survey
 Calculate percent
 Estimate populations by scaling up results of a survey
 List reasons why certain data collection is inaccurate
 List the advantages and disadvantages of four common types of sampling methods
 Collect random samples from students using spinners or graphing calculators
 Make line plots
 Describe and compare variability
 Make and compare box plots
 Calculate mean and find median
 Compare distributions of line plots
 Discuss how well samples of different sizes predict the mean and median for the entire population
Assessments:Formative Assessments: Informal assessments on learning targets
 Partner Quiz
Summative Assessment: Common Core Unit Assessment Samples and Populations
Elements of Instruction:In Grade 6, instructional time focused on four critical areas: (1) connecting ratio and rate to whole number multiplication and division and using concepts of ratio and rate to solve problems; (2) completing understanding of division of fractions and extending the notion of number to the system of rational numbers, which includes negative numbers; (3) writing, interpreting, and using expressions and equations; and (4) developing understanding of statistical thinking.Samples and Populations builds on collecting and organizing data into different contexts. This began during two previous books, How Likely Is It? and What Do You Expect?, which apply the process of statistical investigation to pose questions, identify ways data is collected, determine strategies for analyzing data, and interpret the analysis in order to answer the questions posed in the lessons. This previous work ties together work with statistics and probability. In this unit, students explore ways to select samples, including the use of random sampling techniques.Also, in the Grade 6 book, Data About Us, students find and use range and the shape and distribution of graphs to make inferences and predictions about a data set. These skills are extended in the book Samples and Populations to explain variability in both categorical and numerical data. Finding measures of center in Data About Us is deepened be deciding when to use the mean and median to describe a distribution.Finally, finding percents in the Grade 6 books, Bits and Pieces I, Bits and Pieces III, and Comparing and Scaling, grows during this unit to use counts or percents to report frequencies of occurrence data.Students consider samples and populations, and also use results of analyses of data from samples, to make estimated about population characteristics or behaviors. First, students consider a survey that raises issues about projecting the analysis results of its sample to the entire population. Next, students consider the difference among convenience samples, voluntaryresponse samples, and random samples. They explore techniques for randomly choosing samples from a population such as using spinners, number cubes and randomnumber generations on graphing calculators and think about why random samples are often preferable. Students then investigate the idea that sample size affects the accuracy of population estimates. Through sampling and determining mean and median statistics for each sample, students learn that the statistics of larger samples are more reliably predictive of the population than statistics from smaller samples (Samples and Populations, pg. 3).Major misconceptions by and struggles for students in this unit include: Confusing the definition of “sample” with “population”
 Estimating larger population results using proportions and scaling up from sample results
 Confusing random sampling techniques with other common sampling methods
 Synthesizing conclusions about and describing variability of samples
 Describing the parts and usage of box plots
 Confusing the definitions of “mean” and “median”
Differentiation:Each lesson has differentiation options for each portion of the lesson. Additional differentiation options are listed with directions and student masters in the Teacher’s Guide. Special Needs Handbook
 Unit Projects
 Spanish Additional Practice and Skills guide
 Strategies for English Language Learners Guide
 “Extension” homework questions
 Districtcreated notebooks
Interdisciplinary Connections: Mathematical Reflections
 “Did You Know?” sections
 phschool.com and web codes
 “Connections” homework questions
 The realworld context embedded in lesson problems
Additional Resources / Games:CMP2 and/or the Erie School District provide the following additional resources to aid students in achieving mathematical success. Additional Practice worksheets per investigation
 Skills Review worksheets to target key components of each investigation
 Parent letter to be sent home prior to beginning the unit to share with parents the skills, goals, and expectations of the coming unit.
 Assessment Resources workbook with extra test items (multiple choice, essay, open ended, question bank, etc)
 Investigation specific pregenerated notebooks that include tables, graphs, problem numbers, and all other items students may need to complete the investigation and all its parts. Students are provided with one per unit.
 Reflection questions at the end of each investigation to assess students’ comprehension of key concepts.
 phschool.com and web codes
 Transparencies of models, graphs, etc used within lesson(s)