Major Content Supporting Content Additional Content

Curriculum and Instruction – MathematicsQuarter 3 Grade 7

Introduction

In 2014, the Shelby County Schools Board of Education adopted a set of ambitious, yet attainable goals for school and student performance. The District is committed to these goals, as further described in our strategic plan, Destination 2025. By 2025,

80% of our students will graduate from high school college or career ready 90% of students will graduate on time 100% of our students who graduate college or career ready will enroll in a post-secondary opportunity

In order to achieve these ambitious goals, we must collectively work to provide our students with high quality, college and career ready aligned instruction. The Tennessee State Standards provide a common set of expectations for what students will know and be able to do at the end of a grade. College and career readiness is rooted in the knowledge and skills students need to succeed in post-secondary study or careers. The TN State Standards represent three fundamental shifts in mathematics instruction: focus, coherence and rigor.

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Focus

The Standards call for a greater focus in mathematics. Rather than racing to cover topics in a mile-wide, inch-deep curriculum, the Standards require us to significantly narrow and deepen the way time and energy is spent in the math classroom. We focus deeply on the major work of each grade so that students can gain strong foundations: solid conceptual understanding, a high degree of procedural skill and fluency, and the ability to apply the math they know to solve problems inside and outside the math classroom. For grades K–8, each grade's time spent in instruction must meet or exceed the following percentages for the major work of the grade. 85% or more time spent in instruction in each grade Kindergarten, 1, and 2 align exclusively to the major work of the grade. For grade 7, more than 65% of instructional time is spent on the major focus standards.Supporting Content - informaiont that supports the understanding and implementation of the major work of the grade.Additional Content - content that does not explicitly connect to the major work of the grade yet it is required for proficiency.

Coherence

Thinking across grades:The Standards are designed around coherent progressions from grade to grade. Learning is carefully connected across grades so that students can build new understanding on to foundations built in previous years. Each standard is not a new event, but an extension of previous learning. Linking to major topics:Instead of allowing additional or supporting topics to detract from the focus of the grade, these concepts serve the grade level focus. For example, instead of data displays as an end in themselves, they are an opportunity to do grade-level word problems.

Rigor

Conceptual understanding: The Standards call for conceptual understanding of key concepts, such as place value and ratios. Students must be able to access concepts from a number of perspectives so that they are able to see math as more than a set of mnemonics or discrete procedures. Procedural skill and fluency: The Standards call for speed and accuracy in calculation. Students are given opportunities to practice core functions such as single-digit multiplication so that they have access to more complex concepts and procedures.Application: The Standards call for students to use math flexibly for applications in problem-solving contexts. In content areas outside of math, particularly science, students are given the opportunity to use math to make meaning of and access content.

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Curriculum and Instruction – MathematicsQuarter 3 Grade 7

The Standards for Mathematical Practice describe varieties of expertise, habits of minds and productive dispositions that mathematics educators at all levels should seek to develop in their students. These practices rest on important National Council of Teachers of Mathematics (NCTM) “processes and proficiencies” with longstanding importance in mathematics education. Throughout

the year, students should continue to develop proficiency with the eight Standards for Mathematical Practice.

This curriculum map is designed to help teachers make effective decisions about what mathematical content to teach so that, ultimately our students, can reach Destination 2025. To reach our collective student achievement goals, we know that teachers must change their practice so that it is in alignment with the three mathematics instructional shifts.

Throughout this curriculum map, you will see resources as well as links to tasks that will support you in ensuring that students are able to reach the demands of the standards in your classroom. In addition to the resources embedded in the map, there are some high-leverage resources around the content standards and mathematical practice standards that teachers should consistently access:

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Mathematical Practices(MP)

1. Make sense of problems and persevere in solving them

2. Reason abstractly and quatitatively

3. Construct viable arguments and

crituqe the reasoning of

others

4. Model with mathematics

5. Use appropriate tools strategically

6. Attend to precision

7. Look for and make use of

structure

8. Look for and express regularity

in repeated reasoning

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Curriculum and Instruction – MathematicsQuarter 3 Grade 7

The TN Mathematics StandardsThe Tennessee Mathematics Standards:https://www.tn.gov/education/article/mathematics-standards

Teachers can access the Tennessee State standards, which are featured throughout this curriculum map and represent college and career ready learning at reach respective grade level.

Standards for Mathematical PracticeMathematical Practice Standardshttps://drive.google.com/file/d/0B926oAMrdzI4RUpMd1pGdEJTYkE/view

Teachers can access the Mathematical Practice Standards, which are featured throughout this curriculum map. This link contains more a more detailed explanation of each practice along with implications for instructions.

Purpose of the Mathematics Curriculum Maps

This curriculum framework or map is meant to help teachers and their support providers (e.g., coaches, leaders) on their path to effective, college and career ready (CCR) aligned instruction and our pursuit of Destination 2025. It is a resource for organizing instruction around the TN State Standards, which define what to teach and what students need to learn at each grade level. The framework is designed to reinforce the grade/course-specific standards and content—the major work of the grade (scope)—and provides a suggested sequencing and pacing and time frames, aligned resources—including sample questions, tasks and other planning tools. Our hope is that by curating and organizing a variety of standards-aligned resources, teachers will be able to spend less time wondering what to teach and searching for quality materials (though they may both select from and/or supplement those included here) and have more time to plan, teach, assess, and reflect with colleagues to continuously improve practice and best meet the needs of their students.

The map is meant to support effective planning and instruction to rigorous standards; it is not meant to replace teacher planning or prescribe pacing or instructional practice. In fact, our goal is not to merely “cover the curriculum,” but rather to “uncover” it by developing students’ deep understanding of the content and mastery of the standards. Teachers who are knowledgeable about and intentionally align the learning target (standards and objectives), topic, task, and needs (and assessment) of the learners are best-positioned to make decisions about how to support student learning toward such mastery. Teachers are therefore expected--with the support of their colleagues, coaches, leaders, and other support providers--to exercise their professional judgment aligned to our shared vision of effective instruction, the Teacher Effectiveness Measure (TEM) and related best practices. However, while the framework allows for flexibility and encourages each

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teacher/teacher team to make it their own, our expectations for student learning are non-negotiable. We must ensure all of our children have access to rigor—high-quality teaching and learning to grade-level specific standards, including purposeful support of literacy and language learning across the content areas.

Additional Instructional SupportShelby County Schools adopted our current math textbooks for grades 6-8 in 2010-2011. The textbook adoption process at that time followed the requirements set forth by the Tennessee Department of Education and took into consideration all texts approved by the TDOE as appropriate. We now have new standards; therefore, the textbook(s) have been vetted using the Instructional Materials Evaluation Tool (IMET). This tool was developed in partnership with Achieve, the Council of Chief State Officers (CCSSO) and the Council of Great City Schools. The review revealed some gaps in the content, scope, sequencing, and rigor (including the balance of conceptual knowledge development and application of these concepts), of our current materials. The additional materials purposefully address the identified gaps in alignment to meet the expectations of the CCR standards and related instructional shifts while still incorporating the current materials to which schools have access. Materials selected for inclusion in the Curriculum Maps, both those from the textbooks and external/supplemental resources (e.g., engageNY), have been evaluated by district staff to ensure that they meet the IMET criteria.

How to Use the Mathematics Curriculum Maps

OverviewAn overview is provided for each quarter. The information given is intended to aid teachers, coaches and administrators develop an understanding of the content the students will learn in the quarter, how the content addresses prior knowledge and future learning, and may provide some non-summative assessment items.

Tennessee State StandardsThe TN State Standards are located in the left column. Each content standard is identified as the following: Major Work, Supporting Content or Additional Content.; a key can be found at the bottom of the map. The major work of the grade should comprise 65-85% of your instructional time. Supporting Content are standards that supports student’s learning of the major work. Therefore, you will see supporting and additional standards taught in conjunction with major work. It is the teacher’s responsibility to examine the standards and skills needed in order to ensure student mastery of the indicated standard.

ContentTeachers are expected to carefully craft weekly and daily learning objectives/ based on their knowledge of TEM Teach 1. In addition, teachers should include related best practices based upon the TN State Standards, related shifts, and knowledge of students from a variety of sources (e.g., student work samples, MAP, etc.). Support for the development of these lesson objectives can be found under the column titled ‘Content’. The enduring understandings will help clarify the “big picture” of the standard. The essential questions break that picture down into smaller questions and the objectives provide specific outcomes for that standard(s). Best practices tell us that clearly communicating and making objectives measureable leads to greater student mastery.

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Instructional Support and ResourcesDistrict and web-based resources have been provided in the Instructional Resources column. Throughout the map you will find instructional/performance tasks, i-Ready lessons and additional resources that align with the standards in that module. The additional resources provided are supplementary and should be used as needed for content support and differentiation.

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Topics Addressed in QuarterRandom SamplingComparative Inferences

Probability ModelsScale DrawingsConstructing Triangles

Overview In quarter 3 students begin their study of probability, learning how to interpret probabilities and how to compute probabilities in simple settings. They also learn how to estimate probabilities by conducting experiments and observations (7.SP.C.5, 6), calculate probabilities of compound events using lists, tables, tree diagrams, and simulations (7.SP.C.8) and learn to use probabilities to make decisions and to determine whether or not a given probability model is plausible (7.SP.C.7). Additionally, students build on their knowledge of data distributions that they studied in Grade 6, compare data distributions of two or more populations (7.SP.B.3, 7.SP.B.4), and are introduced to the idea of drawing informal inferences based on data from random samples (7.SP.A.1, 7.SP.A.2). Up to 7th grade, almost all of students’ statistical topics and investigations have dealt with univariate data, e.g., collections of counts or measurements of one characteristic. During eighth grade students will extend their work to bivariate data, applying their experience with the coordinate plane and linear functions in the study of association between two variables related to a question of interest. Near the end of the quarter, students will bring their experience with proportional relationships to the context of scale drawings (7.RP.2b, 7.G.1). Given a scale drawing, students should rely on their background in working with side lengths and areas of polygons (6.G.1, 6.G.3) as they identify the scale factor as the constant of proportionality, calculate the actual lengths and areas of objects in the drawing, and create their own scale drawings of a two-dimensional figure. Students will also construct geometric shapes, mainly triangles provided given conditions, side length and the measurement of the included angle (7.G.A.2) and learn two new concepts about unique triangles. Students develop an intuitive understanding of the structure of a triangle.

Year at a Glance Document Grade Level Standard Type of Rigor Foundational Standards Sample Assessment Items

7.SP.1 Conceptual Understanding 6.SP.1, 6.SP.2 Inside Mathematics Performance Assessment Task 7.SP.1 & 4: Ducklings

7.SP.2 Conceptual Understanding 7.SP.1 Math Shell: Counting Trees7.SP.3 Conceptual Understanding 5.NF.4, 6.NS.1, 6.SP.2 Orglib.com Assessment Items 7.SP.37.SP.4 Conceptual Understanding 7.SP.2, 7.SP.3 Learnzillion: 7.SP.1-47.SP.5 Conceptual Understanding Learnzillion: 7.SP.5-77.SP.6 Conceptual Understanding 7.RP.3, 7.SP.5 Orglib.com Assessment Items 7.SP.57.SP.7 Application 7.RP.3, 7.SP.6 Math Shell: Lottery7.SP.8 Conceptual Understanding,

Procedural Skill & Fluency, Application7.RP.3, 7.SP.7 Inside Mathematics Performance Task: Fair

Game?7.G.1, 7.RP.2b Procedural Skill & Fluency 6.G.1, 7.RP.2 Inside Mathematics Performance Task: Which is

Bigger?7.G.2 Conceptual Understanding Inside Mathematics Performance Assessment

Task 7.G.2 & 7.G.6 Parallelogram

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Fluency NCTM Position

Procedural fluency is a critical component of mathematical proficiency. Procedural fluency is the ability to apply procedures accurately, efficiently, and flexibly; to transfer procedures to different problems and contexts; to build or modify procedures from other procedures; and to recognize when one strategy or procedure is more appropriate to apply than another. To develop procedural fluency, students need experience in integrating concepts and procedures and building on familiar procedures as they create their own informal strategies and procedures. Students need opportunities to justify both informal strategies and commonly used procedures mathematically, to support and justify their choices of appropriate procedures, and to strengthen their understanding and skill through distributed practice.

The fluency standards for 7th grade listed below should be incorporated throughout your instruction over the course of the school year. Click engage ny Fluency Support to access exercises that can be used as a supplement in conjunction with building conceptual understanding.

7.NS.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers. 7.NS.2 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. 7.EE.3 Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form. 7.EE.4 Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by

reasoning about the quantities.

References: https://www.engageny.org/ http://www.corestandards.org/ http://www.nctm.org/ http://achievethecore.org/

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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESStatistics

(Allow approximately 3.5 weeks for instruction, review and assessment)Domain: Statistics and ProbabilityCluster(s): Use random sampling to draw inferences about a population. Draw informal comparative inferences about two populations.

7. SP.A.1 Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population.

7. SP.A.2Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions.

7.SP.B.3 Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability.

7.SP.B.4 Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations.

Enduring Understandings: The rules of probability can lead to more

valid and reliable predictions about the likelihood of an event occurring.

Essential Questions: How is probability used to make informed

decisions about uncertain events?

Objectives: Students will predict actions of a larger

group by using a sample. Students will analyze the variation in multiple

samples of data. Students will calculate measures of center. Students will determine and describe how

changes in data values impact measures of central tendency.

Additional Information: (7.SP.1-2) Students will recognize that it is difficult to

gather statistics on an entire population. Instead a random sample can be representative of the total population and will generate valid predictions.

Students collect and use multiple samples of data to make generalizations about a population.

Example(s): The school food service wants to increase

the number of students who eat hot lunch in the cafeteria. The student council has been asked to conduct a survey of the student body to determine the students’ preferences for hot lunch. They have determined two ways to do the survey. The two methods are listed below. Identify the type of sampling

Focus on the Real-World Examples, Problem Solving and H.O.T. exercises from

the following book lessons.

Glencoe8-3E Use Data to Predict (pp. 468-471)9-1B Measures of Central Tendency (pp.491-496)9-2A Measures of Variation (pp. 498-503)9-2B Box-and-Whisker Plots (pp. 504-509)9-3E Stem-and-Leaf Plots (pp. 526-531)Additional Lesson 14 Multiple Samples of Data p. 807Additional Lesson 15 Visual Overlap of Data Distribution p. 809Additional Lesson 16 Compare Populations 9. 811

Holt7-2 Mean, Median, Mode & Range (pp. 385-389)7-5 Box-and-Whisker Plots (pp.398-401)7-8 Populations and Samples (pp.418-421)

Building Conceptual Understanding:engage ny : Random Sampling/Estimating Population Characteristics (Lessons 13-20)Math Shell Lesson: Comparing Data using Statistical Measures

Choose from the following resources and use them to deepen students' conceptual understanding of mathematical content and develop their ability to apply that knowledge to non-routine problems.

Suggested Additional Lessons:engage ny : Comparing Populations Lessons 21-

Vocabulary: Survey, variability, biased/unbiased sample, sample population, random sampling, mean absolute deviationinferences

Writing in Math:Students will explain the possible ways to use statistics to gain information about a sample set of a population.

Students will explain their knowledge of measures of center.

Graphic Organizer: Students can create Frayer Model for the following terms using a variety of resources available in your classroom (textbook, newspapers, internet resources, prior knowledge, information printed by teacher in advance): Measures of Center Measures of Variation Measures of Spread (note to teacher –

students should discover that measures of spread are the same as measures of variation)

Outliers Mean absolute deviation

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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESused in each survey option. Which survey option should the student council use and why?

1. Write all of the students’ names on cards and pull them out in a draw to determine who will complete the survey.2. Survey the first 20 students that enter the lunch room.3. Survey every 3rd student who gets off a bus.

Below is the data collected from two random samples of 100 students regarding students’ school lunch preferences. Make at least two inferences based on the results.

Solution:Most students prefer pizzaMore people prefer pizza than hamburgers and tacos combined.

Additional Information: (7.SP.3-4) This is the students’ first experience with

comparing two data sets. Students build on their understanding of graphs, mean, median, Mean Absolute Deviation (MAD) and inter-quartile range from 6th grade. Students understand that:

1. a full understanding of the data requires consideration of the measures of variability as well as mean or median,2. variability is responsible for the overlap of two data sets and that an increase in variability can increase the overlap, and3. The median is paired with the inter-quartile

23Better Lesson: 7.SP.3 & 4Math Shell Concept Development Lesson: Comparing Data Using Statistical Measures

Suggested Tasks:Illustrative Math: Mr. Briggs's Class Likes 7.SP.1Illustrative Math Task: Valentine Marbles 7.SP.2Illustrative Math Task: College Athletes 7.SP.3-4Illustrative Math Task: Offensive Lineman 7.SP.3-4Math Shell Task: Temperatures 7.SP.A.2 Math Shell Task: Candy Bars 7.SP.A.2

Suggested Additional Resources:Khan Academy: Mean Absolute Deviation

Correlated iReady Lesson(s): The iReady program includes a variety of resources that can be used to support teacher-led instruction in Tier 1 and guided small-group Tier 1, 2 or 3 instruction.

Random Samples Making Statistical Inferences Using Mean and Mean Absolute

Deviation to Compare Data (Related lesson)

Using Measures of Center to Compare Data (Related lesson)

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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESrange and mean is paired with the mean absolute deviation. Mean Deviation

Measures of center include mean, median, and mode. The measures of variability include range, mean absolute deviation, and inter-quartile range.

Example(s): The two data sets below depict random

samples of the management salaries in two companies. Based on the salaries below which measure of center will provide the most accurate estimation of the salaries for each company?

Company A {1.2 million, 242000, 265500, 140000, 281000, 265000, 211000}

Company B {5million, 154000, 250000, 250000, 200000, 160000, 190000}

Solution:The median would be the most accurate measure since both companies have one value in the million that is far from the other values and would affect the mean.

Probability(Allow approximately 3.5 weeks for instruction, review and assessment)

Domain: Statistics and ProbabilityCluster: Investigate chance processes and develop, use and evaluate probability models.

7.SP.C.5 Understand that the probability of a chance event is a number between 0 and

Enduring Understanding(s): The rules of probability can lead to more

valid and reliable predictions about the likelihood of an event occurring.

Essential Question(s):

Focus on Real-World Examples, Problem Solving and H.O.T. Exercises from the

following book lessons.

Glencoe8-2A Independent and Dependent Events

Vocabulary: Probability, event outcome, theoretical probability, experimental probability, relative frequency, simple event, compound event, tree diagram

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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES1 that expresses the likelihood of the event occurring.

7.SP.C.6 Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability.

7.SP.C.7 Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.

7.SP.C.7a Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events.

7.SP.C.7b Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example: find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies?

7.RP.A.3 Use proportional relationships to solve multistep ratio and percent problems. (This standard was covered in Q1 but it is repeated here because of the strong application of percent in probability.)

How is probability used to make informed decisions about uncertain events?

Objective(s): Students will compute or estimate

probabilities using a variety of methods, including collecting data, using tree diagrams, and using simulations.

Students will find and compare theoretical and experimental probabilities.

Students will predict actions of a larger group by using a sample.

Additional Information: 7.SP.5Students need multiple opportunities to perform probability experiments and compare these results to theoretical probabilities.

Example:The container below contains 2 gray, 1 white, and 4 black marbles. Without looking, if you choose a marble from the container, will the probability be closer to 0 or to 1 that you will select a white marble? A gray marble? A black marble? Justify each of your predictions.

Solution:White marble: Closer to 0Gray marble: Closer to 0Black marble: Closer to 1

Students can use simulations such as Marble Mania on AAAS or the Random Drawing Tool on NCTM’s Illuminations to generate data and examine patterns.Marble Mania

(pp.450-455)8-3A Theoretical & Experimental Probability (pg.458-462)8-3B Extend Simulations (pg. 463)8-3C Problem Solving (pg.466-467)8-3E Use Data to Predict (pp. 468-471)IMPACT Math Unit G, Inv. 2, pp. 108-111

Holt11-1 Probability (pp. 640-643)11-2 Experimental Probability (pp. 644-647)11-4 Theoretical Probability (pp. 652-655)11-5 Making Predictions (pp. 658-661)Experimental and Theoretical Probability Lab (pp. 662-663)11-6 Probability of Independent and Dependent Events (pp. 666-669)

Building Conceptual Understanding:Math Shell Lesson: Analyzing Games of Chance 7.SP.C.6-7engage ny : Module 5 Topic A Lessons for 7.SP.C.5engage ny : Module 5 Topic B Lessons 8-10 for 7.SP.C.6-8

Choose from the following resources and use them to deepen students' conceptual understanding of mathematical content and develop their ability to apply that knowledge to non-routine problems.

Suggested Additional Lessons:engage ny : Module 5 Topic B Lessons 11-12 for 7.SP.C.8Better Lesson: Simple EventsBetter Lesson: Experimental vs Theoretical ProbabilityBetter Lesson: Probability Lab

Writing in Math:Compare and contrast experimental probability and theoretical probability.Have students explain the difference between independent events and dependent events.

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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES7.SP.C.8 Find probabilities of compound

events using organized lists, tables, tree diagrams, and simulation.

7.SP.C.8a Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs

7.SP.C.8b Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., “rolling double sixes”), identify the outcomes in the sample space which compose the event.

7.SP.C.8c Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood.

Random Drawing Tool

Additional Information: 7.SP.6Students can collect data using physical objects or graphing calculator or web-based simulations. Students can perform experiments multiple times, pool data with other groups, or increase the number of trials in a simulation to look at the long-run relative frequencies.

Example:Each group receives a bag that contains 4 green marbles, 6 red marbles, and 10 blue marbles. Each group performs 50 pulls, recording the color of marble drawn and replacing the marble into the bag before the next draw. Students compile their data as a group and then as a class. They summarize their data as experimental probabilities and make conjectures about theoretical probabilities (How many green draws would are expected if 1000 pulls are conducted?10,000 pulls?).

Additional Information: 7.SP.7Students need multiple opportunities to perform probability experiments and compare these results to theoretical probabilities. Critical components of the experiment process are making predictions about the outcomes by applying the principles of theoretical probability, comparing the predictions to the outcomes of the experiments, and replicating the experiment to compare results.

Example:Devise an experiment using a coin to determine whether a baby is a boy or a girl. Conduct the experiment ten times to determine

Suggested Tasks:Math Shell Assessment Task: Spinner Bingo7.SP.C.6-7Math Shell Task: Analyzing Games of Chance 7.SP.C.6Math Shell Task: Charity Fair 7.SP.C.6-7Illustrative Math Task: Red, Blue or Green? 7.SP.C.8Illustrative Math Task: Rolling Twice 7.SP.8.CIllustrative Math Task: Waiting Times 7.SP.8.CIllustrative Math Task: Sitting across from Each Other 7.SP.C.8.a & bIllustrative Math Task: Tetrahedral Dice 7.SP.C.8.a & bShmoop: Simulation of Compound Event 7.SP.C.8.c

Suggested Additional Resources:Learnzillion: Making predictions using proportional reasoning- Probability fair prizesLearnzillion: Analyze independent and dependent events

Correlated iReady Lesson: The iReady program includes a variety of resources that can be used to support teacher-led instruction in Tier 1 and guided small-group Tier 1, 2 or 3 instruction.

Probability Concepts Experimental Probability Probability of Compound Events Simulations of Compound Events

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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESthe gender of ten births. How could a number cube be used to simulate whether a baby is a girl or a boy or girl?

Example:Conduct an experiment using a Styrofoam cup by tossing the cup and recording how it lands.• How many trials were conducted?• How many times did it land right side up?• How many times did it land upside down/• How many times did it land on its side?• Determine the probability for each of the above results.

Additional Information: 7.SP.8Students can use tree diagrams, frequency tables, and organized lists, and simulations to determine the probability of compound events.

Example:How many ways could the 3 students, Amy, Brenda, and Carla, come in 1st, 2nd and 3rd place?Solution:Making an organized list will identify that there are 6 ways for the students to win a raceA, B, CA, C, BB, C, AB, A, CC, A, BC, B, A

Example: Students conduct a bag pull experiment. A bag contains 5 marbles. There is one red marble, two blue marbles and two purple marbles. Students will draw one marble without replacement and then draw another. What is the sample space for this situation? Explain how the sample space was

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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESdetermined and how it is used to find the probability of drawing one blue marble followed by another blue marble.

Example: A fair coin will be tossed three times. What is the probability that two heads and one tail in any order will results?Solution:HHT, HTH and THH so the probability would be 3/8.

Geometry: Draw, Construct & Describe Geometric Figures( Allow approximately 2 weeks for instruction, review and assessment)

Domain: GeometryCluster: Draw, construct and describe geometrical figures and describe the relationships between them.

7.G.A.1 Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

7.RP.2.b Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. (This standard supports proportional reasoning needed to calculate scale factors.)

7.G.A.2 Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

Enduring Understanding(s): Geometric properties can be used to

construct geometric figures. Everyday objects have a variety of

attributes which can be measured in many ways.

Scale factor is the constant ratio of each actual length to its corresponding length in a drawing.

Essential Question(s): What is a scale factor? What is a scale drawing? How can measurements and information

about similar figures be used to solve problems?

Objective(s): Students will solve problems involving

scale drawings. Students will find the relationship between

perimeters and areas of similar figures. Students will determine how changes in

dimensions affect area. Students will use a compass, protractor,

and ruler to draw geometric shapes based on given conditions.

Students will determine whether a set of

The following lessons only provide practice to enhance procedural skill for solving

problems involving scale factor.

Glencoe5-2B Scale Drawings (pgs. 284-290)5-2C Extend Scale Drawings (pg. 291)IMPACT Math Unit D, Inv. 4 Map Scales, pp. 62-64; Inv. 5 Similarity pp. 65-665-3A Similar Figures (pgs.293-298) This lesson focuses on how scale factor can be used to determine if triangles are similar. Remember the focus of 7.G.1 is not on similar triangles.5-3B Perimeter & Area of Similar Figures (pgs.299-302)Additional Lesson 23 Exploring Similarity using Geometer’s Sketchpad pp. 832-8335-3C Extend The Golden Rectangle (pgs. 303)11-2A Make a Model (p. 651 # 3, 4, 6, 8 & 10)11-2B Changes in Scale (p.652 Activity 1, # 1-2)12-1B Explore Triangles12-1CTriangles

Holt4-8 Similar Figures (pp. 248-251) This

Vocabulary: dimensions, scale, scale factor, scale drawings, scale models, triangle, congruent segments, acute triangle, right triangle, obtuse triangle, scalene triangle, isosceles triangle, equilateral triangle

Writing in Math: Have students write a real-world problem that could be solved by making a model. Then solve the problem.Explain why it is impossible to draw an equilateral triangle that is either right or obtuse.

Graphic Organizer(s):Scale Drawing

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Major Content Supporting Content Additional Content

Curriculum and Instruction – MathematicsQuarter 3 Grade 7

TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESgiven conditions for the measures of angle and/or sides of a triangle describe a unique triangle, more than one possible triangle or do not describe a possible triangle.

Additional Information:Students will determine the dimensions of figures when given a scale and identify the impact of a scale on actual length and area.Example(s):Julie showed you the scale drawing of her room. If each 2 cm on the scale drawing equals 5 ft, what are the actual dimensions of Julie’s room? Reproduce the drawing at 3 times its current size.

Solution: 5.6 cm --- 14 ft1.2 cm --- 3 ft2.8 cm --- 7 ft4.4 cm --- 11 ft4 cm --- 10 ft

If the rectangle below is enlarged using a scale factor of 1.5, what will be the perimeter and area of the new rectangle? 7 in. 2 in.

Solution:The perimeter is linear or one-dimensional. Multiply the perimeter of the given rectangle

lesson focuses on proportionality of side lengths.4-9 Using Similar Figures (pp. 252-255) This lesson focuses on indirect measurements.4-10 Scale Drawing and Scale Models (pp. 256-259)Hands-On Lab Make Scale Drawings and Models (pp. 260-261)8-6 Classifying Triangles

Building Conceptual Understanding:Engage NY: Relating Scale Drawings to Ratios and RatesEngage NY: Drawing Geometric ShapesMath Shell Lesson: Describing and Defining TrianglesAchieve The Core: Identifying Proportional and Non-proportional Relationships

Choose from the following resources and use them to deepen students' conceptual understanding of mathematical content and develop their ability to apply that knowledge to non-routine problems.

Suggested Additional Lesson(s):engage ny : Ratios of Scale Drawings Connected Math: Stretching and Shrinking Investigations 1-5Similar Figures LessonMath Shell: Drawing to Scale - A Gardenengage ny : Drawing Parallelograms engage ny : Drawing Triangles

Suggested Task(s):Illustrative Math: Floor PlanIllustrative Math: Map DistanceIllustrative Math: Rescaling Washington ParkIllustrative Math: 7.G.2Achieve the Core: Art Class Task

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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES(18 in.) by the scale factor (1.5) to give an answer of 27 in.Students could also increase the length and width by the scale factor of 1.5 to get 10.5 in. for the length and 3 in. for the width. The perimeter could be found by adding 10.5 + 10.5 + 3 + 3 to get 27 in. The area is two-dimensional so the scale factor must be squared. The area of the new rectangle would be 14 x 1.52 or 31.5 in2.

Additional Information: (7.G.2)Students draw geometric shapes with given parameters. Parameters could include parallel lines, angles, perpendicular lines, line segments, etc.

Example(s):Is it possible to draw a triangle with a 90˚ angle and one leg that is 4 inches long and one leg that is 3 inches long? If so, draw one. Is there more than one such triangle?

Draw a triangle with angles that are 60 degrees. Is this a unique triangle? Why or why not?

Draw an isosceles triangle with only one 80 degree angle. Is this the only possibility or can you draw another triangle that will also meet these conditions?

Through exploration, students recognize that the sum of the angles of any triangle will be 180.

Suggested Additional Resources:Illuminations: Scale Drawings InteractiveIlluminations: Making Triangles 7.G.2 Khan Academy: Constructing Triangles PracticeBetter Lessons 7.G.2

Correlated iReady Lesson(s): The iReady program includes a variety of resources that can be used to support teacher-led instruction in Tier 1 and guided small-group Tier 1, 2 or 3 instruction.

Scale Drawings Constructions of Triangles

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RESOURCE TOOLBOXThe Resource Toolbox provides additional support for comprehension and mastery of grade-level skills and concepts. While some of these resources are imbedded in the map, the

use of these categorized materials can assist educators with maximizing their instructional practices to meet the needs of all students.NWEA MAP Resources: https://teach.mapnwea.org/assist/help_map/ApplicationHelp.htm#UsingTestResults/MAPReportsFinder.htm - Sign in and Click the Learning Continuum Tab – this resources will help as you plan for intervention, and differentiating small group instruction on the skill you are currently teaching. (Four Ways to Impact Teaching with the Learning Continuum)https://support.nwea.org/khanrit - These Khan Academy lessons are aligned to RIT scores.

Textbook Resourceswww.myhrw.comwww.connected.mcgraw-hill.com

Standards SupportTNReady Math StandardsAchieve the CoreEdutoolbox

VideosKhan AcademyWatch Know LearnLearn ZillionVirtual NerdMath PlaygroundStudy Jams

CalculatorTI-73 ActivitiesCASIO ActivitiesTI-Inspire for Middle Grades

Interactive Manipulatives:National Library of Virtual Manipulatives

Additional Sites:PBS: Grades 6-8 Lesson PlansAAA Math: EquationsFrayer Model TemplateGrade 7 Flip Book (This book contains valuable resources that help develop the intent, the understanding and the implementation of the state standards.)

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