Major Content Supporting Content Additional Content

Curriculum and Instruction – Office of Mathematics4th Nine Weeks Grade 6

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, Destination2025. 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 standards-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 Ready Standards are 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.

While the academic standards establish desired learning outcomes, the curriculum provides instructional planning designed to help students reach these outcomes. Educators will use this guide and the standards as a roadmap for curriculum and instruction. The sequence of learning is strategically positioned so that necessary foundational skills and major work of the grade are spiraled in order to facilitate student mastery of the standards.

These standards emphasize thinking, problem-solving and creativity through next generation assessments that go beyond

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Problem Solving

Reasoning and Proof

CommunicationRepresentation

Connecton

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. For grade 6, more than 65% of instructional time is spent on the major focus standards.Supporting Content - information 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 operations on rational numbers 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 – Office of Mathematics4th Nine Weeks Grade 6

multiple-choice tests to increase college and career readiness among Tennessee students. In addition, assessment blueprints (http://www.tn.gov/education/article/tnready-blueprints) have been designed to show educators a summary of what will be assessed in each grade, including the approximate number of items that will address each standard. Blueprints also detail which standards will be assessed on Part I of TNReady and which will be assessed on Part II.

Our collective goal is to ensure our students graduate ready for college and career. The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important “processes and proficiencies” with longstanding importance in mathematics education. The first of these are the NCTM process standards of problem solving, reasoning and proof, communication, representation and connections.

The second are the strands of mathematical proficiency specified in the National Research Council’s report Adding It Up: adaptive reasoning, strategic competence, conceptual understanding (comprehension of mathematical concepts, operations and relations) procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately), and productive disposition (habitual inclination to see mathematics and sensible, useful and worthwhile, coupled with a belief in diligence and one’s own efficacy). Throughout the year, students should continue to develop proficiency with the eight Standards for Mathematical Practice.

How to Use the Mathematics Curriculum Map

This curriculum map is designed to help teachers make effective decisions about what mathematical content to teach so that our

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Mathematical Practices

Make sense of problems and persevere in solving them

Reason abstractly and quatitatively

Construct viable arguments and

critique the reasoning of

others

Model with mathematics

Use appropriate tools

strategically

Attend to precision

Look for and make use of

structure

Look for and express

regularity in repeated reasoning

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Curriculum and Instruction – Office of Mathematics4th Nine Weeks Grade 6

students can reach Destination 2025. To reach our collective student achievement goals, we know that teachers must change their instructional practice in alignment with the three College and Career Ready shifts, as described above, in instruction for Mathematics.

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 standards and teaching practices that teachers should consistently access:

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The TNCore 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.

Mathematical Teaching Practiceshttps://mathprojectsjournal.files.wordpress.com/2015/05/nctm-teaching-practices.pdf

NCTM – Mathematics Teaching Practices

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Curriculum and Instruction – Office of Mathematics4th Nine Weeks Grade 6

Curriculum Maps:

Locate the TDOE Standards in the left column. Analyze the language of the standards and match each standard to an example or additional information about the standards.

Consult your McGraw-Hill or Holt Teachers’ Edition (TE) and other cited references to map out your week(s) of instruction. Plan your weekly and daily objectives, using the standards' explanations provided in the second column. Best practices tell us that

making objectives measureable increases student mastery. Carefully review the web-based resources provided in the 'Content and Tasks' column and use them as you introduce, practice or

assess a particular standard or set of standards. Review the Literacy Connections found in the right column. Make plans to address the content vocabulary, utilizing the suggested

literacy strategies, in your instruction. Examine the other standards and skills you will need to address in order to ensure mastery of the indicated standard. Using your McGraw-Hill or Holt TE and other resources cited in the curriculum map, plan your weekly lessons. Remember to include

differentiated activities for small-group instruction.

Resources

The following tools are available for teachers to assist them in preparing their students for the TNReady Assessments: The Item Sampler (MICA) can be found here: https://micatime.com/ TDOE TNReady Practice Tools homepage : A summary of TNReady practice tools Classroom Chronicles: Using MICA to prepare for TNReady : Hear how other teachers in TN are using MICA! Ten Things to Know about TNReady from the TDOE TNReady Blueprints: Blueprints provide a summary of what will be assessed in each grade, including the number of items that will

address each standard on each part of TNReady as well as the standards addressed in the Performance Task. This webpage also includes the calculator policy and reference sheets for Grades 5-8.

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Curriculum and Instruction – Office of Mathematics4th Nine Weeks Grade 6

Grade 6 Quarter 4 Overview:

During quarter 4 students move from simply representing data into analysis of data.  Students begin to think and reason statistically, first by recognizing a statistical question as one that can be answered by collecting data.  Students learn that the data collected to answer a statistical question has a distribution that is often summarized in terms of center, variability, and shape.  Throughout the module, students see and represent data distributions using dot plots and histograms.  They study quantitative ways to summarize numerical data sets in relation to their context and to the shape of the distribution.  As the module ends, students synthesize what they have learned as they connect the graphical, verbal, and numerical summaries to each other within situational contexts, culminating with a major project.

Standards for this Quarter(Note: Related foundational standards are noted in parenthesis)

Statistics and Probability

Cluster 6.SP.A Develop understanding of statistical variability.

6.SP.A.1: Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. (5.MD.B.2)

6.SP.2: Understand that a set of data collected to answer a statistical question has a distribution, which can be described by its center, spread, and overall shape. (5.MD.B.2)

6.SP.3: Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. (6.SP.A.1, 6.SP.A.2)

Cluster 6.SP.B Summarize and describe distributions.

6.SP.B.4: Display numerical data in plots on a number line, including dot plots, histograms, and box plots. (5.MD.B.2)

6.S P . B .5a: Summarize numerical data sets in relation to their context, such as by reporting the number of observations. (6.SP.A.2, 6.SP.A.3)

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Curriculum and Instruction – Office of Mathematics4th Nine Weeks Grade 6

6.SP.B.5b: Summarize numerical data sets in relation to their context, such as by describing the nature of the attribute under investigation, including how it was measured and its units of measurement. (6.SP.A.2, 6.SP.A.3)

6.SP.B.5c: Summarize numerical data sets in relation to their context, such as by giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. (6.SP.A.2, 6.SP.A.3)

6.SP.B.5d: Summarize numerical data sets in relation to their context, such as by relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. (6.SP.A.2, 6.SP.A.3)

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Curriculum and Instruction – Office of Mathematics4th Nine Weeks Grade 6

TN STATE STANDARDS ENDURING UNDERSTANDINGS CONTENT & TASKS LITERACY CONNECTIONS

Topic: Geometry Volume and Surface Area( 4.5 Weeks)

6. G . A .2: Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.

Enduring Understanding(s):Geometric attributes (such as shapes, lines, angles, figures and planes) provide descriptive information about an object’s properties and position in space and support visualization and problem solving.

Essential Question(s):How is the formula for the area of rectangles used in finding the volume of rectangular prisms?What are two ways to find the volume of a rectangular prism?

Additional Information:Students should understand that the volume of a three-dimensional figure is the number of cubic units needed to fill the space inside the figure. A cubic unit is a cube that measures 1 unit long, 1 unit wide, and 1 unit high.

Students will work with unit cubes that have edge lenghts that are fractions.

Students need multiple opportunities to measure volume by filling rectangular prisms with blocks and looking at the relationship between the total volume and the area of the base. Through these experiences, students derive the volume formula (volume equals the area of the base times the height). Students can explore the connection between filling a box with unit cubes and the volume formula using interactive applets such as the Cubes Tool on NCTM’s Illuminations (

Glencoe9-4A Explore Volume of Rectangular Prisms (page 568)9-4B Volume of Rectangular Prisms (page 569-574)

Holt10 – 7 Hands-on Lab Explore Volume of Prisms Curriculum Companion10 - 7A Explore Volumes of Prisms10 - 7 Volume of Prisms (page 566-569)

Connected Math Investigation: Geometry 6.G.2 p. 35

Engage NY Lessons: 6.G.2

C ube M o d el L e s s o n

Tasks:C o m pu ti ng V o l u m e Task Pro g r e s s i on 1 C o m pu ti ng V o l u m e Task Pro g r e s s i on 2

C o m pu ti ng V o l u m e Task Pro g r e s s i on 3

C o m pu ti ng V o l u m e Task Pro g r e s s i on 4

B anana B r ead Task Shodor I n t e r a c t i v e V o l u m e Graphic Organizers and Other Resources for Solid Figures

MICA Sample Items for 6.G.A.2:IDs 42491 and 43924

Language Objective(s):Students will discuss their reasoning, using appropriate mathematical language, for calculating the volume of figures.

Students will describe how to tell which part of a rectangular prism is the base and which part is the face.

Students will explain the difference between volume and surface area.

Vocabulary:Volume, right rectangular prism, face, prism, face, base, height, edge

Journal/Writing:Below you will find a link to use that will give students 3-D visuals of volume and surface area. Allow students to select problems to work out in their interactive math notebooks, or math journals. They must include the formulas, the work, and written explanations for each problem.Volume and Surface Area of Rectangular Prisms Volume/Surface Area/Rectangular Prisms/Interactive Drop-Down Menu Problems/Explanations

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Curriculum and Instruction – Office of Mathematics4th Nine Weeks Grade 6

TN STATE STANDARDS ENDURING UNDERSTANDINGS CONTENT & TASKS LITERACY CONNECTIONSh tt p :// i l l u m i n ati on s . n c t m . or g / A ct i v i t y Det a il.a s p x ? I D= 6 ).

In addition to filling boxes, students can draw diagrams to represent fractional side lengths, connecting with multiplication of fractions. This process is similar to composing and decomposing two dimensional shapes.

Example(s):Find the volume, in cubic feet, of the right rectangular prism.

V=(2 38

• 8 •3 12

) = 6612

cubic ft (ft3)

Correlated iReady Lessons: Volume with Fractional Length

6. G . A .4: Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.

Enduring Understanding(s):Strategies for finding surface area and volume of any three dimensional figure will work for any similar three dimensional figure.

Essential Question(s):

Glencoe9-4C Explore Surface Area of Rectangular Prisms (page 575-576)

9-4D Surface Area of Rectangular Prisms (page 577-581)

Language Objective:Students will describe ways to determine if a net/flat pattern can be folded to make a certain 3-D figure.

Vocabulary:Surface area, face, net or flat pattern

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Curriculum and Instruction – Office of Mathematics4th Nine Weeks Grade 6

TN STATE STANDARDS ENDURING UNDERSTANDINGS CONTENT & TASKS LITERACY CONNECTIONSHow can a net be used to find the surface area of a pyramid, rectangular or triangular prism?

Additional Information:

Students construct models and nets of three dimensional figures, describing them by the number of edges, vertices, and faces. Solids include rectangular and triangular prisms. Students are expected to use the net to calculate the surface area.

Students can create nets of 3D figures with specified dimensions using the Dynamic Paper Tool on NCTM’s Illuminations (h t tp : / / i l l u m i n a t ion s . n c t m . o r g / A c t i v i t y D e tail . a s p x? I D = 20 5 ).

Students also describe the types of faces needed to create a three- dimensional figure. Students make and test conjectures by determining what is needed to create a specific three-dimensional figure.

Example:Create the net for a given prism or pyramid, and then use the net to calculate the surface area.

Holt10-9 Hands-On Lab Model Three- Dimensional Figures (page 574-575)

10-9 Surface Area (page 576-579)

Math Shell Problem Solving Lesson: Designing 3-D Products

Engage NY Lessons: Nets and Surface Area

Illustrative Math: Christo's Building Task

3D Geometric Shapes Flat Patterns

Virtual Geometric Solids

Resources:Shodor I n t e r a c t i v e Su r f ace A r ea

MICA Sample Items for 6.G.A.4:IDs 23360

Correlated iReady Lessons: Nets and Surface Area

Graphic Organizer:Have students create a Venn Diagram comparing and contrasting surface area and volume.

Students can create a foldable for various 3-D figures. Example 3-D shape foldable Images of various volume and surface area foldables

Geometry Nets

Topic: Data and Statistics

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Curriculum and Instruction – Office of Mathematics4th Nine Weeks Grade 6

TN STATE STANDARDS ENDURING UNDERSTANDINGS CONTENT & TASKS LITERACY CONNECTIONS

( 4.5 Weeks) 6.SP.A.1: Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers.

Enduring Understanding(s):The message conveyed by the data depends on how the data is collected, represented, and summarized.

The results of a statistical investigation can be used to support or refute an argument.

Essential Question(s):How is probability used to make informed decisions about uncertain events?

Additional Information:

Grade 6 is the introduction to the formal study of statistics for students. Students need multiple opportunities to look at data to determine and word statistical questions.

Statistics are numerical data relating to a group of individuals; statistics is also the name for the science of collecting, analyzing and interpreting such data. A statistical question anticipates an answer that varies from one individual to the next and is written to account for the variability in the data. Data are the numbers produced in response to a statistical question. Data are frequently collected from surveys or other sources (i.e. documents).

Questions can result in a narrow or wide range of numerical values (data). For example, asking classmates “How old are the students in my class in years?” will result in less variability than asking “How old are the students in my class in months?”

GlencoeAdditional Lesson 8 p. 807

HoltAdditional Topic A-2 pp. AT4-66-5 Hands on Lab p. 3106-8 Misleading Graphs pp. 318-321

Connected Math lesson: Inv 1 & 3 p. 4 & 47Connected Math Data About Us Resources

Engage NY Lesson 6.SP.1B u tt o n s S t a t i s ti c al Q u e s t i o n Task

I den tif y i ng St a t i s ti c al Q u e s ti o n s

Statistics PowerPoint.

Distinquishing Between Statistical and Non-statistical Questions

Illustrative Math: Identifying Statistical Questions

CPalms: Statistical QuestionsOpus Math: Recognizing Statistical Questions

Correlated iReady Lesson(s): Understanding Statistics

Language Objective(s):Students will define statistics, in their own words, and describe how it is used in real-world situations.

Students will discuss how data is collected.

Students will write statistical questions to use with their classmates.

Vocabulary:Statistics, Data, Variability,

Journal/Writing:Students will write a friendly letter to a friend explaining what a statistical question is and how it relates to real-world situations. Students may use the link below.Friendly or Business Letter Generator

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Curriculum and Instruction – Office of Mathematics4th Nine Weeks Grade 6

TN STATE STANDARDS ENDURING UNDERSTANDINGS CONTENT & TASKS LITERACY CONNECTIONS

Topic: Data and Statistics 6.SP.2: Understand that a set of data collected to answer a statistical question has a distribution, which can be described by its center, spread, and overall shape.

6.SP.3: Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.

Enduring Understanding(s):

The answer to a statistical question is obtained through the treatment of a collection of data that exhibits variability.

Essential Question(s):How do you interpret data by looking at the overall shape of the data distribution?

How do you measure the center of the data?(mean or average, median and mode)

What does the measure of variation or the spread of the data imply?

Glencoe11-1F Appropriate Measures (pages 657-660)Additional Lesson 11 Appropriate Measures p. 821

Holt6 – 3AdditionalData and Outliers (pages 292-295)

Hands-On Lab: Use a Survey to Collect Data p. 310

Connected Math lesson: Inv 2

Engage NY Lesson: 6.SP.2-4

Inside Math Task: Pick a Pocket

MICA Sample Items for 6.SP.A.2:ID 42485

Correlated iReady Lesson(s): Understand MEAN and MAD Understanding Statistics

Language Objective(s):Students will describe statistical distribution.

Students will discuss with a partner the information that can be gathered by looking at the distribution of data.

Students will compare/contrast measure of center and measure of variation.

Vocabulary:Distribution

Topic: Displaying Data 6.SP.B.4: Display numerical data in plots on a number line, including dot plots, histograms, and box plots.

Enduring Understanding(s):Data can be displayed as a dot plot, histogram, and box plot.Data display is essential to organize data

Essential Question(s):How do you measure the variation or the spread of the data? ( range, mean absolute deviation, quartiles)

How is data displayed using a histogram, a

Glencoe11-1E Box-and-Whisker Plots (pages 655-666)11-2A Frequency Tables p. 661-66511-2C Histograms (page 668-672)

Holt6 – 5 Line Plots, Frequency Tables, and

Language Objective(s):Students will use appropriate math language to describe the various characteristics of a given set of data.

Vocabulary:Histogram, box plot, dot plot, frequency table, skewed, minimum, lower quartile, median, upper quartile, maximum

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Curriculum and Instruction – Office of Mathematics4th Nine Weeks Grade 6

TN STATE STANDARDS ENDURING UNDERSTANDINGS CONTENT & TASKS LITERACY CONNECTIONSdot plot or a box plot?

Additional Information:Students will display data graphically using number lines. Dot plots, histograms and box plots are the three graphs that will be explored.

In order to display numerical data in dot plots, histograms or box plots, students need to make decisions and perform calculations. Students are expected to display data graphically in a format appropriate for that data set as well as reading data from graphs generated by other students or contained in reference materials.

Dot plots are simple plots on a number line where each dot represents a piece of data in the data set. Dot plots are suitable for small to moderate size data sets and are useful for highlighting the distribution of the data including clusters, gaps, and outliers.

A box plot is a graphical depiction of groups of numerical data through their quartiles which is created from the five number summary of a data set consisting of the minimum, maximum, median, and two quartile values.

Students can readily compare two sets of data if they are displayed with side by side box plots on the same scale. Box plots display the degree of spread of the data and the ‘skewness’ of the data.

A histogram shows the distribution of continuous data using intervals on the number line. The height of each bar represents the number of data values in that interval.

Histograms (pages 304-307)

Tasks:Illustrative Math: Puppy Weights Task

Illustrative Math: Describing Distributions Task

Inside Math Task: Through the Grapevine

D a t a C o ll e c t i on A c ti v i t y

Resources:Creating Box Plots Lesson

R .11 C r e a t e h i s t o g r am

Illuminations Box Plot Tool

Illuminations Histogram Tool

H i s t o g r am and Bar G r aph P r a c ti c e

D a t a a nd g r aph s : R .12 I n t e r p r et B ox and Wh i s k er Pl o t s

C r ea t i ng a Box a nd W h i s ke r Pl o t

Spor t s P l o t A c ti v it y

D a t a C o ll e c t i o n : C r e a t i ng B ox and W h i s k er Plo t s Ac t i v it y

M e an and M e d i an

NB A St at i s t i cs

Journal/Writing:Have students explain the difference between a histogram and a bar graph.Graphic Organizer:Students will use a Venn Diagram to compare and contrast a histogram and bar graph.Venn Diagram Templates

Students will create a foldable or Frayer model for box plots and dot plots.

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Curriculum and Instruction – Office of Mathematics4th Nine Weeks Grade 6

TN STATE STANDARDS ENDURING UNDERSTANDINGS CONTENT & TASKS LITERACY CONNECTIONS

Example(s):Grade 6 students were collecting data for a math class project. They decided they would survey the other two grade 6 classes to determine how many DVDs each student owns. A total of 48 students were surveyed. The data are shown in the table below in no specific order. Create a data display. What are some observations that can be made from the data display?

A histogram using 5 bins (0-9, 10-19, …30-39) to organize the data is displayed below.

T he Pi z z a Pa l a ce

MICA Sample Items for 6.SP.B.4:ID 42487

Correlated iReady Lesson(s): Histograms Box Plots Dot Plots

Topic: Descriptive Statistics 6.S P . B .5a: Summarize numerical data sets in relation to their context, such as by reporting the number of observations.

6.SP.B.5b: Summarize numerical data sets in relation to their context, such as by describing the nature of the attribute under investigation, including how it was measured and its units of measurement.

Enduring Understanding(s):The measure of the variation or spread of the data is obtained in different ways such as the range, interquartile range and the mean absolute deviation.

The measure of the center and the measure of the variation are essential to analyze data.

Data can be displayed as a dot plot,

Glencoe11-1B Mean (pages 644-648)11-1D Median, Mode, and Range (pages 650-654)Additional Lesson 9 p. 809Additional Lesson 10 p. 81511-1F Appropriate Measures (pages 657-660)

Language Objective(s):Students will explain the various ways to describe sets of data.

Graphic Organizer:Students will create a brochure outlining the most pertinent characteristics and uses of various types of graphs with measures of central tendency. Below you find links where students can create their own graph brochures.

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Curriculum and Instruction – Office of Mathematics4th Nine Weeks Grade 6

TN STATE STANDARDS ENDURING UNDERSTANDINGS CONTENT & TASKS LITERACY CONNECTIONS

6.SP.B.5c: Summarize numerical data sets in relation to their context, such as by giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.

6.SP.B.5d: Summarize numerical data sets in relation to their context, such as by relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.

histogram, and box plot.

Data display is essential to organize data.

Essential Question(s):What does the measure of variation or the spread of the data imply?

How do you measure the variation or the spread of the data? ( range, mean absolute deviation, quartiles)

How is data displayed using a histogram, a dot plot or a box plot?

Additional Information:Students summarize numerical data by providing background information about the attribute being measured, methods and unit of measurement, the context of data collection activities, the number of observations, and summary statistics.

When using measures of center (mean, median, and mode) and range, students are describing a data set in a single number.

The measure of center that a student chooses to describe a data set will depend upon the shape of the data distribution and context of data collection.The mode is the value in the data set that occurs most frequently. The mode is the least frequently used as a measure of center because data sets may not have a mode, may have more than one mode, or the mode may not be descriptive of the data set.

The mean is a very common measure of center computed by adding all the numbers in

Additional Lesson 11 p. 821Holt

6 – 2 Mean, Median, Mode, and Range (pages 288-291)6 – 3Additional Data and Outliers (pages 292-295)

Tasks:MARS Task: Mean, Mode, Median, and RangeIllustrative Math: Puzzle Times TaskResources:What A r e O u t l i e r s i n D a t a?

Find i ng O u tl i e r s

C r ea t e Your Ow n M e a n, M ed i a n , and Mode

Pr a c ti c e P r ob l e m s

M e an M e d i an Mo d e I n t e r a c ti v e A c ti v it y

Lea r n A l b e rt a

Videos:

K han A cade m y

Virtual Nerd: Mean Mode, Median, Range Video

M e an M e d i an Mo d e Vid e o M e a s u r e s of C en t r a l T en de ncy

Printing Press Explanation and PlanPrinting Press Generator for Flyers, Brochures, & NewspapersPlanning Sheet for Printing Press

Journal/Writing:Explain in your own words what you would say to your parents to describe how they could use median, mean, mode, or range in their lives, or in your own life (your grades, temperatures, scores from games, etc.).

To illustrate, you may say, “Mom, you can use mean to calculate the average of several bills you have that must be paid every month. Let’s say you spend $300 on the light bill, $900 on the mortgage, $300 on food, $200 on gas, and $100 on water. When you add the 5 bills together, you must spend a total sum of $1,800 per month. You can calculate the average of these bills by dividing the sum total by the number of bills which is five ($1,800/5 = $360). So the mean is $360. The median of these 5 bills can be calculated by writing the bills in order from least to greatest ($100, $200, $300, $300, and $900) and selecting the bill in the middle ($300 food). If you have six amounts, you must add the two numbers in the middle and divide them by two to attain the mean. You can attain the range by subtracting the smallest bill from the largest bill ($900-$100 = $800), or by subtracting the minimum value from the maximum value. Of all of these measures of central tendency, I think the mode is the easiest to solve. You simply have to select the number that occurs the most ($300). However, sometimes you may not have a mode based on the amount of your bills.

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Major Content Supporting Content Additional Content

Curriculum and Instruction – Office of Mathematics4th Nine Weeks Grade 6

TN STATE STANDARDS ENDURING UNDERSTANDINGS CONTENT & TASKS LITERACY CONNECTIONSthe set and dividing by the number of values. The mean can be affected greatly by a few data points that are very low or very high. In this case, the median or middle value of the data set might be more descriptive. In data sets that are symmetrically distributed, the mean and median will be very close to the same. In data sets that are skewed, the mean and median will be different, with the median frequently providing a better overall description of the data set.

The range provides a single number that describes how the values vary across the data set. The range can also be expressed by stating the minimum and maximum values.

MICA Sample Items for 6.SP.B.5:6.SP.B.5b: ID 424886.SP.B.5c: IDs 42489 and 43936

Correlated iReady Lesson(s): Choice of Measures of Center and

Variability

Teach students writing strategies such as climbing and diving or double-entry to write about what they learned, and record these entries into their interactive math notebook or math journal. Using Writing in Math to Deepen Student Learning, Refer to p. 14These strategies and other summary strategies are explained in the link below from the National Council of Teachers of Mathematics (pg. 12).Writing Strategies in Mathematics NCTM

Graphic Organizer(s):Have students fill out a Frayer model using all vocabulary words (mean, median, mode, range, measures of central tendency, averages, outlier, and multi-modal, maximum value, minimum value).They can write the definitions in their own words besides the book definition to also assess for understanding.Frayer Model Template and Explanation of Frayer Model

Frayer Models with Explanations of Mean, Median, Mode, and RangeGo to Week of 10-4.

Have students to fill out a measure of central tendency foldable and glue it inside their interactive math notebooks or math journals. It is your decision whether to grade for grammar or not on each activity. Below, you will find an example of a math journal, and a rubric generator for any skill, project, or grammar requirements.Interactive Math Journal Sample Rubric

Mean, Median, Mode, and Range Foldable Example

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Major Content Supporting Content Additional Content

Curriculum and Instruction – Office of Mathematics4th Nine Weeks Grade 6

TN STATE STANDARDS ENDURING UNDERSTANDINGS CONTENT & TASKS LITERACY CONNECTIONSMeasures of Central Tendency with Max and Min Value

Students will use a diamante poem format to explain characteristics of mean, median, mode, and range. This type of poem will assist students with thinking deeper about the concepts they learn. Also, they will learn more about parts of speech, gerunds, and synonyms and antonyms required to write this poem. In the links below you will find the diamante poem generator as well as instructions with a lesson plan.Interactive Diamante Poem GeneratorImages of Math Diamante Poems

RESOURCE TOOLBOXNWEA 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 Resources CCSST N C o r e http://www.ccsstoolbox.org

Videos

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Major Content Supporting Content Additional Content

Curriculum and Instruction – Office of Mathematics4th Nine Weeks Grade 6

w w w . c o n n ec t e d . m c g r a w - h i l l.com h t t p :// m y. h r w . c o m http://my.hrw.com/nsmedia/osp/2010/ma/msm1/temp/Tennessee/index.htm(This link will take you to the Holt Middle School Math Material on-line. Click on the section that says additional Common Core Material to access the Curriculum Companion.)

I ns i de M a t he m a ti c s https://www. engageny .org/

KhanAcademy

www.learnzillion.com

www.virtualnerd.comStudy Jams

Math Playground

Calculatorw w w . ed u c a t io n . t i.com

w w w . c asioe d u c a t io n . c om

Interactive ManipulativesN a ti o n al L i b r a r y of V i r t u a l M a n i pu l a t i v es - N L V M

Other:CREATING BOX AND WHISKER PLOTS:https://app.activateinstruction.org/playlist/resource-sview/id/53b9f1c8f07787bd20f1a969/rid/53b9fbd7f07787f820f1a96a/bc0/explore/bc1/playlisthttps://www.brainingcamp.com/content/box-and-whisker-plots/lesson.phphttps://www.schooltube.com/video/2817f4cf68f544abae49/6th%20Grade%20-%20Box%20and%20Whisker%20Plotshttp://betterlesson.com/lesson/435648/box-and-whiskers-analyzing-and-creatinghttp://illuminations.nctm.org/lesson.aspx?id=2643

Additional SitesMEAN, MEADIAN, MODE, AND RANGE:http://www.purplemath.com/modules/meanmode.htmhttps://www.khanacademy.org/math/probability/descriptive-statistics/central_tendency/v/ mean - median -and- mode http://www.studyzone.org/mtestprep/math8/e/meanmedmode6l.cfmhttp://www.gameclassroom.com/skills/6/math/range,%20mean,%20median,%20mode,%20outliers%20and%20central%20tendency

HISTOGRAMS:https://www.khanacademy.org/math/cc- sixth - grade -math/cc- 6th -data-statistics/creating- histograms /v/ histograms -intro https://www.khanacademy.org/...sixth-grade...6th...histograms/.../creating- histogramshttps://www.engageny.org/sites/default/files/resource/attachments/math-g6-m6-teacher-materials.pdfHISTOGRAM AND FREQUENCY TABLE PROJECT:https://app.activateinstruction.org/playlist/resource-sview/id/53b9f1c8f07787bd20f1a969/rid/53bca55af07787bd40f1a96c/bc0/explore/bc1/playlistBOX AND WHISKER PLOTS WORKSHEETS:http://www.mathworksheetsland.com/stats/1boxandwhiskersset.html

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