common core state standards grade 6 - tech-connect -...

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Common Core State Standards Grade 6Connected Mathematics 2, Grade 6 Units

Connected Mathematics (CMP) is a field-tested and research-validated program that focuses on a few big ideas at each grade level. Students explore these ideas in depth, thereby developing deep understanding of key ideas that they carry from one grade to the next. The sequencing of topics from grade to grade, the result of lengthy field-testing and validation, helps to ensure the development of students’ deep mathematical understanding and strong problem-solving skills. By the end of grade 8, CMP students will have studied all of the content and skills in the Common Core State Standards (CCSS) for middle grades (Grades 6-8).

The sequence of content and skills in CMP2 varies in some instances from that in the CCSS, so in collaboration with the CMP2 authors, Pearson has created a set of investigations for each grade level to further support and fully develop students’ understanding of the CCSS.

The authors are confident that the CMP2 curriculum supplemented with the additional investigations at each grade level will address all of the content and skills of the CCSS, but even more, will contribute significantly to advancing students’ mathematical proficiency as described in the Mathematical Practices of the CCSS. Through the in-depth exploration of concepts, students become confident in solving a variety of problems with flexibility, skill, and insightfulness, and are able to communicate their reasoning and understanding in a variety of ways.

The following alignment of the Common Core State Standards for Mathematics ( June 2, 2010 release) to Pearson’s Connected Mathematics 2 (CMP2) ©2009 program includes the supplemental investigations that complete the CMP2 program. These supplemental investigations will be available this fall from your Pearson Prentice Hall Account Representative.

CCSS Mathematical Practices and CMP2

The Common Core State Standards (CCSS) articulate a set of Mathematical Practices that have been central to the development of the Connected Mathematics Project (CMP) materials from their inception. CMP focuses on developing mathematical situations that give students opportunities to incorporate the mathematical practices into their ways of thinking and reasoning.

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ImplementIng the Common Core StAte StAndArdS

Standards for Mathematical Practices 1. Make sense of problems and persevere in solving them.

This goal is fundamental to the CMP approach. CMP is a problem-centered curriculum. To be effective, problems must embody critical concepts and skills and have the potential to engage students in making sense of mathematics. Students build understanding by reflecting, connecting, and communicating.

The problems themselves are developed to be engaging to students and to support these practices. The contexts of the problems support the development of students’ mathematical reasoning abilities and understanding. The demands of the problems lead students into thinking and reasoning about problem contexts and the mathematics needed to solve the problems embedded in the contexts.

The questions in the problems provide the scaffolding needed for students to engage with the context and to make progress on solving the problem. The CMP teacher materials give suggestions to help teachers develop classroom cultures in which students learn to engage in mathematics discourse and articulate their reasoning and solution strategies around problems.

Practice in the Applications, Connections, and Extensions problems assures that all students are given opportunities to develop successful practices for engaging with a new problem situation.

Throughout program; for examples see: Bits and Pieces I (Inv. 3); Bits and Pieces II (Inv. 3); Bits and Pieces III (Inv. 4); Prime Time (Inv. 2); Data About Us (Inv. 1); How Likely Is It? (Inv. 4); Covering and Surrounding (Inv. 2); Shapes and Designs (Inv. 1)

2. Reason abstractly and quantitatively.

CMP provides help to teachers in creating classroom environments where students have opportunities to “talk” mathematics, to engage in mathematical arguments, and to grow in their ability to persevere in solving problems. These environments promote the acquisition of mathematical language and mathematical ways of reasoning that are the underpinning of both abstract and quantitative mathematical reasoning.

A key to establishing such classrooms at this level is the teacher’s commitment to developing a classroom culture in which explanation of one’s thinking and reasoning is an expectation at all times. In order to support the building of such classroom norms, the problems students engage with need to capture students’ interest and systematically push students to higher levels of thinking. This has always been at the forefront of the authors’ problem development. A growing body of evidence from the cognitive sciences shows that students make sense of mathematics if concepts and skills are embedded within a context or problem. This research is a cornerstone for developing the problem situations in CMP.

Throughout program; for examples see: Prime Time (Inv. 2 p. 25); Bits and Pieces I (Inv. 3 pp. 40–41); Bits and Pieces II (Inv. 3 pp. 36–38); Bits and Pieces III (Inv. 3 p. 46); Data About Us (Inv. 3 pp. 54–55); How Likely Is It? (Inv. 2 pp. 22–23); Covering and Surrounding (Inv. 5 p. 88); Shapes and Designs (Inv. 3 p. 69)

The chart that follows highlights the opportunities these materials create to make the Mathematical Practices a reality for students. It explains how CMP supports the development of the Mathematical Practices and provides some examples of how each standard for Mathematical Practices is embedded in the CMP materials.

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Standards for Mathematical Practices

3. Construct viable arguments and critique the reasoning of others.

A classroom environment in which students expect to explain the reasoning that led to the solution they put forth changes mathematics from the dreaded subject it is for many students to a subject that makes sense and provides challenges that students are willing to undertake. Every module in CMP provides problems that help create such an environment. The teacher guides provide questions for teachers to use as they work to create a classroom culture that focuses on argument and critique as a part of making sense of and solving mathematical problems.

Reasoning and justification are central to all three grade levels—6, 7, and 8. However, the sophistication of the problem situations and mathematical discussions around the problem solutions grows over the grades. The teacher materials provide help for teachers in creating classroom norms that establish expectations around classroom mathematical discourse.

The lens the authors used in creating and critiquing problems in the curriculum is the following: A problem must have important, useful mathematics embedded in it; investigation of the problem should contribute to students’ conceptual development of important mathematical ideas; work on the problem should promote skillful use of mathematics; and problems should create opportunities for teachers to assess what students are learning. Problems at all grade levels are developed to promote opportunities to construct mathematical arguments and to critique other students’ solutions and strategies.

Throughout program; for examples see: Bits and Pieces I (Inv. 1 pp. 7–8, 10, Inv. 2 pp. 24–25, Inv. 4 pp. 56–58, 60); Bits and Pieces II (Inv. 4 p. 54); Bits and Pieces III (Inv. 3 p. 39); Prime Time (Inv. 1 p. 10); Data About Us (Inv. 2 p. 33); How Likely Is It? (Inv. 3); Covering and Surrounding (Inv. 1 pp. 6–8); Shapes and Designs (Inv. 2 pp. 36–37)

4. Model with mathematics.

In grades 6, 7, and 8, CMP engages students in learning to construct, make inferences from, and interpret concrete symbolic, graphic verbal, and algorithmic models of mathematical relationships in problem situations as well as translating information from one model to another. Building a standard set of mathematical modeling tools begins in grade 6 and continues to grow in sophistication throughout grades 7 and 8.

The basic set of modeling tools in CMP are number strips, number lines, squares, diagrams, graphs, tables, equations, functions, and technological supports such as calculators and computers. Partitioning squares, strips, and lines support students’ insight into rational numbers and rational number computation. Diagrams help students model a problem situation and determine whether a solution is correct. Graphs are fundamental to understanding equations and functions. Students explore the relationships among members of a set of functions such as linear, quadratic, and exponential through graph models and algebraic models. These models give students insight into the overall behavior of a particular kind of function and allow students to make comparisons between functions.

In data analysis, additional models are introduced that give opportunities for students to experience a different kind of reasoning—one based on seeing and reporting trends, anomalies, outliers, and other aspects of the data as it is displayed in various representations. Statistical thinking and reasoning is extremely important to everyone in our society. Making decisions, understanding survey data, reading newspaper reports, and being a savvy consumer are all enhanced by developing tools for analyzing and interpreting statistical claims that are ubiquitous in our society. CMP provides a substantive data analysis module at each grade level.

Throughout program; for examples see: Bits and Pieces I (Inv. 3 pp. 36–38, 40–41); Bits and Pieces II (Inv. 3 pp. 34–35); Bits and Pieces III (Inv. 4 p. 58) Prime Time (Inv. 2 p. 25); Data About Us (Inv. 1 pp. 18–20) How Likely Is It? (Inv. 4 pp. 57–58); Covering and Surrounding (Inv. 2 p. 30); Shapes and Designs (Inv. 1 pp. 14–15)


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5. Use appropriate tools strategically.

CMP chose a small set of tools as the primary vehicles for exploring problem situations. Students use these tools to gain insight into situations, to compute, and to represent relationships in tables, graphs, and spreadsheets. Students use calculators in many ways: to compute, to check their thinking, to explore possibilities, to see whether an approach makes sense, and to use the graphing capability to examine functions to see how they behave – what is common and what is different in the behavior of classes of functions.

In addition, students use tools such as polystrips, plastic two-dimensional shapes, and three-dimensional shapes to explore mathematics. The polystrips allow students to explore the rigidity of triangle forms and the lack of rigidity of square forms. The two-dimensional shapes support many kinds of mathematical explorations. For example, students explore the question of what shape has the greatest area when built from a given number of squares. Graphing tools have become essential in classrooms to give students support in engaging with mathematics both in exploratory ways to “see into a problem situation” and to find solutions to problems.

Through out grades 6, 7, and 8, students are encouraged to determine the reasonableness of answers by using “benchmarks” to estimate measures and other strategies to approximate a calculation and to compare estimates.

Throughout program; for examples see: Shapes and Designs (Inv. 2, 4); Bits and Pieces I (Inv. 1); Bits and Pieces II (Inv. 3); Prime Time (Inv. 1, 2); How Likely Is It? (Inv. 1, 2, 3, 4)

6. Attend to precision.

As students transition from elementary programs into CMP, a key goal is learning to “talk” mathematics using precise terms and definitions. The clarity of a student’s thinking is dependent on the student’s precise understanding of mathematical language. CMP is judicious in supporting the use of mathematical language. The key mathematical goals determine which important mathematical terms, definitions, and ways of thinking and reasoning are highlighted. Student books include mathematical definitions that are student-friendly. For example, the definition of congruent figures is: Two figures are congruent if one is the image of the other under a translation, a reflection, a rotation, or some combination of these transformations. The goal is to develop students’ facility in talking mathematics at an appropriate level of mathematical maturity.

In addition to supporting the development of precise use of mathematical language, CMP supports students in developing precision in their presentation of arguments. The series of questions in a problem pushes students to think more deeply and to articulate more clearly their solutions and the processes by which they reached these solutions.

A regular feature of the CMP student materials is the Mathematical Reflections (MR) pages that occur at the end of each investigation. The MR pages consist of a set of questions that help students synthesize and organize their understandings of important concepts and strategies. After thinking about the questions and sketching their own ideas, students discuss the questions with their teacher and classmates, and then write a summary of their findings.

Throughout program; for examples see: Shapes and Designs (Inv. 2)

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7. Look for and make use of structure.

The CMP materials were designed to build mathematics in ways that illuminate and make use of mathematical structure. In grade 6, for example, students examine data tables and look for patterns in the data, and they analyze numbers to determine their prime structure.

In grade 7, students examine proportional reasoning situations of various kinds and develop tools for solving proportions. They examine the structure of algebraic expressions, algebraic operations, equations, and equation solving. In all grades, students see structure in measurement. They examine formulas, create algorithms for computation with rational numbers, and compare algorithms for scope of use and efficiency.

In grade 8, students examine the structure of linear, exponential, and quadratic relationships. They examine graphical representations of functions and develop ways of solving equations of each kind. Although it is unusual to examine quadratic and exponential functions in middle school, the mathematical payoff for examining these three kinds of relationships is very great. Linearity is amazingly complex for students. The contrast with two other kinds of functions helps students understand the structure of a function and to see what is revealed about the function through its structure.

Throughout program; for examples see: Bits and Pieces I (Inv. 1, 2, 3); Bits and Pieces II (Inv. 2, 3, 4); Bits and Pieces III (Inv. 1, 2, 5); Prime Time (Inv. 1, 2, 4); Covering and Surrounding (Inv. 1, 2, 3, 4, 5); How Likely Is It? (Inv. 2, 4); Data About Us (Inv. 1, 2, 3); Shapes and Designs (Inv. 1, 2, 3, 4)

8. Look for and express regularity in repeated reasoning.

The CMP curriculum was developed expressly to engage students in making sense of mathematics, in seeing regularity, in learning to apply strategies and tools developed in one context to a very different problem context, in seeking mathematical connections, and in recognizing and using powerful mathematical ways of thinking and reasoning. The materials provide repeated opportunities for students to examine mathematical situations, presented in a context or in mathematical form, and to look for connections to previous problems and previous solution strategies.

Students are aided in seeing opportunities to use strategies previously used to solve a problem in order to solve a new problem that looks on the surface to be very different. This kind of thinking and reasoning about solving problems promotes a view of mathematics as connected in many different ways, rather than as an endless set of problems to be solved and forgotten.

The CMP teacher materials tell how to create a learning environment that promotes student-to-student discourse around mathematics. The problems are written to be engaging to students in the middle grades and to encourage the development of mathematical thinking and reasoning. Even the titles of the materials express the importance the authors place on making connections–all kinds of mathematics connections. Noting such connections is fundamental in seeing mathematics as a connected whole rather than an endless string of algorithms or processes to be learned.

Throughout program; for examples see: Prime Time (Inv. 2, 3); Bits and Pieces I (Inv. 3); Bits and Pieces II (Inv. 2, 3); Shapes and Designs (Inv. 1, 3); Covering and Surrounding (Inv. 1, 2, 4)


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Common Core State Standards Grade 6Meeting the Common Core State Standards

with Connected Mathematics 2 (CMP2)

Ratios and Proportional Relationships

Understand ratio concepts and use ratio reasoning to solve problems.

6.RP.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”

Bits and Pieces I (Inv. 4)

6.RP.2 Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”

NOTE: Expectations for unit rates in this grade are limited to non-complex fractions.

CCSS Investigation 1: Ratios and Rates

6.RP.3Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

Bits and Pieces I (Inv. 3, 4)

Shapes and Designs (Inv. 2 ACE 29–35)

How Likely Is It? (Inv. 1, 2, 3, 4)

6.RP.3.aMake tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.



6.RP.3.b Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?



6.RP.3.c Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.

Bits and Pieces III (Inv. 4, 5)

6.RP.3.d Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.


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The Number System

Apply and extend previous understandings of multiplication and division to divide fractions by fractions.

6.NS.1 Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?

Bits and Pieces II (Inv. 4)

Compute fluently with multi-digit numbers and find common factors and multiplies.

6.NS.2 Fluently divide multi-digit numbers using the standard algorithm.


Bits and Pieces III (Inv. 3)

6.NS.3 Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

Bits and Pieces III (Inv. 1, 2, 3)

6.NS.4 Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4(9 + 2).

Prime Time (Inv. 2, 3)

CCSS Investigation 2: Number Properties and Algebraic Equations

Apply and extend previous understandings of numbers to the system of rational numbers.

6.NS.5 Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.

Bits and Pieces II (Inv. 2 ACE 51)

6.NS.6 Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.

Bits and Pieces I (Inv. 1, 2, 3, 4)

Bits and Pieces II (Inv. 1, 2, 3, 4)

Bits and Pieces III (Inv. 1, 2, 3, 4)


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6.NS.6.a Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite.


CCSS Investigation 3: Integers and the Coordinate Plane

6.NS.6.b Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.


6.NS.6.c Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.


6.NS.7 Understand ordering and absolute value of rational numbers.

Bits and Pieces I (Inv. 1, 2, 3)

6.NS.7.a Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right.

Bits and Pieces I (Inv. 1, 2, 3, 4)


6.NS.7.b Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write –3 °C > –7 °C to express the fact that –3 °C is warmer than –7 °C.


Bits and Pieces III (Inv. 1 ACE 58)

6.NS.7.c Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars.


6.NS.7.d Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars.


6.NS.8 Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.

Covering and Surrounding (Inv. 2)

Data About Us (Inv. 2)


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Expressions and Equations

Apply and extend previous understandings of arithmetic to algebraic expressions.

6.EE.1 Write and evaluate numerical expressions involving whole-number exponents.

Prime Time (Inv. 4)

6.EE.2 Write, read, and evaluate expressions in which letters stand for numbers.

Bits and Pieces II (Inv. 2, 3, 4)



6.EE.2.a Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y.


6.EE.2.b Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2(8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms.

Prime Time (Inv. 1, 3, 4, 5)




6.EE.2.c Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems.Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2.

Covering and Surrounding (Inv. 1, 2, 3, 4, 5)


6.EE.3 Apply the properties of operations to generate equivalent expressions.For example, apply the distributive property to the expression 3(2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6(4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.


6.EE.4 Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.



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Reason about and solve one-variable equations and inequalities.

6.EE.5 Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.



6.EE.6 Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.


6.EE.7 Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.


6.EE.8 Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.


Represent and analyze quantitative relationships between dependent and independent variables.

6.EE.9 Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.


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Geometry

Solve real-world and mathematical problems involving area, surface area, and volume.

6.G.1 Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.

Covering and Surrounding (Inv. 1, 2, 3, 4, 5)

6.G.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 = lwh and V = bh to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.

CCSS Investigation 4: Measurement

6.G.3 Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems.


6.G.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.

Covering and Surrounding (Inv. 3 ACE 39)

CCSS Investigation 4: Measurement


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Statistics and Probability

Develop understanding of statistical variability.

6.SP.1 Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages.

Data About Us (Inv. 1, 2, 3, Unit Project p. 64)

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.

Data About Us (Inv. 1, 2, 3)

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.


Summarize and describe distributions.

6.SP.4 Display numerical data in plots on a number line, including dot plots, histograms, and box plots.

Data About Us (Inv. 1, 3)

CCSS Investigation 4: Histograms and Box Plots

6.SP.5 Summarize numerical data sets in relation to their context, such as by:


6.SP.5.a Reporting the number of observations.

How Likely Is It? (Inv. 1, 2, 3, 4)

6.SP.5.b Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.

Data About Us (Inv. 1, 2)

6.SP.5.c 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.


CCSS Investigation 4: Histograms and Box Plots

6.SP.5.d 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.


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