This document provides a 6th grade math curriculum map that outlines the standards, units, and clusters to be taught over the school year. It includes essential questions, big ideas, vocabulary, and resources for each cluster. The curriculum is organized into units on ratios and proportional relationships, the number system including fractions, decimals, percents, and integers, and decimal operations. Standards are prioritized and paired with mathematical practices. Suggested formative assessments, projects, and resources are included to support instruction.
Dynamic Question Answer Generator An Enhanced Approach to Question Generationijtsrd
Teachers and educational institutions seek new questions with different difficulty levels for setting up tests for their students. Also, students long for distinct and new questions to practice for their tests as redundant questions are found everywhere. However, setting up new questions every time is a tedious task for teachers. To overcome this conundrum, we have concocted an artificially intelligent system which generates questions and answers for the mathematical topic –Quadratic equations. The system uses i Randomization technique for generating unique questions each time and ii First order logic and Automated deduction to produce solution for the generated question. The goal was achieved and the system works efficiently. It is robust, reliable and helpful for teachers, students and other organizations for retrieving Quadratic equations questions, hassle free. Rahul Bhatia | Vishakha Gautam | Yash Kumar | Ankush Garg ""Dynamic Question Answer Generator: An Enhanced Approach to Question Generation"" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-4 , June 2019, URL: https://www.ijtsrd.com/papers/ijtsrd23730.pdf
Paper URL: https://www.ijtsrd.com/computer-science/artificial-intelligence/23730/dynamic-question-answer-generator-an-enhanced-approach-to-question-generation/rahul-bhatia
Secondary mathematics wednesday august 22 2012brearatliff
Using CSCOPE for Instructional Planning - a PowerPoint outlining how to use the YAG, TEKS Verification Document, IFD, VAD, and EITG for effective lesson planning.
Dynamic Question Answer Generator An Enhanced Approach to Question Generationijtsrd
Teachers and educational institutions seek new questions with different difficulty levels for setting up tests for their students. Also, students long for distinct and new questions to practice for their tests as redundant questions are found everywhere. However, setting up new questions every time is a tedious task for teachers. To overcome this conundrum, we have concocted an artificially intelligent system which generates questions and answers for the mathematical topic –Quadratic equations. The system uses i Randomization technique for generating unique questions each time and ii First order logic and Automated deduction to produce solution for the generated question. The goal was achieved and the system works efficiently. It is robust, reliable and helpful for teachers, students and other organizations for retrieving Quadratic equations questions, hassle free. Rahul Bhatia | Vishakha Gautam | Yash Kumar | Ankush Garg ""Dynamic Question Answer Generator: An Enhanced Approach to Question Generation"" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-4 , June 2019, URL: https://www.ijtsrd.com/papers/ijtsrd23730.pdf
Paper URL: https://www.ijtsrd.com/computer-science/artificial-intelligence/23730/dynamic-question-answer-generator-an-enhanced-approach-to-question-generation/rahul-bhatia
Secondary mathematics wednesday august 22 2012brearatliff
Using CSCOPE for Instructional Planning - a PowerPoint outlining how to use the YAG, TEKS Verification Document, IFD, VAD, and EITG for effective lesson planning.
Transitioning to the Common Core is not going to be easy. Hear what we've learned from educators across the country about what's different and what you should look for in new materials.
Preparing K-5 Students for the Focus, Coherence and Rigor of the Common Core ...npsmath
This is the powerpoint presentation presented by Shelbi Cole, Director of Mathematics at Smarter Balanced. Please contact Jill Bessette, April Schultz or Jackie Walsh if you would like to meet for an overview or a PLC session on the contents.
New York Survey DataInstructionsA consulting firm was hired to.docxcurwenmichaela
New York Survey Data
Instructions
A consulting firm was hired to perform a survey on people living in New York City. The survey was completed monthly for six months by 445 randomly selected people in different boroughs. There were a number of items on the survey, but six basic biographical items will be studied for this exercise. The data for the people surveyed in one of these monthly surveys can be found in the Excel file SURVEY. The variables that were used for the basic biographical data are found on the last page of the exercise.
In this exercise, some of the estimation techniques presented in the module will be applied to the New York survey results. You may assume that these respondents represent a simple random sample of all potential respondents within the community, and that the population is large enough that application of the finite population correction would not make an appreciable difference in the results.
New York City governmental agency personnel like to have point estimates regarding variables describing the biographical information of the people living within the different boroughs. It is very helpful for them to have some idea regarding the likely accuracy of these estimates as well. Therein lies the benefit of the techniques presented in this module and applied here.
1. Item A in the description of the data collection instrument lists variables 1 through 5, which represent the respondent’s general attitude toward each of the five boroughs. Each of these variables has numerically equal distances between the possible responses, and for purposes of analysis they may be considered to be of the interval scale of measurement.
1. Determine the point estimate, and then construct the 95% confidence interval for μ1= the average attitude toward Manhattan.
2. Repeat part (a) for μ2through μ5, the average attitudes toward Brooklyn, Queens, The Bronx and Staten Island, respectively.
2. Given the breakdown of responses for variable 6 (highest level of education), determine the point estimate, then construct the 95% confidence interval for π6= the population proportion of doctoral degrees.
3. Given the breakdown of responses for variable 7 (marital status of respondent), determine the point estimate, and then construct the 95% confidence interval for π7 = the population proportion in the “single or other” category.
4. Assume the governmental agencies requested estimates of the mean attitudes towards each borough with a margin of error of 0.05 for each borough. If the governmental agency personnel want to have 95% confidence that the sample mean will fall within this margin of error, how large should the sample sizes be for each borough?
Paper Requirements
· Write a report that uses the Written Assignment Requirements under the heading Expectations for APA format.
· Items that should be included, at a minimum, are a title page, an introduction, a body that answers the questions posed in the problem, and a conclusion paragraph that add ...
Welcome to TechSoup New Member Orientation and Q&A (May 2024).pdfTechSoup
In this webinar you will learn how your organization can access TechSoup's wide variety of product discount and donation programs. From hardware to software, we'll give you a tour of the tools available to help your nonprofit with productivity, collaboration, financial management, donor tracking, security, and more.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
Francesca Gottschalk - How can education support child empowerment.pptxEduSkills OECD
Francesca Gottschalk from the OECD’s Centre for Educational Research and Innovation presents at the Ask an Expert Webinar: How can education support child empowerment?
A Strategic Approach: GenAI in EducationPeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
Embracing GenAI - A Strategic ImperativePeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
Acetabularia Information For Class 9 .docxvaibhavrinwa19
Acetabularia acetabulum is a single-celled green alga that in its vegetative state is morphologically differentiated into a basal rhizoid and an axially elongated stalk, which bears whorls of branching hairs. The single diploid nucleus resides in the rhizoid.
1. 6th Grade Math Curriculum Map
6th Grade Math Curriculum Map
Introduction
This document contains all mandated 2010 Arizona Mathematical Standards for 6th grade mathematics. The standards have been organized into
units and clusters. The units represent the major domain under which the identified standards fall. The cluster represents the collection of similar
concepts within the larger domain. Within these units and clusters the performance objectives have been sequenced to represent a logical progression
of the content knowledge. It is expected that all teachers follow the sequence of units and clusters as described in the following document.
Organization
Approximate Time
Approximate times are based on a 60-minute instructional session for grades 6-8. All units and clusters must be taught prior to the 2013 AIMS
assessment.
Essential Questions
Essential Questions are to be posed to the students at the beginning of the cluster and revisited throughout the cluster. They are designed to facilitate
conceptual development of the content and can be used as a tool for making connections, higher order thinking and inquiry. The students should be
able to answer these on their own by the end of the cluster.
Big Ideas
Big Ideas are the essential understandings that are critical for students’ learning. These are the enduring understandings we want students to carry
with them from grade level to grade level. Answering the Essential Questions is indicative of a student mastering the Big Idea, however they are not
always synonymous. Thus, in cases that the answer to the Essential Question does not include all components of the Big Idea, the Big Idea (for teacher
use) has been provided in italics.
Common Misconceptions
These are common misunderstandings students bring to the learning process. Being aware of such misconceptions allows us to plan for them during
instruction.
Content Standards and Mathematical Practices
This document has been organized by content standards and mathematical practices. The content standards are those that represent knowledge
specific to the mathematical standard (The five domains). The mathematical practices 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 content standards and mathematical standards have been paired to represent possible combinations of content standards
with mathematical practices. As described in the Arizona state standards, the content standards are not intended to be taught in isolation; thus, the
pairing of these standards provides a possible context for teaching these standards. Each time, the performance objective should be taught to a
deeper level of understanding and/or should be connected to the other standards in the cluster.
9/10/2012 1 Isaac Elementary School District
2. 6th Grade Math Curriculum Map
Common Core/Cross Curricular
The standards in the Common Core/Cross Curricular column represent possible reading, writing, math and language standards that can be reinforced
or taught through the mathematical content standards with which they are paired.
Priority
With input from grade level teachers, standards have been prioritized in two ways. The content standards have been prioritized using a three-point
scale. Essential standards represent those that are heavily weighted on state/national exams, foundational, and/or applicable in multiple contexts.
Important standards are those that are applicable in many contexts and less heavily weighted on state/national exams. Useful standards are those
with the least weight on state/national exams and are likely only useful in a specific context. This is denoted in the priority column with the codes E
(essential), I (important) and U (useful). This label applies to the content standards only. The skill/process standards that are a priority for this
grade level are highlighted in blue and are expected to be mastered at this grade level.
Key Vocabulary
The key vocabulary that should be taught for each of the performance objectives is listed under key vocabulary. These vocabulary words are coded
as tier one (1), tier two (2) or tier three (3). Tier one words are those that are very common and should not be explicitly taught. Tier two words are
high utility words that can be used across content areas or contexts. Tier three words are content specific words.
Resources
The two types of resources listed are the Web Resources resources and the Core Resources. All are suggestions that teachers may use to support
instruction. They are aligned to the standards listed in the same row. The web resources are useful Internet links that can be used for the teacher’s
edification prior to instruction or as a tool during instruction. The core resources are suggested pages from the adopted texts.
Unit/Cluster Project
The Unit/Cluster Projects are possible projects that teachers can use to support students in making connections, critical thinking, higher order thinking,
and/or spiraling curriculum. Unit projects support standards from all clusters within a unit while cluster project support the standards in a particular
cluster. While it is not required that a teacher do a project with every unit or cluster these resources will support project-based instruction and
practice should the teacher choose to implement them.
Assessment
The assessment section of the map has been left blank for teachers to plan the dates that they will give a formative assessment for the cluster. It is
expected that each cluster be assessed using a common formative assessment.
Other
Standards may appear more than once. Each time they should be taught within the context of the cluster and/or revisited to a deeper level of
knowledge. Underlined segments of a standard indicate an additional piece of the standard that was likely not covered in previous clusters.
[Brackets] will occasionally appear though out the document and indicate clarification of the standard. Bracketed information is not a part of the
standard itself.
9/10/2012 2 Isaac Elementary School District
3. 6th Grade Math Curriculum Map
Unit: Ratios and Proportional Relationships
Cluster: Ratios and Rates
Approximate Time: 1 week
Essential Questions Big Ideas
How are parts of a number represented? The same number can be written as a rate and a
How are ratios and rates related? ratio.
Why is it important to know the equivalent form of numbers?
Priority Standard Mathematical Common Core/Cross Key Vocabulary Resources
Practices Curricular Web Resources Core
6.RP.1. Understand the concept of 6.MP.2 6-8.RST.4 Ratio Comparing Ratios and MC: 6-1
a ratio and use ratio language to 6.MP.6 6-8.WHST.2d Rate Rates Worksheet
describe a ratio relationship Unit rate
between two quantities. Equivalent Ratios
Worksheet
Introduction
6.RP.2. Understand the concept of 6.MP.2 6-8.RST.4 Ratio Example Problems for MC: 6-1
a unit rate a/b associated with a 6.MP.6 Rate Solving Unit Rates
ratio a:b with b 0, and use rate Unite rate
language in the context of a ratio Ratio and Rate Venn
relationship. Diagram
6.RP.3. Use ratio and rate 6.MP.1 6.EE.9 Double number line Types of Ratios MC: 6-2
reasoning to solve real-world and 6.MP.2 6-8.RST.7 Diagrams
mathematical problems, e.g., by 6.MP.4 ET06-S6C2-03 Equations
reasoning about tables of 6.MP.5 SC06-S2C2-03 Equivalent ratios
equivalent ratios, tape diagrams, 6.MP.7 Rate
double number line diagrams, or Ratio
equations. Tape diagrams
Unit
Project:
Assessment:
9/10/2012 3 Isaac Elementary School District
4. 6th Grade Math Curriculum Map
Unit: The Number System
Cluster: Fractions, Decimals, and Percents
Approximate Time: 5 weeks
Essential Questions Big Ideas
How are parts of a number represented? The same number can be written as a fraction,
How are fractions, decimals, and percents related? decimal, and percent.
Why is it important to know equivalent forms of numbers?
Why is it important to know the percent of a number? How a number is represented depends on the given
What are the strategies we use to multiply and divide fractions? situation and/or need.
9/10/2012 4 Isaac Elementary School District
5. 6th Grade Math Curriculum Map
Priority Standard Mathematical Common Core/Cross Key Vocabulary Resources
Practices Curricular Web Resources Core
6.NS.1. Interpret and compute 6.MP.1 6-8.RST.7 Compute Dividing Fractions MC: 5-7, 5-8, 5-9,
quotients of fractions, and solve 6.MP.2 Equations Student Copy 5-10
word problems involving division 6.MP.3 Fractions
of fractions by fractions, e.g., by 6.MP.4 Improper fraction Dividing Fractions CM: Bits & Pieces II
using visual fraction models and 6.MP.7 Product Teacher Copy Investigation 3 & 4
equations to represent the 6.MP.8 Interpret
problem. Mixed number Fractions in Division
Quotient Word Problems
Reciprocal
Simplest form Math Is Fun-Dividing
Fractions
6.NS.4. Find the greatest common 6.MP.7 6-8.RST.4 Composite numbers LCM and GCF MC: 1-2, 4-1, 4-5
factor of two whole numbers less Multiple
than or equal to 100 and the Distributive property Prime factorization CM: Prime Time
least common multiple of two Factor Investigation 1, 3-5
whole numbers less than or equal GCF Factor Game
to 12. Use the distributive LCM
property to express a sum of two Prime factorization
whole numbers 1–100 with a Prime numbers
common factor as a multiple of a Sum
sum of two whole numbers with no Whole number
common factor.
6.NS.9. Convert between 6.MP.2 Annex Changing fractions, MC: 4-7, 4-8, 7-1,
expressions for positive rational 6.MP.8 Convert percents, and decimals 7-3
numbers, including fractions, Decimal
decimals, and percents Equivalent PowerPoints
Fraction CM: Bits & Pieces 1
Percent Converting Game 3.4, 4.4
Rational number
Introduction
*S1C1PO 4. Compare and order Ascending order MC: 3-2, 4-6
integers; and positive fractions, Compare
decimals, and percents. Descending order CM: Bits & Pieces 1
Fractions 3.5, Investigation 2
Integers
Least common
denominator
Percents
Unit
Project:
Assessment:
9/10/2012 5 Isaac Elementary School District
6. 6th Grade Math Curriculum Map
Unit: The Number System
Cluster: Decimal Operations
Approximate Time: 2 weeks
Essential Questions Big Ideas
What are the strategies we use to add, subtract, multiply, and divide Decimal placement affects the value of the solution.
decimals?
Priority Standard Mathematical Common Core/Cross Key Vocabulary Resources
Practices Curricular Web Resources Core
6.NS.2. Fluently divide multi-digit 6.MP.2 6-8.RST.3 Algorithm Math Live MC: 5th Grade: 4-4
numbers using the standard 6.MP.7 Dividend
algorithm. 6.MP.8 Divisor
Quotient
6.NS.3. Fluently add, subtract, 6.MP.2 6-8.RST.3 Addend Math Live MC: 3-4, 3-5, 3-6,
multiply, and divide multi-digit 6.MP.7 Algorithm 3-7, 3-8, 3-9
decimals using the standard 6.MP.8 Difference Fluency with Decimals
algorithm for each operation. Dividend CM: Bits & Pieces III
Divisor 1.2, 2.3, 3.3
Factor
Minuend
Product
Quotient
Subtrahend
Sum
Unit
Project:
Assessment:
9/10/2012 6 Isaac Elementary School District
7. 6th Grade Math Curriculum Map
Unit: The Number System
Cluster: Absolute Value and Integers
Approximate Time: 2 weeks
Essential Questions Big Ideas
What is absolute value? Integers are used in a wide array of contexts.
How do you order integers?
How do you model integers?
9/10/2012 7 Isaac Elementary School District
8. 6th Grade Math Curriculum Map
Priority Standard Mathematical Common Core/Cross Key Vocabulary Resources
Practices Curricular Web Resources Core
6.NS.5. Understand that positive 6.MP.1 6-8.RST.4 Integers Introduction MC: 2-9
and negative numbers are used 6.MP.2 6-8.WHST.2d MC: 7th Grade: 2-1
together to describe quantities 6.MP.4
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.
6.NS.6. Understand a rational 6.MP.2 6-8.RST.7 Coordinate axes Whole Numbers and MC: 2-9
number as a point on the number 6.MP.4 SS06-S1C1-03 Line diagrams Integers MC: 7th Grade: 2-1
line. Extend number line diagrams Rational numbers
and coordinate axes familiar from
previous grades to represent
points on the line and in the plane
with negative number coordinates.
6.NS.7. Understand ordering and 6.MP.1 6-8.WHST.1c Absolute value Absolute Value War MC: 11-1
absolute value of rational 6.MP.2 6-8.WHST.2a Ascending order LA: 2-4
numbers. 6.MP.4 Descending order Absolute Value
6. Greater than Worksheet
7. a. Interpret statements of Inequality
inequality as statements about the Integers Khan Academy
relative position of two numbers on Less than
a number line diagram. For Line diagram AAAMath
example, interpret –3 > –7 as a Rational numbers
statement that –3 is located to the Number Balls
right of –7 on a number line
oriented from left to right. Coolmath
b. Write, interpret, and explain Eduplace
statements of order for rational
numbers in real-world contexts.
For example, write –3 oC > –7 oC
to express the fact that –3 oC is
warmer than –7 oC.
c. Understand the absolute value
of a rational number as its
distance from 0 on the number
line; interpret absolute value as
9/10/2012 8 Isaac Elementary School District
9. 6th Grade Math Curriculum Map
Priority Standard Mathematical Common Core/Cross Key Vocabulary Resources
Practices Curricular Web Resources Core
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.
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.
*S1C2PO1. Apply and interpret the Integers Addition MC: 11-2, 11-3
concepts of addition and subtraction Zero pairs
with integers using models. Subtraction
Gizmo with Number
Lines
Gizmo with Chips
Unit
Project:
Assessment:
9/10/2012 9 Isaac Elementary School District
10. 6th Grade Math Curriculum Map
Unit: Expressions and Equations
Cluster: Expressions and Order of Operations
Approximate Time: 2 weeks
Essential Questions Big Ideas
What is an algorithm? Algorithms are useful strategies for computing.
What argument can you provide to explain your solution? The order of operations will affect solutions.
9/10/2012 10 Isaac Elementary School District
11. 6th Grade Math Curriculum Map
Priority Standard Mathematical Common Core/Cross Key Vocabulary Resources
Practices Curricular Web Resources Core
6.EE.1. Write and evaluate numerical expressions 6.MP.2 6-8.RST.4 Base Order of MC: 1-3,
involving whole-number exponents. Exponents Operations 1-4
Order of operations
Parentheses Order of
Powers Operations
Whole number Examples
Evaluate
Expressions
Order of
Operations
Lessons/Practice
6.EE.2. Write, read, and evaluate expressions in 6.MP.1 6-8.RST.4 Coefficient Translate to MC: 1-5
which letters stand for numbers. 6.MP.2 6-8.WHST.2d Exponent Algabraic
6.MP.3 Expressions Expressions
a. Write expressions that record operations with 6.MP.4 Factor
numbers and with letters standing for numbers. 6.MP.6 Order of operations
For example, express the calculation “Subtract y Parenthesis Gizmos to
from 5” as 5 – y. Product Translate
Quotient Algebraicl
b. Identify parts of an expression using Substitution Expressions
mathematical terms (sum, term, product, factor, Sum
quotient, coefficient); view one or more parts of Term
an expression as a single entity. For example, Variable Worksheet
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 Translate to
Algebraic
c. Evaluate expressions at specific values of their Equations
variables. Include expressions that arise from
formulas used in real-world problems. Perform
arithmetic operations, including those involving Substitution
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=6 s2 to
find the volume and surface area of a cube with
sides of length s=1/2.
*S1C1PO 6. Express the inverse relationships Cube root Perfect Squares MC: 7th
between exponents and roots for perfect squares Cubed Grade: 1-
and cubes. Exponents 3
Inverse
Perfect Cubes
9/10/2012 11 Isaac Elementary School District
12. 6th Grade Math Curriculum Map
Priority Standard Mathematical Common Core/Cross Key Vocabulary Resources
Practices Curricular Web Resources Core
Perfect Squares
Radical sign
Square root
Squared
Unit
Project:
Assessment:
9/10/2012 12 Isaac Elementary School District
13. 6th Grade Math Curriculum Map
Unit: Expressions and Equations
Cluster: Properties
Approximate Time: 1 week
Essential Questions Big Ideas
What are the math properties and why do we use them? Distributive Property
a(b + c) = a(b) + a(c)
a(b) + a(c) = a(b + c)
Commutative Property
a+b=b+a
a*b=b*a
Associative Property
a + (b + c) = (a + b) + c
a * (b * c) = (a * b) * c
Identity Property
a+0=a
a*1=a
9/10/2012 13 Isaac Elementary School District
14. 6th Grade Math Curriculum Map
Priority Standard Mathematical Common Core/Cross Key Vocabulary Resources
Practices Curricular Web Resources Core
6.EE.3. Apply the properties of 6.MP.2 6-8.RST.4 Associative property Basic Number MC: 12-1, 12-2
operations to generate equivalent 6.MP.3 Identity property Properties
expressions. 6.MP.4 Distributive property MC: 7th Grade: 1-
6.MP.6 Commutative More Basic Number 8
6.MP.7 property Properties
Equivalent
expressions Distributive Property
6.EE.4. Identify when two 6.MP.2 6-8.RST.5 Combine like terms Combining Like Terms MC: 12-2
expressions are equivalent 6.MP.3 Equivalent
6.MP.4 expressions Combining Like Terms
6.MP.6 Game
6.MP.7
Equivalent Expressions
Worksheet
Unit
Project:
Assessment:
9/10/2012 14 Isaac Elementary School District
15. 6th Grade Math Curriculum Map
Unit: Expressions and Equations
Cluster: Solving Equations
Approximate Time: 3 weeks
Essential Questions Big Ideas
What does a variable represent? Variables represent numbers.
How do you solve/interpret equations? Algebra is used to solve real world situations.
What are the multiple ways you can represent the process and solution? Estimates can be used to verify the reasonableness of
a result.
9/10/2012 15 Isaac Elementary School District
16. 6th Grade Math Curriculum Map
Priority Standard Mathematical Common Core/Cross Key Vocabulary Resources
Practices Curricular Web Resources Core
6.EE.5. Understand solving an 6.MP.1 6-8.RST.7 Equation MC: 12-3, 12-4,
equation or inequality as a 6.MP.2 Inequality 12-5
process of answering a question: 6.MP.4 Inverse operations
which values from a specified set, 6.MP.7 Inverse properties MC: 7th Grade: 5-
if any, make the equation or Substitution 6
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 6.MP.2 6-8.RST.4 Expression Expressions and MC: 12-3, 12-4,
numbers and write expressions 6.MP.4 Variable 12-5
when solving a real-world or 6.MP.7 Equations
mathematical problem; MC: 7th Grade: 3-
understand that a variable can Writing Expressions 1, 5-6
represent an unknown number, or,
depending on the purpose at
hand, any number in a specified
set.
6.EE.7. Solve real-world and 6.MP.1 6-8.RST.7 Equation One-step Equations MC: 12-3, 12-4,
mathematical problems by writing 6.MP.2 Rational numbers 12-5
and solving equations of the form x 6.MP.3 Equation Game
+ p = q and px = q for cases in 6.MP.4 MC: 7th Grade: 3-
which p, q and x are all nonnegative 6.MP.7 Solving One-step 1, 5-6
rational numbers
Equation Video
*S3C3PO 2. Create and solve two- Coefficient Two-step Equations MC: 7th Grade: 3-
step equations that can be solved Equation 5
using inverse properties with Inverse properties Equation Game
fractions and decimals. Term
Two-step equations Multi-step equation
Variable
Video
Unit
Project:
Assessment:
9/10/2012 16 Isaac Elementary School District
17. 6th Grade Math Curriculum Map
Unit: Expressions and Equations
Cluster: Inequalities
Approximate Time: 2 weeks
Essential Questions Big Ideas
What is an inequality? When ≤ or ≥ are used, the circle on the graph is filled
in to show that the number is included in the solution.
What symbol represents greater/less than and greater/less than or equal
to?
What symbol represents the phrase not equal to?
9/10/2012 17 Isaac Elementary School District
18. 6th Grade Math Curriculum Map
Priority Standard Mathematical Common Core/Cross Key Vocabulary Resources
Practices Curricular Web Resources Core
6.EE.8. Write an inequality of the 6.MP.1 6-8.RST.7 Inequality Solving Inequalities Video MC: 7th Grade:
form x > c or x < c to represent 6.MP.2 Infinite pg. 740
a constraint or condition in a 6.MP.3 Number line Solving Linear Inequalities:
real-world or mathematical 6.MP.4 diagrams Addition/Subtraction MC: 8th Grade: 8-
problem. Recognize that 6.MP.7 Solution 6, 8-7, 8-8
inequalities of the form x > c or Online Quiz: Solving
x < c have infinitely many Linear Inequalities:
solutions; represent solutions of Addition/Subtraction
such inequalities on number line
diagrams. Solving Linear Inequalities:
Multiplication/Division
Online Quiz: Solving
Linear Inequalities:
Multiplication/Division
Real Life Problems
Worksheet
Graphing Inequalities
Foldable-Student Copy
Solving Inequalities
Foldable-Teacher Copy
6.EE.9. Use variables to 6.MP.1 6.RP.3 Dependent variable Graphing From Function MC: 1-6, 6-6
represent two quantities in a 6.MP.2 6-8. RST.7 Equation Tables
real-world problem that change 6.MP.3 ET06-S1C2-01 Function
in relationship to one another; 6.MP.4 ET06-S1C2-02 Input (x) Function Machine
write an equation to express one 6.MP.7 ET06-S1C2-03 Output (y)
quantity, thought of as the 6.MP.8 ET06-S6C2-03 In/out table Stop That Creature
dependent variable, in terms of SC06-S2C2-03 Independent variable
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.
Unit
Project:
Assessment:
9/10/2012 18 Isaac Elementary School District
19. 6th Grade Math Curriculum Map
Unit: Geometry
Cluster: Coordinate Plane
Approximate Time: 2 weeks
Essential Questions Big Ideas
How do you use a coordinate plane? Ordered pairs show an exact location on a coordinate
plane.
How do you find a missing coordinate?
What are the features of a coordinate plane?
How do values on a coordinate plane relate to integers?
9/10/2012 19 Isaac Elementary School District
20. 6th Grade Math Curriculum Map
Priority Standard Mathematical Common Core/Cross Key Vocabulary Resources
Practices Curricular Web Resources Core
6.NS.8. Solve real-world and 6.MP.1 6.G.3 Coordinate plane The Math Worksheet MC: 4-9, 11-7
mathematical problems by 6.MP.2 6-8.RST.7 Ordered pairs Site
graphing points in all four 6.MP.4 Quadrant
quadrants of the coordinate 6.MP.5 Origin Coordinate Plane
plane. Include use of coordinates 6.MP.7 X-axis
and absolute value to find Y-axis Coordinate Plane
distances between points with the Game
same first coordinate or the same
second coordinate. Khan Academy
Coordinate Plane
Template
Distance Between Points
Worksheet
6.G.3. Draw polygons in the 6.MP.1 6.NS.8 Coordinate plane Galileo
coordinate plane given 6.MP.2 6-8.RST.7 Ordered pair Study Island
coordinates for the vertices; use 6.MP.4 Origin
coordinates to find the length of a 6.MP.5 Polygon
side joining points with the same 6.MP.7 Parallelogram
first coordinate or the same Quadrilateral
second coordinate. Apply these Vertex (vertices)
techniques in the context of
solving real-world and
mathematical problems.
*S4C2PO1. Identify a simple Coordinate plane Introduction MC: 11-8
translation or reflection and model Origin
its effect on a 2-dimensional figure Quadrants
on a coordinate plane using all four Reflection
quadrants. Translation
X-axis
Y-axis
*S4C2PO2. Draw a reflection of a Coordinate plane MC: 11-9
polygon in the coordinate plane Horizontal line
using a horizontal or vertical line of Origin
reflection. Reflection
X-axis
Y-axis
Unit
Project:
Assessment:
9/10/2012 20 Isaac Elementary School District
21. 6th Grade Math Curriculum Map
Unit: Geometry
Cluster: Area, Volume, and Surface Area
Approximate Time: 4 weeks
Essential Questions Big Ideas
What real world use is there for knowing area, volume, and surface area? Measures of length are expressed in linear units,
measures of area are expressed in square units, and
measures of volume are expressed in cubic units.
9/10/2012 21 Isaac Elementary School District
22. 6th Grade Math Curriculum Map
Priority Standard Mathematical Common Core/Cross Key Vocabulary Resources
Practices Curricular Web Resources Core
6.G.1. Find the area of right 6.MP.1 6-8.RST.7 Area Decomposing Polygons MC: 1-9, 10-4
triangles, other triangles, special 6.MP.2 6-8.WHST.2b,d Length to find Area
quadrilaterals, and polygons by 6.MP.3 ET06-S1C2-02 Polygons MC: 7th Grade: 3-
composing into rectangles or 6.MP.4 Quadrilaterals 6, 11-2, 11-6
decomposing into triangles and other 6.MP.5 Right triangles
shapes; apply these techniques in the 6.MP.6 Width CM: Covering and
context of solving real-world and 6.MP.7 Surrounding
mathematical problems. 6.MP.8
6.G.2. Find the volume of a right 6.MP.1 6-8.RST.4 Area of the base MC: 10-6
rectangular prism with fractional 6.MP.2 ET06-S1C2-02 Edge
edge lengths by packing it with unit 6.MP.3 Face
cubes of the appropriate unit 6.MP.4 Height
fraction edge lengths, and show 6.MP.5 Rectangular prism
that the volume is the same as 6.MP.6 Vertex
would be found by multiplying the 6.MP.7 Volume
edge lengths of the prism. Apply 6.MP.8
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.
6.G.4. Represent three-dimensional 6.MP.1 6-8.RST.7 Edge Surface Area and Nets MC: 10-7, LA20
figures using nets made up of 6.MP.2 6-8.WHST.2b Face Foldable
rectangles and triangles, and use the 6.MP.3 ET06-S1C2-02 Nets MC: 7th Grade: 12-
nets to find the surface area of these 6.MP.4 ET06-S1C2-03 Surface area Surface Area and Nets 4
figures. Apply these techniques in the 6.MP.5 Three-dimensional Foldable-Teacher Copy
context of solving real-world and 6.MP.6 Vertex
mathematical problems. 6.MP.7 Surface Area and Nets
6.MP.8 Cut Outs
PowerPoint
*S4C4PO 5. Solve problems Area MC: 10-1
involving area and perimeter of Irregular polygon
regular and irregular polygons Perimeter CM: Covering and
Regular polygon Surrounding
*S4C1PO1. Define (pi) as the Circle MC: 10-2
ratio between the circumference and Circumference
diameter of a circle and explain the Diameter CM: Covering and
relationship among the diameter, Pi Surrounding
radius, and circumference. Radius
9/10/2012 22 Isaac Elementary School District
23. 6th Grade Math Curriculum Map
Priority Standard Mathematical Common Core/Cross Key Vocabulary Resources
Practices Curricular Web Resources Core
*S4C1PO 2. Solve problems using Complementary MC: LA 10
properties of supplementary, angles
complementary, and vertical angles. Supplementary MC: 7th Grade:
angles 10-1, 10-2
Vertical angles
Unit
Project:
Assessment:
9/10/2012 23 Isaac Elementary School District
24. 6th Grade Math Curriculum Map
Unit: Statistics and Probability
Cluster: Graphing and Measures of Central Tendency
Approximate Time: 4 weeks
Essential Questions Big Ideas
How can you collect, organize, and display data? Charts, tables, and graphs help us make valid
inferences, decisions, and arguments.
How does the type of data influence the choice of graph?
Appropriate graphs need to be used in specific
How do you use modes of central tendency? situations.
How do we determine which information is relevant or missing?
9/10/2012 24 Isaac Elementary School District
25. 6th Grade Math Curriculum Map
Priority Standard Mathematical Common Core/Cross Key Resources
Practices Curricular Vocabulary Web Resources Core
6.SP.1. Recognize a statistical question as one 6.MP.1 Galileo
that anticipates variability in the data related to 6.MP.3
the question and accounts for it in the answers. 6.MP.6 Study Island
6.SP.2. Understand that a set of data collected to 6.MP.2 6-8.RST.4 Maximum Teacher Tube MC: 2-6, 2-7
answer a statistical question has a distribution 6.MP.4 Mean Lesson
that can be described by its center, spread, and 6.MP.5 Median MC: 7th Grade:
overall shape. 6.MP.6 Minimum Jeopardy Game 8-1, 8-2
6.MP.7 Mode
Outliers CM: Data About
Range Us
6.SP.3. Recognize that a measure of center for a 6.MP.2 6-8.RST.4 Absolute Galileo
numerical data set summarizes all of its values with 6.MP.4 deviation
a single number, while a measure of variation 6.MP.5 Standard Study Island
describes how its values vary with a single number. 6.MP.6 deviation
6.MP.7
6.SP.4. Display numerical data in plots on a 6.MP.2 6-8.RST.7 Box and whiskers Box Plots MC: 2-5, LA25
number line, including dot plots, histograms, and 6.MP.4 ET06-S6C2-03 Dot plot
box plots. 6.MP.5 SC06-S1C4-01 Histogram Histograms MC: 8th Grade:
6.MP.6 SC06-S1C4-02 Interquartile 8-1, 8-4
6.MP.7 SS06-S1C1-02 Line plot Box Plots
SS06-S1C2-02 Lower quartile Foldable-Student MC: 8th Grade:
SS06-S1C4-01 Maximum Copy 11-6
Minimum Box Plots
Stem and leaf Foldable-Teacher CM:
plot Copy Data About Us
Upper quartile Investigation 2
6.SP.5. Summarize numerical data sets in relation 6.MP.2 6-8.WHST.2a-f Absolute Grab a Handful
to their context, 6.MP.3 ET06-S6C2-03 deviation Box Plot Activity
a. Reporting the number of observations. 6.MP.4 Box and whiskers
6.MP.5 Dot plot Minute to Win It
b. Describing the nature of the attribute under 6.MP.6 Histogram Box Plots
investigation, including how it was measured and 6.MP.7 Interquartile Recording Sheet
its units of measurement Line plot
Lower quartile Minute to Win It
c. Giving quantitative measures of center (median Maximum Games
and/or mean) and variability (interquartile range Mean
and/or mean absolute deviation), as well as Median Box and Whiskers
describing any overall pattern and any striking Minimum Task Analysis
deviations from the overall pattern with reference Mode
to the context in which the data were gathered. Outliers
d. Relating the choice of measures of center and Range
9/10/2012 25 Isaac Elementary School District
26. 6th Grade Math Curriculum Map
Priority Standard Mathematical Common Core/Cross Key Resources
Practices Curricular Vocabulary Web Resources Core
variability to the shape of the data distribution Standard
and the context in which the data were gathered. deviation
Stem and leaf
plot
Upper quartile
*S2C1P2. Formulate and answer questions by Histograms Histograms MC: 2-4
interpreting, analyzing, and drawing inferences Stem-and-leaf Stem-and-Leaf Plot
from displays of data, including histograms and plots
stem-and-leaf plots.
Unit
Project:
Assessment:
9/10/2012 26 Isaac Elementary School District
27. 6th Grade Math Curriculum Map
Unit: Probability
Cluster: Theoritical and Experimental Probability
Approximate Time: 1 week
Essential Questions Big Ideas
How are theoretical probability and experimental probability different? Probability is a form of estimation.
What is a sample space and how is it used? Using a systematic approach can confirm solutions.
What is a conjecture?
Why do we replicate an experiment?
What are the multiple ways you can represent a sample space?
9/10/2012 27 Isaac Elementary School District
28. 6th Grade Math Curriculum Map
Priority Standard Mathematical Common Core/Cross Key Vocabulary Resources
Practices Curricular Web Resources Core
*S2C2PO1. Use data collected Certain Expressing MC: 7-4
from multiple trials of a single event Experimental probability Likelihood
to form a conjecture about the Conjecture CM: How likely is
theoretical probability. Favorable outcomes it?
Possible outcomes
Impossible
Probability
Random
Theoretical probability
Tree diagram
*S2C2PO 2. Use theoretical Certain Theoretical MC: 7-4
probability to Experimental Probability
predict experimental Conjecture CM: How likely is
outcomes, Favorable outcomes it?
compare the outcome of the Possible outcomes
experiment to the Impossible
prediction, and Probability
replicate the experiment and Random
compare results Theoretical
Tree diagram
*S2C2PO3. Determine all possible Possible outcomes Sample Space MC: 7-5
outcomes (sample space) of a given Probability
situation using a systematic Sample space CM: How likely is
approach. Tree diagram it?
*S2C3PO 1. Build and explore tree Certain MC: 7-5
diagrams where items repeat. Conjecture
Favorable outcomes CM: How likely is
Possible outcomes it?
Impossible
Probability
Random
Repeat
Sample space
Tree diagram
Unit
Project:
Assessment:
9/10/2012 28 Isaac Elementary School District
29. 6th Grade Math Curriculum Map
Unit: Measurement
Cluster: U.S. Customary and Metric System
Approximate Time: 2 weeks
Essential Questions Big Ideas
What are the units in the U.S. customary system? There are appropriate units of measure for different
situations.
What are the units in the metric system?
How do you convert between units?
9/10/2012 29 Isaac Elementary School District
30. 6th Grade Math Curriculum Map
Priority Standard Mathematical Common Core/Cross Key Vocabulary Resources
Practices Curricular Web Resources Core
*S4C4PO 1. Determine the Clock CM: Chapter 8
appropriate unit of measure for a Protractor
given context and the appropriate Ruler
tool to measure to the needed Scale
precision (including length, capacity,
angles, time, and mass).
*S4C4PO 2. Solve problems Capacity CM: Chapter 8
involving conversion within the U.S. Centi
Customary and within the metric Cup
system Customary
Feet
Fluid ounce
Gallon
Gram
Inch
Kilo
Length
Liter
Mass
Meter
Metric
Mile
Milli
Ounce
Pint
Pound
Quart
Ton
Weight
Yard
*S4C4PO 3. Estimate the measure Scale CM: 7th Grade: 6-8
of objects using a scale drawing or Scale drawing
map. Scale factor
Scale model
Unit
Project:
Assessment:
9/10/2012 30 Isaac Elementary School District