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West Deptford Middle School 6th Grade Advanced Math Curriculum Unit 2: Integers and Rational Numbers
West Deptford Middle School
675 Grove Rd, Paulsboro, NJ 08066 wdeptford.k12.nj.us
(856) 848-1200
* All Enduring Understandings and Essential Questions for each standards are suggested samples and can be modified or removed at the discretion of the teacher(s).
**Assessments and Resources could be altered or added at the discretion of the teacher(s). All assessments and resources used will cover the standards.
***CRP stands for Career Ready Practices.
West Deptford Township Schools
Course of Study/Curriculum Guide
Curricular Area: Mathematics Course Title: Integers and Rational Numbers Grade Level: 6 Written by: Kelley Mason and Tom Shown Reviewed by: Laura Sandy Approved by: Shawnequa Carvalho Board of Education Approval: September 2017
* All Enduring Understandings and Essential Questions for each standards are suggested samples and can be modified or removed at the discretion of the teacher(s).
**Assessments and Resources could be altered or added at the discretion of the teacher(s). All assessments and resources used will cover the standards.
***CRP stands for Career Ready Practices.
Unit 2- Integers and Rational Numbers Timeline: 5 weeks
Standards Math
Practices (MP)
Focus Math Concepts Critical Knowledge and Skills
Prerequisite Skills Common Misunderstanding
6.NS.C.5
Understand that positive and negative numbers are used together to describe quantities having opposite directions or values; use positive and negative numbers and quantities in real-world contexts, explaining the meaning of 0 n each situation.
MP.2 MP.7 MP.8
Understand positive integers.
Students do not always make the connection between the negative sign and the meaning “opposite”.
Enduring Understanding:
❏ use positive and negative numbers. Essential Questions:
❏ How do I identify opposites of integers? ❏ How do I use integers to represent real-world quantities and
explain the meaning of 0 in each context?
CRP
***
CRP1 CRP3 CRP4 CRP6
* All Enduring Understandings and Essential Questions for each standards are suggested samples and can be modified or removed at the discretion of the teacher(s).
**Assessments and Resources could be altered or added at the discretion of the teacher(s). All assessments and resources used will cover the standards.
***CRP stands for Career Ready Practices.
Unit 2- Integers and Rational Numbers Timeline: 5 weeks
Standards Math
Practices (MP)
Focus Math Concepts Critical Knowledge and Skills
Prerequisite Skills Common Misunderstanding
6.NS.C.6a
Recognize opposite signs of numbers as indicating 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 ) is its own opposite.
MP.2 MP.7 MP.8
Students should have a solid understanding of placing positive rational numbers on a number line.
Students will often place -1.5 between 0 and -1. They struggle with the more negative rational number being further to the left.
Enduring Understanding:
❏ represent rational numbers using a number line.
Essential Questions:
❏ How do I use integers to represent real-world quantities and explain the meaning of 0 in each context?
❏ How do I plot rational numbers on a number line? ❏ How do I compare and order integers? ❏ How do I compare and order rational numbers?
CRP
CRP1 CRP3 CRP4 CRP6
* All Enduring Understandings and Essential Questions for each standards are suggested samples and can be modified or removed at the discretion of the teacher(s).
**Assessments and Resources could be altered or added at the discretion of the teacher(s). All assessments and resources used will cover the standards.
***CRP stands for Career Ready Practices.
* All Enduring Understandings and Essential Questions for each standards are suggested samples and can be modified or removed at the discretion of the teacher(s).
**Assessments and Resources could be altered or added at the discretion of the teacher(s). All assessments and resources used will cover the standards.
***CRP stands for Career Ready Practices.
Unit 2- Integers and Rational Numbers Timeline: 5 weeks
Standards Math Practices
(MP)
Focus Math Concepts Critical Knowledge and Skills
Prerequisite Skills Common Misunderstanding
6.NS.C.6b
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.
MP.7 MP.8
Students should be able to fluently represent real-world and mathematical problems by graphing points in the first quadrant of the coordinate plane.
Students will often confuse the x- and y- coordinates, erroneously graphing them in the first quadrant.
Enduring Understanding:
❏ graph points with rational coordinates on a coordinate plane. Essential Questions:
❏ How do I identify and graph points with rational coordinates on the coordinate plane?
❏ How do I reflect points with rational coordinates across both axes?
CRP
CRP1 CRP3 CRP4 CRP6
* All Enduring Understandings and Essential Questions for each standards are suggested samples and can be modified or removed at the discretion of the teacher(s).
**Assessments and Resources could be altered or added at the discretion of the teacher(s). All assessments and resources used will cover the standards.
***CRP stands for Career Ready Practices.
Unit 2- Integers and Rational Numbers Timeline: 5 weeks
Standards Math Practices
(MP)
Focus Math Concepts Critical Knowledge and Skills
Prerequisite Skills Common Misunderstanding
6.NS.C.6c
Find and position integers and other rational numbers on a horizontal or vertical number lines; find and position pairs of integers and other rational numbers on a coordinate plane.
MP.2 MP.7 MP.8
Students should have a solid understanding of placing positive rational numbers on a number line.
Students will often place -1.5 between 0 and -1. They struggle with the more negative rational number being further to the left.
Enduring Understanding:
❏ represent rational numbers using a number line.
Essential Questions:
❏ How do I use integers to represent real-world quantities and explain the meaning of 0 in each context?
❏ How do I plot rational numbers on a number line? ❏ How do I compare and order integers? ❏ How do I compare and order rational numbers?
CRP
CRP1 CRP3 CRP4 CRP6
* All Enduring Understandings and Essential Questions for each standards are suggested samples and can be modified or removed at the discretion of the teacher(s).
**Assessments and Resources could be altered or added at the discretion of the teacher(s). All assessments and resources used will cover the standards.
***CRP stands for Career Ready Practices.
Unit 2- Integers and Rational Numbers Timeline: 5 weeks
Standards Math
Practices (MP)
Focus Math Concepts Critical Knowledge and Skills
Prerequisite Skills Common Misunderstanding
6.NS.C.7a
Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram.
MP.2 MP.3 MP.7 MP.8
Students should be comfortable placing rational positive numbers and their opposites on the number line.
Students have difficulty differentiating between opposites and absolute value. Many will “switch the sign” for absolute value.
Enduring Understanding: ❏ find, order, and interpret rational numbers
Essential Question:
❏ How do I plot, order, and compare rational numbers? ❏ How do I use rational numbers to represent real-world situation?
CRP
CRP1 CRP3 CRP4 CRP6
* All Enduring Understandings and Essential Questions for each standards are suggested samples and can be modified or removed at the discretion of the teacher(s).
**Assessments and Resources could be altered or added at the discretion of the teacher(s). All assessments and resources used will cover the standards.
***CRP stands for Career Ready Practices.
Unit 2- Integers and Rational Numbers Timeline: 5 weeks
Standards Math
Practices (MP)
Focus Math Concepts Critical Knowledge and Skills
Prerequisite Skills Common Misunderstanding
6.NS.C.7b
Write, interpret, and explain statements of order for rational numbers in real-world contexts.
MP.2 MP.3 MP.7
Students should be comfortable placing rational positive numbers and their opposites on the number line.
Students will struggle with differentiating between translation of > or <. Students will have difficulty accurately placing negative decimals on the number line. Students will be confused that negative numbers closer to zero are greater.
Enduring Understanding:
❏ How do I make sense of rational numbers? Essential Question:
❏ How do I plot, order, and compare rational numbers?
CRP
CRP1 CRP3 CRP4 CRP6
* All Enduring Understandings and Essential Questions for each standards are suggested samples and can be modified or removed at the discretion of the teacher(s).
**Assessments and Resources could be altered or added at the discretion of the teacher(s). All assessments and resources used will cover the standards.
***CRP stands for Career Ready Practices.
Unit 2- Integers and Rational Numbers Timeline: 5 weeks
Standards Math
Practices (MP)
Focus Math Concepts Critical Knowledge and Skills
Prerequisite Skills Common Misunderstanding
6.NS.C.7c Understand 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.
MP.2 MP.3
Students should be comfortable placing rational positive numbers and their opposites on the number line.
Many will “switch the sign” for absolute value. Students will struggle with differentiating between translation of > or <.
Enduring Understanding: ❏ How do I make sense of rational numbers?
Essential Question:
❏ How do I plot, order, and compare rational numbers? ❏ How do I use absolute value to represent a number’s distance from
zero? ❏ How do I interpret absolute value in real-world situations?
CRP
CRP1 CRP3 CRP4 CRP6
* All Enduring Understandings and Essential Questions for each standards are suggested samples and can be modified or removed at the discretion of the teacher(s).
**Assessments and Resources could be altered or added at the discretion of the teacher(s). All assessments and resources used will cover the standards.
***CRP stands for Career Ready Practices.
Unit 2- Integers and Rational Numbers Timeline: 5 weeks
Standards Math
Practices (MP)
Focus Math Concepts Critical Knowledge and Skills
Prerequisite Skills Common Misunderstanding
6.NS.C.7d Distinguish comparisons of absolute value from statements about order.
MP.2 MP.3
Students should be comfortable placing rational positive numbers and their opposites on the number line.
Many will “switch the sign” for absolute value. Students will struggle with recognizing the farther a negative number is from 0, the greater the absolute value and the closer the number is from 0, the greater the value.
Enduring Understanding: ❏ make sense of absolute value as it relates to rational number?
Essential Question:
❏ use absolute value to represent a number’s distance from zero? ❏ interpret absolute value in real-world situations?
CRP
CRP1 CRP3 CRP4 CRP6
* All Enduring Understandings and Essential Questions for each standards are suggested samples and can be modified or removed at the discretion of the teacher(s).
**Assessments and Resources could be altered or added at the discretion of the teacher(s). All assessments and resources used will cover the standards.
***CRP stands for Career Ready Practices.
Unit 2- Integers and Rational Numbers Timeline: 5 weeks
Standards Math
Practices (MP)
Focus Math Concepts Critical Knowledge and Skills
Prerequisite Skills Common Misunderstanding
6.NS.C.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.
MP.2 MP.3 MP.7 MP.8
Students should be able to establish a scale on a number line and plot rational numbers.
Students can often confuse the x and y coordinates, associating x with vertical position and y with horizontal position. Students may think that they can find the distance between any two points by adding or subtracting the absolute values of the coordinates.
Enduring Understanding:
❏ use absolute value to find distance on a coordinate plane. ❏ find side lengths of a polygon on a coordinate plane.
Essential Question:
❏ use absolute value to find the distance between two points that lie on the same horizontal or vertical line on a coordinate plane?
❏ solve real-world and mathematical problems involving distances on the coordinate plane?
❏ find side lengths of polygons on the coordinate plane? ❏ find the perimeter of polygons on the coordinate plane?
CRP
CRP1 CRP3 CRP4 CRP6
* All Enduring Understandings and Essential Questions for each standards are suggested samples and can be modified or removed at the discretion of the teacher(s).
**Assessments and Resources could be altered or added at the discretion of the teacher(s). All assessments and resources used will cover the standards.
***CRP stands for Career Ready Practices.
Unit 2- Integers and Rational Numbers Timeline: 5 weeks
Standards Math
Practices (MP)
Focus Math Concepts Critical Knowledge and Skills
Prerequisite Skills Common Misunderstanding
6.G.A.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.
MP.2 MP.3 MP.8
Students should be able to find the distance between two points that share an x coordinate or y coordinate. Students should be able to plot points in the first quadrant.
Students will often assume the number of blocks is the same as the number of units for distance, ignoring the scale of the coordinate grid.
Enduring Understanding:
❏ Find side lengths of polygons on the coordinate plane. Essential Question:
❏ Find the side lengths and perimeter of polygons on the coordinate plane?
CRP
CRP3 CRP6 CRP11
* All Enduring Understandings and Essential Questions for each standards are suggested samples and can be modified or removed at the discretion of the teacher(s).
**Assessments and Resources could be altered or added at the discretion of the teacher(s). All assessments and resources used will cover the standards.
***CRP stands for Career Ready Practices.
Unit 2- Integers and Rational Numbers Timeline: 5 weeks
Standards Math Practices
(MP)
Focus Math Concepts Critical Knowledge and Skills
Prerequisite Skills Common Misunderstanding
7.NS.A.1a Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged.
MP1, MP2, MP3, MP4
Grade 6:
Understand that integers can describe quantities having opposite values or directions.
Used integers to represent real-world quantities.
Absolute value sign confused as a “1”
Connecting opposites to absolute value
Enduring Understanding:
❏ Understand how integers, their opposites and absolute values are related
❏ Apply this understanding to models (number lines) and use these to solve real-world problems.
Essential Question:
❏ How are integers and their opposites related? CRP
***
CRP2, CRP3, CRP4, CRP7, CRP8, CRP11
* All Enduring Understandings and Essential Questions for each standards are suggested samples and can be modified or removed at the discretion of the teacher(s).
**Assessments and Resources could be altered or added at the discretion of the teacher(s). All assessments and resources used will cover the standards.
***CRP stands for Career Ready Practices.
Unit 2- Integers and Rational Numbers Timeline: 5 weeks
Standards Math Practices
(MP)
Focus Math Concepts Critical Knowledge and Skills
Prerequisite Skills Common Misunderstanding
7.NS.A.2d Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.
MP1, MP2, MP6, MP7
Understand a rational number as a point on a number line.
Write, interpret, and explain statements of order for rational numbers in real-world situations.
Understanding division of fractions to convert to decimal equivalents
Understanding the use of repeating decimals
Enduring Understanding:
❏ Identify rational numbers ❏ Convert rational numbers expressed as fractions to terminating
or repeating decimals Essential Question:
❏ How are rational numbers written as decimals? CRP
CRP2, CRP3, CRP4, CRP7, CRP8, CRP11
* All Enduring Understandings and Essential Questions for each standards are suggested samples and can be modified or removed at the discretion of the teacher(s).
**Assessments and Resources could be altered or added at the discretion of the teacher(s). All assessments and resources used will cover the standards.
***CRP stands for Career Ready Practices.
Unit 2- Integers and Rational Numbers Timeline: 5 weeks
Standards Math Practices
(MP)
Focus Math Concepts Critical Knowledge and Skills
Prerequisite Skills Common Misunderstanding
7.NS.A.1b Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.
MP2, MP3, MP4, MP5, MP7
Understand that movement on a number line requires opposite directions for positive and negative directions. Applied and extended their understanding of the system of rational numbers
Understanding positive and negative numbers in real life situations Positive and negative directions on a vertical/horizontal number line Converting a mixed number to a fraction
Enduring Understanding: ❏ Add positive and negative integers
❏ Add and subtract positive and negative rational numbers
❏ Use number lines to model addition and subtraction as a movement or distance between rational numbers
Essential Questions: ❏ How do you use what you know about absolute value to add
integers?
❏ How are adding and subtracting integers related to adding and subtracting other rational numbers?
CRP
CRP2, CRP3, CRP4, CRP6, CRP8, CRP11
* All Enduring Understandings and Essential Questions for each standards are suggested samples and can be modified or removed at the discretion of the teacher(s).
**Assessments and Resources could be altered or added at the discretion of the teacher(s). All assessments and resources used will cover the standards.
***CRP stands for Career Ready Practices.
Unit 2- Integers and Rational Numbers Timeline: 5 weeks
Standards Math Practices
(MP)
Focus Math Concepts Critical Knowledge and Skills
Prerequisite Skills Common Misunderstanding
7.NS.A.1d Apply properties of operations as strategies to add and subtract rational numbers.
MP2, MP3, MP4, MP5, MP7
Understand that movement on a number line requires opposite directions for positive and negative directions. Applied and extended their understanding of the system of rational numbers Understand that positive and negative integers are used to describe quantities having opposite values or directions Applied sums of integer numbers to solve real world problems
Understanding positive and negative numbers in real life situations Positive and negative directions on a vertical/horizontal number line Converting a mixed number to a fraction Ordering rational numbers based on value (least to greatest)
Enduring Understanding: ❏ Add positive and negative integers
❏ Add and subtract positive and negative rational numbers
❏ Model integer addition in real-life applications
❏ Understand subtraction of integers as adding the additive inverse, p - q = p + (-q)
❏ Use addition and subtraction rules to solve real-world problems
Essential Questions: ❏ How do you use what you know about absolute value to add
integers?
❏ How is subtracting integers related to adding integers?
❏ How are adding and subtracting integers related to adding and subtracting other rational numbers?
CRP
CRP2, CRP3, CRP4, CRP6, CRP8, CRP11
* All Enduring Understandings and Essential Questions for each standards are suggested samples and can be modified or removed at the discretion of the teacher(s).
**Assessments and Resources could be altered or added at the discretion of the teacher(s). All assessments and resources used will cover the standards.
***CRP stands for Career Ready Practices.
Unit 2- Integers and Rational Numbers Timeline: 5 weeks
Standards Math Practices
(MP)
Focus Math Concepts Critical Knowledge and Skills
Prerequisite Skills Common Misunderstanding
7.NS.A.1c Understand subtraction of rational numbers as adding the additive inverse, p - q = p + (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.
MP2, MP3, MP4, MP5, MP7
Applied and extended their understanding of the system of rational numbers Understand that positive and negative integers are used to describe quantities having opposite values or directions Applied sums of integer numbers to solve real world problems
Positive and negative directions on a vertical/horizontal number line Converting a mixed number to a fraction Ordering rational numbers based on value (least to greatest)
Enduring Understanding: ❏ Add and subtract positive and negative rational numbers
❏ Understand subtraction of integers as adding the additive inverse, p - q = p + (-q)
❏ Use addition and subtraction rules to solve real-world problems
Essential Question:
❏ How is subtracting integers related to adding integers?
❏ How are adding and subtracting integers related to adding and subtracting other rational numbers?
CRP
CRP1, CRP2, CRP3, CRP4, CRP6, CRP8, CRP9, CRP11
* All Enduring Understandings and Essential Questions for each standards are suggested samples and can be modified or removed at the discretion of the teacher(s).
**Assessments and Resources could be altered or added at the discretion of the teacher(s). All assessments and resources used will cover the standards.
***CRP stands for Career Ready Practices.
Unit 2- Integers and Rational Numbers Timeline: 5 weeks
Standards Math Practices
(MP)
Focus Math Concepts Critical Knowledge and Skills
Prerequisite Skills Common Misunderstanding
7.NS.A.2a
Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1)=1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts
MP.4 MP.6
Earlier in this topic: added and subtracted integers with the same signs or different signs
Using inverse operations Multiplying a negative by a negative turns the solution into a positive Converting a mixed number to a fraction or a decimal
Enduring Understanding: ❏ Multiply positive and negative integers
❏ Use models and mathematical properties to develop a deep understanding of fluency with multiplying integers
❏ Multiply with rational numbers
❏ Apply operations with rational numbers to real-world contexts
Essential Questions:
❏ How do the signs of factors affect their product?
❏ How is multiplying rational numbers like multiplying integers?
CRP
CRP1,CRP2, CRP4,CRP7, CRP8, CRP12
* All Enduring Understandings and Essential Questions for each standards are suggested samples and can be modified or removed at the discretion of the teacher(s).
**Assessments and Resources could be altered or added at the discretion of the teacher(s). All assessments and resources used will cover the standards.
***CRP stands for Career Ready Practices.
Unit 2- Integers and Rational Numbers Timeline: 5 weeks
Standards Math Practices
(MP)
Focus Math Concepts Critical Knowledge and Skills
Prerequisite Skills Common Misunderstanding
7.NS.A.2c
Apply properties of operations as strategies to multiply and divide rational numbers
MP.4 MP.6
Earlier in this topic: added and subtracted integers with the same signs or different signs Understood that the product of two integers with the same sign is positive and two integers with different signs is negative. Used number lines and reasoning to solve real-world multiplication problems
Dividing fractions is the same as multiplying by the reciprocal Using inverse operations Multiplying a negative by a negative turns the solution into a positive Converting a mixed number to a fraction or a decimal
Enduring Understanding: ❏ Understand how signs of factors affect the product
❏ Multiply positive and negative integers
❏ Use models and mathematical properties to develop a deep understanding of fluency with multiplying integers
❏ Multiply with rational numbers
❏ Apply operations with rational numbers to real-world contexts
❏ Use the relationship between multiplication and division to divide integers
❏ Determine which quotients of integers are equivalent
❏ Understand how the signs of integers in a multiplication sentence relate to the signs in a related division sentence
❏ Extend the knowledge about multiplying rational numbers and
CRP
CRP1,CRP2, CRP4,CRP7, CRP8, CRP12
* All Enduring Understandings and Essential Questions for each standards are suggested samples and can be modified or removed at the discretion of the teacher(s).
**Assessments and Resources could be altered or added at the discretion of the teacher(s). All assessments and resources used will cover the standards.
***CRP stands for Career Ready Practices.
Learned to divide integers
dividing integers to division of rational numbers
Essential Questions:
❏ How do the signs of factors affect their product?
❏ How is multiplying rational numbers like multiplying integers?
❏ How does dividing integers relate to multiplying integers?
❏ How is dividing rational numbers like dividing integers?
Unit 2- Integers and Rational Numbers Timeline: 5 weeks
Standards Math Practices
(MP)
Focus Math Concepts Critical Knowledge and Skills
Prerequisite Skills Common Misunderstanding
7.NS.A.2b
Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q)=(-p)/q=p/(-q). Interpret quotients of rational numbers by describing real-world contexts
MP.7 MP.8
Earlier in this topic: understood that the product of two integers with the same sign is positive and two integers with different signs is negative. Used number lines and reasoning to solve real-world multiplication problems
Dividing fractions is the same as multiplying by the reciprocal Using inverse operations Multiplying a negative by a negative turns the solution into a positive
Enduring Understanding: ❏ Use the relationship between multiplication and division to
divide integers
❏ Determine which quotients of integers are equivalent
❏ Understand how the signs of integers in a multiplication sentence relate to the signs in a related division sentence
❏ Extend the knowledge about multiplying rational numbers and dividing integers to division of rational numbers
Essential Question:
❏ How does dividing integers relate to multiplying integers?
CRP
CRP1,CRP2, CRP4,CRP7, CRP8, CRP12
* All Enduring Understandings and Essential Questions for each standards are suggested samples and can be modified or removed at the discretion of the teacher(s).
**Assessments and Resources could be altered or added at the discretion of the teacher(s). All assessments and resources used will cover the standards.
***CRP stands for Career Ready Practices.
Learned to divide integers
Converting a mixed number to a fraction or a decimal
❏ How is dividing rational numbers like dividing integers?
Unit 2- Integers and Rational Numbers Timeline: 5 weeks
Standards Math Practices
(MP)
Focus Math Concepts Critical Knowledge and Skills
Prerequisite Skills Common Misunderstanding
7.NS.A.3
Solve real-world and mathematical problems involving the four operations with rational number
MP.2 MP.4
Earlier in topic: added and subtracted rational numbers Multiplied and divided rational numbers
Positive and negative directions on a vertical/horizontal number line Understanding positive and negative numbers in real life situations Dividing fractions is the same as multiplying by the reciprocal Using inverse operations Multiplying a negative by a negative
Enduring Understanding: ❏ Decide which operations to use to solve
problems with rational numbers
Essential Question:
❏ How do you decide which rational number operations to use to solve problems?
CRP
CRP1,CRP2, CRP3,CRP4, CRP5,CRP6,CRP7,CRP8, CRP9,CRP10, CRP11,
* All Enduring Understandings and Essential Questions for each standards are suggested samples and can be modified or removed at the discretion of the teacher(s).
**Assessments and Resources could be altered or added at the discretion of the teacher(s). All assessments and resources used will cover the standards.
***CRP stands for Career Ready Practices.
CRP12 turns the solution into a positive Converting a mixed number to a fraction or a decimal
Unit 2- Integers and Rational Numbers Timeline: 5 weeks
Standards Math Practices
(MP)
Focus Math Concepts Critical Knowledge and Skills
Prerequisite Skills Common Misunderstanding
7.EE.B.3
Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the
MP.2 MP.4
Earlier in topic: added and subtracted rational numbers Multiplied and divided rational numbers
Positive and negative directions on a vertical/horizontal number line Understanding positive and negative numbers in real life situations Dividing fractions is
Enduring Understanding: ❏ Decide which operations to use to solve problems with
rational numbers
Essential Question:
❏ How do you decide which rational number operations to use to solve problems?
CRP
CRP1,CRP2, CRP3,CRP4, CRP5,CRP6,CRP7,CRP8, CRP9,CRP10, CRP11,
* All Enduring Understandings and Essential Questions for each standards are suggested samples and can be modified or removed at the discretion of the teacher(s).
**Assessments and Resources could be altered or added at the discretion of the teacher(s). All assessments and resources used will cover the standards.
***CRP stands for Career Ready Practices.
reasonableness of answers using mental computation and estimation strategies
CRP12 the same as multiplying by the reciprocal Using inverse operations Multiplying a negative by a negative turns the solution into a positive Converting a mixed number to a fraction or a decimal
Unit 2- Integers and Rational Numbers Timeline: 5 weeks
District / School Formative Assessment Plan District/School Summative Assessment Plan Topic 2 Readiness Assessment – Used a pre-assessment to measure knowledge of the Topic prior to anything being covered or taught. This will set up the pacing guide for the duration of Topic 2. Lesson Quizzes – Used at the discretion of the teacher. Will be used after each lesson to ensure that concepts and standards were covered and students retained the information. Additional support for students will be provided for those that still need additional practice and examples of concepts not shown with mastery.
Topic 2 Mid Topic Assessment – Used after Topics 2.1 – 2.3 have been covered. Will assess to see growth from the Readiness Assessment and measure mastery of concepts and standards covered this far. Topic 2 Assessment – Covering all standards and concepts connected in Topic 2. Testing will be done online with the Pearson envisions program. Test can be modified by the teacher online and printed out for those that are provided a printed copy of the assessment.
District / School Primary and Supplementary Resources Primary Resources Supplementary Resources
* All Enduring Understandings and Essential Questions for each standards are suggested samples and can be modified or removed at the discretion of the teacher(s).
**Assessments and Resources could be altered or added at the discretion of the teacher(s). All assessments and resources used will cover the standards.
***CRP stands for Career Ready Practices.
enVisions 2.0 o Math XL Assignments o Virtual Nerd Videos o Additional Examples / Support o Online Assessments o Fluency Practice o Three (3) Act Math o Performance Task Assessment
Additional outside Resources: Topic 2 Virtual Nerd Links
Technology Aspect
● Google Products o Google Classroom - Used for daily interactions with the students covering a vast majority of different educational resources (Daily Notes, Exit
Tickets, Classroom Polls, Quick Checks, Additional Resources/ Support, Homework, etc.) o GAFE (Google Apps For Education) - Using various programs connected with Google to collaborate within the district, co-teachers, grade level
partner teacher, and with students to stay connected with the content that is covered within the topic. Used to collect data in real time and see results upon completion of the assignments to allow for 21st century learning.
● Pearson enVisions 2.0 o Online Assessment (Pre and Post Assessments, Math XL, Tests, Quizzes, Interactive Videos and homework helper, etc.) o Interactive Lessons
● One to One Student's laptop o All students within the West Deptford School District are given a computer, allowing for 21st century learning to occur within every lesson/topic.
* All Enduring Understandings and Essential Questions for each standards are suggested samples and can be modified or removed at the discretion of the teacher(s).
**Assessments and Resources could be altered or added at the discretion of the teacher(s). All assessments and resources used will cover the standards.
***CRP stands for Career Ready Practices.
● Teacher Created Videos and Notes that coincide with Unit 2 ● Teacher Curated Khan Academy Exercises that directly relate to Unit 2 standards. ● Students that struggles with basic math facts will utilize Xtra Math.
Differentiated Instruction
Gifted Students (N.J.A.C.6A:8-3.1)
❏ Within each lesson, the Gift Students are to be given the Enrichment Questions. ❏ These questions are to push the knowledge of each portion of the lesson. Refer to the bottom of your Teacher Edition to see this portion of the lesson.
English Language Learners (N.J.A.C.6A:15)
❏ Within each lesson, the English Language Learners are given three levels of questioning. Each level is accommodating to the level of learning that the individual student(s) is learning at.
❏ Beginning
* All Enduring Understandings and Essential Questions for each standards are suggested samples and can be modified or removed at the discretion of the teacher(s).
**Assessments and Resources could be altered or added at the discretion of the teacher(s). All assessments and resources used will cover the standards.
***CRP stands for Career Ready Practices.
❏ Intermediate ❏ Advanced
❏ All assignments have been created in the student’s native language. ❏ Work with ELL Teacher to allow for all assignments to be completed with extra time.
Risk Students (N.J.A.C.6A:8-4.3c)
❏ Within each lesson, the Response to Intervention section is for the at risk students. Within these sections of the Teacher Edition, common mistakes are brought up and intervention plans are provided. Refer to the bottom of your Teacher Edition to see these examples.
Special Education Students (N.J.A.C.6A:8-3.1)
❏ Utilize Differentiated Intervention resources at the bottom of Teacher’s Manual in each lesson (“Reteach to Build Understanding”, “Additional Vocabulary Support”, and “Build Mathematical Literacy” exercises).
Interdisciplinary Connections****
Math Science ELA
In the STEM project, students use rational numbers to represent costs and other measurements as they gather relevant data. They will use numbers to represent quantities in a solution proposal.
Students apply the engineering design process to find possible solutions to the problem identified.
Students will be asked to routinely criticize reasoning and explain their thinking in open constructed response questions. Evidence will be used to support their reasons. Students will use Frayer Model (graphic organizer)
* All Enduring Understandings and Essential Questions for each standards are suggested samples and can be modified or removed at the discretion of the teacher(s).
**Assessments and Resources could be altered or added at the discretion of the teacher(s). All assessments and resources used will cover the standards.
***CRP stands for Career Ready Practices.
to sort and categorize math terms used in this topic. Teachers will encourage students to utilize text features (highlighted bold terms, examples, and Key Concept boxes) in order to identify and connect with frequently communicated key ideas about the vocabulary terms
Fine Arts/ Performing Arts World Language Technology
Students think like an engineer and apply the engineering design process as they work toward a proposed solution. The solution may require implementation of established or innovative technologies.
Careers Global Awareness Other
Students will choose a problem identified in the Topic 1 STEM project and apply the engineering design process to research, plan, test, propose, and present a solution.
In “The Ultimate Throw” 3-Act, students will discover there are many ways to throw a flying disc. In particular, Ultimate is played by millions of people across the globe, from casual games to professional leagues.
