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Goddard: Sixth Grade Common Core State Standards (CCSS) Mathematics

Quarter Taught: Quarter 1 Quarter 2 Quarter 3 Quarter 4 Domain: The Number System Code: 6.NS.1Cluster: Apply and extend previous understandings of multiplication and division to divide fractions by fractions.Standard: 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?

Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☒Level 3: Strategic Thinking ☐ Level 4: Extended Thinking ☐

Know (nouns) DefinitionList the key concepts (nouns/noun phrases) and provide a common definition of the nouns/noun phrases as used in this context.

Quotients – Solution to a division problem Fractions – Part of a whole with a numerator & denominator, mixed and/or improper Equation – Mathematical operation w/ an equal sign Reciprocal – The inverse of a fraction, flip numerator & denominator

Be Able to Do (Verbs) Level I Level II Level III Level IV Level V

List the verbs that are key learning targets, then determine the cognitive demand level (Bloom’s/SEC) with verbs in context by placing a checkmark in the appropriate square:

Knowledge/ Remembering

Memorize facts, definitions, &

formulas

Comprehension/ Understanding

Perform Procedures

ApplicationDemonstrate

understanding of math

AnalysisConjecture,

Generalize, Prove

Synthesis/Evaluate/ Create; Solve non-routine problems; make connections

Interpret/Compute use visual fraction models and equations to represent the problem

☐ ☒ ☒ ☐ ☐

Solve ☒ ☒ ☒ ☐ ☐ Find the inverse ☒ ☒ ☒ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)

Understand & solve the division of fractions as equations and real world problems Interpret data to set up a division equation Divide fractions by fractions using mathematical reasoning Solve real world problems using division of fractions and interpret the quotient

1

Essential Questions:

Can I find the quotient of two given fractions Can I create a story context to demonstrate the quotient of two given fractions In what ways can rational numbers be useful? Can I create a story problem to represent the given problem? What learning progressions are needed to master this standard? Give specific, measurable skill statements.

Learning Sequence Prior skill(s) needed Check Level of Rigor/Cognitive Demand(Depth of Knowledge

1 Multiplication facts I ☒ II ☐ III ☐ IV ☐ V ☐2 Vocabulary – numerator, denominator, reciprocal I ☒ II ☐ III ☐ IV ☐ V ☐3 Change mixed fraction to improper I ☐ II ☒ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐Assessments: (What will be acceptable evidence the student has achieved the desired results?)

Instructional Resources/Tools:

Assessment Item Type: Selected Response ☒ Extended Constructed Response ☒ Technology Enhanced ☒ Performance Task ☒ Oral Response ☐ Eligible as summative item ☒Example: Provide possible instructional learning example/formative assessment item(s) for this standard:

Example 1: Example 2: Example 3:

2

Quarter Taught: Quarter 1 Quarter 2 Quarter 3 Quarter 4 Domain: The Number System Code: 6.NS.2Cluster: Compute fluently with multi-digit numbers and find common factors and multiples.Standard: Fluently divide multi-digit numbers using the standard algorithm.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☐

Level 3: Strategic Thinking ☐ Level 4: Extended Thinking ☐Know (nouns) Definition

List the key concepts (nouns/noun phrases) and provide a common definition of the nouns/noun phrases as used in this context. Multi-digit number – Has more than one digit Common Factor – A number that is a factor of two or more numbers. 5 is a common factor of 15 & 20 Multiples – The result of multiplying Algorithm – A procedure to solve mathematical problems, steps in a process Factor – Numbers multiplied together to get another number





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


Divide- Separate into equal parts ☒ ☒ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)

Divide using up to 3 digit divisors Can I use a procedure to fluently divide multi digit numbersEssential Questions:

Can I divide multi digit numbers accurately? Can I use an algorithm to divide multi digit numbers? What learning progressions are needed to master this standard? Give specific, measurable skill statements.

Learning Sequence Prior skill(s) needed Check Level of Rigor/Cognitive Demand

3

(Depth of Knowledge1 Multiplication facts I ☒ II ☐ III ☐ IV ☐ V ☐2 Place value I ☒ II ☐ III ☐ IV ☐ V ☐3 How to use division algorithms I ☒ II ☒ III ☐ IV ☐ V ☐4 Subtraction facts I ☒ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐Assessments: (What will be acceptable evidence the student has achieved the desired results?)




4

Quarter Taught: Quarter 1 Quarter 2 Quarter 3 Quarter 4 Domain: The Number System Code: 6.NS.3Cluster: Compute fluently with multi-digit numbers and find common factors and multiples.Standard: Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☐


List the key concepts (nouns/noun phrases) and provide a common definition of the nouns/noun phrases as used in this context. Addition – The combination of two or more numbers to arrive at a total Subtract – The difference between two or more numbers Multiply – The product of two or more numbers Division – Separate into equal parts Multi digit decimals – A number that uses a decimal point showing values less than 1 Algorithm - A procedure to solve mathematical problems, steps in a process





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


Fluently compute the addition & subtraction of decimals

☒ ☒ ☐ ☐ ☐

Fluently compute the product of decimals ☒ ☒ ☐ ☐ ☐ Fluently compute the quotient of decimals ☒ ☒ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)

Manipulate decimals using addition, subtraction, multiplication & division Quickly & efficiently add and subtract, multiply and divide multi digit decimalsEssential Questions:

Can I use math facts with decimals? Do I know how to add & subtract decimals? Do I know how to multiply & divide decimals? Can I correctly place the decimal in the answer to questions? (+, -, x, /) What learning progressions are needed to master this standard? Give specific, measurable skill statements.

5


1 +, -, X & /; using decimals I ☒ II ☒ III ☒ IV ☐ V ☐2 Explain place values from 100,000 to 100,000ths I ☒ II ☒ III ☐ IV ☐ V ☐3 Use algorithms (+, -, x, /) I ☒ II ☒ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐Assessments: (What will be acceptable evidence the student has achieved the desired results?)




6

Quarter Taught: Quarter 1 Quarter 2 Quarter 3 Quarter 4 Domain: The Number System Code: 6.NS.4Cluster: Compute fluently with multi-digit numbers and find common factors and multiples.Standard: 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).

Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☐Level 3: Strategic Thinking ☐ Level 4: Extended Thinking ☐


Greatest Common Factor (GCF) – Greatest factor which divides two numbers Least Common Multiple (LCM) – The smallest number which is a multiple of two or more numbers Distributive Property – An algorithm in which the product of a number and the sum is equal to the sum of the individual products of addends and the

number. A(B+C) = AB + AC





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


Calculate the GCF of two whole numbers ☒ ☒ ☐ ☐ ☐ Calculate the LCM of two whole numbers ☒ ☒ ☐ ☐ ☐ Apply the distributive property to rewrite addition

problems☐ ☒ ☒ ☐ ☐

☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)

Apply the distributive property to rewrite addition problems by factoring out the GCF Using the distributive property to solve by adding or subtracting the multiples Calculate the GCF of two whole numbers less than 100 Calculate the LCM of two whole numbers less than or equal to 12 All factors for a given number less than 100 List multiples less than or equal to 12 Use the distributive property to rewrite a simple addition problem when the addend have a common factorEssential Questions:

7

Can I find the GCF of two given numbers less than 100? Can I find the LCM of two given numbers less than 12? Do I understand the Distributive Property? What learning progressions are needed to master this standard? Give specific, measurable skill statements.


2 Explain factors I ☒ II ☐ III ☐ IV ☐ V ☐3 Explain multiples I ☒ II ☐ III ☐ IV ☐ V ☐4 Use algorithms I ☐ II ☒ III ☐ IV ☐ V ☐1 Multiplication facts I ☒ II ☐ III ☐ IV ☐ V ☐5 Use divisibility rules I ☒ II ☒ III ☐ IV ☐ V ☐Assessments: (What will be acceptable evidence the student has achieved the desired results?)



Example 1: Use the “L” method/chart to find GCF, LCMExample 2: Use the “T” method/chart to find all factors of a given numberExample 3:

8

Quarter Taught: Quarter 1 Quarter 2 Quarter 3 Quarter 4 Domain: The Number System Code: 6.NS.5Cluster: Apply and extend previous understandings of numbers to the system of rational numbers.Standard: 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.

Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☒Level 3: Strategic Thinking ☐ Level 4: Extended Thinking ☐


Positive numbers – Numbers greater than 0 Negative numbers – Numbers less than 0 Quantities – A numbered amount Opposite – Inverse of any number; Two numbers with the same magnitude but with different signs





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


Describe quantities having opposite values (directions) ☐ ☐ ☒ ☐ ☐ Recognize/Understand positive & negative signs

represent opposite values☒ ☐ ☐ ☐ ☐

Explain the number 0 is the point at which direction or value will change

☒ ☐ ☐ ☐ ☐


Will be able use positive, negative numbers along with zero to represent and understand real world situations Recognize positive and negative signs and their opposite values Explain the number zero is the point at which the direction of values change Using positive and negative numbers with zeros to represent real world situations Understand and explain rational numbersEssential Questions:

In what ways are positive and negative numbers be useful?

9

Given two rational numbers, can I give the value of the distance between them? Can I determine the value of a positive and negative? What learning progressions are needed to master this standard? Give specific, measurable skill statements.


4 Explain rational numbers I ☐ II ☒ III ☒ IV ☐ V ☐2 Understand negative numbers are less than zero I ☐ II ☒ III ☒ IV ☐ V ☐1 Able to use the number line; create and use an integer/number line I ☒ II ☒ III ☐ IV ☐ V ☐3 Explain rational and whole numbers I ☐ II ☒ III ☒ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐Assessments: (What will be acceptable evidence the student has achieved the desired results?)



Example 1: Use temperature to illustrate addition & subtraction numbersExample 2: Use sea level & altitude to illustrate addition & subtraction numbersExample 3: Use bank account & accounting to illustrate addition & subtraction numbers (in the red, in the black)

10

Quarter Taught: Quarter 1 Quarter 2 Quarter 3 Quarter 4 Domain: The Number System Code: 6.NS.6Cluster: Apply and extend previous understandings of numbers to the system of rational numbers.Standard: 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.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☐


List the key concepts (nouns/noun phrases) and provide a common definition of the nouns/noun phrases as used in this context.Rational Numbers – The set of all positive and negative numbers Number Line – A line which numbers are placed in the correct position both greater than or less than zero; in ascending & descending order Coordinate Plane – A plane spanned of the X & Y axes which are perpendicular Ordered Pairs – Numbers written in the order of X & Y Integer s- The set of all positive and negative numbers





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


Recognize opposite signs of numbers on a number line ☒ ☒ ☐ ☐ ☐ Understand the signs of numbers in ordered pairs as

indicate location in quadrants☐ ☒ ☐ ☐ ☐

Find and position of pairs of integers or rational numbers on a coordinate plane

☐ ☒ ☒ ☐ ☐


Show and explain why every rational number can be represented by a point on a number line/coordinate plane Plot a number and its opposite on a number line and recognize their distance from zero Find the opposite of any given number including zero? Use the signs of the coordinates to determine the location of an ordered pair Reason about the location of two ordered pairs that have the same value but different signs; absolute value Read a point from a number line or a coordinate plane


11

Can I a plot rational numbers on a coordinate plane? What learning progressions are needed to master this standard? Give specific, measurable skill statements.


2 Locate a point on a number line I ☐ II ☒ III ☐ IV ☐ V ☐3 Explain number lines & coordinate axes – horizontal & vertical lines as a coord. plane? I ☐ II ☒ III ☐ IV ☐ V ☐1 Explain rational and whole numbers I ☐ II ☒ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐Assessments: (What will be acceptable evidence the student has achieved the desired results?)



Example 1: Aircraft fly on coordinate planes – left/right/up/downExample 2: Example 3:

12

Quarter Taught: Quarter 1 Quarter 2 Quarter 3 Quarter 4 Domain: The Number System Code: 6.NS.6aCluster: Apply and extend previous understandings of numbers to the system of rational numbers.Standard: 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.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☐


List the key concepts (nouns/noun phrases) and provide a common definition of the nouns/noun phrases as used in this context. Opposite - Inverse of any number; Two numbers with the same magnitude but with different signs Opposite of the Opposite – Is the number itself; Zero is its own opposite





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


Recognize an opposite of an opposite and the opposite of zero is zero

☐ ☒ ☐ ☐ ☐

Plot a number and its opposite on a number line and recognize they are equal distance from zero

☐ ☒ ☒ ☐ ☐

Explain absolute value – an integers ☐ ☐ ☐ ☐ ☐ Distance from zero ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)

Recognize an opposite of an opposite is the number itself and the opposite of zero is zero Describe the relative position of two numbers on a number line Can interpret any inequality in terms of real world situations Define absolute value as it applies to a number line Describe absolute value as the magnitude of the number line in a real world situation


13

What learning progressions are needed to master this standard? Give specific, measurable skill statements.


3. Explain rational and whole numbers I ☐ II ☐ III ☒ IV ☐ V ☐2. Explain number lines & coordinate axes I ☒ II ☒ III ☒ IV ☐ V ☐1. Plot a point on a number line I ☒ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐Assessments: (What will be acceptable evidence the student has achieved the desired results?)



Example 1: Temperature (number line)Example 2: altitude; sea levelExample 3:

14

Quarter Taught: Quarter 1 Quarter 2 Quarter 3 Quarter 4 Domain: The Number System Code: 6.NS.6bCluster: Apply and extend previous understandings of numbers to the system of rational numbers.Standard: 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.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☐


List the key concepts (nouns/noun phrases) and provide a common definition of the nouns/noun phrases as used in this context. Coordinate Plane – A plane spanned of the X & Y axes which are perpendicular – better def. Ordered Pairs – Numbers written in the specific order of X & Y axis Reflections – Transformation resulting from a flip; Opposite position across an axis





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


Recognize the plane spanned of the X & Y axes are perpendicular

☒ ☐ ☐ ☐ ☐

Understand X represents horizontal axis and Y represents vertical axis by creating a coordinate plane

☒ ☒ ☒ ☐ ☐

Construct a reflection across an axis ☐ ☒ ☒ ☐ ☒ Demonstrate ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)

Be able to create a coordinate plane and demonstrate a reflection on the coordinate plane Graph points in any quadrant on a coordinate plan Use absolute value to find the distance of any two pointsEssential Questions:

In what ways can rational numbers be useful? Can I correctly create & label a coordinate plane?

15

Do I understand Absolute Value? What learning progressions are needed to master this standard? Give specific, measurable skill statements.

Learning Sequence Prior skill(s) needed Check Level of Rigor/Cognitive Demand(Depth of Knowledge)

2 Create a coordinate plane I ☒ II ☐ III ☐ IV ☐ V ☐1 Understand positive & negative numbers I ☐ II ☒ III ☐ IV ☐ V ☐3 Understand absolute value I ☐ II ☐ III ☒ IV ☐ V ☐4 Locate points on a coordinate plane I ☒ II ☐ III ☐ IV ☐ V ☐5 Perform a reflection across 1 or both axis I ☐ II ☒ III ☐ IV ☐ V ☐Assessments: (What will be acceptable evidence the student has achieved the desired results?)




16

Quarter Taught: Quarter 1 Quarter 2 Quarter 3 Quarter 4 Domain: The Number System Code: 6.NS.6cCluster: Apply and extend previous understandings of numbers to the system of rational numbers.Standard: 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.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☐


List the key concepts (nouns/noun phrases) and provide a common definition of the nouns/noun phrases as used in this context. Integers – All positive and negative whole numbers including zero Rational Numbers – A number which can be expressed as a ratio of two integers Horizontal – A line with zero slope Vertical – A line with a 0 to 1 slope





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


Plot a point on a number line or coordinate plane ☐ ☐ ☒ ☐ ☐ Read a point on a number line or coordinate plane ☐ ☐ ☒ ☐ ☐ Explain/Describe the location of ordered pairs ☐ ☐ ☐ ☐ ☒ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)

Show and explain how every number can be located on a number line or coordinate planeEssential Questions:

Can I plot a point on a coordinate plane? Can I correctly read an ordered pair? What learning progressions are needed to master this standard? Give specific, measurable skill statements.

17

Learning Sequence Prior skill(s) needed Check Level of Rigor/Cognitive Demand(Depth of Knowledge)

2 Understand positive & negative numbers on a number line & coordinate plane I ☐ II ☒ III ☒ IV ☐ V ☐1 Understand rational numbers I ☐ II ☒ III ☒ IV ☐ V ☐3 Understand ordered pairs and their place on a coordinate plane I ☐ II ☒ III ☒ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐Assessments: (What will be acceptable evidence the student has achieved the desired results?)




18

Quarter Taught: Quarter 1 Quarter 2 Quarter 3 Quarter 4 Domain: The Number System Code: 6.NS.7Cluster: Apply and extend previous understandings of numbers to the system of rational numbers.Standard: Understand ordering and absolute value of rational numbers.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☒


List the key concepts (nouns/noun phrases) and provide a common definition of the nouns/noun phrases as used in this context. Absolute Value – The distance of an integer from zero; The positive value of an integer Rational Numbers – A number which can be expressed as the ratio of two integers (x/y)





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


Ordering rational numbers from least to greatest and greatest to least on a number line

☒ ☒ ☒ ☐ ☒

Understand absolute value in the integers distance from zero

☒ ☐ ☒ ☐ ☐

☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)

Order integers from G to L and/or L to G; Understand Absolute Value as an integers distance from zeroEssential Questions:

Can I determine values of integers using a number line? Can I place integers in order from G to L; L to G? Do I understand absolute value means the distance from zero? What learning progressions are needed to master this standard? Give specific, measurable skill statements.

19


2 Understand positive & negative numbers on a number line I ☐ II ☒ III ☒ IV ☐ V ☐1 Order numbers by value from G to L; L to G I ☒ II ☒ III ☒ IV ☐ V ☐3 Understand absolute value of integers I ☐ II ☐ III ☒ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐Assessments: (What will be acceptable evidence the student has achieved the desired results?)




20

Quarter Taught: Quarter 1 Quarter 2 Quarter 3 Quarter 4 Domain: The Number System Code: 6.NS.7aCluster: Apply and extend previous understandings of numbers to the system of rational numbers.Standard: 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.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☒


List the key concepts (nouns/noun phrases) and provide a common definition of the nouns/noun phrases as used in this context. Inequality – a state of not being equal Relative Position – Position based on the location of a given point Number Line – A line in which every point represents a rational number





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


Interpret means to describe the meaning of… ☐ ☐ ☒ ☒ ☒ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)

Describe the relative position of two numbers on a number line when given an inequality Explain where an integer goes on a number line and which is larger/smaller in an inequal statementEssential Questions:

Can I place integers on a number line? Can I decide which integer is larger or smaller in a given inequality? What learning progressions are needed to master this standard? Give specific, measurable skill statements.

21


1 Number lines are constructed for root numbers I ☐ II ☒ III ☒ IV ☐ V ☐2 Correct placement of integers on a number line I ☐ II ☐ III ☒ IV ☒ V ☐3 Determine greater than/less than values in an equaltiy I ☐ II ☐ III ☒ IV ☒ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐Assessments: (What will be acceptable evidence the student has achieved the desired results?)




22

Quarter Taught: Quarter 1 Quarter 2 Quarter 3 Quarter 4 Domain: The Number System Code: 6.NS.7bCluster: Apply and extend previous understandings of numbers to the system of rational numbers.Standard: Write, interpret, and explain 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.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☒


List the key concepts (nouns/noun phrases) and provide a common definition of the nouns/noun phrases as used in this context. Rational Numbers – A number which can be expressed as a ratio of two integers on a number line Real World Contexts – Applying math concepts to real world situations





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


Describe the meaning of ☐ ☒ ☒ ☒ ☐ Order rational numbers in words ☐ ☐ ☐ ☒ ☒ ☐ ☐ ☐ ☐ ☐ Explain the value of ☐ ☒ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)

Explain how integers show value such as in temperature, altitude, sea level, bank accounts – in the real worldEssential Questions:

Can I determine the value of rational numbers in an everyday situation? What learning progressions are needed to master this standard? Give specific, measurable skill statements.


23

(Depth of Knowledge2 Value of rational numbers I ☐ II ☒ III ☐ IV ☐ V ☐3 Order rational numbers I ☐ II ☐ III ☒ IV ☐ V ☐1 Definition of rational numbers I ☒ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐Assessments: (What will be acceptable evidence the student has achieved the desired results?)



Example 1: TemperatureExample 2: attitude/sea levelExample 3: bank account

24

Quarter Taught: Quarter 1 Quarter 2 Quarter 3 Quarter 4 Domain: The Number System Code: 6.NS.7cCluster: Apply and extend previous understandings of numbers to the system of rational numbers.Standard: 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.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☒


List the key concepts (nouns/noun phrases) and provide a common definition of the nouns/noun phrases as used in this context. Absolute Value – The distance of a number from zero; The positive value of an integer Rational Number - A number which can be expressed as a ratio of two integers Number Line – The line in which every point represents a rational number Magnitude – Greatness of size or amount, value





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


Interpret and explain the absolute value of an integer ☒ ☒ ☒ ☐ ☐ Interpret/describe the meaning (distance from zero) ☐ ☐ ☐ ☐ ☐ Explain/make clear to someone ☐ ☐ ☐ ☐ ☐ ☐ ☒ ☒ ☒ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)

Describe absolute value as a value of a number in a real world situationEssential Questions:

Can I tell how far away an integer is from zero in either direction? Can I understand that even though an integer is negative, it has an absolute value, distance, in positive form What learning progressions are needed to master this standard? Give specific, measurable skill statements.


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(Depth of Knowledge2 Locating points on a number line I ☒ II ☒ III ☒ IV ☐ V ☐1 Telling the distance from zero I ☒ II ☒ III ☐ IV ☐ V ☐3 Definition of absolute vale I ☒ II ☒ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐Assessments: (What will be acceptable evidence the student has achieved the desired results?)



Example 1: Phantom Tollbooth - MathmagicianExample 2: Bank accounts when overdrawn – you owe that money in positive formExample 3:

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Quarter Taught: Quarter 1 Quarter 2 Quarter 3 Quarter 4 Domain: The Number System Code: 6.NS.7dCluster: Apply and extend previous understandings of numbers to the system of rational numbers.Standard: 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.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☒


List the key concepts (nouns/noun phrases) and provide a common definition of the nouns/noun phrases as used in this context. Absolute Value – The distance of a number from zero; The positive value of a number





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


Perceive/point out a difference between absolute value and ordering integers

☐ ☐ ☒ ☒ ☒

☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)

Accurately compare and order using integers in real world situationsEssential Questions:

Do I understand the absolute value is the distance from zero, but NOT the integer’s value? Do I understand the definition of absolute value as the distance from zero? Do I understand negative integers are less than zero regardless of their absolute zero? Do I understand when ordering integers, order is determined by the sign and relative position on the number line and NOT its absolute value? What learning progressions are needed to master this standard? Give specific, measurable skill statements.

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3 Definition of absolute value I ☒ II ☒ III ☒ IV ☒ V ☐1 Use of integers & number line I ☒ II ☒ III ☒ IV ☐ V ☐2 Ordering integers I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐Assessments: (What will be acceptable evidence the student has achieved the desired results?)



Example 1: bank account – negative balance means you owe the bank that amount in positive formExample 2: Example 3:

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Quarter Taught: Quarter 1 Quarter 2 Quarter 3 Quarter 4 Domain: The Number System Code: 6.NS.8Cluster: Apply and extend previous understandings of numbers to the system of rational numbers.Standard: 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.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☒


List the key concepts (nouns/noun phrases) and provide a common definition of the nouns/noun phrases as used in this context. Four Quadrants – The four areas of a coordinate plane represented by ++. -+, -- & +- (Cartesian Plane) Coordinate plane – plane formed by the intersection or a horizontal (x axis) and vertical (y axis) number lines





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


Solve – To find the answer or explanation ☐ ☐ ☒ ☒ ☐ Graph – Drawing to represent date ☒ ☒ ☒ ☐ ☐ Find – To locate ☐ ☒ ☒ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)

Graph points in all quadrants of a coordinate plane Use absolute value to find distance between two opposite pointsEssential Questions:

Do I know all 4 quadrants on the coordinate plane and their signs? Can I accurately graph points on a coordinate plane? Can I determine a point’s distance from zero (absolute value) on a coordinate plane? What learning progressions are needed to master this standard? Give specific, measurable skill statements.

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1 Placing points on a number line I ☒ II ☒ III ☒ IV ☐ V ☐2 Construction of a coordinate plane I ☒ II ☒ III ☒ IV ☐ V ☐3 Locating points on a coordinate plane in all 4 quadrants I ☐ II ☒ III ☒ IV ☐ V ☐4 Determine absolute value of opposite points I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☒ III ☒ IV ☒ V ☐Assessments: (What will be acceptable evidence the student has achieved the desired results?)




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