Topic Proficiency Scale Domain: The Number System Topic: Rational Numbers. I know all of the Simple and Complex Learning Goals.

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1 Topic Proficiency Scale Domain: The Number System Topic: Rational Numbers 4.0 Going Beyond I know all of the Simple and Complex Learning Goals and my understanding goes beyond the grade level target. I know all of the Simple and Complex Learning Goals. 3.0 Complex Goals Grade Level Target C1: Write, interpret, and explain statements of order for rational numbers in real-world contexts. (Example: writing -3 C>-7 C to express the fact that -3 C is warmer than -7 C.) (6.NS.7b) C2: Interpret absolute value as a magnitude for a positive or negative quantity in a real-world situation. (Example: given $-143, $-203, $-198, $-350 who owes more?) (6.NS.7c) C3: Distinguish comparisons of absolute value from statements about order. (-1,000<-400 and > -400 ) (6.NS.7d) 2.5 I know all of the Simple Learning Goals plus some of the Complex Learning Goals. I know all of the Simple Learning Goals. cademic Vocabulary: V1: absolute value V2: integer 2.0 Simple Goals S1: Use positive and negative numbers to represent quantities in real-world context explaining the meaning of zero in each situation. (Example: elevation, checking account, temperature, etc.) (6.NS.5) S2: Know opposite signs of numbers as indicating locations on opposite sides of 0 on the number line. (6.NS.5) S3: Know that the opposite of the opposite of a number is the number itself. (Example: -(-3)=3) (6.NS.6a) S4: Find and position rational numbers on a number line. (6.NS.6c) S5: Interpret statements of inequality as statements about the relative position of two negative numbers on a number line diagram. (Example: -3>-7) (6.NS.7a) 1 I know some of the Simple Learning Goals. 0.5 I know only one of the Simple Learning Goals. 0 evidence of knowing the Learning Goals.

2 Teacher Resources Domain: The Number System Topic: Rational and Irrational Numbers CCSS in this Topic 6.NS.5 Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. 6.NS.6 Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. 6.NS.6a 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. 6.NS.6c Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. 6.NS.7 6.NS.7a 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. 6.NS.7b Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write 3 o C > 7 o C to express the fact that 3 o C is warmer than 7 o C. 6.NS.7c Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of 30 dollars, write 30 = 30 to describe the size of the debt in dollars. 6.NS.7d 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. gile Mind Resources ll lesson descriptions and needed resources can be found in gile Mind. To find: Click on View and Professional Support. Prepare Instruction link can be found under each topic.

3 The Number System (NS) pply and extend previous understandings of the system Explanations and Examples Standards Students are expected to: 6.NS.5 6.NS.6a,c 6.NS.7a,b,c,d Number lines can be used to show numbers and their opposites. Both 3 and -3 are 3 units from zero on the number line. Graphing points and reflecting across zero on a number line extends to graphing and reflecting points across axes on a coordinate grid. The use of both horizontal and vertical number line models facilitates the movement from number lines to coordinate grids. gile Mind Topics Topic 8: Extending the number system Case 1: Two positive numbers 5 > 3 5 is greater than 3 Case 2: One positive and one negative number 3 > -3 positive 3 is greater than negative 3 negative 3 is less than positive 3 Case 3: Two negative numbers -3 > -5 negative 3 is greater than negative 5 negative 5 is less than negative 3 One of the thermometers shows -3 C and the other shows -7 C. Which thermometer shows which temperature? Which is the colder temperature? How much colder? Write an inequality to show the relationship between the temperatures and explain how the model shows this relationship. Teaching tes!!

4 Grade 6 Evidence Statements Topic: Rational Numbers Subclaim Evidence Statement Text 6.NS.5 6.NS.6a 6.NS.6c-1 Evidence Statement Text Understand that positive and negative numbers are used together to describe quantities having opposite direction 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 realworld contexts, explaining the meaning of 0 in each situation. 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. a. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., -(-3) = 3, and that 0 is its own opposite. 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. Clarifications, limits, emphases, & other information intended to ensure appropriate variety in tasks Tasks do not require students to perform any computations. Students may be asked to recognize the meaning of 0 in the situation, but will not be asked to explain. Tasks have thin context 2 or no context. Tasks have thin context 2 or no context. Coordinates are not limited to integers. Relationship to MPs MP.8 Calculator c. Find and position integers and other rational numbers on a horizontal or vertical number line diagram.

5 Tasks do not have a context. 6.NS.7a a. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret -3 > -7 as a statement that -3 is located to the right of -7 on a number line oriented from left to right. 6.NS.7b b. Write interpret, and explain statements of order for rational numbers in realworld contexts, Tor example, Write -3 > -7 to express the fact that -3 is warmer than -7. For the explain aspect of 6.NS.7b, see 6.C.4 MP.3 B C 6.NS.7c-1 6.NS.7c-2 6.NS.7d 6.C.4 c. Understand the absolute value of a rational number as its distance from 0 on the number line. c. 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 the absolute value of 30 equal 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. Base explanations/reasoning on a number line diagram (whether provided in the prompt or constructed by the student in his/her response). Tasks do not have a context. Tasks do not have a context. Tasks may or may not have a context. Prompts do not present students with a number line diagram, but students may draw a number line diagram as a strategy. - MP.3 Yes Content Scope: Knowledge and skills articulated in 6.NS.6, 6.NS.7 MP.6

6 D D 6.D.1 6.D.3 Solve multi-step contextual word problems with degree of difficulty appropriate to Grade 6, requiring application of knowledge and skills articled in Type 1 Evidence Statements. Reasoned estimates: Use reasonable estimates of known quantities in a chain of reasoning that yields an estimate of unknown quantity. Tasks may have scaffolding, if necessary, in order to yield a degree of difficulty appropriate to Grade 6. Tasks may have scaffolding, if necessary, in order to yield a degree of difficulty appropriate to Grade 6. Content Scope: Knowledge and skills articulated in Type 1 Evidence Statements. Source: 2016 PRCC Evidence Statement Tables Grade 6 Mathematics MP.1 MP.4 MP.7 MP.1 MP.4 MP.7 Yes Yes Type 1 Type 2 Type 3 2 Thin context is a sentence or phrase that established a concrete referent for the quantity/quantities in the problem, in such a way as to provide meaningful avenues for mathematical intuition to operate, yet without requiring any sort of further analysis of the contest. For example, a task could provide a reason for the use of scientific notation such as, The number represents the distance between two planets.