Grade 6 - Claim 1 - Target D
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Target D
Apply and extend previous understandings of numbers to the system of rational numbers
Sample Item
Grade 6Test
Claim 1
Concepts and Procedures
Standards
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...
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...
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.,...
NS-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...
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.
NS-7
Understand ordering and absolute value of rational numbers.
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...
NS-7b
Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write -3ᵒC
>-7ᵒC to express the fact that -3ᵒC is warmer than -7ᵒC.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...
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.
NS-8
Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first...
Clarifications
Tasks for this claim will ask students to place numbers on a number line (positive and negative rational numbers, including those expressed using absolute value notation). Some tasks will ask students to interpret the...
Range Achievement Level Descriptors
Evidence Required
1
The student uses positive and negative numbers to represent quantities in real-world contexts.
2
The student can identify the location of ordered pairs on the coordinate plane based on the signs of the numbers in an ordered pair.
3
The student locates and positions integers and other rational numbers on a number line.
4
The student positions ordered pairs of integers and other rational numbers on a coordinate plane.
5
[Evidence Required statement retired]
6
The student writes and interprets statements about the order of rational numbers in real-world contexts.
7
The student represents the absolute value of a rational number as the distance from zero on a number line.
8
The student can make comparisons of absolute value from statements about order.
9
The student solves real-world and mathematical problems by graphing ordered pairs on a coordinate plane and using coordinates and absolute value to find the distances between points with same first coordinate or...
Item Guidelines
Depth of Knowledge
M-DOK1
Recall includes the recall of information such as fact, definition, term, or a simple procedure, as well as performing a simple algorithm or applying a formula. That is, in mathematics a one-step, well-defined, and straight algorithmic procedure should be...
M-DOK2
Skill/Concept includes the engagement of some mental processing beyond a habitual response. A Level 2 assessment item requires students to make some decisions as to how to approach the problem or activity, whereas Level 1 requires students to demonstrate a...
Allowable Item Types
- Equation/Numeric
- Graphing
- Multiple Choice, single correct response
- Matching Tables
- Drag and Drop
Allowable Stimulus Materials
horizontal and vertical number lines, coordinate planes
Key/Construct Relevant Vocabulary
positive, negative, integer, absolute value, coordinate, ordered pair, coordinate grid/plane, quadrant, number line, relative position, magnitude
Allowable Tools
None
Target-Specific Attributes
None
Accessibility
Item writers should consider the following Language and Visual Element/Design guidelines [1] when developing items. Language Key Considerations: Use simple, clear, and easy-to-understand language needed to assess the construct or aid in the understanding of the...
Development Notes
Claim 3 tasks will integrate the work of this target by incorporating students’ understanding of interpretations and explanations of common misconceptions related to inequalities for negative rational numbers (e.g., explaining that –3$^{o}$C is warmer...
Task Models
Task Model 1
Item Types
Equation/NumericDepth of Knowledge
M-DOK1Standards
NS-5
Target Evidence Statement
The student uses positive and negative numbers to represent quantities in real-world contexts.
Allowable Tools
None
Task Description
Prompt Features: The student is prompted to interpret negative numbers in context. Stimulus Guidelines: Context should be familiar to students 11 to 13 years old. The context should involve quantities where negative values can be interpreted in...
Stimulus
The student is presented with a context that can be unambiguously represented by a negative number or zero.
Example 1
Example Stem: A Fahrenheit thermometer shows that the temperature is 15 degrees below zero.
Enter the integer that represents the temperature in degrees Fahrenheit in the response box.
Rubric: (1 point) The student enters the correct number (e.g., –15).