6NS-Apply+and+extend+previous+understandings+of+numbers+to+the+system+of+rational+numbers

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. 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. b. 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. c. 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.Understand ordering and absolute value of rational numbers. 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.// b. 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.// c. 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.// 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.// 6.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 coordinate or the same second coordinate. || ===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Anchor Standard/Mathematical Practice(s)**=== ===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Learning Target/Task Analysis**===
 * ===**Common Core Standard**s===
 * Make sense of problems and persevere in solving them.
 * Reason abstractly and quantitatively.
 * Model with mathematics.
 * Use appropriate tools strategically.
 * Look for and make sense of structure. ||
 * ===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Information Technology Standard**=== || ===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Revised Bloom's Level of thinking: Applying, Analyzing, Evaluating, Creating**=== ||

Students use rational numbers (fractions, decimals, and integers) to represent real-world contexts and understand the meaning of 0 in each situation.

Students extend the number line to represent all rational numbers and recognize that number lines may be either horizontal or vertical (i.e. thermometer) which facilitates the movement from number lines to coordinate grids. Students recognize that a number and its opposite are equidistance from zero (reflections about the zero).

Students recognize the point where the x-axis and y-axis intersect as the origin. Students identify the four quadrants and are able to identify the quadrant for an ordered pair based on the signs of the coordinates.

Students understand the relationship between two ordered pairs differing only by signs as reflections across one or both axes.

Students use inequalities to express the relationship between two rational numbers, understanding that the value of numbers is smaller moving to the left on a number line.

Students recognize the distance from zero as the absolute value or magnitude of a rational number. Students need multiple experiences to understand the relationships between numbers, absolute value, and statements about order.

Students write statements using to compare rational number in context. However, explanations should reference the context rather than “less than” or “greater than”.

Students understand absolute value as the distance from zero and recognize the symbols | | as representing absolute value.

Students find the distance between points when ordered pairs have the same x-coordinate (vertical) or same y-coordinate (horizontal).

Students graph coordinates for polygons and find missing vertices based on properties of triangles and quadrilaterals

===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**I can...Apply and extend previous understanding of numbers to the set of rational numbers.**===


 * I can identify an integer and its opposite.
 * I can use integers to represent quantities in real world situations.
 * I can explain the meaning of zero in the relationship to integers.
 * I can use a number line to identify rational numbers.
 * I can identify the quadrant of an ordered pair.
 * I can plot and identify ordered pairs on a coordinate plane.
 * I can recognize a reflection according to the ordered pair.
 * I can order rational numbers on a number line.
 * I can use inequality symbols to compare and order numbers.
 * I can identify the absolute value of a number.
 * I can graph points in all four quadrants of the coordinate plane.
 * I can use the absolute value to calculate the distance between points.

‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Essential Vocabulary:**

rational numbers, opposites, absolute value, greater than, >, less than, <, greater than or equal to, ≥, less than or equal to, ≤, origin, quadrants, coordinate plane, ordered pairs, x-axis, y-axis, coordinates

‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Sample Assessments**
Daily Spiral Review Signaling Questioning Teacher Observation Thinkgate

‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Differentiation**
Teaching the Common Core Math Standards with Hands-On Activities: Finding the Opposite (page 19) Teaching the Common Core Math Standards with Hands-On Activities: Activity 1 Graphing on a Number Line (page 22) Teaching the Common Core Math Standards with Hands-On Activities: Activity 2 Bonk the Mole (page 24) Teaching the Common Core Math Standards with Hands-On Activities: An Old Fashioned Number Line (page 25) Teaching the Common Core Math Standards with Hands-On Activities: The Maze Game (page 27) Quantiles 1

‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Intervention:**
Activities will be used from Instructional Resources List

‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Enrichment:**
TI-73 Graphing Ordered Pairs Activity

===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Instructional Resources:**===

Mathematics Station Activities for Common Core State Standards Grade 6 (pages 22 and 29) Carnegie Learning: Chapter 10, Chapter 11 DPI Indicators: Pages 34-36 Page 53 DPI Strategies: Inequality Race (page 81) Draw It Again Sam (page 51) Review (page 51)

Coordinate Grid
Unit Notes Notes/Examples Practice 1 Practice 2 Practice 3

===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Notes and Additional Information**===