ALEX Classroom Resource

  

Grade 6 Mathematics Module 3, Topic C: Rational Numbers and the Coordinate Plane

  Classroom Resource Information  

Title:

 Grade 6 Mathematics Module 3, Topic C: Rational Numbers and the Coordinate Plane

URL:

 https://www.engageny.org/resource/grade-6-mathematics-module-3-topic-c-overview

Content Source:

 EngageNY
Type: Lesson/Unit Plan

Overview:

In Module 3, Topic C, students extend their understanding of the ordering of rational numbers in one dimension (on a number line) to the two-dimensional space of the coordinate plane. They construct the plane’s vertical and horizontal axes, discovering the relationship between the four quadrants and the signs of the coordinates of points that lie in each quadrant (6.NS.C.6b, 6.NS.C.6c). Students build upon their foundational understanding from 5th Grade (5.G.1, 5.G.2) of plotting points in the first quadrant and transition to locating points in all four quadrants. Students apply the concept of absolute value to find the distance between points located on vertical or horizontal lines and solve real-world problems related to distance, segments, and shapes (6.NS.C.8).

Content Standard(s):
Mathematics
MA2015 (2016)
Grade: 6
9 ) 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-NS6]

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. [6-NS6a]

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. [6-NS6b]

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-NS6c]

NAEP Framework
NAEP Statement::
8A2c: Graph or interpret points represented by ordered pairs of numbers on a rectangular coordinate system.

NAEP Statement::
8NPO1d: Write or rename rational numbers.

NAEP Statement::
8NPO1e: Recognize, translate or apply multiple representations of rational numbers (fractions, decimals, and percents) in meaningful contexts.

NAEP Statement::
8NPO1g: Find or model absolute value or apply to problem situations.

NAEP Statement::
8NPO1h: Order or compare rational numbers (fractions, decimals, percents, or integers) using various models and representations (e.g., number line).

NAEP Statement::
8NPO5e: Apply basic properties of operations.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.6.9a- Identify positive and negative numbers on a number line.
M.AAS.6.9b- Locate or plot positive and negative numbers on a number line.
M.AAS.6.9c - Find given points between -10 and 10 on both axes of a coordinate plane.
Mathematics
MA2019 (2019)
Grade: 6
11. Find the position of pairs of integers and other rational numbers on the coordinate plane.

a. Identify quadrant locations of ordered pairs on the coordinate plane based on the signs of the x and y coordinates.

b. Identify (a,b) and (a,-b) as reflections across the x-axis.

c. Identify (a,b) and (-a,b) as reflections across the y-axis.

d. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane, including finding distances between points with the same first or second coordinate.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Create and interpret coordinate axes with positive and negative coordinates.
  • Given ordered pairs made up of rational numbers, locate and explain the placement of the ordered pair on a coordinate plane.
  • Given two ordered pairs that differ only by signs, locate the points on a coordinate plane and explain the relationship of the locations of the points as reflections across one or both axes.
  • Given real-world and mathematical problems where a coordinate graph will aid in the solution and given a graph of a real-world or mathematical situation, interpret the coordinate values of the points in the context of the situation including finding vertical and horizontal distances.
Teacher Vocabulary:
  • Coordinate plane
  • Quadrants
  • Coordinate values
  • ordered pairs
  • x axis
  • y axis
  • Reflection
Knowledge:
Students know:
  • Strategies for creating coordinate graphs.
  • Strategies for finding vertical and horizontal distance on coordinate graphs.
Skills:
Students are able to:
  • Graph points corresponding to ordered pairs,
  • Represent real-world and mathematical problems on a coordinate plane.
  • Interpret coordinate values of points in the context of real-world/mathematical situations.
  • Determine lengths of line segments on a coordinate plane when the line segment joins points with the same first coordinate (vertical distance) or the same second coordinate (horizontal distance).
Understanding:
Students understand that:
  • A graph can be used to illustrate mathematical situations and relationships. These representations help in conceptualizing ideas and in solving problems,
  • Distances on lines parallel to the axes on a coordinate plane are the same as the related distance on the axis (number line).
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.6.11.1: Define quadrant, coordinate plane, coordinate axes (x-axis and y-axis), horizontal, vertical, and reflection.
M.6.11.2: Demonstrate an understanding of an extended coordinate plane.
M.6.11.3: Draw a four-quadrant coordinate plane.
M.6.11.4: Draw and extend vertical and horizontal number lines.
M.6.11.5: Interpret graphing points in all four quadrants of the coordinate plane in real-world situations.
M.6.11.6: Recall how to graph points in all four quadrants of the coordinate plane.
M.6.11.7: Define ordered pairs.
M.6.11.8: Name the pairs of integers and/or rational numbers of a point on a coordinate plane.
M.6.11.9: Demonstrate when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.
M.6.11.10: Identify which signs indicate the location of a point in a coordinate plane.
M.6.11.11: Recall how to plot ordered pairs on a coordinate plane.
M.6.11.12: Define reflections.
M.6.11.13: Calculate the distances between points having the same first or second coordinate using absolute value.

Prior Knowledge Skills:
  • Model writing ordered pairs.
  • Identify the x- and y- values in ordered pairs.
  • Label the vertical axis (y).
  • Label the horizontal axis (x).
  • Define ordered pair of numbers, quadrant one, coordinate plane, and plot points.
  • Locate positive numbers on a vertical number line.
    Examples: thermometer, map.
  • Locate positive numbers on a horizontal number line.
  • Locate negative numbers on a horizontal number line.
  • Label x- and y-axis and zero on a coordinate.
  • Illustrate vertical and horizontal number lines.
  • Specify locations on the coordinate system.
  • Define x-axis, y-axis, and zero on a coordinate.
  • Define ordered pair of numbers.
  • Locate positive numbers on a horizontal number line.
  • Locate negative numbers on a horizontal number line.
  • Define symmetry.
  • Identify lines of symmetry on one-dimensional figures.
Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.6.11 Graph or identify ordered pairs in the first quadrant of the coordinate plane between 0 and 5, limited to whole numbers.
Tags: absolute value, coordinate plane, distance, graphing, integer, negative, number line, ordered pair, positive, rational number
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Comments

There are six lessons in this topic.

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Author: Hannah Bradley
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