6.NS.8 - About the Math, Learning Targets, and Increasing Rigor
Grade 5AGL The Number System
6.NS.8
Full 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.
Learning Targets (I can)
- Explain the distance between 2 coordinates in the context of a problem.
- Graph points to solve problems.
About the Math
- Explain the distance between 2 coordinates in the context of a problem.
- Graph points to solve problems.
Students find the distance between points when ordered pairs have the same x-coordinate (vertical) or same y-coordinate (horizontal).
Example 1: What is the distance between (–5, 2) and (–9, 2)? Solution: The distance would be 4 units. This would be a horizontal line since the y-coordinates are the same. In this scenario, both coordinates are in the same quadrant. The distance can be found by using a number line to find the distance between –5 and –9. Students could also recognize that –5 is 5 units from 0 (absolute value) and that –9 is 9 units from 0 (absolute value). Since both of these are in the same quadrant, the distance can be found by finding the difference between the distances 9 and 5. (| 9 | - | 5|). Coordinates could also be in two quadrants and include rational numbers. Students graph coordinates for polygons and find missing vertices based on properties of triangles and quadrilaterals.
Essential vocabulary for this standard includes: rational numbers, opposites, absolute value, quadrants, coordinate plane, ordered pairs, x-axis, y-axis, and coordinates.
Progression of Standard within Grade 6 (5 AGL)
This progression informs how to develop the standard within the grade level. This progression is provided by HCPSS Elementary Mathematics.
| Quarter 1 | Quarter 2 | Quarter 3 | Quarter 4 |
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Progression of this Standard Across Grades
This progression is informed by the Achieve the Core Coherence Map Links to an external site.. Information is not the complete standard.
| Grade 5 | Grade 8 |
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TASKS
These tasks can be used with small group or whole group instruction.
- What quadrants will two points fall if they share the same x-coordinates? Explain your answer by providing an example. Is there another possible answer? (if they share the same positive x value, they will be in quadrants 1 & 4 and if they share the same negative x value, they will be in quadrants 2 & 3.)
- Plot the point (5,-7) on the coordinate grid. If this point is reflected over the x-axis, what will be the resulting point?
- If each unit on the x and y axis represents one mile and travel can only occur horizontally or vertically, how many miles does Sally travel when she moves from (4,5) to (7,11)?
- Without actually graphing the points (2,3), (2,6) and (2,1), will the graph result in a horizontal, diagonal, or vertical line?
- Plot 4 points on the coordinate grid that are each 5 points from the point (2,3).
SLIDE-BASED TASKS
These links are HCPSS created instructional tasks. These tasks are provided in Google slides. These tasks should be used for inspiration and resources, but instruction should start with students having the opportunity to engage with the math first (often involving physical and/or visual models) followed by discussion and explicit instruction to ensure student understanding.
Module 9 • Positive and Negative Numbers
Solve Real-World and Mathematical Problems by Graphing Points on a Coordinate Plane:
Additional Tasks
These links provide instructional ideas connected to this standard.
- Lesson 7.12 - Constructing the Coordinate Plane Links to an external site. (Illustrative Math)
- Lesson 7.13 -Interpreting Points on a Coordinate Plane Links to an external site. (Illustrative Math)
- Lesson 7.14 - Distances on a Coordinate Plane Links to an external site.(Illustrative Math)
- Lesson 7.15 - Shapes on a Coordinate Plane Links to an external site.(Illustrative Math)
- Distances between Points (Links to an external site.) Links to an external site. (Illustrative Math)
- Area of a Quadrilateral on a Coordinate Plane Links to an external site. (Open Middle)
- Battleship Download Battleship (Lesson Collection)
- Outdoor Ed Download Outdoor Ed (HCPSS Lesson)
Tasks From Print Resources
These publications have been provided for each school. They are typically stored in team closets or the media center. Check with your team leader if you cannot find them.
| Book Thumbnail | Book Title | Grade | Pages |
|---|---|---|---|
| Hands-On Standards Common Core | 6 | 30 (Lesson 3) |
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Centers
These print resources can be used during independent or center time. These resources could also be used as lesson seeds.
INDEPENDENT PRACTICE/HOMEWORK/ASSESSMENT
These resource sheets can be used for independent practice, homework, or assessment. They are intended to reinforce procedures and concepts. They should not be used as a source of direct instruction or whole-group practice.
- Solve Problems on a Coordinate Plane a Links to an external site.
- Solve Problems on a Coordinate Plane b Links to an external site.
- Identify and Explain Distance Between Points on a Coordinate Grid Links to an external site.
- Identify and Explain Distance Between Points on a Coordinate Grid_2 Links to an external site.
- Graph Points to Solve Problems Links to an external site.
- Graph Points to Solve Problems_2 Links to an external site.
- Graph and Reason About Points to Solve Problems Links to an external site.
- Graph and Reason About Points to Solve Problems_2 Links to an external site.
- Graph and Reason About Points to Solve Problems_3 Links to an external site.
Performance Based Task
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Learning Targets
- Explain the distance between 2 coordinates in the context of a problem.
- Graph points to solve problems.
Learning targets identify what students should be able to do. This rubric can be applied to tasks and observations for assessment and/or grading.
Rubric for Tasks Links to an external site.
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Links to an external site. license. Content in this course can be considered under this license unless otherwise noted.