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Grade 5 Mathematics Module 6, Topic B: Patterns in the Coordinate Plane and Graphing Number Patterns from Rules

  Classroom Resource Information  

Title:

Grade 5 Mathematics Module 6, Topic B: Patterns in the Coordinate Plane and Graphing Number Patterns from Rules

URL:

https://www.engageny.org/resource/grade-5-mathematics-module-6-topic-b-overview

Content Source:

EngageNY
Type: Lesson/Unit Plan

Overview:

In Module 6, Topic B, students plot points and use them to draw lines on the plane (5.G.1).  Students begin by investigating patterns relating the x- and y-coordinates of the points on the line and reasoning about the patterns in the ordered pairs, which lays important groundwork for Grade 6 work with proportional reasoning. Topic B continues as students use given rules (e.g., multiply by 2, and then add 3) to generate coordinate pairs, plot points, and investigate relationships. Patterns in the resultant coordinate pairs are analyzed to discover that such rules produce collinear sets of points or lines. Students next generate two number patterns from two given rules, plot the points, and analyze the relationships within the sequences of the ordered pairs and graphs (5.OA.3).  Patterns continue to be the focus as students analyze the effect on the steepness of the line when the second coordinate is produced through an addition rule as opposed to a multiplication rule (5.OA.3). They also create rules to generate number patterns, plot the points, connect those points with lines, and look for intersections.

Content Standard(s):
Mathematics
MA2015 (2016)
Grade: 5
2 ) Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. [5-OA2]

Examples: Express the calculation "add 8 and 7, then multiply by 2" as 2 x (8 + 7). Recognize that 3 x (18,932 + 921) is three times as large as 18,932 + 921, without having to calculate the indicated sum or product.


Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.5.2- Select the expression that represents a given calculation (include parentheses).


Mathematics
MA2015 (2016)
Grade: 5
23 ) Use a pair of perpendicular number lines, called axes, to define a coordinate system with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). [5-G1]


NAEP Framework
NAEP Statement::
4A2c: Graph or interpret points with whole number or letter coordinates on grids or in the first quadrant of the coordinate plane.

NAEP Statement::
4G4a: Describe relative positions of points and lines using the geometric ideas of parallelism or perpendicularity.



Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.5.23- Identify quadrant 1 and the origin on a coordinate system grid.


Mathematics
MA2019 (2019)
Grade: 5
2. Generate two numerical patterns using two given rules and complete an input/output table for the data.

a. Use data from an input/output table to identify apparent relationships between corresponding terms.

b. Form ordered pairs from values in an input/output table.

c. Graph ordered pairs from an input/output table on a coordinate plane.
Unpacked Content
Evidence Of Student Attainment:
Students:
Use two related rules to
  • Generate numerical patterns and record as ordered pairs.
  • Graph ordered pairs consisting of corresponding terms.
  • Identify and explain relationships between corresponding terms.

  • Example: Given the rule "add 1 starting at 0", and "add 2 starting at 0," explain the terms in one sequence as 1/2 the corresponding terms in the other sequence, or the terms in one sequence are twice the corresponding terms in the other sequence.
Teacher Vocabulary:
  • Number pattern
  • Graph
  • Coordinate plane
  • X-axis
  • Y-axis
  • Origin
  • X-coordinate
  • Y-coordinate
  • Ordered pair
  • Generate
  • Sequence
Knowledge:
Students know:
  • Strategies to identify numerical patterns and recognize the relationship between the terms in the pattern.
  • Reasoning strategies to generate a numerical pattern which follow a given rule.
Skills:
Students are able to:
  • Generate two numerical patterns using two given rules.
  • Complete an input/output table for data.
  • Identify relationship between terms in an input/output table.
  • Form ordered pairs from an input/output table.
  • Graph ordered pairs on a coordinate plane.
Understanding:
Students understand that:
  • relationships between two numerical patterns can be represented by ordered pairs and graphed in the first quadrant of the coordinate plane.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.5.2.1: Construct repeating and growing patterns with a variety of representations.
M.5.2.2: Continue an existing pattern.
M.5.2.3: Identify arithmetic patterns (including patterns in the addition table or multiplication table).

Prior Knowledge Skills:
  • Generate two numerical patterns using two given rules.
  • Complete an input/output table for data.
  • Identify relationship between terms in an input/output table.
  • Form ordered pairs from an input/output table.
  • Graph ordered pairs on a coordinate plane.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.5.2 Given a rule, Identify and extend numerical patterns (e.g., given the rule "Add 3" and the starting number 0).


Tags: axes, axis, coordinate pairs, coordinate plane, numerical patterns, ordered pairs, relationships, rules
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Comments

There are six lessons in this topic.

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Author: Hannah Bradley