Standard

Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.

Student Language:

• "I can use numerical rules and patterns to form ordered pairs.
• "I can graph the ordered pairs on a coordinate plane."

Explanation

About the Math, Learning Targets, and Rigor

This standard extends the work from Fourth Grade, where students generate numerical patterns when they are given one rule. In Fifth Grade, students are given two rules and generate two numerical patterns. The graphs that are created should be line graphs to represent the pattern.

Use the rule “add 3” to write a sequence of numbers. Starting with a zero, students write 0, 3, 6, 9, 12 . . . Use the rule “add 6” to write a sequence of numbers. Starting with zero, students write 0, 6, 12, 18, 24 . . . After comparing these two sequences, the students notice that each term in the second sequence is twice the corresponding terms of the first sequence.

Once students can describe that the second sequence of numbers is twice the corresponding terms of the first sequence, the terms can be written in ordered pairs and then graphed on a coordinate grid. They should recognize that each point on the graph represents two quantities in which the second quantity is twice the first quantity.

Common Misconceptions: Students reverse the points when plotting them on a coordinate plane. They count up first on the y-axis and then count over on the x-axis. The location of every point in the plane has a specific place. Have students plot points where the numbers are reversed such as (4, 5) and (5, 4). Begin with students providing a verbal description of how to plot each point. Then, have them follow the verbal description and plot each point.

Resources

Videos

• Khan Academy
  • Scroll to 5.OA.3, click on skill, find videos on left side of each skill
• Learn Zillion
• Virtual Nerd

EngageNY Lessons

Extra Practice

• North Carolina Tasks
• Illustrative Math Tasks
• Howard County Tasks
  • Click on 5th grade at bottom, then 5.OA.3
• Common Core Sheets

Released Assessment Questions

PARCC

Common Core State Standards

5.OA.3

Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.

STUDENT SAMPLE RESPONSE

Performance Indicators: 5.OA.3

Level 5: Exceeds Expectations

Represents real-world and mathematical problems by locating and graphing points in the first quadrant of a coordinate plane and interprets coordinate values of points in the context of the situation.

Level 4: Meets Expectations

Represents real-world and mathematical problems by locating and graphing points in the first quadrant of a coordinate plane.