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Operations and Algebraic Thinking: Patterns and Ordered Pairs CCSS 5.OA.3 Facts & Worksheets

Finding patterns and correlations among different sets of numbers is an important skill in elementary algebra.

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Worksheets /Math /Grade 5 (ages 10-11) /Operations and Algebraic Thinking: Patterns and Ordered Pairs CCSS 5.OA.3 Facts & Worksheets
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Finding patterns and correlations among different sets of numbers is an important skill in elementary algebra. Different rules and patterns can be set for different sets of numbers, and it requires critical thinking and an open mind to be able to see these patterns.

See the fact file below for more information on the Operations and Algebraic Thinking: Patterns and Ordered Pairs or alternatively, you can download our 29-page Operations and Algebraic Thinking: Patterns and Ordered Pairs CCSS 5.OA.3 worksheet pack to utilise within the classroom or home environment.

Key Facts & Information

LEARNING OBJECTIVE:

  • At the end of the lesson, students will be able to generate patterns using given rules, identify the relationships between these patterns, form ordered pairs based on these patterns, and graph these ordered pairs on a coordinate plane.

A NOTE FOR THE TEACHER

  • When finding patterns and ordered pairs, take note of the following:
    • Always find a generalization based on all the terms in the table
    • If lost, trial and error is usually a good strategy to use
    • Don’t rush, since it’s very easy to make careless mistakes

THEORY:

  • Finding patterns and correlations among different sets of numbers is an important skill in elementary algebra. Different rules and patterns can be set for different sets of numbers, and it requires critical thinking and an open mind to be able to see these patterns.
  • Take, for example, 2 sets of data, x, and y respectively.
  • Rule 1: For the data of x, start with 1, and add 1 to each succeeding term
  • Rule 2: For the data of y, start with 5, and add 5 to each succeeding term

  • What relationship can we get from data x and data y?
  • If we look closely, we can notice that in every column, the terms in y are 5 times the terms in x. This is the main generalization we can make from the two data sets.
  • Terms in algebra usually come in the form of inputs (x) and outputs (y). Different rules can be made on these inputs to produce specific outputs.
  • Take, for example, the following:
  • Rule 1: Multiply the input by 5
  • Rule 2: Add 3 to the result to get the output

  • The terms from x and y can be written in what we call ordered pairs, with the notation (x, y), where x and y are replaced with the corresponding terms. For the previous example, the ordered pairs are as follows:
    • (2 , 13), (4 , 23), (6 , 33), (8 , 43)
  • Knowing how to graph these ordered pairs is an important skill, as it lets us visualize patterns and trends within given data sets. Take, for instance, this example, where the terms of the outputs (y) are twice that of the inputs (x)
  • The ordered pairs are the following:
    • (1 , 2) (2 , 4)  (3 , 6)  (4 , 8)
  • On the coordinate plane, we graph all of the x-values from the inputs along the horizontal axis called the x-axis. Subsequently, all of the y-values from the outputs are plotted along the vertical axis called the y-axis.
  • The intersection of the x-values and y-values of each ordered pair along the coordinate axis is called a point.

Operations and Algebraic Thinking: Patterns and Ordered Pairs CCSS 5.OA.3 Worksheets

This is a fantastic bundle that includes everything you need to know about Operations and Algebraic Thinking: Patterns and Ordered Pairs across 29 in-depth pages. These are ready-to-use worksheets that align with the Common Core CCSS code 5.OA.3 for Operations and Algebraic Thinking: Patterns and Ordered Pairs.

Table of contents

  • A lesson plan
  • Warm up activity
  • Math theory explained
  • Assisted learning activities
  • Independent learning activities
  • Extension activities and games
  • Answer keys

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Use With Any Curriculum

These worksheets have been specifically designed for use with any international curriculum. You can use these worksheets as-is, or edit them using Google Slides to make them more specific to your own student ability levels and curriculum standards.

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