Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 56260
Exploring Related Patterns
Students are asked to complete one of two number patterns, write ordered pairs composed of corresponding terms, graph the ordered pairs, and
identify a relationship between corresponding terms of the patterns.
Subject(s): Mathematics
Grade Level(s): 5
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, numerical patterns, rules, terms, ordered pairs, coordinate plane, quadrant one, x-axis, y-axis
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_Exploring Related Patterns_Worksheet.docx
FORMATIVE ASSESSMENT TASK
Instructions for Implementing the Task
This task can be administered individually, in small groups, or whole group.
1. The teacher shows the student the two rules and the table on the attached Graphing Exploring Related Patterns worksheet, and reads aloud to the student:
Pattern A begins at one and increases by two each step.
Pattern B begins at five and increases by two each step.
2. The teacher then asks the student to complete the table based on the given rules.
3. The teacher asks the student to write ordered pairs in which the values for Pattern A are the x-coordinates and the corresponding values for Pattern B are the
y-coordinates and to graph the ordered pairs on the given coordinate grid.
4. Finally, the teacher asks the student to identify a relationship between corresponding terms. If necessary, the teacher can prompt the student by asking, “What do you
notice about the values one and five; how do they compare to the next set of values three and seven?”
page 1 of 3 TASK RUBRIC
Getting Started
Misconception/Error
The student is unable to write the ordered pairs correctly.
Examples of Student Work at this Level
The student completes the table correctly but reverses the order of the coordinates in the ordered pairs. The student pairs non-corresponding values when writing the
ordered pairs.
The student incorrectly calculates values in the table.
Questions Eliciting Thinking
When we plot these points we want to use the values in pattern A as the x-coordinates and the corresponding values in pattern B as the y-coordinates. Where does the xcoordinate go when you write an ordered pair?
What does it mean to increase by one? Increase by two?
How could we continue this pattern?
Instructional Implications
Provide the student with two simple number patterns and show the student how to create ordered pairs using corresponding terms of the patterns. For example, give the
student the multiples of three and the multiples of four (3, 6, 9, 12, 15, 18 and 4, 8, 12, 16, 20, 24) and have the student create ordered pairs with the x-coordinate as
the multiples of three and the y-coordinate as the multiples of four yielding (3, 4), (6, 8), (9, 12), (12, 16), (15, 20), and (18, 24). Emphasize that the x-coordinate is given
first in the ordered pair and the y-coordinate is given second.
Provide additional problems for the student in which the first few terms of a pattern are given. Ask the student to continue the pattern by writing three more terms. Have
the student describe the rule he or she discerned in the pattern and how additional terms were calculated.
Moving Forward
Misconception/Error
The student is unable to graph the ordered pairs.
Examples of Student Work at this Level
The student continues the pattern and writes the ordered pairs correctly but is unable to correctly or accurately graph them on the coordinate grid, e.g., the student
interchanges the x-and y-coordinates when graphing.
Questions Eliciting Thinking
Which line on the grid is the x-axis and which is the y-axis?
When you plot points on a graph what do you do first?
Which point in the ordered pair goes with each axis?
What does each number tell me to do on the coordinate grid?
Instructional Implications
Explain the relationship between an ordered pair of numbers of the form (x, y) and the location of the point in the coordinate plane that corresponds to the ordered pair.
Have the student identify the coordinates of graphed points and graph given ordered pairs, focusing on points in the first quadrant and on the positive portions of the axes
as well as at the origin.
Almost There
Misconception/Error
The student needs prompting to describe a relationship between the two patterns of numbers.
Examples of Student Work at this Level
The student correctly completes the table, writes and graphs the ordered pairs, yet is unable to describe a relationship between the corresponding terms. The student
needs much prompting to explain how the terms are related.
Questions Eliciting Thinking
What do you notice about the values one and five? How do they compare to the next set of values three and seven?
How much more is five than one? Is that the same for three and seven? Will that work for every pair of terms? Why or why not?
Instructional Implications
Guide the student to see that the second pattern contains numbers that are four more than the corresponding term in the first pattern.
Provide the student with several different pairs of related patterns. Model for the student how to relate the patterns by describing how to calculate one term from the
corresponding term of the other pattern. Emphasize that a good rule must work for every pair of corresponding terms in the patterns. Provide additional examples for the
student to explore and ask the student to find rules.
Got It
page 2 of 3 Misconception/Error
The student successfully completes the task using and justifying an appropriate strategy.
Examples of Student Work at this Level
The student correctly completes the table, writes and graphs the ordered pairs, and says each term in pattern B is always four more than the corresponding term from
pattern A.
Questions Eliciting Thinking
Can you find a way to describe how the coordinates of these ordered pairs are related: (1, 2), (2, 4), (3, 6), 4, 8)?
Can you think of two more related patterns and write the corresponding terms as ordered pairs?
Instructional Implications
Provide the student with a graphed number pattern and have the student describe a rule that relates the x- and y-coordinates of the points.
Have the student create more related patterns, write the corresponding terms as ordered pairs, and graph the ordered pairs.
Provide instruction on how to plot points in the second, third, and fourth quadrants.
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
Exploring Related Patterns worksheet
SOURCE AND ACCESS INFORMATION
Contributed by: MFAS FCRSTEM
Name of Author/Source: MFAS FCRSTEM
District/Organization of Contributor(s): Okaloosa
Is this Resource freely Available? Yes
Access Privileges: Public
License: CPALMS License - no distribution - non commercial
Related Standards
Name
MAFS.5.OA.2.3:
Description
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.
page 3 of 3