Math  /  5th Grade  /  Unit 7: Patterns and the Coordinate Plane

Patterns and the Coordinate Plane

Students are introduced to the coordinate plane and use it to represent the location of objects in space, as well as to represent patterns and real-world situations.

Math

Unit 7

5th Grade

Unit Summary

In Unit 7, the final unit of the 5th grade course, students are introduced to the coordinate plane and use it to represent the location of objects in space, as well as to represent patterns and real-world situations. 

Students have coordinated numbers and distance before, namely with number lines. Students were introduced to number lines with whole-number intervals in 2nd grade and used them to solve addition and subtraction problems, helping to make the connection between quantity and distance (2.MD.5—6). Then in 3rd Grade Math, students made number lines with fractional intervals, using them to understand the idea of equivalence and comparison of fractions, again connecting this to the idea of distance (3.NF.2). For example, two fractions that were at the same point on a number line were equivalent, while a fraction that was further from 0 than another was greater. Then, in 4th Grade Math, students learned to add, subtract, and multiply fractions in simple cases using the number line as a representation, and they extended it to all cases, including in simple cases involving fraction division, throughout 5th grade (5.NF.1—7). Students’ preparation for this unit is also connected to their extensive pattern work, beginning in Kindergarten with patterns in counting sequences (K.CC.4c) and extending through 4th grade work with generating and analyzing a number or shape pattern given its rule (4.OA.3).  

Thus, students start the unit thinking about the number line as a way to represent distance in one dimension and then see the usefulness of a perpendicular line segment to define distance in a second dimension, allowing any point in two-dimensional space to be located easily and precisely (MP.6). After a lot of practice identifying the coordinates of points as well as plotting points given their coordinates with coordinate grids of various intervals and scales, students begin to draw lines and figures on a coordinate grid, noticing simple patterns in their coordinates. Then, after students have grown comfortable with the coordinate plane as a way to represent two-dimensional space, they represent real-world and mathematical situations, as well as two numerical patterns, by graphing their coordinates. This visual representation allows for a rich interpretation of these contexts (MP.2, MP.4).

This work is an important part of “the progression that leads toward middle-school algebra” (6—7.RP, 6—8.EE, 8.F) (K–8 Publishers’ Criteria for the Common Core State Standards for Mathematics, p. 7). This then deeply informs students’ work in all high school courses. Thus, 5th grade ends with additional cluster content, but that designation should not diminish its importance this year and for years to come. 

Pacing: 16 instructional days (14 lessons, 1 flex day, 1 assessment day)

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Assessment

The following assessments accompany Unit 7.

Pre-Unit

Have students complete the Pre-Unit Assessment and Pre-Unit Student Self-Assessment before starting the unit. Use the Pre-Unit Assessment Analysis Guide to identify gaps in foundational understanding and map out a plan for learning acceleration throughout the unit.

Mid-Unit

Have students complete the Mid-Unit Assessment after Lesson 7.

Post-Unit

Use the resources below to assess student understanding of the unit content and action plan for future units.

Expanded Assessment Package

Use student data to drive instruction with an expanded suite of assessments. Unlock Pre-Unit and Mid-Unit Assessments, and detailed Assessment Analysis Guides to help assess foundational skills, progress with unit content, and help inform your planning.

Unit Prep

Intellectual Prep

Unit Launch

Before you teach this unit, unpack the standards, big ideas, and connections to prior and future content through our guided intellectual preparation process. Each Unit Launch includes a series of short videos, targeted readings, and opportunities for action planning to ensure you're prepared to support every student.

Intellectual Prep for All Units

  • Read and annotate “Unit Summary” and “Essential Understandings” portion of the unit plan. 
  • Do all the Target Tasks and annotate them with the “Unit Summary” and “Essential Understandings” in mind. 
  • Take the Post-Unit Assessment.

Essential Understandings

  • Just as the understanding of number and length can be applied in one dimension using a number line, number and length can be coordinated across two dimensions to understand the location of objects in a space. 
  • The point (2, 3) can be viewed in two different ways: (1) as instructions, “right 2, up 3,” and (2) as the point defined by being a distance 2 from the y-axis and a distance 3 from the x-axis. In these two interpretations the 2 is associated with the x-axis (in the first interpretation) and with the y-axis (in the second interpretation).
  • Just as relationships can exist between terms in one pattern, relationships can exist between corresponding terms in two patterns. This is the basis for all functional understanding. 
  • Graphing coordinate points that represent a real-world situation or patterns can help illuminate trends and features that may have otherwise been difficult to identify. 

Vocabulary

axis/x-axis/y-axis

corresponding terms

coordinate pair

coordinate/x-coordinate/y-coordinate

coordinate plane

ordered pair

origin

term

To see all the vocabulary for Unit 7 , view our 5th Grade Vocabulary Glossary.

Materials

  • Markers or crayons (3 per student)
  • Graph paper (5 sheets per student) — You can provide students with Inch Grid Paper if you don't have enough printed graph paper.
  • Optional: Quarter Inch Graph Paper (5 per student) — This is optional in case you don't have graph paper.

Unit Practice

Word Problems and Fluency Activities

Help students strengthen their application and fluency skills with daily word problem practice and content-aligned fluency activities.

Lesson Map

Topic A: Introduction to the Coordinate Plane

Topic B: Drawing Figures and Shapes in the Coordinate Plane

Topic C: Real-World Problems and Patterns on the Coordinate Plane

Common Core Standards

Key

Major Cluster

Supporting Cluster

Additional Cluster

Core Standards

Geometry

  • 5.G.A.1 — 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.G.A.2 — Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.

Operations and Algebraic Thinking

  • 5.OA.B.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.

Foundational Standards

Geometry

  • 4.G.A.1
  • 4.G.A.3
  • 5.G.B.4

Measurement and Data

  • 2.MD.B.6

Number and Operations—Fractions

  • 3.NF.A.2

Operations and Algebraic Thinking

  • 4.OA.C.5

Future Standards

Expressions and Equations

  • 6.EE.C.9

Geometry

  • 6.G.A.3

Ratios and Proportional Relationships

  • 6.RP.A.3

The Number System

  • 6.NS.C.6
  • 6.NS.C.8

Standards for Mathematical Practice

  • CCSS.MATH.PRACTICE.MP1 — Make sense of problems and persevere in solving them.

  • CCSS.MATH.PRACTICE.MP2 — Reason abstractly and quantitatively.

  • CCSS.MATH.PRACTICE.MP3 — Construct viable arguments and critique the reasoning of others.

  • CCSS.MATH.PRACTICE.MP4 — Model with mathematics.

  • CCSS.MATH.PRACTICE.MP5 — Use appropriate tools strategically.

  • CCSS.MATH.PRACTICE.MP6 — Attend to precision.

  • CCSS.MATH.PRACTICE.MP7 — Look for and make use of structure.

  • CCSS.MATH.PRACTICE.MP8 — Look for and express regularity in repeated reasoning.

Next

Define a coordinate plane and identify the coordinates of given points.

Lesson 1
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