Mathematics 2016-17—Grade 5
Weeks 32-33—May
enVisionmath2.0—Topic 14
Standards for Mathematical Practice
Beyond the Critical Area(s): Numerical Relationships and the Coordinate Plane
FOCUS for Grade 5
Supporting Work
20% of Time
5.MD.A.1
5.MD.B.2
Major Work
Additional Work
70% of time
10% of Time
5.NBT.A.1-2-3-4
5.OA.A.1-2
5.NBT.B.5-6-7
5.OA.B.3
5.NF.A.1-2
5.G.1-2
5.NF.B.3-4-5-6-7
5.G.B.3-4
5.MD.C.3-4-5
Required Fluency Standard: 5.NBT.B.5
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Standards in bold are specifically targeted within instructional materials.
Domains:
Geometry
Clusters:
Clusters outlined in bold should drive the learning for this period of instruction.
5.G.A Graph points on the coordinate plane to solve real-world and mathematical problems.
Standards:
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.
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Mathematics 2016-17—Grade 5
Weeks 32-33—May
enVisionmath2.0—Topic 14
Foundational Learning
4.MD.B.4
5.MD.B.2
Future Learning
5.OA.B.3
6.NS.C
6.EE.C.9
Key Student Understandings
Assessments
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Formative Assessment Strategies
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Evidence for Standards-Based Grading
Students understand the coordinate plane and its relationship to the number line.
Students understand that data can be represented in a coordinate graph, and the graph can be
analyzed to solve problems.
Common Misconceptions/Challenges
5.G.A Graph points on the coordinate plane to solve real-world and mathematical problems.
 Students may believe the order in plotting a coordinate point is not important. Have students plot points so that the position of the coordinates is
switched. For example, have students plot (3, 4) and (4, 3) and discuss the order used to plot the points. Have students create directions for others to
follow so that they become aware of the importance of direction and distance.
 Students commonly reverse the order of (x, y) coordinates. Teachers should be explicit when modeling coordinate graphing, by audibly and visually
counting along the horizontal axis, followed by counting up vertically to along the y-axis to reach the desired point. Careful modeling of writing ordered
pairs is crucial as well.
Instructional Practices
Domain: 5.G
Cluster: 5.G.A Graph points on the coordinate plane to solve real-world and mathematical problems.
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 ycoordinate).

5.G.A.1 and 5.G.A.2 deal with only the first quadrant (positive numbers) in the coordinate plane.

Students need to understand the underlying structure of the coordinate system and see how axes make it possible to locate points anywhere on a
coordinate plane. It is important that students create the coordinate grid themselves. This can be related to two number lines, allowing students to build
on previous experiences with moving along a number line.
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Mathematics 2016-17—Grade 5
Weeks 32-33—May
enVisionmath2.0—Topic 14

Students need multiple experiences plotting points. Provide multiple coordinates on a grid and have students explain how to get to a specified location.
Encourage students to articulate directions as they plot points.
o Example 1:
Students can use a classroom size coordinate grid to physically locate the coordinate point (5, 3) by
starting at the origin point (0,0), walking 5 units along the x axis to find the first number in the pair (5), and
then walking up 3 units for the second number in the pair (3). The ordered pair names a point on the grid.
o Example 2:
Graph and label the points below on a coordinate plane.
A (0, 0) “I moved over 0 units, then up 0 units.”
B (2, 4) “I moved 2 units to the right along the x-axis, then 4 units up.”
C (5, 5) “I moved to 5 on the x-axis, and then counted up 5 units to land at (5,5).”
D (4, 1) “I moved 4 units along the horizontal axis, and then I moved up one unit.”
E (2.5, 6) “I moved to halfway between 2 and 3 on the x-axis, and then I moved up 6 units vertically.”
F (3, 2) “I moved 3 units to the right, and then 2 units up to land at (3,2).
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Although students can often “locate a point,” students need understanding beyond simple skills. For example, initially, students often fail to distinguish
between two different ways of viewing the point (2, 3), say, as instructions: “right 2, up 3”; and as the point defined by being a distance 2 from the y-axis
and a distance 3 from the x-axis. In these two descriptions the 2 is first associated with the x-axis, then with the y-axis. Provide varied experiences such
as the examples below.
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Mathematics 2016-17—Grade 5
Weeks 32-33—May
enVisionmath2.0—Topic 14
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Mathematics 2016-17—Grade 5
Weeks 32-33—May
enVisionmath2.0—Topic 14
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.

This standard references real-world and mathematical problems, including the traveling from one point to another
and identifying the coordinates of missing points in geometric figures, such as squares, rectangles, and
parallelograms.
o Example:
Using the coordinate grid at right, which ordered pair represents the location of the School? Explain a
possible path from the school to the library.

Provide students with stories they can represent graphically, with multiple graphs created. How does changing a
variable affect the graph?
o Example 1:
Sara has saved $20. She earns $8 for each hour she works. If Sara saves all of her money, how much will she have after working 3 hours? 5
hours? 10 hours? Create a graph that shows the relationship between the hours Sara worked and the amount of money she has saved. What
other information do you know from analyzing the graph?
o Example 2:
Use the graph below to determine how much money Jack makes after working exactly 9 hours.

Provide opportunities for students to explain how they moved (using appropriate math vocabulary) on the coordinate grid. Surface the relationship
between the symbols in the equation, story or table, and the graphical representation. Make certain students are developing flexible strategies for
explaining the symbols and the graphs, and are able to create the ordered pairs from the graph, and the graph from the ordered pairs.
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Mathematics 2016-17—Grade 5
Weeks 32-33—May
enVisionmath2.0—Topic 14
Differentiation
5.G.A Graph points on the coordinate plane to solve real-world and mathematical problems .
 Have students create shapes or pictures on the coordinate grid, e.g., letter M: What coordinates (x,y) correspond
to the shape points?
 Have students move between plotting a letter or shape from the coordinates, and finding the coordinates from a
plotted shape or letter. Give less able students easier shapes to work with. Several shapes/letters can be plotted
on the same grid.
The Common Core Approach to Differentiating Instruction (engageny How to Implement a Story of Units, p. 14-20)
Linked document includes scaffolds for English Language Learners, Students with Disabilities, Below Level Students, and
Above Level Students.
Literacy Connections
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Academic Vocabulary Terms
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Vocabulary Strategies
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Literacy Strategies
Resources
enVisionmath2.0
Developing Fluency
Multiplication Fact Thinking Strategies
Topic 14 Pacing Guide
Grade 5 Games to Build Fluency
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Property of MPS
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