Gary School Community Corporation
Mathematics Department Unit Document
Unit Number: 7
Grade: 5th
Unit Name: Graphing Coordinate Planes
Duration of Unit: 10 days
UNIT FOCUS
Standards for Mathematical Content
Standard Emphasis
Critical
5.AT.5: Solve real-world problems involving addition, subtraction,
multiplication, and division with decimals to hundredths, including
problems that involve money in decimal notation (e.g. by using
equations to represent the problem).
Important
Additional
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5.AT.6: Graph points with whole number coordinates on a coordinate
plane. Explain how the coordinates relate the point as the distance
from the origin on each 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).
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5.AT.8: Define and use up to two variables to write linear expressions
that arise from real-world problems, and evaluate them for given
values
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5.AT.7: Represent real-world problems and equations by graphing
ordered pairs in the first quadrant of the coordinate plane, and
interpret coordinate values of points in the context of the situation.
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Mathematical Process Standards:
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PS.1: Make sense of problems and persevere in solving them.
PS.2: Reason abstractly and quantitatively
PS.3: Construct viable arguments and critique the reasoning of others
PS.4: Model with mathematics
PS.5: Use appropriate tools strategically
PS.6: Attend to Precision
PS.7: Look for and make use of structure
PS.8: Look for and express regularity in repeated reasoning
Big Ideas/Goals
Essential Questions/
Vertical Articulation documents for K – 2, 3 – 5, and 6 – 8 can be found at:
http://www.doe.in.gov/standards/mathematics (scroll to bottom)
“I Can” Statements
Learning Targets
On the coordinate plane, a point
represents the two facets of
information associated with an
ordered pair.
How does coordinate system
work?
Coordinate grid is a visual
method for showing
relationships between numbers.
How do coordinate grids help
you organize information?
I can identify the x- and y- axis.
I can locate the origin on the
coordinate system.
I can identify coordinates of a
point on a coordinate system.
I can interpret information in an
organized way from coordinate
grid.
Given two rules, students can
generate two numerical
patterns. Students create line
graphs from the patterns. This
explains a linear function and
why straight lines are generated
from the pattern.
What relationship can be
determined by analyzing two
sets of given rules?
I can analyze two set of given
rules to determine relationships.
The relationships are shown on
a coordinate grid. A coordinate
grid has two perpendicular
lines, or axes, labeled like
number lines. The horizontal
axis is called the x-axis. The
vertical axis is called the y-axis.
The point where the x-axis and
y-axis intersect is called the
origin.
How might a coordinate grid
help me understand the
relationship between two
numbers?
I can identify relationships
between corresponding terms.
Given two rules with an
apparent relationship, students
should be able to identify the
relationship between the
resulting sequences of the terms
in one sequence to the
corresponding terms in the
other sequence.
How can we represent
numerical patterns on a
coordinate grid?
I can recognize and describe the
connection between the ordered
pair and the x- and y- axis (from
the origin).
Graphical representations can
be used to make predictions ad
interpretations about real world
situations.
How can a coordinate system
help you better understand
other map systems?
I can use the coordinate system
to help me understand other
map systems.
I can graph points in the all
quadrants
I can generate two numerical
patterns using two given rules
and form ordered pairs
consisting of corresponding
terms form the two patterns,
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UNIT ASSESSMENT TIME LINE
Beginning of Unit – Pre-Assessment
Assessment Name: Coordinate Graph Pre-Assessment
Assessment Type: Pre-Assessment
Assessment Standards: 5.AT.5, 5.AT.6, 5.AT.7, 5.AT.8
Assessment Description: Students should be pre-assessed on the following skills to help focus your
lessons in this unit. They write expressions to express a calculation, e.g., writing to express the
calculation “add 8 and 7, then multiply by 2.” They also evaluate and interpret expressions, e.g., using
their conceptual understanding of multiplication to interpret as being three times as large as
18932+921, without having to calculate the indicated sum or product. Thus, students in Grade 5 begin
to think about numerical expressions in ways that prefigure their later work with variable expressions
(e.g., three times an unknown length is 3 L). In Grade 5, this work should be viewed as exploratory
rather than for attaining mastery; for example, expressions should not contain nested grouping
symbols, and they should be no more complex than the expressions one finds in an application of the
associative or distributive property, e.g., . Note however that the numbers in expressions need not
always be whole numbers.
Throughout the Unit – Formative Assessment
Assessment Name: Fly on the Ceiling
Assessment Type: Practice Presentation
Assessing Standards: 5.AT.6, 5.AT.7
Assessment Description: In this task student will grasp why Identifying points on a coordinate grid is
important in understanding how the coordinate system works and in constructing simple line graphs
to display data or to plot points. These skills further help us to examine algebraic functions and
relationships. The skills developed in this lesson can be applied cross- curricular to reading latitude
and longitude on a map and to plotting data points. An introductory activity to introduce the concept
of coordinate planes would be to ask students to look at the ceiling and ask them what they see. (In
most schools, you will have a modified grid system on the ceiling from the ceiling tiles. You may also
use floor tiles, be sure to arrange desk appropriately. If you do not have this, skip this.) If you have a
metal frame supporting the ceiling tiles, use these to create a coordinate grid. You might want to label
them just below the ceiling on the wall. (If no metal frame is visible, you may need to point out the grid
that is created where the ceiling tiles meet.) Be sure to label the lines created by the grid and not the
tiles themselves. Turn the lights out and pretend you found a fly. Using a flashlight, shine the light on
an intersection in the ceiling grid. Ask students to identify the ordered pair. Continue on until the class
has grasped the concept. Then give the students flashlights and call out different ordered pairs for
students to identify with the flashlight. Teacher can read the book Fly on the Ceiling by Julie Glass or a
similar book.
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Assessment Name: Battle Ship
Assessment Type: Game/ Exit Ticket
Assessing Standards: 5.AT.7, 5.AT.6
Assessment Description: The purpose of this task is to give students practice plotting points in the
first quadrant of the coordinate plane and naming coordinates of points. It could be easily adapted to
plotting points with negative coordinates. It also provides teachers with a good opportunity to assess
how well their students understand how to plot ordered pairs and identify the coordinates of points.
Students can play this after the teacher demonstrates how to find the point on the coordinate plane
that corresponds to an ordered pair. The teacher should help students set up their game boards the
first time they play and visit with each group of students to listen and watch what they are doing to
assess their understanding of the game and how to find ordered pairs. Also, it is good to listen to see if
they are properly labeling their axes and generating, identifying, forming, and correctly graphing the
ordered pairs on the coordinate plane.
Students play in pairs sitting opposite each other and take turns calling out ordered pairs. Players
should keep a list of the ordered pairs they call out written in (x, y) form on a piece of paper that both
players can see so there is no disagreement later on about what has been called (it is common for
students to transpose the coordinates). Then they are to mark the ordered pair they call out on the top
coordinate plane. They should mark in black if they missed and red if they hit their opponent’s boat.
On the bottom half of the grid paper they are to color black for the ordered pairs their opponent calls
out and color red for the ordered pairs that hit their ship.
Assessment Name: Catch a Thief
Assessment Type: Performance Task/ PBL
Assessing Standards: 5.AT.5, 5.AT.7, 5.AT.8
Assessment Description: This lesson reviews math skills related to time and money while introducing the
coordinate grid. Students will use these skills, as well as problem solving, reasoning, and
communication skills to solve a real-world problem. The objectives of the lesson include the following:
Students will plot points in all four quadrants of a coordinate grid that represents the map of a city.
Students will find the distance between points with the same x-values or the same y-values.
Students will calculate elapsed time in minutes.
In addition to the time and point data, students will use given clues to determine where a thief likely
left a briefcase of stolen money.
End of Unit – Summative Assessments
Assessment Name: Tell Me a Story
Assessment Type: Performance Task
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Assessing Standards: 5.AT.6, 5.AT.7, 5.AT.8
Assessment Description: In this lesson students will review plotting points and labeling axis.
Students generate a set of random points all located within the first quadrant. Students will plot and
connect the points and then create a short story that could describe the graph. Students must ensure
that the graph is labeled correctly and that someone could recreate their graph from their story.
PLAN FOR INSTRUCTION
Unit Vocabulary
Key terms are those that are newly introduced and explicitly taught with expectation of student
mastery by end of unit. Prerequisite terms are those with which students have previous
experience and are foundational terms to use for differentiation.
Key Terms for Unit
Prerequisite Math Terms
Axis/ axes
Coordinates
Coordinate Plane
First
Quadrant
Horizontal
Intersection of lines
Line
Ordered pairs
Origin
Parallel lies
Perpendicular lines
Point
Rule
Vertical
x-axis
x-coordinate
y-axis
y-coordinate
Unit Resources/Notes
Include district and supplemental resources for use in weekly planning
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Targeted Process Standards for this Unit
PS.1: Make sense of problems and persevere in solving them
Mathematically proficient students start by explaining to themselves the meaning of a problem and
looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They
make conjectures about the form and meaning of the solution and plan a solution pathway, rather than
simply jumping into a solution attempt. They consider analogous problems and try special cases and
simpler forms of the original problem in order to gain insight into its solution. They monitor and
evaluate their progress and change course if necessary. Mathematically proficient students check their
answers to problems using a different method, and they continually ask themselves, “Does this make
sense?” and "Is my answer reasonable?" They understand the approaches of others to solving complex
problems and identify correspondences between different approaches. Mathematically proficient
students understand how mathematical ideas interconnect and build on one another to produce a
coherent whole.
PS.2: Reason abstractly and quantitatively.
Mathematically proficient students make sense of quantities and their relationships in problem
situations. They bring two complementary abilities to bear on problems involving quantitative
relationships: the ability to decontextualize—to abstract a given situation and represent it
symbolically and manipulate the representing symbols as if they have a life of their own, without
necessarily attending to their referents—and the ability to contextualize, to pause as needed during
the manipulation process in order to probe into the referents for the symbols involved. Quantitative
reasoning entails habits of creating a coherent representation of the problem at hand; considering the
units involved; attending to the meaning of quantities, not just how to compute them; and knowing
and flexibly using different properties of operations and objects.
PS.3: Construct viable arguments and critique the reasoning of others
Mathematically proficient students understand and use stated assumptions, definitions, and
previously established results in constructing arguments. They make conjectures and build a logical
progression of statements to explore the truth of their conjectures. They analyze situations by
breaking them into cases and recognize and use counterexamples. They organize their mathematical
thinking, justify their conclusions and communicate them to others, and respond to the arguments of
others. They reason inductively about data, making plausible arguments that take into account the
context from which the data arose. Mathematically proficient students are also able to compare the
effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is
flawed, and—if there is a flaw in an argument—explain what it is. They justify whether a given
statement is true always, sometimes, or never. Mathematically proficient students participate and
collaborate in a mathematics community. They listen to or read the arguments of others, decide
whether they make sense, and ask useful questions to clarify or improve the arguments.
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PS.4: Model with mathematics
Mathematically proficient students apply the mathematics they know to solve problems arising in
everyday life, society, and the workplace using a variety of appropriate strategies. They create and use
a variety of representations to solve problems and to organize and communicate mathematical ideas.
Mathematically proficient students apply what they know and are comfortable making assumptions
and approximations to simplify a complicated situation, realizing that these may need revision later.
They are able to identify important quantities in a practical situation and map their relationships using
such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They analyze those
relationships mathematically to draw conclusions. They routinely interpret their mathematical results
in the context of the situation and reflect on whether the results make sense, possibly improving the
model if it has not served its purpose.
PS.5: Use appropriate Tools Strategically
Mathematically proficient students consider the available tools when solving a mathematical problem.
These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a
spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software.
Proficient students are sufficiently familiar with tools appropriate for their grade or course to make
sound decisions about when each of these tools might be helpful, recognizing both the insight to be
gained and their limitations. For example, mathematically proficient high school students analyze
graphs of functions and solutions generated using a graphing calculator. They detect possible errors
by strategically using estimation and other mathematical knowledge. When making mathematical
models, they know that technology can enable them to visualize the results of varying assumptions,
explore consequences, and compare predictions with data. Mathematically proficient students at
various grade levels are able to identify relevant external mathematical resources, such as digital
content located on a website, and use them to pose or solve problems. They are able to use
technological tools to explore and deepen their understanding of concepts.
PS.6: Attend to precision
Mathematically proficient students communicate precisely to others. They use clear definitions,
including correct mathematical language, in discussion with others and in their own reasoning. They
state the meaning of the symbols they choose, including using the equal sign consistently and
appropriately. They express solutions clearly and logically by using the appropriate mathematical
terms and notation. They specify units of measure and label axes to clarify the correspondence with
quantities in a problem. They calculate accurately and efficiently and check the validity of their results
in the context of the problem. They express numerical answers with a degree of precision appropriate
for the problem context.
PS.7: Look for and make use of structure
Mathematically proficient students look closely to discern a pattern or structure. They step back for an
overview and shift perspective. They recognize and use properties of operations and equality. They
organize and classify geometric shapes based on their attributes. They see expressions, equations, and
geometric figures as single objects or as being composed of several objects.
PS.8: Look for and express regularity in repeated reasoning
Mathematically proficient students notice if calculations are repeated and look for general methods
and shortcuts. They notice regularity in mathematical problems and their work to create a rule or
formula. Mathematically proficient students maintain oversight of the process, while attending to the
details as they solve a problem. They continually evaluate the reasonableness of their intermediate
results.
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