Download Gary School Community Corporation Unit of Study: 5 Grade: 5th Unit

Gary School Community Corporation
Mathematics Department Unit Document
Unit of Study: 5
Grade: 5th
Unit Name: Geometry- Polygons and Circles
Duration of Unit: 15 days
UNIT FOCUS
Standards for Mathematical Content
Standard Emphasis
Critical
5.M.3: Develop and use formulas for the area of triangles,
parallelograms and trapezoids. Solve real-world and other
mathematical problems that involve perimeter and area of triangles,
parallelograms and trapezoids, using appropriate units for measures
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5.G.1: Identify, describe, and draw triangles (right, acute, obtuse) and
circles using appropriate tools (e.g., ruler or straightedge, compass and
technology). Understand the relationship between radius and
diameter.
5.G.2: Identify and classify polygons including quadrilaterals,
pentagons, hexagons, and triangles (equilateral, isosceles, scalene,
right, acute and obtuse) based on angle measures and sides. Classify
polygons in a hierarchy based on properties
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.5: Use appropriate tools strategically
PS.6: Attend to Precision
PS.7: Look for and make use of structure
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)
Important
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Additional
Essential Questions/
Learning Targets
Big Ideas/Goals
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Polygons can be classified
according to their attributes
A shape is a quadrilateral
when it has exactly 4 sides
and is a polygon.
To be a polygon the figure
must be a closed plane figure
with at least three straight
sides.
Triangles can be named and
classified according to their
angles or their sides.
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Geometry is the mathematics •
of space and shape.
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Attributes of quadrilaterals
can determine how they are
classified.
A square is always a
rectangle because a square
will always have 4 right
angles like a rectangle.
A rectangle does not have to
have 4 equal sides like a
square. It can have 4 right
angles without 4 equal sides.
Therefore, a rectangle is not
always a square.
A square is always a
rhombus because it has 4
equal sides like a rhombus
and it is also a rectangle
because it has 4 right angles
like a rectangle.
A rhombus does not have to
have right angles like a
square. It can have 4 equal
sides without having 4 right
angles. Therefore a rhombus
is not always a square.
A parallelogram can be a
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What attributes are needed
classify different types of
quadrilaterals?
What attributes are needed
to classify different types of
triangles?
How do we use triangle
sides to classify triangles?
How do the angle measures
of a triangle determine the
way it is named?
What are some examples of
geometric shapes and
objects in your everyday
world?
• What are properties of a
quadrilateral?
• What attributes distinguish
a square from a rhombus?
How are they alike?
• What attributes distinguish
a rectangle from a
parallelogram?
“I Can” Statements
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I can classify quadrilaterals
according to their attributes.
I can describe the attributes
that distinguish different
triangles.
•
I can determine whether a
triangle is acute, right, or
obtuse.
• I can classify and name a
triangle by measuring its
angles.
• I can name and identify
geometric shapes and
objects around me.
•
•
I can describe, analyze,
create, and compare
properties of 2-D and 3-D
figures.
I can justify the classification
of different quadrilaterals.
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rectangle if it has 4 right
angles.
UNIT ASSESSMENT TIME LINE
Beginning of Unit – Pre-Assessment
Assessment Name: Show Me What You Know
Assessment Type: Constructed Response
Assessment Standards: 5.M.3, 5.G.1, 5.G.2
Assessment Description:
By the conclusion of this unit, students should be able to demonstrate the following competencies:
Classify quadrilaterals (square, rectangle, parallelogram, kite, trapezoid, and rhombus).
Classify the different types of triangles by their attributes.
Identify and sort two-dimensional and geometric figures by their properties. (circle, half/quarter circle,
triangle, quadrilaterals, pentagon, hexagon)
Classify two-dimensional figures in a hierarchy based on properties.
Classify polygons by attribute
A pre-assessment of the above skills
Throughout the Unit – Formative Assessment
Assessment Name: Investigating Triangles
Assessment Type: Exit Ticket
Assessing Standards: 5.G.1
Assessment Description: Angles are difficult, complicated figures for students to understand because
they must be understood as a rotation from one place to the next, as a geometric shape, and a combination
of both when measuring . Be prepared to help students identify individual angles in a triangle and deal
with misconceptions about those angles.
Assessment Name: Investigating Polygons
Assessment Type: Exit Ticket
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Assessing Standards: 5.G.2
Assessment Description: The purpose of this task is for students to become familiar with the
properties of quadrilaterals.. They will classify two-dimensional shapes into a hierarchy based on
properties. Details learned in earlier grades need to be used in the descriptions of the attributes of
shapes. The more ways that students can classify and discriminate shapes, the better they can
understand them. They will identify the attributes of each quadrilateral, then compare and contrast
the attributes of different quadrilaterals The shapes are not limited to quadrilaterals.
Assessment Name: Quadrilateral Check for Understanding
Assessment Type: Selected Response, Constructed Response
Assessing Standards: 5.G.2
Assessment Description: The purpose of this task is to motivate students to examine relationships
among geometric properties. According to Van Heile, the students move from recognition or description to
analysis. When asked to describe geometric figures, students rarely mention more than one property or
describe how two properties are related. In this activity, by having to choose figures according to a pair of
properties, students should go beyond simple recognition to an analysis of the properties and how they
interrelate
End of Unit – Summative Assessments
Assessment Name: Quadrilateral Hierarchy Diagram
Assessment Type: Performance Task
Assessing Standards: 5.M.3, 5.G.1, 5.G.2
Assessment Description:
The students will create a Hierarchy Diagram using the terms: quadrilaterals, parallelogram, non
parallelograms, rectangle, square, rhombus, trapezoid, kite, and other:
Classify quadrilaterals (square, rectangle, parallelogram, kite, trapezoid, and rhombus).
Classify the different types of triangles by their attributes.
Identify and sort two-dimensional and geometric figures by their properties. (circle, half/quarter
circle, triangle, quadrilaterals, pentagon, hexagon)
Classify two-dimensional figures in a hierarchy based on properties.
Classify polygons by attribute
PLAN FOR INSTRUCTION
Unit Vocabulary
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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
Rhombus
Quadrilateral
Area
Polygon
Square
Triangle
Rectangle
Parallelogram
Pentagon
Hexagon
Cube
Trapezoid
Right triangle
Kite
Attribute
Hierarchy
Unit Resources/Notes
Include district and supplemental resources for use in weekly planning
Targeted Process Standards for this Unit
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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.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.
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