Download Grade 4 Math Unit 5 - Cleburne Independent School District

Grade 4 Math
Unit 5
Title
Suggested Time Frame
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5 and 6 Six Weeks
Suggested Duration: 30 days
Guiding Questions
Unit 5 – Geometry
Big Ideas/Enduring Understandings
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Relationships between geometric figures can be described and
compared.
Geometric figures can be described, compared, and transformed
using symmetry and congruence.
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What angles are formed by each set of lines?
Can lines be both intersecting and perpendicular?
How do you differentiate between angles?
How do you differentiate between transformations?
How can you determine if a figure has symmetry?
What are the attributes of a two-dimensional or three-dimensional
shape?
Vertical Alignment
*TEKS one level below*
*TEKS one level below*
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TEA MATH VERTICAL ALIGNMENT—K-6 Grade
Sample Assessment Question
Coming soon!
CISD Math Grade 4-Unit 5
Updated May18, 2015
The resources included here provide teaching examples and/or meaningful learning experiences to address the District Curriculum. In order to address the TEKS to the proper
depth and complexity, teachers are encouraged to use resources to the degree that they are congruent with the TEKS and research-based best practices. Teaching using only the
suggested resources does not guarantee student mastery of all standards. Teachers must use professional judgment to select among these and/or other resources to teach the
district curriculum. Some resources are protected by copyright. A username and password is required to view the copyrighted material. District Specificity/Examples TEKS
clarifying examples are a product of the Austin Area Math Supervisors TEKS Clarifying Documents.
Ongoing TEKS
4.01 Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding.
The student is expected to:
(A) apply mathematics to problems arising in everyday life, society, and the workplace;
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Focus is on application
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Students should assess which tool to apply rather
than trying only one or all
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Students should evaluate the effectiveness of
representations to ensure they are communicating
mathematical ideas clearly
Students are expected to use appropriate
mathematical vocabulary and phrasing when
communicating ideas
Students are expected to form conjectures based on
patterns or sets of examples and non-examples
(B) use a problem-solving model that incorporates analyzing given information, formulating a plan
or strategy, determining a solution, justifying the solution, and evaluating the problem-solving
process and the reasonableness of the solution;
(C) select tools, including real objects, manipulatives, paper and pencil, and technology as
appropriate, and techniques, including mental math, estimation, and number sense as appropriate,
to solve problems;
(D) communicate mathematical ideas, reasoning, and their implications using multiple
representations, including symbols, diagrams, graphs, and language as appropriate;
(E) create and use representations to organize, record, and communicate mathematical ideas;
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(F) analyze mathematical relationships to connect and communicate mathematical ideas; and
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(G) display, explain, and justify mathematical ideas and arguments using precise mathematical
language in written or oral communication
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CISD Math Grade 4-Unit 5
Updated May18, 2015
Precise mathematical language is expected.
Knowledge and Skills with
Student Expectations
District Specificity/ Examples
Vocabulary
Resources
Resources listed and
categorized to indicate
suggested uses. Any
additional resources must be
aligned with the TEKS.
GEOMETRY---15 days
MAT.4.06 Geometry and
measurement. The student
applies mathematical
process standards to
analyze geometric
attributes in order to
develop generalizations
about their properties. The
student is expected to:
(A) Identify points, lines,
line segments, rays, angles,
and perpendicular and
parallel lines
Supporting vocabulary – straight angle
4.06A
This standard asks students to draw two-dimensional geometric
objects and to also identify them in two-dimensional figures. This
is the first time that students are exposed to rays, angles, and
perpendicular and parallel lines. Examples of points, line
segments, lines, angles, parallelism, and perpendicularity can be
seen daily. Students may not easily identify lines and rays
because they are more abstract.
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**Visual Representations…next page.
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CISD Math Grade 4-Unit 5
Updated May18, 2015
Angles
Geometric
attributes
Lines
Line segments
Parallel line
Perpendicular line
Points
Rays
Congruent
Lines of symmetry
Symmetry
Two-dimensional
Acute angles
Obtuse angles
Right angles
Attributes
Polygons
Rhombus,
parallelogram,
trapezoid,
rectangle, square,
quadrilateral
Sides
Vertex (vertices)
HMH GoMath
Module 13
Region 11
Livebinder
http://illuminations
.nctm.org/
(B) Identify and draw one or
more lines of symmetry, if
they exist, for a twodimensional figure
CISD Math Grade 4-Unit 5
Updated May18, 2015
4.06B
Students need experiences with figures which are symmetrical and
on-symmetrical. Figures include both regular and on-regular
polygons. Folding cut-out figures will help students determine
whether a figure has one or more lines of symmetry.
This standard only includes line symmetry not rotational
symmetry.
(C) Apply knowledge of
right angles to identify
acute, right, and obtuse
triangles;
4.06C
Given a set of different triangles, students measure the angles
(using a protractor or geometry exploration software) and classify
triangles according to their properties. Students organize their data
in a table and analyze patterns to match triangles with the most
appropriate name.
Right triangles can be a category for classification. A right triangle
has one right angle. There are different types of right triangles. An
isosceles right triangle has two or more congruent sides and a
scalene right triangles has no congruent sides.
(D) Classify two-dimensional 4.06D
figures based on the
Two-dimensional figures may be classified using different
characteristics such as, parallel or perpendicular or by angle
presence or absence of
measurement.
parallel or perpendicular
lines or the presence or
Parallel or Perpendicular Lines:
absence of angles of a
Students should become familiar with the concept of parallel and
perpendicular lines. Two lines are parallel if they never intersect
specified size
and are always equidistant. Two lines are perpendicular if they
intersect in right angles.
CISD Math Grade 4-Unit 5
Updated May18, 2015
CISD Math Grade 4-Unit 5
Updated May18, 2015
MAT.4.07 Geometry and
measurement. The student
applies mathematical
process standards to solve
problems involving angles
less than or equal to 180
degrees. The student is
expected to:
(A) Illustrate the measure of
an angle as the part of a
circle whose center is at the
vertex of the angle that is
"cut out" by the rays of the
angle. Angle measures are
limited to whole numbers
CISD Math Grade 4-Unit 5
Updated May18, 2015
4.07A
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Grade 4 introduces illustrating the measure of an angle as the part of
a circle whose center is at the vertex of the angle that is "cut out" by
the rays of the angle. Angle measures are limited to whole numbers.
Before students begin measuring angles with protractors, they need to
have some experiences with benchmark angles. They transfer their
understanding that a rotation about a point makes a complete circle to
recognize and sketch angles that measure approximately and . They
extend this understanding and recognize and sketch angles that measure
approximately and . They use appropriate terminology (acute, right and
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Center
Measure of an angle
Part of a circle
Rays
Vertex of an angle
Angle
Angle vertex
Degrees
1/360 of a circle
One degree
Center mark
Inner scale
Line
Outer scale
Protractor
Zero adge
HMH GoMath
Module 14
Region 11
Livebinder
http://illuminations
.nctm.org/
obtuse) to describe angles and rays (perpendicular).
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This standard brings up a connection between angles and circular
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measurement (360 degrees). Angle measure is a “turning point” in the
study of geometry. Students often find angles and angle measure to be
difficult concepts to learn, but that learning allows them to engage in
interesting and important mathematics. An angle is the union of two rays,
a and b, with the same initial point P. The rays can be made to coincide
by rotating one to the other about P, this rotation determines the size of
the angle between a and b. The rays are sometimes called the sides of the
angles.
(B) Illustrate degrees as the
units used to measure an
angle, where 1/360 of any
circle is one degree and an
angle that "cuts" n/360 out
of any circle whose center is
at the angle's vertex has a
measure of n degrees.
Angle measures are limited
to whole numbers
4.07B
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Grade 4 introduces illustrating degrees as the units used to measure
an angle, where
of any circle is one degree and an angle that
"cuts"
out of any circle whose center is at the angle's vertex has
a measure of n degrees. Angle measures are limited to whole
numbers.
Another way of saying this is that each ray determines a direction and the
angle size measures the change from one direction to the other. Angles
are measured with reference to a circle with its center at the common
endpoint of the rays, by considering the fraction of the circular arc
between the points where the two rays intersect the circle. An angle that
turns through 1/360 of a circle is called a “one-degree angle,” and
degrees are the unit used to measure angles in elementary school. A full
rotation is thus 360 degrees.
Two angles are called complementary if their measurements have the
sum of 90o. Two angles are called supplementary if their measurements
have the sum of 180o. Two angles with the same vertex that overlap only
at a boundary (ie share a side) are called adjacent angles. These terms
may come up in classroom discussion. This concept is developed
thoroughly in middle school.
CISD Math Grade 4-Unit 5
Updated May18, 2015
Adjacent angles
Non-overlapping
Like length, area and volume, angle measure is additive. The sum of
measurements of adjacent angles is the measurement of the angle
formed by their union. This leads to other important properties. If a right
angle is decomposed into two adjacent angles, the sum is , thus they are
complementary. Two adjacent angles that compose a “straight angle” of
180 must be supplementary.
(Source: Kaufman ISD Clarifying Docs)
CISD Math Grade 4-Unit 5
Updated May18, 2015
(C) Determine the
approximate measures of
angles in degrees to the
nearest whole number
using a protractor
(D) Draw an angle with a
given measure
CISD Math Grade 4-Unit 5
Updated May18, 2015
4.07C & 4.07D
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Grade 4 introduces determining the approximate measures of
angles in degrees to the nearest whole number using a protractor.
(E) Determine the measure
of an unknown angle
formed by two nonoverlapping adjacent angles
given one or both angle
measures
REVIEW – 15 days
CISD Math Grade 4-Unit 5
Updated May18, 2015
4.07E