Download IM7 - Unit 7 Geometric Figures.docx

Wentzville School District
Curriculum Development Template
Stage 1 – Desired Results
Unit 7 - Geometric Figures
Unit Title: Geometric Figures
Course: Integrated 7
Brief Summary of Unit: Students will use the properties that exist in and between angles and triangles to solve
problems. Students will also examine properties of three-dimensional figures to describe the real-world. Finally,
students will use the idea of scale factor to make enlargements and reductions of a given model.
Textbook Correlation: Glencoe Math Course 2 Chapter 7 (including 7-3 lab - Create Triangles and Problem-Solving
Investigation)
Time Frame: 3.5 weeks
Note: If you can get access to appropriate student technology, plan to include 7-3 lab - Draw Triangles (Geometer’s
Sketchpad), 7-4 lab - Investigate Online Maps and Scale Drawings, and 7-4 lab - Scale Drawings (Geometer’s
Sketchpad)
WSD Overarching Essential Question
Students will consider…
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How do I use the language of math (i.e. symbols,
words) to make sense of/solve a problem?
How does the math I am learning in the classroom
relate to the real-world?
What does a good problem solver do?
What should I do if I get stuck solving a problem?
How do I effectively communicate about math
with others in verbal form? In written form?
How do I explain my thinking to others, in written
form? In verbal form?
How do I construct an effective (mathematical)
argument?
How reliable are predictions?
Why are patterns important to discover, use, and
WSD Overarching Enduring Understandings
Students will understand that…
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Mathematical skills and understandings are used
to solve real-world problems.
Problem solvers examine and critique arguments
of others to determine validity.
Mathematical models can be used to interpret and
predict the behavior of real world phenomena.
Recognizing the predictable patterns in
mathematics allows the creation of functional
relationships.
Varieties of mathematical tools are used to
analyze and solve problems and explore concepts.
Estimating the answer to a problem helps predict
and evaluate the reasonableness of a solution.
Clear and precise notation and mathematical
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generalize in math?
How do I create a mathematical model?
How do I decide which is the best mathematical
tool to use to solve a problem?
How do I effectively represent quantities and
relationships through mathematical notation?
How accurate do I need to be?
When is estimating the best solution to a
problem?
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vocabulary enables effective communication and
comprehension.
Level of accuracy is determined based on the
context/situation.
Using prior knowledge of mathematical ideas can
help discover more efficient problem solving
strategies.
Concrete understandings in math lead to more
abstract understanding of math.
Transfer
Students will be able to independently use their learning to…
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Reason and solve problems about two-dimensional and three-dimensional objects by knowing the attributes of
geometric figures.
Read and analyze maps, scale drawings, blueprints, etc.
Meaning
Essential Questions
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How does geometry help us describe realworld objects?
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Understandings
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Geometric shapes have specific attributes
that are used to describe and solve problems
about the shape..
What tools could best be used to draw
geometric shapes?
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Triangles can be classified by angles and/or
sides.
How can knowing the properties of angles and
triangles help us find missing measurements?
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The relationships between the angles made
by intersecting lines can be used to solve
problems.
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Angle relationships can be used to find
unknown angle measurement in a figure.
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Three-dimensional figures’ cross sections are
two-dimensional figures.
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By analyzing cross sections of a threedimensional figure, we can better understand
How can angle relationships help us solve for
unknown angle measurements?
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How can angle measurements be determined
without using a protractor?
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What patterns are there in the measures of the
angles that are formed when lines intersect?
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How are supplementary, complementary,
vertical, and adjacent angles similar? How are
they different?
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How can you use a scale factor to represent
real-world objects on a piece of paper or
model?
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How can you use a map to estimate the
distance between two locations?
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How does drawing the different views of a
three-dimensional figure help you have a
better understanding of the figure?
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How does the slope and position of a plane
cutting through a three-dimensional figure
affect the resulting cross section?
the properties of the figure.
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Scale is the relationship between an actual
object and a drawing or model of that object.
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Scale drawings can be used to find real
lengths and areas.
Acquisition
Key Knowledge
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Line segment
acute triangle
adjacent angles
base
complementary angles
cone
congruent
congruent segments
coplanar
cross section
cylinder
diagonal
edge
equilateral triangle
face
isosceles triangle
obtuse triangle
plane
polyhedron
prism
pyramid
right triangle
scale
scale drawing
scale factor
Key Skills
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Classify angles, and identify vertical and
adjacent angles.
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Use properties of vertical and adjacent angles
to solve for missing angles and/or values.
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Classify angles, and Identify supplementary
and complementary angles.
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Use properties of complementary and
supplementary angles to solve for missing
angles and/or values.
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Draw triangles using given angles or given
side lengths.
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Identify and classify triangles and find missing
angles. (Using triangle sum theorem.)
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Make a model in order to solve problems.
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Solve problems involving scale drawings
(using scale factors, models, drawings, and
actual dimensions).
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Draw three-dimensional figures given the top,
side and front views and vice versa.
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scale model
scalene triangle
supplementary angles
triangle sum theorem
vertex
vertical angle
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Identify and draw three-dimensional figures,
including naming the specific parts of threedimensional figures.
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Name the two-dimensional cross-section when
a three dimensional figure is sliced with a
plane in various directions.
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Use protractors, rulers, and technology to
create specified geometric shapes.
Standards Alignment
MISSOURI LEARNING STANDARDS
Draw, construct, and describe geometrical figures and describe the relationship between them.
(7.G.1) Solve problems involving scale drawings of geometric figures, including computing actual lengths and
areas from a scale drawing and reproducing a scale drawing at a different scale.
(7.G.2) Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given
conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions
determine a unique triangle, more than one triangle, or no triangle.
(7.G.3) Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane
sections of right rectangular prisms and right rectangular pyramids.
Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
(7.G.5) Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step
problems to write and solve simple equations for an unknown angle in a figure.
MP.1 Make sense of problems and persevere in solving them.
MP.2 Reason abstractly and quantitatively.
MP.3 Construct viable arguments and critique the reasoning of others.
MP.4 Model with mathematics.
MP.5 Use appropriate tools strategically.
MP.6 Attend to precision.
MP.7 Look for and make use of structure.
MP.8 Look for and express regularity in repeated reasoning.
SHOW-ME STANDARDS
Goals:
1.1, 1.4, 1.5, 1.6, 1.7, 1.8
2.2, 2.3, 2.7
3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, 3.8
4.1, 4.4, 4.5, 4.6
Performance:
Math 1, 2, 5