MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 8
Unit Description
Big Idea(s)
What enduring
understandings are essential
for application to new
situations within or beyond
this content?
Unit 11
Angle Relationships
Suggested Length: 3 weeks
Enduring Understandings
Develop an understanding of two- and three- dimensional space and
figures.
When parallel lines are cut by a transversal, corresponding, alternate
interior and alternate exterior angles are congruent.
Two shapes are similar if the lengths of all the corresponding sides are
proportional and all the corresponding angles are congruent.
Two similar figures are related by a scale factor, which is the ratio of the
lengths of the corresponding sides.
Congruent figures have the same size and shape.
Enduring Skills Rubric measures competency of the following skills:
Understand similar figures have angles with the same measure and sides
that are proportional and understand that a scale factor greater than one
will produce an enlargement in the figure, while a scale factor less than
one will produce a reduction in size.
Use exploration and deductive reasoning to determine relationships that
exist between a) angle sums and exterior angle sums of triangles, b) angles
created when parallel lines are cut by a transversal, and c) the angle-angle
criterion for similarity of triangle.
Use deductive reasoning to find the measure of missing angles.
Essential Question(s)
How can I tell if two figures are similar?
What questions will provoke
and sustain student
engagement while focusing
learning?
In what ways can I represent the relationships that exist between similar
figures using the scale factors, length ratios, and area ratios?
What strategies can I use to determine missing side lengths and areas of
similar figures?
Under what conditions are similar figures congruent?
When I draw a transversal through parallel lines, what are the special angle
and segment relationships that occur?
Why do I always get a special angle relationship when any two lines
intersect?
Standards
Curriculum and Instruction
Standards for Mathematical Practice
3. Construct viable arguments and critique the reasoning of others.
In grade 8, students construct arguments using verbal or written
2015-2016
Page 1 of 5
MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 8
explanations accompanied by expressions, equations, inequalities, models,
and graphs, tables, and other data displays (i.e. box plots, dot plots,
histograms, etc.). They further refine their mathematical communication
skills through mathematical discussions in which they critically evaluate their
own thinking and the thinking of other students. They pose questions like
“How did you get that?”, “Why is that true?” “Does that always work?” They
explain their thinking to others and respond to others’ thinking.
Standards for Mathematical Content
8.G.5 Use informal arguments to establish facts about the angle sum and
exterior angle of triangles, about the angles created when parallel lines are
cut by a transversal, and the angle‐angle criterion for similarity of triangles.
For example, arrange three copies of the same triangle so that the three
angles appear to form a line, and give an argument in terms of transversals
why this is so.
Supporting Standard(s)
Which related standards will
be incorporated to support
and enhance the enduring
standards?
Instructional Outcomes
What must students learn
and be able to do by the
end of the unit to
demonstrate mastery?
Essential Vocabulary
What vocabulary must
students know to
understand and
communicate effectively
about this content?
Resources/Activities
What resources could we
use to best teach this unit?
Curriculum and Instruction
8.G.4 Understand that a two‐dimensional figure is similar to another if the
second can be obtained from the first by a sequence of rotations,
reflections, translations, and dilations; given two similar two‐dimensional
figures, describe a sequence that exhibits the similarity between them.
I am learning to…
• Create angles using parallel lines and a transversal.
• Identify and analyze angle relationships. (ie; linear pairs, interior/exterior,
adjacent, complementary, supplementary, vertical, corresponding and
alternate interior/exterior).
• Recognize that similar triangles have congruent angles and
corresponding proportional sides.
• Apply properties of angles to create similar triangles.
Essential Vocabulary
exterior angles, interior angles, alternate interior angles, angle-angle
criterion, deductive reasoning, vertical angles, adjacent, supplementary,
complementary, corresponding, scale factor, transversal, parallel lines
Supporting Vocabulary
Similar, Congruent, Triangle, proportional
Resources/Activities
www.estimation180.com
www.visualpatterns.org
101Questions
http://www.101qs.com/
Dan Meyer’s Website
http://blog.mrmeyer.com/
Dan Meyer has created many problem-based learning tasks. The tasks
have great hooks for the students and are aligned to the standards.
Andrew Stadel
https://docs.google.com/spreadsheet/ccc?key=0AkLk45wwjYBudG9LeX
2015-2016
Page 2 of 5
MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 8
Rad0lHM0E0VFRyOEtRckVvM1E#gid=0
Andrew Stadel has created many problem-based learning tasks using
the same format as Dan Meyer.
Robert Palinsky
http://robertkaplinsky.com/lessons/
Robert Palinsky has created many tasks that engage students with real
life situations.
Geoff Krall’s Emergent Math
http://emergentmath.com/my-problem-based-curriculum-maps/
Geoff Krall has created a curriculum map structured around problembased learning tasks.
Mathematics in Movies
http://www.math.harvard.edu/~knill/mathmovies/
Short movie clips related to a variety of math topics.
Mathematical Fiction
http://kasmana.people.cofc.edu/MATHFICT/browse.php
Plays, short stories, comic books and novels dealing with math.
The Shodor Educational Foundation
http://www.shodor.org/interactivate/lessons/byAudience/
This website has extensive notes, lesson plans and applets aligned with
the standards.
NEA Portal Arkansas Video Lessons on-line
http://neaportal.k12.ar.us/index.php/9th-12th-grades-mathematics/
The NEA portal has short videos aligned to each standard. This resource
may be very helpful for students who need review at home.
Learnzillion
http://learnzillion.com/common_core/math/hs
This is another good resource for parents and students who need a
refresher on topics.
Math Words
http://www.mathwords.com/
This is a good reference for math terms.
National Library of Virtual Manipulatives
http://nlvm.usu.edu/en/nav/vlibrary.html
Java must be enabled for this applet to run. This website has a wealth of
virtual manipulatives helpful for use in presentation. Listed by domain.
Geogebra Download
http://www.geogebra.org/cms/download
Free software similar to Geometer’s Sketchpad. This program has
applications for algebra, geometry & statistics.
Remember there are other sources in your school that may not be listed
on this common resources list due to variation in each individual
school. Examples of other great resources your school may have
access to include: Everyday Math Games, Investigations, Everyday
Partner Games, AVMR file folders, Ongoing Assessment Project, etc. The
Kentucky Numeracy Project is also a great resource that can be
Curriculum and Instruction
2015-2016
Page 3 of 5
MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 8
searched by AVMR strand, CCSS, and grade level. Find this resource at
http://knp.kentuckymathematics.org/#!/page_knphome. Kentucky
teachers can use it for free. Just put in your school email address and the
username “mathfun”, and password is “859”.
Curriculum and Instruction
2015-2016
Page 4 of 5
Curriculum and Instruction
2015-2016
Page 5 of 5