Summer School Course Guide
Geometry
CURRICULUM AND INSTRUCTION
Time Management In Summer School
Each day in a summer school course lasts over 4 hours. To make planning more manageable and maintain
student interest, each day should be divided into manageable periods – each with clear learning objectives.
Examples of time-management plans for these independent periods are:
10 min
45 min
Bell Ringer / Warm Up
Lesson
Break class into 3 groups and
have them rotate between a
tech activity*, a group
activity and guided practice.
Bell Ringer / Warm Up
Lesson
Use a Kagan-style strategy*
in small groups,
10 min
10 min
5 min
Wrap Up
Quiz
Break
Next Period
Student Report-Out
Wrap Up
Break
Next Period
Review
Lesson
Mini-Lecture followed by:
o guided practice
o applications & problem solving
o writing or performance task
Wrap Up
Quiz
Break
Next Period
Curriculum Map
Summer school courses have approximately 60 hours of instructional time over 15 days for each session (a
single semester of material is taught in each session). This “Approximate Timeline” coordinates this available
time with the District’s curriculum map. See the curriculum map* for more information regarding the State
standards to which “Big Ideas” and “Essential Questions” correlate.
Approximate
Timeline
Note: Emphasis
should be given to
topics on which
the SBA focuses.
Additional time
will be used for
exams, etc.
Day 1
Big Ideas &
Essential Questions
Session 1
(1st Semester Material)
How do we use the language
of Geometry to express
mathematical ideas and
situations?

Geometry contains the
symbolic language and
Illutstrations & Potential Strategies
Note: A “Potential Strategy” is a tip on how to present/teach either in
general or for a specific topic. They should not be considered a
complete list of strategies. Many should be considered as
strategies to use on an ongoing basis, not limited to teaching a
particular concept.
Potential Strategy: Class & Team Activities (e.g. Kagan*) to
develop teams to work together in
subsequent learning.
Potential Strategy: Word wall.
Day 2

Day 3
Day 4
Day 5
Day 6
Day 7
Day 8
Day 9
Day 10
Day 11
Day 12
vocabulary for common
ideas including
undefined terms.
Definitions, postulates,
properties, and theorems
form the framework of
geometry.
How can inductive &
deductive reasoning be used
to prove geometric concepts?

Define inductive &
deductive reasoning.

Logical arguments
consist of a set of
hypotheses and
conclusions.
Potential Strategy: Have students watch video instruction
from the Khan Academy*.
Illustration: Julia drives from Belen to Albuquerque. She
stops in Los Lunas after driving 14 miles. If the
total distance she drove is 35 miles, how far is it
from Los Lunas to Albuquerque?
Potential Strategy:
Small group discussion.
Illustration: Identify the next term in the sequence: 5, 8,11, ...
and know which type of reasoning they are
using.
Illustration: Assume the following statement is true: “If it
rains, then my head gets wet.” Explain how you
know whether or not the converse is true.
How do geometric
Potential Strategy:
relationships and their
applications help us to solve
real world problems?
Illustration: Baker Avenue and Oak Steet intersect at an angle

Parallel lines cut by a
of 99. Pine Street is parallel to Oak Street and
transversal form angles
also intersects Baker Avenue. An alley meets
with specific
these roads at their intersection,
relationships.
forming a 30 angle with Pine

Triangles are classified
Street. A road crew must
99
by their angles and
determine the value of one-third
sides.
3x
the angle between the alley and

Triangles are congruent
Baker Avenue. Find this value
30
if their corresponding
for them.
parts are congruent.

Corresponding parts of
congruent triangles are
Illustration: Determine whether the triangles in the diagram
congruent.
are congruent and, if they are, explain why.

Recognizing congruency
in geometric figures
contributes to solving
real world problems.
How do geometric
relationships and their
applications help us to solve
real world problems?

Classification of
polygons, including
triangles and
quadrilaterals.

Measurement of interior
and exterior angles
within polygons.
Potential Strategy: Have students identify and categorize
various polygons (e.g. outdoor activity or
in the classroom).
Illustration:
Students should be able to find the value of x
in from the following diagram:
x°
35°


Day 13
Day 14
Day 15

Similar geometric
figures have
proportional attributes.
Ratios of similar shapes
are used in reduction
and enlargement, such
as in cartoons, drafting,
and digital animation.
Midpoint and distance
formula within a
coordinate plane.
Illustration:
Potential Strategy: Let students investigate how to find the
distance and midpoint in small groups,
then share their strategies with the class.*
Illustration:
Note: Formative
assessments may
dictate deviations
from this timeline.
Day 1
Day 2
Day 3
Day 4
Day 5
Day 6
Students should be able to find the length of
EF from the following diagram:
Draw segment AB on the coordinate plane
with endpoints A(2,5) and B(6,7). Find the
length of AB as well as the midpoint of AB .
Session 2
(2 Semester Material)
nd
How do geometric
relationships and their
applications help us to solve
real world problems?

Similar geometric
figures have
proportional attributes.

Ratios of similar shapes
are used in reduction
and enlargement, such
as in cartoons, drafting,
and digital animation.

Pythagorean Theorem
has real world
applications in civil
engineering,
architecture, mapmaking
& GPS.

Right triangles can be
used to determine
distances in the real
world, such as surveying
or navigation.
Potential Strategy: Start Session 2 with a review of material
taught in Session 1.
Illustration: An irregularly shaped object is moved as
depicted in the diagram below. Identify how it
was moved.
Potential Strategy: Indirect measurement of real world
objects using similarity (e.g. outdoor
activity).
Illustration: A hot-air balloon is 202 feet above the point on
the ground where it took off. If you are 136 feet
from that point, what is the angle of elevation
you need to use to look directly at the balloon?
202 ft
x
136 ft
Day 7
Day 8
Day 9
Day 10
Day 11
Day 12
Day 13
Day 14
How do we measure 2D &
3D figures and apply the
results to real world
situations?

AREA: Understanding
the measurements of
area helps solve real
world problems – such
as the use of floor plans.

SURFACE AREA:
Understanding the
measurements of surface
area helps solve real
world problems – such
as determining the
coverage of point.

VOLUME:
Understanding the
measurements of
volume helps solve real
world problems – such
as determining the flow
rates of liquids into a
tank.
Day 15
* Web Links to Activities and Strategies
The APS curriculum map for geometry is located on the APS Blackboard site at:
aps.blackboard.com/webapps/portal/frameset.jsp?tab_tab_group_id=null&url=/webapps/blackboard/
execute/courseMain?course_id=_117122_1
Examples of activities involving technology are available from:
Geometers’ Sketchpad: sketchexchange.keypress.com
NCTM Illuminations: illuminations.nctm.org/
Khan Academy: www.khanacademy.org
Texas Instruments: education.ti.com/calculators/downloads/US/
Kagan Structures to use in activities are located at: www.kaganonline.com
A summary of many of them is located at:
learningservicesnvsd44.edublogs.org/files/2011/11/kagan_strats-1-sp46vb.pdf
An example of a lesson in which students investigate how to find distance and midpoint is available at:
alex.state.al.us/lesson_view.php?id=26361.