Focus Plan
Texarkana Independent School District
GRADING
PERIOD:
Teacher:
1st six weeks
PLAN CODE:
10M6 coordinates
Dottie Johnson
Course/subject:
Math 10
Grade(s):
10
Time allotted
for instruction:
1 class period on block
Title:
Finding Midpoints of Segments
Lesson TOPIC:
The student will use various methods to find the midpoint of segments
including paper folding, geomirrors, compass and straightedge, and
measuring with rulers. When the segments are drawn on number lines
or the coordinate graph the student will discover and use a
mathematical rule for finding the midpoint.
Objective 6: The students will demonstrate an understanding of
geometric relationships and spatial reasoning.
TAKS Objective:
FoCUS TEKS and
Student Expectation:
Geometry G.7C The student develops and uses formulas including
distance and midpoint.
Supporting TEKS and
Student Expectations:
Geometry G.7A, 7B The student understands that coordinate systems
provide convenient and efficient ways of representing geometric figures
and uses them accordingly.
aligned TEKS and
Student Expectations
for modifications:
Concepts
Enduring Understandings/Generalizations/Principles
The student will understand that
Finding midpoints of
segments with paper
folding
Finding the midpoints
of segments with a
geomirror
Finding the midpoints
of segments with a
compass
Finding the midpoints
of segments with
rulers
folding a segment where endpoint is placed on top of endpoint
gives a crease or line in the paper that passes through the
midpoint of the segment.
reflecting a segment back on top of itself where endpoint is
reflected on top of endpoint gives a line of reflection that
crosses the midpoint of the segment.
the two intersections of arcs drawn from the opposite ends of a
segment form a line that crosses the segment at the midpoint.
the length of a segment in units divided by 2 gives the distance
from either endpoint to the midpoint of the segment using the
same units.
 Division of Curriculum and Instruction  School Improvement Department  Texarkana Independent School District
Finding the midpoints
of segments on
number lines
Finding the midpoints
of segments on the
coordinate system
Finding a missing
endpoint when one
endpoint and the
midpoint is known
the location of the midpoint of a segment on a number line is
found by adding the location of the endpoints and dividing the
sum by 2.
 x  x1 
Mathematically:  2
 where x2 and x1 are the endpoints
 2 
of the segment
the x coordinate of the midpoint of a segment on a coordinate
graph is found by adding the x-values of the endpoints and
dividing by 2 and the y coordinate of the midpoint of a segment
on a coordinate graph is found by adding the y-values of the
endpoints and dividing by 2.
 x  x1 y 2  y1 
Mathematically;  2
,
 where
2 
 2
( x1 , y1 ) and ( x2 , y2 ) are the coordinates of the endpoints of the
segment.
There are two ways to find the minissing endpoint when one
endpoint and the midpoint is known. The student can draw the
problem on a coordinate grid and count the rise and the run.
The students can use algebra and the formula for the midpoint
of a segment.
 Division of Curriculum and Instruction  School Improvement Department  Texarkana Independent School District
I.
Sequence of Activities (Instructional Strategies)
A.
Focus/connections
Being able to take a segment and divide it into smaller, but equal pieces is an important
skill for many people working as carpenters, machinists, plumbers, and architects. There
are several methods of finding the midpoints of segments. The method you would use in
the workforce would depend on the materials you were working with and the tools that
were available. We will briefly go over several different ways, but will spend the majority
of our time finding the midpoint of a segment that is located on the coordinate plane.
This method could be used by rescue workers who often have to work with maps with the
overlay of a coordinate graph.
B.
Instructional activities
(demonstrations, lectures, examples, hands-on experiences, role play, active
learning experience, art, music, modeling, discussion, reading, listening, viewing,
etc.)
Students will fold paper, use a geomirror (Mira), use a compass and straightedge, use a
ruler and then discover a pattern (rule or formula) for finding the midpoint on a number
line or the coordinate graph.
C.
Guided activity or strategy
The teacher will guide and help the students in the activities on the introduction sheet.
Graphing calculators should be used beginning with A. 4.
When using formulas the students will need guidance in using the calculators. Students
especially need to understand that the x-value and the y-value are found separately when
using the midpoint formula. Many students want to put both parts of the midpoint formula
into the calculator at one time.
The teacher should next work from the textbook page 40-41 problems 6-10,12,13 with
the students.
D.
Accommodations/modifications
Some students will need much more help than others on the instructional activities.
These students may be paired with a partner or given extra guidance from the instructor.
E.
Enrichment
Students can complete problem number 45, Critical Thinking, on page 42 for an
enrichment activity.
II.
STUDENT PERFORMANCE
A.
Description
Students will complete the discovery lesson individually or with a partner. They will follow
the instructions of the teacher on part A of the discovery activity. On parts B and C and D
many students can work at their own pace. At the end of the discussion students will
 Division of Curriculum and Instruction  School Improvement Department  Texarkana Independent School District
have the discovery sheet completed with all questions answered. The final problem on
part D is an important exercise to help review the students algebra skills.
Students should copy the examples worked by the teacher from pages 40-41 problems
6-10, 12, 13 from the textbook.
Students will then work on their own to complete the assignment from the textbook, page
41 15-38,
B.
Accommodations/modifications
Students with modifications may have difficulties using the compass and straightedge of
A. 3. This problem can be deleted. Explaining how they arrived at their answers on B. 1,
2, and 3 may also be deleted. All formulas should be given to these students ahead of
time. Some students will have difficulty with the last problem D 2. This may need to be
deleted for the modified student.
The assignment for students with modifications should be limited to 15-37 odds only.
C.
Enrichment
If students complete the discovery lesson early with little or no guidance, they should be
encouraged to complete the assignment in order to have time to work on the enrichment
activity. All problems should be correctly completed before the enrichment activity is
begun.
.
iii.
Assessment of Activities
A.
Description
The teacher should circulate among the students to make sure the discovery activity is
correctly completed. The teacher should remind students to copy the examples as they
are worked by the teacher. Assignment answers should be checked and discussed
when completed.
B.
Rubrics/grading criteria
Students should be given a daily completion grade for the discovery activity. A
class work / homework grade should be given for the individual assignment.
C.
Accommodations/modifications
Students should complete modified discovery sheet and modified assignment.
D.
Enrichment
Bonus points should be given to any students completing enrichment activity correctly.
E.
Sample discussion questions
Discussion questions are listed on the discovery activity.
F.
Sample TAKS questions (attached)
 Division of Curriculum and Instruction  School Improvement Department  Texarkana Independent School District
IV.
TAKS Preparation
A.
Transition to TAKS context
Students must be made aware that the formula for finding the midpoint of a segment on
the coordinate plane is on the formula card. They should use the formula card daily and
know where the midpoint formula is found. They should also be aware that the formula
for finding the midpoint of a segment on a number line is not on the formula card. There
is likewise no information about finding the other endpoint of a segment when one
endpoint and the midpoint is known. These concepts are tested on the TAKS.
B.
V.
Sample TAKS questions (attached)
Key Vocabulary
midpoint of a segment
bisector of a segment
perpendicular bisector of a segment
congruent segments
VI. Resources
A.
B.
VII.
Textbook Geometry by Glencoe
Chapter 1 lesson 5
Practice Masters from textbook lesson 1-5
Graphing calculators
follow up activities
(reteaching, cross-curricular support, technology activities, next lesson in sequence, etc.)
The next lesson will be on the Pythagorean Theorem which is then followed by finding the
distance on the coordinate plane. These three lessons will be tested together.
VIII.
Teacher Notes
A. For a class of 10th grade Algebra II students, give the sample TAKS questions first. Students
not scoring 3/4 should work half of the textbook assignment. The Discovery Activity should not be
necessary with these students.
B. This lesson should be covered in one day on the block schedule. Adjustments in the
discovery activity and / or the assignment may need to be made in order to accommodate this.
 Division of Curriculum and Instruction  School Improvement Department  Texarkana Independent School District