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Distance
Formula
Designed by: Melanie B. Moorer
School: Dreher High School
Grade
Level: 9-10 Subject:
Mathematics (Geometry)
Core
Curriculum Objective: Apply the distance
formula.
Overview:
Students will work independently and in
small groups to develop strategies to find
distance and apply their knowledge in everyday
situations. Students will use various
instructional strategies such as:
demonstrations, presentations, critical
thinking, and deduction. As a culminating
assessment, students will use a blue print of
the school sectioned off in coordinates to
measure the distance from the classroom to the
closest exit of the building in order to
determine the quickest exit in case of an
emergency.
Purpose/Essential Question(s): How do
you find distance?
Time Frame: This lesson is designed for
two ninety-minute class periods.
Resources
and Instructional Materials:
Geometry:
An Integrated Approach
D. C. Heath and Company
Lexington, Massachusetts / Toronto, Ontario
Pages 71-76
Transparencies
Overhead
Projector
Blue
print of school building
Rulers
Calculators
Day One
Bell- Work: (work to be done when the
student enters the class before the tardy
bell)
Have
students copy the following formula for
distance off a ready-made transparency:
Motivating
the lesson:
Draw the figure below on a transparency. Write
below it: How many different routes can be
traced from point A to point B if the
movements must be to the right or down?
Answer:
36
Work through the following teacher-led
examples:
1.Let
A = (-2, 5) and B = (4, 1). Find the distance
between the two points using the distance
formula.
2. On a city map, the streets are 100 feet
apart horizontally and 250 feet apart
vertically. On a coordinate plane where the
capital building is at the origin, north is
directing up the positive y-axis, south is
directing down the negative y - axis, east is
directing right on the positive x - axis, and
west is directing left on the negative x -
axis, find the walking distance from the City
Hall (1, 2) to the Riverfront Park (-2, 3).
Then find the distance as a bird would fly
(directly from each point - using the distance
formula)
Activity
One:
Have students work independently on Worksheet
A for 15 minutes. Then let the students get
with their partner (already selected by the
teacher when designating collaborative pairs)
compare work and reach a consensus on what the
correct answers are. After another ten
minutes, randomly select student pairs to come
up and find distances on the overhead for the
class to see.
For
homework, give the students some problems
similar to those on Worksheet A.
Day Two
Allow students to go over their homework
problems by comparing answers with
their partners. The teacher will ask for any
questions and go over any problems the
students may still be having trouble with.
Activity
Two
Pair students with a partner. Students will
receive Culminating Activity Sheet and the
rubric for this lesson. In this activity, the
students will demonstrate their ability to
find distances by finding the closest exit out
of the building in case of an emergency. The
teacher will demonstrate how to draw a
coordinate plane on the blue print of the
school building. The students will then follow
the steps on the sheet in order to find the
distance from the classroom to the closest
exit of the building. The teacher will
evaluate the culmninating assessment with the
following rubric:
| Culminating
Activity |
Excellent
25-18 |
Acceptable
17-14 |
Unacceptable
13-0 |
| Coordinate
Plane Drawn Correctly |
Coordinate
plane drawn neatly with correct origin |
Coordinate
plane drawn neatly without correct
origin |
Coordinate
plane not drawn neatly without correct
origin |
| Points
Labeled Correctly |
Both
points labeled correctly |
One
point labeled correctly |
No
points labeled correctly |
| Correct
Distance Formula Used |
Correct
distance formula used |
Incorrect
distance formula used |
| Calculations |
Calculations
are correct and work is shown |
Calculations
are correct but no work is shown |
Calculations
are incorrect |
Worksheet
A
Finding Distance Date
(Click here
for a printable Adobe Acrobat version of this
page)
Name________________________________________________________
Date__________________________________________
Find
the distance between the two points. Use you
calculators for those that do not come out as
perfect square roots. Round your answers to
two decimal places.
1. A = (4, 3) and B = (-2, -5)
2.
C = (-4, 1) and D (6, -1)
3.
E = (-3, 3) and F = (5, -1)
4.
G = (2, 8) and H (4, 8)
5.
I = (5, 9) and J = (5, -2)
6.
K = (2.5, 3.6) and L = (7.4, 3.2)
7.
M = (0, 4) and N = (8, 0)
8.
O = (0, 0) and P = (-3,-6)
9.
Q = (-I, 4) and R = (3, -1)
10.
S = (8,7) and T = (5,-3)
Culminating
Activity for the
Distance Formula
(Click
here for a printable Adobe Acrobat version of
this page)
Materials
Needed: Blue print of school building,
Ruler, Calculator
Procedures:
1. Meet with your partner and begin to draw
the coordinate plane as instructed by the
teacher.
2. Design your coordinate plane so that the
main off ice of the school is at the origin.
3. Find the doorway to the classroom and the
closest exit to the classroom. Label each of
these points on the blue print as follows:
a.
The doorway to the classroom = C
b. The closest exit = E
c. Main Office= O
4.
Draw straight lines down hallways and
staircases (if needed) beginning at the
doorway to the classroom and ending at the
exit.
5.
Find the distance from the classroom to the
nearest exit by finding the distances of each
of the line segments drawn.
6.
On the back of the blue print, make sure to
show all your work when using the distance
formula!
**Make
sure you put your name and your partner's name
on the back of the blue print! You'll be
presenting these to the class, so be familiar
with your results and how you got them. |
