CENTENARY COLLEGE - Education Department
Student Teaching-Grade 8: Algebra
Lisa Tran
Curriculum Dimensions:
Content – The Distance Formula
Product – Graph paper; notes
Process – Students will find the distance between two given points. They will learn how to find a missing
coordinate by apply the distance formula. After students practice solving problems as a class, they will apply
their skills to a math game. The game involves students finding a missing coordinate on a map.
Time Frame- 40 minutes
Research
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Academic and Professional Standards. 2006. NJ Department of Education. 20 Jan. 2009
<http://www.state.nj.us/education/cccs/>.
Holliday, Berchie, Gilbert J. Cuevas, Beatrice Luchin, John A. Carter et al.. Algebra 1. New York:
Glencoe McGraw-Hill, 2008.
New Jersey Core Curriculum Content StandardsSTANDARD 4.1.8.B.3 (Number and numerical operations): Find square and cube roots of numbers and
understand the inverse nature of powers and roots.
STANDARD 4.2.8.A.2 (Geometry and measurement): Understand and apply the Pythagorean theorem.
STANDARD 4.5.8.A.4 (Mathematical processes): Pose problems of various types and levels of difficulty.
STANDARD 4.5.8.B.1 (Mathematical processes): Use communication to organize and clarify their
mathematical thinking.
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Reading and writing
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Discussion, listening, and questioning
STANDARD 4.58.B.4 (Mathematical processes): Use the language of mathematics to express mathematical
ideas precisely.
Learning Objectivities:
Students will be able to:
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Write the distance formula (Knowledge).
Summarize the steps in finding the distance between two points (Comprehension).
Find the distance between two points on the coordinate plane using the distance formula (Application).
Find a point that is a given distance from a second point on a plane using the distance formula
(Application).
Instructional Activities:
The teacher will:
1. Motivate by:
 Playing two truths and a lie. This activity will introduce the topic students will be learning.
2.
Introduce/Review/Extend CONTENT by:
a. Discussion.
b. Find the distance between two points.
c. Find a missing coordinate.
d. Play a math game.
3.
Introduce/Review/Extend PROCESS by:
a. Discussion:
1) Where else might you use the Distance Formula?
1. Finding the distance between two places on a map.
2. Finding the distance of an object in sports (ex. golf, football)
3. Geometry: length of the hypotenuse
b. Find the distance between two points:
1) What happens if you switch the points, would it change the outcome?
2) What do you notice when you square numbers? (always a positive result)
c. Find a missing coordinate:
1) What happens when there is a missing coordinate? How would you solve it?
d. Play a math game (using SMART Board)
1) Group will be separated into 3 groups of 3 or 4 people.
2) Students will plot coordinates on a map.
3) Each group will find a missing coordinate.
4. Introduce/Review/Extend the PRODUCT by:
a. Having student collect materials (listed below).
b. What are the steps in solving the distance formula?
5. Explain/List ASSESSMENT criteria:
a. Evaluate students’ ability to apply the distance formula by checking homework (15 out of 15).
b. Check students’ in-class work if there are able to illustrate the steps in finding the distance
between two points and finding a missing coordinate.
c. Gauge students’ comprehension through oral questions.
6. Provide feedback and evaluation:
c. Circulate around the classroom, answer questions, and help students while they are working on
problems.
d. Ask questions:
i. What if the points are switched in the distance formula, would it affect the outcome?
ii. What if there was a missing coordinate? How could you solve the problem?
7. Close the lesson: Ask students to summarize in their own words the steps in finding the distance using
the Distance Formula.
Materials:
1. Pencils
2. Papers
3. Graph Papers
Differentiation:
Less-abled learner: SMART Board visual; use calculators to compute and check problems; write/draw to
explain steps; get information from demonstration and group discussions.
More-abled learner: model their thinking process; create challenging problems and questions during group
discussions;
Visual- vocabulary terms and numbers written on SMARTboard; visual pictures; examples
Bodily- Kinesthetic- draw and perform steps during the math game.
Interpersonal- group discussions, math game.
Intrapersonal- completing homework assignment, complete seat work, write notes.
Linguistic- explaining the purpose of this lesson, discussion with the whole class; explaining examples
Logical-Mathematical- discussing the thinking process aloud during activity; recognizing patterns in numbers.
Extension Activities:
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Create a mnemonic device to help you remember the distance formula.
Motivation:
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The Distance Formula is based on the Pythagorean Theorem.
You can use the distance formula to find the distance between any two points in the coordinate plane.
The Distance Formula is only used in math or science classes.
Example A: Page
Example B: A triangle has vertices A(12,5), B(5,3), and C(12, 1).
Example C:
DIRECTIONS:
1) Plot the points and write your coordinates on your map:
(1,7)
(3,1)
(9,3)
(7, a)
2) Label each point using the first letter of the state's name:
For example:
New Jersey: N (1,7)
Pennsylvania: P (3,1)
Maine: M (9,3)
Rhode Island: R (7,10)
3) Find the value of a so that each side of all the points has the same
length.