Download 8.16A Plan17.patterns - Texarkana Independent School District

Focus Plan
Texarkana Independent School District
GRADING
PERIOD:
Teacher:
3rd Six Weeks
PLAN CODE:
Tipton
Course/subject:
Mathematics
Grade(s):
8
Time allotted
for instruction:
1 – 1 ½ hours
Title:
What is the Pattern?
Lesson TOPIC:
Patterns and Sequence
TAKS Objective:
Objective 6: The student will demonstrate an understanding of the
mathematical processes and tools used in problem solving.
FoCUS TEKS and
Student Expectation:
(16) Underlying processes and mathematical tools. The student uses
logical reasoning to make conjectures and verify conclusions. The
student is expected to:
(A) make conjectures from patterns or sets of examples and
nonexamples
(5) Patterns, relationships, and algebraic thinking. The student uses
graphs, tables, and algebraic representations to make predictions and
solve problems. The student is expected to:
(B) use an algebraic expression to find any term in a sequence
Supporting TEKS and
Student Expectations:
Concepts
Pattern
Enduring Understandings/Generalizations/Principles
The student will understand that
A pattern is a recognizable shape or arrangement of things (numbers).
Sequence
A sequence is an ordered list of numbers.
Term
A term is an element or number in a sequence.
 Division of Curriculum and Instruction  School Improvement Department  Texarkana Independent School District
I.
Sequence of Activities (Instructional Strategies)
A.
Focus/connections
Prior to students entering the class, write the following numbers on the board:
8, 16, 24, 32,……
After students are seated, ask them to look for a pattern that describes the relationship between the
numbers. Have the class predict what the next five numbers would be.
B.
Instructional activities
(demonstrations, lectures, examples, hands-on experiences, role play, active
learning experience, art, music, modeling, discussion, reading, listening, viewing,
etc.)
Explain to the class that the purpose of this lesson is to develop skills in the problem solving strategy of
discovering and describing patterns in mathematical situations. Students must use inductive and
deductive reasoning as they recognize and use patterns to explain, create and predict situations. Write
the numbers 1, 3, 5, and 7 on the chalkboard. Ask the students to predict what number comes next.
Next ask the students to brainstorm what the 75th number in the sequence would be. Discuss that it
would take a long time to find the 75th term by repeatedly adding the common difference. Now show the
class how you can find any term by writing an expression that describes the sequence. With the
numbers on the board you could create the following table:
1st Term
2nd Term
3rd Term
4th Term
5th Term
1
3
5
7
9
1 + 2(1)
1 + 2(2)
1 + 2(3)
1 + 2(4)
Have the class look at the table. What do the expressions for all of the terms have in common? Now
have the students predict what the 75th term would be. Next predict what the 150th term in the sequence
would be. The class should understand that the study of patterns supports learning to see relationships,
to find connections, and to make generalizations and predictions. Understanding patterns nurtures the
kind of mathematical thinking that helps students become problem solvers and abstract thinkers.
C.
Guided activity or strategy
Have students get in groups of 2 - 3. Write the following numbers on the board: 1, 2, 4, 7, 11, ….
Have the groups work together to determine the following:
 Find the next 5 numbers in the sequence
 Write an expression to describe the sequence
 Find the 62nd term in the sequence
After pairs have been given time to work, go over the correct answers with the class.
D.
Accommodations/modifications
Students requiring modifications may work with a peer for the guided activity.
E.
Enrichment
Students requiring enrichment may reteach the lesson in the small group setting for the guided activity..
II.
STUDENT PERFORMANCE
A.
Description
Students may complete the Pattern Worksheet individually.
B.
Accommodations/modifications
C.
Enrichment
 Division of Curriculum and Instruction  School Improvement Department  Texarkana Independent School District
iii.
Assessment of Activities
A.
Description
Individual student grades may be taken on the Pattern Worksheet.
B.
Rubrics/grading criteria
Grades may be taken based on the Pattern Worksheet Answer Key and Grading Rubric.
C.
Accommodations/modifications
D.
Enrichment
E.


IV.
Sample discussion questions
Why is it important to know how to work with patterns?
In what real world settings do you see patterns?
TAKS Preparation
A.
Transition to TAKS context
The teacher will lead the students in a discussion of how pattern or sequence problems may look in test
format by placing the following TAKS questions on the overhead/board.
B.
Sample TAKS questions
1. A pattern of equations is shown below.
1% of 800 = 8
2% of 400 = 8
4% of 200 = 8
8% of 100 = 8
16% of 50 = 8
Which statement best describes this pattern of equations?
A. When the percent is doubled and the other number is halved, the answer is 8.
B. When the percent is doubled and the other number is doubled, the answer is 8.
C. When the percent is increased by 2 and the other number remains the same, the answer is 8.
D. When the percent remains the same and the other number is increased by 2, the answer is 8.
2. The expression shown below describes a pattern of numbers.
n(n – 1) + 4
If n represents a number’s position in the sequence, which pattern of numbers does the expression
describe?
A. 4, 6, 8, 10, 12….
B. 1, 4, 6, 10, 16….
C. 4, 6, 10, 16, 24….
D. 4, 10, 18, 28, 40….
 Division of Curriculum and Instruction  School Improvement Department  Texarkana Independent School District
3. Which expression can be used to find the nth term in the following arithmetic sequence, where n
represents a number’s position in the sequence?
Position in
Sequence
Term
A.
B.
C.
D.
1
2
3
4
n
5
9
13
17
?
n+4
3n + 4
5n
4n + 1
4. Let n represent the position of a number in the following arithmetic sequence.
1/2, 1, 3/2, 2, ….
Which expression can be used to find any term in the sequence?
F. 2n
G. 1/2 n
H. 3/2 n
J. 5/2 n
V.
Key Vocabulary
Pattern, Sequence, Term
VI.
Resources
A.
Textbook
Math Advantage ~ Middle School II
Chapter 6: Writing and Simplifying Expressions
 Sequences and Expressions, pp. 134-137
Chapter 18: Growing and Shrinking Patterns
 Repeated Doubling and Halving, pp. 362-363
 Patterns in Sequences, pp. 379-381


B.
Supplementary materials
Pattern Worksheet
Pattern Worksheet Answer Key and Grading Rubric
C.
Technology
Students may be taken to the computer lab to utilize the following websites with pattern/sequencing
activities:
http://www.funbrain.com/cracker/index.html
http://www.kidport.com/Grade7/TAL/Patterns.htm
VII.
follow up activities
(reteaching, cross-curricular support, technology activities, next lesson in sequence, etc.)
A good follow-up lesson would be one dealing with patterns while using exponents.
VIII.
Teacher Notes
Another good introduction to this lesson would be to read a children’s book that has a predictable pattern
that repeats over and over. Examples: The Little Red Hen, The House that Jack Built
 Division of Curriculum and Instruction  School Improvement Department  Texarkana Independent School District