Download 8.5B Plan21.sequence - Texarkana Independent School District

Focus Plan
Texarkana Independent School District
GRADING
PERIOD:
Teacher:
4th Six Weeks
PLAN CODE:
Tipton
Course/subject:
Mathematics
Grade(s):
8
Time allotted
for instruction:
1 – 1 ½ hours
Title:
More Practice with Patterns!
Lesson TOPIC:
Using Algebraic Expressions to find terms in a sequence
TAKS Objective:
Objective 2: The student will demonstrate an understanding of
patterns, relationships, and algebraic reasoning.
FoCUS TEKS and
Student Expectation:
(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
(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
Supporting TEKS and
Student Expectations:
Concepts
Term
Sequence
Algebraic Expression
Enduring Understandings/Generalizations/Principles
The student will understand that
A term is a number in a sequence.
A sequence is a list of numbers in a certain order, such as, 0, 1, 2, 3…
An algebraic expression is a combination of variables, numbers, and at
least one operation.
 Division of Curriculum and Instruction  School Improvement Department  Texarkana Independent School District
I.
Sequence of Activities (Instructional Strategies)
A.
Focus/connections
This lesson is to be used after the lesson titled: “What is the Pattern”. Students sometimes need
additional practice while developing skills in recognizing and extending patterns. The goal of this lesson
is to reinforce for your students about understanding the change in patterns and extending it to
predictions for terms in the sequence.
Place the following pattern on the board:
1, 4, 9, 16, …
Ask your students to predict what the next five terms in the sequence will be.
B.
Instructional activities
(demonstrations, lectures, examples, hands-on experiences, role play, active
learning experience, art, music, modeling, discussion, reading, listening, viewing,
etc.)
Remind students that the first step while dealing with patterns is to identify the algebraic expression for
each sequence. The expression must be true for each stage of the sequence. Work with the class to
determine the algebraic expression for the example on the board. Place the following table on the board
if you wish:
1st Term
1
2nd Term
4
(2)ˆ
3rd Term
9
(3)ˆ
4th Term
16
(4)ˆ
5th Term
25
(5)ˆ
Urge your students to test the algebraic expression each time with the numbers in the original sequence.
Remind the class that you can find any term in a sequence by writing an expression that describes the
sequence. Once the algebraic expression has been determined, find the 75th term in the sequence.
C.
Guided activity or strategy
Have students get into groups of two or three. Place the following on the board: 1, 1/2, 1/4, 1/8,…
Ask the groups to do the following:
 Find the next two terms in the sequence
 Determine the algebraic expression for the sequence
 Find what the 25th term in the expression would be
After groups have had time to work, go over the correct answers with the class and discuss.
D.
Accommodations/modifications
Students requiring modifications may work in a small group setting to complete the guided activity.
E.
Enrichment
Students requiring enrichment may reteach the lesson in a small group setting.
II.
STUDENT PERFORMANCE
A.
Description
Students will complete the Algebraic Expressions in Patterns 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 Algebraic Expressions in Patterns Worksheet.
B.
Rubrics/grading criteria
Grades may be taken based on the Algebraic Expressions in Patterns Worksheet Answer Key and
Grading Rubric.


IV.
C.
Accommodations/modifications
D.
Enrichment
E.
Sample discussion questions
In what real world settings do you see patterns?
Why is it important to know how to find the algebraic expression with a pattern?
TAKS Preparation
A.
Transition to TAKS context
The teacher will lead the students in a discussion of how algebraic expressions in pattern 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
Term, Sequence, Algebraic Expression
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
Algebraic Expressions in Patterns Worksheet
Algebraic Expressions in Patterns Worksheet Answer Key and Grading Rubric
C.
Technology
VII.
follow up activities
(reteaching, cross-curricular support, technology activities, next lesson in sequence, etc.)
Students may be taken to the computer lab to utilize the following websites for reinforcement:
http://www.glencoe.com/sec/math/studytools/cgi-bin/msgQuiz.php4?isbn=0-02-8332407&chapter=5&lesson=9&headerFile=6&state=tx
http://www.glencoe.com/sec/math/studytools/cgi-bin/msgQuiz.php4?isbn=0-02-8332407&chapter=6&lesson=8&headerFile=6&state=tx
 Division of Curriculum and Instruction  School Improvement Department  Texarkana Independent School District