Download GRADE 7 MATHEMATICS PARENT GUIDE Six Weeks 4

GRADE 7 MATHEMATICS
(7.4) Patterns, relationships, and algebraic thinking. The student represents a relationship in numerical, geometric, verbal, and symbolic
form. The student is expected to: (C) use words and symbols to describe the relationship between the terms in an arithmetic sequence
(with a constant rate of change) and their positions in the sequence.
PARENT GUIDE
Six Weeks 4 – Lesson 7
7.4C INSTRUCTIONAL LESSON & ASSESSMENT
For this TEKS students should be able to use words and symbols to describe the relationship between the
terms in an arithmetic sequence (with a constant rate of change) and their positions in the sequence.
MATH BACKGROUND
Understanding how to describe the relationship between the terms in a sequence and their positions in
the sequence
A sequence of numbers is a set of numbers written in a particular order. For example, 7, 11, 15, 19 is a
sequence of four numbers. The number 7 is the first term in the sequence, 11 is the second term, 15 is the
third term, and 19 is the fourth term.
An arithmetic sequence is a sequence of n numbers where the difference between the successive terms is
constant. For example: 4, 8, 12, 16, 20 ... is the first five terms of an arithmetic sequence. The number 4 is
the first term in the sequence, 8 is the second term, 12 is the third term, 16 is the fourth term, and 20 is the
fifth term.
The common difference in an arithmetic sequence can be identified by finding the difference between the
terms in the sequence.
+4
+4
+4
+4
4, 8, 12, 16, 20, . . .
In the sequence 4, 8, 12, 16, 20, . . ., the common difference is 4. The value of the term in position 1 is 4.
Multiply the common difference times term’s position number.
common difference
4 1 = 4
position number
The value of the term in position 1 is 4, therefore multiplying the common difference times position 1 gives
the value of the term in position 1.
Check to see if multiplying the common difference times the second position gives the value of the term in
position 2.
common difference
4 2 = 8
position number
The value of the term in position 2 is 8, therefore multiplying the common difference times position 2 gives
the value of the term in position 2.
TEKSING TOWARD TAKS
2009
6 Weeks 4 - Lesson 7
Page 1
GRADE 7 MATHEMATICS
(7.4) Patterns, relationships, and algebraic thinking. The student represents a relationship in numerical, geometric, verbal, and symbolic
form. The student is expected to: (C) use words and symbols to describe the relationship between the terms in an arithmetic sequence
(with a constant rate of change) and their positions in the sequence.
A rule can be used to find the nth term in this arithmetic sequence. Multiply 4 times n, the position of the
term. The rule can be expressed algebraically as 4n.
A rule can be used to find the nth term in any arithmetic sequence. The nth term in an arithmetic sequence
can be found by multiplying the common difference by n, the position of the term in the sequence, and
adding or subtracting from the product to get the correct value of the term. The rule can be expressed
algebraically.
Follow these guidelines to find a rule or expression that can be used to find the nth term in an arithmetic
sequence:
Use the common difference to find a pattern that shows the relationship between a term’s position number
and the value of the term.
State the pattern as a rule.
Check to see whether the rule works for the next two terms in the sequence.
Represent the rule as an algebraic expression.
The numbers in a sequence can be organized in a table to find the relationship between the terms in the
sequence and their positions.
Position
1
2
3
4
n
Value of Term
4
7
10
13
+3
+3
+3
The “position” column indicates a value’s position in the sequence: first, second, and so on.
The “value of term” column shows the actual numbers in the sequence: 4, 7, 10, 13, etc.
Use the common difference to find a pattern that shows the relationship between a term’s position number
and the value of the term.
In the sequence 4, 7, 10, 13. . ., the common difference is 3. The value of the term in position 1 is 4.
Multiply the common difference times the term’s position number.
3 1 = 3
The term in position 1 is 4, not 3, therefore you must add or subtract from 3 to find the value of the term in
position 1.
3 1 = 4
The term in position 1 is 4. Maybe each term in this sequence is equal to 3 times its position number in the
sequence and add 1.
State the pattern as a rule.
A rule can be used to find the nth term in this arithmetic sequence. Multiply 3 times the position of the
term and add 1.
\
Check to see whether the rule works for the next two terms in the sequence.
The term in position 2 is 7 and (3 2) + 1 = 7. The term in position 3 is 10 and (3 3) + 1 = 10.
Represent the rule as an algebraic expression.
The value of the nth term is (3 n) + 1, or 3n + 1.
TEKSING TOWARD TAKS
2009
6 Weeks 4 - Lesson 7
Page 2