Download 7.4c student activity #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.
7.4C STUDENT ACTIVITY #1
Problem #1: Find the relationship in the arithmetic sequence 7, 14, 21, 28, 35, …
The common difference in an _______________ ________________ can be identified by finding
the difference between the terms in the sequence.
+7
+7
+7
+7
7, 14, 21, 28, 35, . . .
In the sequence 7, 14, 21, 28. 35, …, the common difference is _____. The value of the term in
position 1 is _____. Multiply the ______________ ________________ times the term’s position.
_____ _____ = _____
The value of the term in position 1 is _____, therefore multiplying the ______________
________________ times position 1 gives the value of the term in position _____.
Check to see if multiplying the ______________ ________________ times the second position
gives the value of the term in position _____.
_____ _____ = _____
The value of the term in position 2 is _____, therefore multiplying the ______________
________________ times the second position gives the value of the term in position _____.
A rule can be used to find the nth term in this arithmetic sequence. Multiply _____ times n, the
position of the term. The rule can be expressed algebraically as _____n.
The 9th term in this sequence is ____________.
The 25th term in this sequence is ____________.
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 ____________ _______________ times _____, the
position of the term in the sequence, and adding or subtracting from the ______________ to get
the correct value of the term. The rule can be expressed ____________________.
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.
Problem #2: Here is a sequence of numbers: 6, 12, 18, 24,…
The table below shows the same ___________________. Complete the table.
Position
1
2
3
4
7
10
n
Value of Term
6
12
18
24
The “position” column indicates a value’s ____________ in the ____________ : first,
___________, and so on.
The “value of term” column shows the actual numbers in the ________________: 6, 12, 18, 24,
and so on.
Use the ______________ __________________ to find a pattern that shows the relationship
between a term’s _______________ number and the _______________ of the term.
The common difference is _____. _______________ the common difference times the position
number in the sequence. _____ _____ = _____ and the value of the first term is _____.
State the pattern as a _______________.
Multiply _____ times the term’s position to find the value of the ____________.
Check to see whether the _____________ works for the next two terms in the ______________.
_____ _____ = _____ and the value of the second term is _____.
_____ _____ = _____ and the value of the third term is _____.
Each value in the sequence is _____ times its _____________ number.
Represent the rule as an algebraic expression.
The rule for this sequence can be represented by the algebraic expression ________.
The 12th term in this sequence is ____________.
The 42nd term in this sequence is ____________.
TEKSING TOWARD TAKS
2009
6 Weeks 4 - Lesson 7
Page 2
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.
Problem #3: What expression can be used to find the nth term in this sequence?
1
1
1
, 1, 1 , 2, 2 , ...
2
2
2
Use the common difference to find a _______________ that shows the relationship between a
term’s ____________ number and the value of the ______________.
Position
Value of Term
1
1
2
2
1
+1
2
In the sequence
3
1
1
2
+1
2
4
5
1
2
2
2
+1
2
n
?
+1
2
1
1
1
, 1, 1 , 2, 2 , ...., the common difference is _____. The value of the term in
2
2
2
position 1 is _____. Multiply the common ____________ times the term’s position ___________.
_____ _____ = _____
The value of the first term is _____.
State the _______________ as a rule.
Multiply _____ times the term’s position to find the value of the ____________.
Check to see whether the _____________ works for the next two terms in the ______________.
_____ _____ = _____ and the value of the second term is _____.
_____ _____ = _____ and the value of the third term is _____.
Each value in the sequence is _____ times its _____________ number.
Represent the rule as an algebraic expression.
The rule for this sequence can be represented by the algebraic expression ________.
The 8th term in this sequence is ____________.
The 17th term in this sequence is ____________.
TEKSING TOWARD TAKS
2009
6 Weeks 4 - Lesson 7
Page 3
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.
7.4C STUDENT ACTIVITY #2
Problem #1: What expression can be used to find the nth term in this sequence?
3, 5, 7, 9, ...
Use the common difference to find a _______________ that shows the relationship between a
term’s ____________ number and the value of the ______________.
Position
Value of Term
1
3
2
5
+2
3
7
+2
4
9
…
…
n
?
+2
In the sequence 3, 5, 7, 9, …, the common difference is _____. The value of the term in position
1 is _____. Multiply the common ________________ times the term’s position _____________.
2 1 = 2
The term in position 1 is _____, not 2, therefore you must add or subtract from _____ to find the
value of the term in position _____.
2 1 = 3
The term in position 1 is _____. Maybe each term in this sequence is equal to _____ times its
position number in the sequence and add _____.
State the pattern as a __________.
. A rule can be used to find the nth term in this arithmetic sequence. ______________ 2 times the
_____________ of the term and add _____.
Check to see whether the rule works for the next two __________ in the _______________.
The term in position 2 is _____ and (_____ _____) + _____ = _____.
The term in position 3 is _____ and (_____ _____) + _____ = _____.
Represent the rule as an algebraic expression.
The value of the nth term is (_____ _____) + _____, or _____n + _____.
The 14th term in this sequence is ____________.
TEKSING TOWARD TAKS
2009
6 Weeks 4 - Lesson 7
Page 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.
Problem #2: Look at this sequence of numbers: 4, 12, 20, 28, 36,…
Which of these three expressions can you use as the rule to find the value of the nth term in the
sequence?
4n
2n + 2
8n 4
Check the first expression, 4n.
When n = 1, the expression 4n = _______.
When n = 2, the expression 4n _______. But the second term should be _______.
Check the second expression, 2n + 2.
When n = 1, the expression 2n + 2 = _______ + _______ = _______.
When n = 2, the expression 2n + 2 = _______ + _______ = _______. But the second term
should be _______.
Check the third expression, 8n 4.
When n = 1, the expression 8n 4= _______  _______ = _______.
When n = 2, the expression 8n 4= _______  _______ = _______.
When n = 3, the expression 8n 4= _______  _______ = _______.
When n = 4, the expression 8n 4= _______  _______ = _______.
When n = 5, the expression 8n 4= _______  _______ = _______.
The expression ________________ can be used as the rule to find the value of the nth term in this
sequence.
The 15th term in this sequence is ____________.
The 32nd term in this sequence is ____________.
TEKSING TOWARD TAKS
2009
6 Weeks 4 - Lesson 7
Page 5
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.
7.4C OPEN ENDED #1
A sequence is defined by the expression 4n 3, where n is the position in the sequence.
Write the first 5 terms of the arithmetic sequence.
Find the 20th term in the sequence.
Does 103 belong in this sequence? _______
If so, which term is it? _______
If not, name a term in the sequence that is near 103. _______
1. What mathematical concepts and vocabulary do I need to know to be able to work this problem?
2. Will the Grade 7 Mathematics Formula Chart be helpful on this problem? Why or why not?
3. Is this relationship a proportional relationship? How do you know?
4. What problem-solving strategy or strategies will I use to help solve this problem?
5. Extension (7.7A): Draw a graph of the first three terms of this sequence using the term
position as x and the value of the term as y. Determine an appropriate scale for the axes of the
graph.
y
x
TEKSING TOWARD TAKS
2009
6 Weeks 4 - Lesson 7
Page 6
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.
NAME___________________
DATE___________
SCORE ___/5
7.4C Homework #1
1.
Write the first five terms of the sequence represented by the rule 5n 1 , where n represents the position in the sequence.
2.
Write the rule that represents the terms of the sequence whose first 5 terms are 3, 6, 9, 12, 15...
3.
Complete the table below that represents the sequence that is represented by the rule
Position
2
Term value
2
2
3
1
3
3
3
4
1
2
3
n 2
4
5
4.
5.
Write a description that shows the relationship between a term and n, its position in the sequence.
Position
1
2
3
4
Value of the Term
5
10
15
20
n
Find the following terms in the sequence that is defined by the rule 3n 4 , where n represents the position of the term in the
sequence.
10th term: _____________
TEKSING TOWARD TAKS
2009
20th term: _____________
6 Weeks 4 - Lesson 7
45th term: _____________
Page 7
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.
NAME___________________
DATE___________
SCORE ___/5
7.4C Homework #2
1.
Write the first five terms of the sequence defined by the expression 4 n 5 , where n represents the position in the sequence.
2.
Write the rule that defines the terms of the sequence whose first 5 terms are 5, 7, 9, 11, 13...
3.
Complete the table below to show the sequence that is defined by the expression 0.5n 2.5 .
Position
1
2
3
4
5
4.
Term value
3
3.5
4
Following is a description that shows the relationship between a term and n, its position in the sequence.
Multiply n by 2 and then subtract 0.5.
Write the first five terms of the sequence.
5.
Fill in the missing terms in the sequence below.
4, 7, 10, ___, 16, ___, 22
Write a verbal description of how the value of a term can be found using the position of the term in the sequence.
TEKSING TOWARD TAKS
2009
6 Weeks 4 - Lesson 7
Page 8