Download 7th Grade Math

7th Grade Math
Unit 5: Algebraic Expressions & Equations
Students will be able to effectively represent everyday problem situations by writing an
expression or equation and vice versa. Students will be able to generate different
representations of data given one representation. Students will use the common
difference in an arithmetic sequence to generate the expression relating the value of the
term and its position in the sequence.
EXPRESSION – a mathematical representation consisting of symbols,
operations and/or variables.
Ex: 2x-3
EQUATIONS – a mathematical sentence made up of more than one
expression connected by an equal sign.
Ex: 3x+7=x-3
TERMS – all the parts of expressions or equations. In an arithmetic
sequence, terms are the values (or numbers) in the list.
ARITHMETIC SEQUENCES – a list of numbers that have a common
difference (constant rate of change) between each pair of consecutive
numbers.
The numbers are called the terms in the sequence and the order that
they are written gives the term’s position, n. Also called nth term.
Ex: 4, 8, 12, 16, …. (this means it keeps going)
The first number is 4 so its in the 1st position (or n=1)
The second number is 8 so its in the 2nd position (or n=2)
The third number is 12 so its in the 3rd position (or n=3)
FIND THE RULE OF THE SEQUENCE - (this is the expression that
relates the term to its position)
1. you must first figure out what the common difference is
2. multiply the common difference times n
3. test the rule with n=1 to see if it equals the 1st term, n=2 to
see if it equals the 2nd term, n=3 to see if it equals the 3rd
term.
4. if yes to all three, then your rule is the common difference
times n
if no, then you must figure out what you need to add OR
subtract from the product to get the 1st term, 2nd term, etc…
Ex1: 4, 8, 12, 16, … Question: What is the rule?
4
4
4 , the common difference is 4 because
8-4=4, 12-8=4, 16-12=4
***so we start with 4n as the rule
substitute 1 for n and see if = 1st term…then substitute 2 for
n and see if = 2nd term, then substitute 3 for n to see if = 3rd
term….4(1)=4
4(2)=8
4(3)=12
YES…4, 8, 12 are the first three numbers in the sequence, so
the rule is 4n for this sequence
Ex 2: Question: What is the rule for the sequence:
Position (n)
1
2
3
4
Term
5
13
21
29
The sequence is organized in a table, but it’s the same thing
as writing:
5, 13, 21, 29, …
the common
8(1) =
8(2) =
8(3) =
difference is 8 so we write 8n
8–3=5
So you must subtract 3
16 – 3 = 13
from the rule in order for
it to work for all the
24 – 3 = 21
terms.
The rule is:
8n – 3
Ex3: Question: Using the rule, 8n – 3, find the 30th term in the
sequence.
If you need to find the 30th term, that means you have to
find term in the 30th position. This means n = 30. So substitute 30 for n
in the rule and it will equal to the 30th term.
8(30) – 3
240 – 3
237 is the 30th term