1. Topic-
Operations with Rational Numbers
 
2. Content-
opposite, absolute value, absolute value, rational number, integer, rational number, additive inverse, commutative property, associative property, distributive property, integer, terminating decimal, rational number, commutative property, associative property, sum, difference, product, quotient
 
3. Goals: Aims/Outcomes-
Domain: Operations with Rational Numbers (7.NS)

Clusters: Apply and extend previous understandings of numbers to the system of rational numbers.

Standards:
7.NS.1: APPLY and EXTEND previous understandings of addition and subtraction to add and subtract rational numbers; REPRESENT addition and subtraction on a horizontal or vertical number line diagram.
DESCRIBE situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charges because its two constituents are oppositely charged.

UNDERSTAND p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. SHOW that a number and its opposite have a sum of 0 (are additive inverses). INTERPRET sums of rational numbers by describing real-world contexts.

UNDERSTAND subtraction of rational numbers as adding the additive inverse, p "� q = p + ("�q). SHOW that the distance between two rational numbers on the number line is the absolute value of their difference, and APPLY this principle in real-world contexts.

APPLY properties of operations as strategies to add and subtract rational numbers.


7.NS.2: APPLY and EXTEND previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

UNDERSTAND that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as ("�1)("�1) = 1 and the rules for multiplying signed numbers. INTERRUPT products of rational numbers by describing real-world contexts.

UNDERSTAND that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then "�(p/q) = ("�p)/q = p/("�q). INTERRUPT quotients of rational numbers by describing real-world contexts.

APPLY properties of operations as strategies to multiply and divide rational numbers.

a rational number to a decimal using long division, know that the decimal form of a rational number terminates in 0s or eventually repeats.


7.NS.3: SOLVE real-world and mathematical problems involving the four operations with rational numbers.
Note: Computations with rational numbers extend the rules for manipulating fractions to complex fractions.
 
Procedures/Methods-

A. Introduction-

Vocabulary key "�
Transaction = debit or credit from an account
Debit (withdrawal) = Check or debit card usage written out of the checking account
Credit= Deposit of money put in the account

Situation #1:
Use the ledger to record the information and answer the questions.
Note: On August 12, your beginning balance is $0.00

1. On August 16, you receive a check from your Grandmother for $40 for your birthday.

2. On August 16, you receive a check from your Parents for $100 for your birthday.

3. On August 17, you purchase a pair of pants from Old Navy for $23.42.

4. On August 18, you find $5.19 in change during the day.

5. On August 19, you purchase socks from Wal-Mart for $12.76.
DATE
TRANSACTION
PAYMENT (-)
DEPOSIT (+)
BALANCE
8/16
Beginning balance
$0.00

A. What is your balance after five transactions?

B. How much money did you deposit (show as a positive value)?

C. How much money did you pay or withdraw (show as a negative value)?

Situation #2:
Use the ledger to record the information and answer the questions.
Note: On May 5, your beginning balance is $8.00

1. On May 6, you spent $4.38 on a gallon of ice cream at Marty's Ice Cream Parlor.

2. On May 7, you spent $3.37 on crackers, a candy bar, and a coke from Circle H convenience store.

3. On May 8, you received $10 for cutting the neighbor's grass.

4. On May 8, you spent $14.80 on a downloaded book for your Kindle.

DATE
TRANSACTION
PAYMENT (-)
DEPOSIT (+)
BALANCE

A. What is your balance after four transactions?

B. How much money did you deposit (show as a positive value)?

C. How much money did you pay or withdraw (show as a negative value)?

D. Can you really afford to spend $14.80 on a book for your Kindle? If not, how much money do you need to earn to have an account balance of $0?

Situation #3:
Use the ledger to record the information and answer the questions.
Note: On July 4, your beginning balance is (-$40).
Requirements:
- Use at least eight transactions, four of which are debits and four are credits.
- You must have an ending balance of $145.
- You must include debit and credit amounts that have cents in at least five of your transactions.
Be sure to fill out the ledger as you go.

DATE
TRANSACTION
PAYMENT (-)
DEPOSIT (+)
BALANCE
 

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