Numeracy requires the ability to work flexibly with quantities in order to recognize, reason, and solve situations of varying contexts in everyday life, society, and the work place.

• • How is numeracy like literacy?

  • What are some examples of numeracy in everyday life, society, and the work place?

  • How does context influence understanding of a quantity?

  • Why is the ability to work flexibly with quantities essential to developing the foundations of numeracy?

Rational numbers create a more sophisticated number system where new relationships exist within and between sets and subsets of numbers (counting numbers; whole numbers; integers; rational numbers).

• • What representations can be used to visually demonstrate relationships between sets and subsets of numbers?

  • How does organizing numbers in sets and subsets aid in understanding the relationships between rational numbers?

  • What relationships exist between sets and subsets of numbers?

  • How are the elements in counting (natural) numbers, whole numbers, integers, and rational numbers related?

  • How can a number belong to the same set of numbers but not necessarily the same subset of numbers?

  • What relationship exists between rational numbers and the other number sets?

Unit Vocabulary:

• Number and Operations

  • Number

    • Counting (natural) numbers

    • Whole numbers

    • Integers

    • Rational numbers

  • Number Representations

    • Sets and subsets

  • Relationships and Generalizations

    • Numerical

    • Equivalence

  • Representations

  • Fluency

  • Earned wages

  • Financial asset

  • Financial liability

  • Income tax

  • Net worth

  • Sales tax

Assignment 1:

Analyze the situation(s) described below. Organize and record your work for each of the following tasks. Using precise mathematical language, justify and explain each mathematical process.

1. Number sets are interrelated.

   1. Create a visual representation to organize and display the relationship of the sets and subsets of numbers:

      • counting (natural) numbers

      • integers

      • rational numbers

      • whole number

   2. Include 3 elements in each of the number sets in the visual representation.

   3. In writing, describe the relationships between sets of rational numbers.

For each expression below, determine the solution and complete each generalization.

1. When adding two rational numbers, if a pair of addends has the same sign, then the sum will have the __________ of both addends.
   

2. When adding two rational numbers, if a pair of addends has opposite signs, then the sum will have the sign of the addend with the _________ ____________ _____________.
   

3. When subtracting two non-zero positive rational numbers (with the subtrahend larger than the minuend), the difference will always be ____________ than the minuend and be ____________.
   

4. When multiplying two non-zero positive rational numbers, where at least one of the factors is greater than one, the product always will be __________ than the smallest factor.
   

5. When dividing two non-zero positive rational numbers, where the dividend is greater than the divisor, the quotient will always be ___________ than one.
   

6. When multiplying two or more rational numbers with a(n) __________ number of negative signs, then the product is ___________________.

Rational Numbers in the Real World

Estimation strategies can be used to mentally approximate solutions and determine reasonableness of solutions (rational numbers).

• • What strategies can be used to estimate solutions to problems?

  • When might an estimated answer be preferable to an exact answer?

  • How can an estimation aid in determining the reasonableness of an actual solution?

  • When might one estimation strategy be more beneficial than another?

Recognizing and understanding operational relationships in a variety of problem situations leads to efficient, accurate, and flexible representations and solution strategies (rational numbers).

• • How does the context of a problem situation affect the representation, operation(s), and/or solution strategy that could be used to solve the problem?

  • How does understanding …

    • relationships within and between operations

    • properties of operations

    • relationships between fractions, decimals, and percents

  • … aid in determining an efficient strategy or representation to investigate and solve problem situations?

  • Why is it important to understand when and how to use standard algorithms?

  • Why is it important to be able to perform operations with rational numbers fluently?

Understanding taxes and net worth helps one make informed financial management decisions, which promotes a more secured financial future.

• • How does the understanding operations with rational numbers aid in calculating …

    • sales tax for a given purchase?

    • income tax for earned wages?

  • What is the process for calculating …

    • sales tax for a given purchase?

    • income tax for earned wages?

  • How does understanding sales tax and income tax help promote a more secured financial future?

  • What are examples of financial …

    • assets?

    • liabilities?

  • What is the process of …

    • creating and organizing a financial assets and liabilities record?

    • constructing a net worth statement?

  • What factors affect the amount of income tax paid to the federal government?

  • What are some examples of a financial …

    • asset?

    • liability?

  • What is the relationship between an individual’s financial assets and liabilities when they have a negative or positive net worth?

  • How does understanding assets, liabilities, and net worth help promote a more secured financial future?

Assignment 2:

Analyze the problem situation(s) described below. Organize and record your work for each of the following tasks. Using precise mathematical language, justify and explain each solution process.

1. The thermometer outside reads that the current temperature is degrees Celsius. If the temperature drops each hour by of a degree, how many hours will pass before the temperature outside reaches 0°C?

2. Drew has decided it is time to purchase a new car. He has shopped around and decided which car he would like to purchase.

   1. The price of the car Drew wants to purchase is $17,998. This price includes all fees associated with the purchase of a vehicle, such as title and registration fees; however, the price does not include the required sales tax. In Texas, the sales tax rate for automobiles is 6%. Calculate the sales tax and final price of the new car.