Standard 6: Number Systems and Number Theory

In grades 5-8, the mathematics curriculum should include the study of number systems and number theory so that students can:

• Understand and appreciate the need for numbers beyond the whole numbers

 
Benchmarks 12B (Habits of Mind: Computation and Estimation)
Grades K-2, page 290
Use whole numbers and simple, everyday fractions in ordering, counting, identifying, measuring, and describing things and experiences.

Benchmarks 8E (The Designed World: Information Processing)
Grades 6-8, page 202
Most computers use digital codes containing only two symbols, 0 and 1, to perform all operations. Continuous signals (analog) must be transformed into digital codes before they can be processed by a computer.

Benchmarks 9A (The Mathematical World: Numbers)
Grades 6-8, page 213
A number line can be extended on the other side of zero to represent negative numbers. Negative numbers allow subtraction of a bigger number from a smaller number to make sense, and are often used when something can be measured on either side of some reference point (time, ground level, temperature, budget).
 

• Extend their understanding of whole number operations to fractions, decimals, integers, and rational numbers

Benchmarks 9A (The Mathematical World: Numbers)
Grades 6-8, page 213
There have been systems for writing numbers other than the Arabic system of place values based on tens. The very old Roman numerals are now used only for dates, clock faces, or ordering chapters in a book. Numbers based on 60 are still used for describing time and angles.

Benchmarks 9A (The Mathematical World: Numbers)
Grades 6-8, page 213
Numbers can be represented by using sequences of only two symbols (such as 1 and 0, on and off); computers work this way.

Benchmarks 9A (The Mathematical World: Numbers)
Grades 6-8, page 213
A number line can be extended on the other side of zero to represent negative numbers. Negative numbers allow subtraction of a bigger number from a smaller number to make sense, and are often used when something can be measured on either side of some reference point (time, ground level, temperature, budget).

Benchmarks 9A (The Mathematical World: Numbers)
Grades 6-8, page 213
Numbers can be written in different forms, depending on how they are being used. How fractions or decimals based on measured quantities should be written depends on how precise the measurements are and how precise an answer is needed.
 

• Understand how the basic arithmetic operations are related to one another

Benchmarks 9A (The Mathematical World: Numbers)
Grades 6-8, page 213
The operations + and – are inverses of each other one undoes the other; likewise ´ and ¸ .

Benchmarks 9A (The Mathematical World: Numbers)
Grades 6-8, page 213
The expression a/b can mean different things: a parts of size 1/b each, a divided by b, or a compared to b.
 

• Develop and apply number theory concepts (e.g., primes, factors, and multiples) in real-world and mathematical problem situations