### Standard 5: Number and Number Relationships

In grades 5-8, the mathematics curriculum should include the continued development of number relationships so that students can:
• Understand, represent, and use numbers in a variety of equivalent forms (integer, fraction, decimal, percent, exponential, and scientific notation) in real-world and mathematical problem situations

•   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).

• Develop number sense for whole numbers, fractions, decimals, integers, and rational numbers
• Benchmarks 11D (Common Themes: Scale)
Grades 3-5, page 277
Almost anything has limits on how big or small it can be.

• Understand and apply ratios, proportions, and percents in a wide variety of situations
• Benchmarks 11D (Common Themes: Scale)
Grades 6-8, page 278
Properties of systems that depend on volume, such as capacity and weight, change out of proportion to properties that depend on area, such as strength or surface properties.

• Investigate relationships among fractions, decimals, and percents
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.

• Represent numerical relationships in one- and two-dimensional graphs
• Benchmarks 9C (The Mathematical World: Shapes)
Grades 3-5, page 223
If 0 and 1 are located on a line, any other number can be depicted as a position on the line.

Benchmarks 9C (The Mathematical World: Shapes)
Grades 6-8, page 224
It takes two numbers to locate a point on a map or any other flat surface. The numbers may be two perpendicular distances from a point, or an angle and a distance from a point.

Benchmarks 9C (The Mathematical World: Shapes)
Grades 6-8, page 224
The scale chosen for a graph or drawing makes a big difference in how useful it is.