Benchmark
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. (2 of 7)
Standard 6-3, page 91, Grades 5-8
Extend their understanding of whole number operations to fractions,
decimals, integers, and rational numbers
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). (2 of 7)
Standard 4-1 page 32, Grades K-4
Link conceptual and procedural knowledge
Standard 5-1, page 87, Grades 5-8
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
Standard 6-1, page 91, Grades 5-8
Understand and appreciate the need for numbers beyond the whole numbers
Standard 6-2, page 91, Grades 5-8
Develop and use order relations for whole numbers, fractions, decimals,
integers, and rational numbers
Standard 6-3, page 91, Grades 5-8
Extend their understanding of whole number operations to fractions,
decimals, integers, and rational numbers
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. (3 of 7)
Standard 12-1 page 57, Grades K-4
Develop concepts of fractions, mixed numbers, and decimals
Standard 12-2 page 57, Grades K-4
Develop number sense for fractions and decimals
Standard 4-2 page 32, Grades K-4
Relate various representations of concepts or procedures to one another
Standard 5-4, page 87, Grades 5-8
Investigate relationships among fractions, decimals, and percents
Standard 6-3, page 91, Grades 5-8
Extend their understanding of whole number operations to fractions,
decimals, integers, and rational numbers
The operations + and – are inverses of each other one undoes the other;
likewise x and / . (4 of 7)
Standard 6-4, page 91, Grades 5-8
Understand how the basic arithmetic operations are related to one another
The expression a/b can mean different things: a parts of size 1/b each,
a divided by b, or a compared to b. (5 of 7)
Standard 6-4, page 91, Grades 5-8
Understand how the basic arithmetic operations are related to one another
Numbers can be represented by using sequences of only two symbols (such
as 1 and 0, on and off); computers work this way. (6 of 7)
Standard 4-2 page 32, Grades K-4
Relate various representations of concepts or procedures to one another
Standard 6-3, page 91, Grades 5-8
Extend their understanding of whole number operations to fractions,
decimals, integers, and rational numbers
Standard 14-3 page 184, Grades 9-12
Appreciate that seemingly different mathematical systems may be essentially
the same
