Topic: The Number System |
Common Core Mathematics 6-8 |
| Cluster Compute fluently with multi-digit numbers and find common factors
and multiples. |
| | Grade 6 |
| | | 6.NS.2. | Fluently divide multi-digit numbers using the standard algorithm. |
| | | 6.NS.3. | Fluently add, subtract, multiply, and divide multi-digit decimals using
the standard algorithm for each operation. |
| | | 6.NS.4. | Find the greatest common factor of two whole numbers less than or
equal to 100 and the least common multiple of two whole numbers
less than or equal to 12. Use the distributive property to express a
sum of two whole numbers 1–100 with a common factor as a multiple
of a sum of two whole numbers with no common factor. For example,
express 36 + 8 as 4 (9 + 2). |
| Cluster Apply and extend previous understandings of numbers to the system
of rational numbers. |
| | Grade 6 |
| | | 6.NS.5. | Understand that positive and negative numbers are used together
to describe quantities having opposite directions or values (e.g.,
temperature above/below zero, elevation above/below sea level,
credits/debits, positive/negative electric charge); use positive and
negative numbers to represent quantities in real-world contexts,
explaining the meaning of 0 in each situation. |
| | | 6.NS.6. | Understand a rational number as a point on the number line. Extend
number line diagrams and coordinate axes familiar from previous
grades to represent points on the line and in the plane with negative
number coordinates. |
| | | 6.NS.6.a. | Recognize opposite signs of numbers as indicating locations
on opposite sides of 0 on the number line; recognize that the
opposite of the opposite of a number is the number itself, e.g.,
–(–3) = 3, and that 0 is its own opposite. |
| | | 6.NS.6.b. | Understand signs of numbers in ordered pairs as indicating
locations in quadrants of the coordinate plane; recognize that
when two ordered pairs differ only by signs, the locations of the
points are related by reflections across one or both axes. |
| | | 6.NS.6.c. | Find and position integers and other rational numbers on a
horizontal or vertical number line diagram; find and position pairs
of integers and other rational numbers on a coordinate plane. |
| | | 6.NS.7.a. | Interpret statements of inequality as statements about the relative
position of two numbers on a number line diagram. For example,
interpret –3 > –7 as a statement that –3 is located to the right of –7 on
a number line oriented from left to right. |
| | | 6.NS.7.d. | Distinguish comparisons of absolute value from statements about
order. For example, recognize that an account balance less than –30
dollars represents a debt greater than 30 dollars. |
| | | 6.NS.8. | Solve real-world and mathematical problems by graphing points in all
four quadrants of the coordinate plane. Include use of coordinates and
absolute value to find distances between points with the same first
coordinate or the same second coordinate. |
| Cluster Apply and extend previous understandings of operations with
fractions to add, subtract, multiply, and divide rational numbers. |
| | Grade 7 |
| | | 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. |
| | | 7.NS.1.a. | Describe situations in which opposite quantities combine to
make 0. For example, a hydrogen atom has 0 charge because its two
constituents are oppositely charged. |
| | | 7.EE.1.b. | 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. |
| | | 7.NS.1.c. | 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. |
| | | 7.NS.1.d. | 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. |
| | | 7.NS.2.a. | 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. Interpret products of rational
numbers by describing real-world contexts. |
| | | 7.NS.6.b. | 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). Interpret quotients of rational numbers by describing realworld
contexts. |
| | | 7.NS.6.c. | Apply properties of operations as strategies to multiply and
divide rational numbers. |
| | | 7.NS.6.d. | Convert 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.[1Computations with rational numbers extend the rules for manipulating fractions to
complex fractions] |
| Cluster Know that there are numbers that are not rational, and approximate
them by rational numbers. |
| | Grade 8 |
| | | 8.NS.1. | Know that numbers that are not rational are called irrational.
Understand informally that every number has a decimal expansion; for
rational numbers show that the decimal expansion repeats eventually,
and convert a decimal expansion which repeats eventually into a
rational number. |
| | | 8.NS.2. | Use rational approximations of irrational numbers to compare the size
of irrational numbers, locate them approximately on a number line
diagram, and estimate the value of expressions (e.g., ƒÎ2). For example,
by truncating the decimal expansion of ã2, show that ã2 is between 1 and
2, then between 1.4 and 1.5, and explain how to continue on to get better
approximations. |