

Unit 2 Integers
and Rational Numbers Grade
7 Math 

Unit
Length and Description: 30 days Students
continue to build an understanding of the number line in Unit 2 from their
work in Grade 6. They develop a unified understanding of numbers, recognizing
fractions, decimals (that have a finite or repeating decimal representation),
and percents as different representations of rational numbers. Students should apply and extend their
understanding of addition, subtraction, multiplication, and division to add,
subtract, multiply and divide within the entire set of rational numbers.
Students should begin this unit representing addition and subtraction on a
horizontal or vertical number line diagram and finish the unit being able to
apply properties of operations as strategies to add, subtract, multiply and
divide rational numbers. They should also apply their understanding of
positive and negative numbers to establish the rules for multiplying signed
numbers. Additionally students should understand that integers can be
divided, provided that the divisor is not zero, and develop an understanding
that the quotient of integers (with nonzero divisors) is a rational
number. Students should leave this
unit with a deeper conceptual understanding of positive and negative rational
numbers and be able to use them to solve realworld and mathematical problems
including realworld problems where the sum is zero. Although procedural
skill and fluency should be improved through this unit, conceptual
understanding should be the basis for discovery and instruction. Unit 2 includes rational numbers as they
appear in expressions and equations—work that is continued in Unit 3. A focus on equivalent expressions is
important as student prepare for work with equations and inequalities in Unit
3. 

Standards: 7.NS.A.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. 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. 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. 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. d. Apply properties of
operations as strategies to add and subtract rational numbers. 7.NS.A.2 Apply and extend previous
understandings of multiplication and division and of fractions to multiply
and divide rational numbers. 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. 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 real‐world contexts. c. Apply properties of
operations as strategies to multiply and divide rational numbers. 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.A.3 Solve real‐world and mathematical problems
involving the four operations with rational numbers. o
Standards
Clarification: Computations with
rational numbers extend the rules for manipulating fractions to complex
fractions. 7.EE.A.2 Understand that rewriting an
expression in different forms in a problem context can shed light on the
problem and how the quantities in it are related. For
example, a + 0.05a = 1.05a means that “increase by 5%” is the same as
“multiply by 1.05.” o
Standards
Clarification: In this unit, this
standard is applied to expressions with rational numbers in them. Focus Standards of
Mathematical Practice: MP.1 Make
sense of problems and persevere in solving them. MP.2 Reason
abstractly and quantitatively. MP.3 Construct
viable arguments and critique the reasoning of others. MP.4 Model
with mathematics. MP.5 Use
appropriate tools strategically. MP.6 Attend
to precision. MP.7 Look for
and make use of structure. MP.8 Look for
and express regularity in repeated reasoning. Instructional
Outcomes: Full Development of the Major Clusters,
Supporting Clusters, Additional Clusters and Mathematical Practices for this
unit could include the following instructional outcomes: 7.NS.A.1a ·
I can describe
situations in which opposite quantities combine to make 0. ·
I can apply the
principal of subtracting rational numbers in realworld contexts. 7.NS.A.1b ·
I can represent and
explain how a number and its opposite have a sum of 0 and are additive
inverses. ·
I can demonstrate and
explain how adding two numbers, p + q, if q is positive, the sum of p and q
will be lql spaces to the right of p on the number line. ·
I can demonstrate and
explain how adding two numbers, p + q, if q is negative, the sum of p and q
will be lql spaces to the left of p on the number line. ·
I can interpret sums
of rational numbers by describing realworld contexts. ·
I can explain and
justify why the sum of p + q is located a distance of lql in the positive or
negative direction from p on a number line. ·
I can represent the
distance between two rational numbers on a number line is the absolute vale
of their difference and apply this principal in realworld contexts. ·
I can apply
properties of operations as strategies to add and subtract rational numbers. 7.NS.A.1c ·
I can identify
subtraction of rational numbers as adding the additive inverse property to
subtract rational numbers, pq= p+ (q). ·
I can apply and
extend previous understanding to represent addition and subtraction problems
of rational numbers with a horizontal or vertical number line. ·
I can apply
properties of operations as strategies to add and subtract rational numbers. 7.NS.A.1d ·
I can identify
properties of addition and subtraction when adding and subtracting rational
numbers. ·
I can apply
properties of operations as strategies to add and subtract rational numbers. 7.NS.A.2a ·
I can recognize that
the process for multiplying fractions can be used to multiply rational
numbers including integers. ·
I can recognize and
describe the rules when multiplying signed numbers. ·
I can apply the
properties of operations, particularly distributive property, to multiply
rational numbers. ·
I can interpret the
products of rational numbers by describing realworld contexts. 7.NS.A.2b ·
I can explain why
integers can be divided except when the divisor is 0. ·
I can describe why
the quotient is always a rational number. ·
I can comprehend and
describe the rules when dividing signed numbers, integers. ·
I can recognize that
–(p/q) = p/q = p/q. ·
I can interpret the
quotient of rational numbers by describing realworld contexts. 7.NS.A.2c ·
I can identify how
properties of operations can be used to multiply and divide rational numbers
(such as distributive property, multiplicative inverse property,
multiplicative identity, commutative property for multiplication, associative
property for multiplication, etc.). ·
I can apply
properties of operations as strategies to multiply and divide rational
numbers. 7.NS.A.2d ·
I can convert a
rational number to a decimal using long division. ·
I can explain the
decimal form of a rational number terminates (stops) in zeroes or repeats. 7.NS.A.3 ·
I can add rational
numbers. ·
I can subtract rational
numbers. ·
I can multiply
rational numbers. ·
I can divide rational
numbers. ·
I can solve
realworld mathematical problems by adding, subtracting, multiplying, and
dividing rational numbers, including complex fractions. 7.EE.A.2 ·
I can write
equivalent expressions with fractions, decimals, and integers. ·
I can rewrite an
expression in a equivalent form in order to provide insight about how
quantities are related in a problem context. 

Enduring
Understandings: ·
Rational
numbers use the same properties as whole numbers. ·
Rational
numbers can be used to represent and solve reallife situation problems. ·
Rational
numbers can be represented with visuals (including distance models),
language, and reallife contexts. ·
A number
line model can be used to represent the unique placement of any number in
relation to other numbers. ·
There are
precise terms and sequences to describe operations with rational numbers. 
Essential
Questions: ·
Why
do I need mathematical operations? ·
What
is the relationship between properties of operations and types of numbers? ·
How
do I know which mathematical operation (+, , x, ÷, exponents, etc.) to use? ·
How
do I know which computational method (mental math, estimation, paper and
pencil, and calculator) to use? ·
How
do you add rational numbers? ·
How
do you subtract rational numbers? ·
How
do you multiply rational numbers? ·
How
do you divide rational numbers? ·
How
is computation with rational numbers similar to and different from whole
number computation? ·
How
are rational numbers used and applied in reallife and mathematical
situations? ·
How
does the ongoing use of fractions and decimals apply to reallife situations? 
