7.NS.1
2012
Domain: The Number System
Cluster: Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide
rational numbers.
Standards: 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.
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.
Essential Questions
Enduring Understandings
Activities, Investigation, and Student Experiences
 What are the different
types of rational
numbers?
 It is helpful to use previous
understandings of adding,
subtracting, multiplying and
dividing whole and positive
numbers in order to solve
more complex problems with
decimals and fractions.
Examples:
 Use a number line to add -5 + 7.
 7 – 5, the difference is the distance between 7 and 5, or
2, in the direction of 5 to 7 (positive). Therefore the
answer would be 2.
 Use a number line to subtract: -6 – (-4)
 Use a number line to illustrate:
 p – q ie. 7 – 4
 p + (-q) ie. 7 + (– 4)
 Is this equation true p – q = p + (-q)?
 Students explore the above relationship when p is
negative and q is positive and when both p and q
are negative.
 Is this relationship always true?
 What kinds of problems
can you solve using
rational numbers?
 When is it helpful to use
a number’s opposite?
 How do the properties of
operations help you add
and subtract rational
numbers?
 Addition and subtraction can
be represented on a horizontal
or vertical number line
diagram.
 p + q represents the number
located a distance |q| from p.
7.NS.1
 How does the opposite
of a number differ from
the absolute value of it?
Content Statements
 Classify numbers.
 Find the absolute value
of a number.
 Identify opposites.
 Find sums and
differences of rational
numbers in practice and
real world context.
 Solve problems
involving rational
numbers using number
lines, and the additive
inverse.
 Identify and apply the
Commutative,
Associative, and Identity
properties to simplify
rational numbers.
 Find the distance
between two rational
numbers on the number
line using the absolute
 Opposite quantities combine
to make 0.
2012

Morgan has $4 and she needs to pay a friend $3. How
much will Morgan have after paying her friend?
Solution: 4 + (-3) = 1 or (-3) + 4 = 1
 Number and its opposite have
a sum of 0. (additive inverse)
 Subtraction of rational
numbers means adding the
additive inverse,
p – q = p + (–q).
 Subtraction is really finding
the distance between two
numbers on a number line.
 Apply the Associative,
Commutative, and Identity
Properties to solve problems.
Activities:
 Use algebra counters/tiles to model addition of integers.

Use a number line to model addition of integers.

Provide students with debits and credits for an account.
Students should determine what values would be needed
to “zero out an account.”

Stock market: Give 5 stock values and their daily
increases and decreases, students need to determine
increased for following day to “break even” using
appropriate signs. The lesson should be modeled on a
number line.
Temperature:
 Create a table of a city’s high and low temperatures
for a week. Be mindful to choose a city whose
temperatures include positive and negative numbers.
 Pair the students to answer questions such as “How
much warmer is Sunday’s high temperature than
Sunday’s low temperature?
7.NS.1
value of their difference.
Assessments

Last week, Jane made deposits of $64, $25, and $37
into her checking account. She then wrote checks for
$52 and $49. What is the overall change in Jane’s
account balance?

A submarine submerges at a depth of -40ft dives 57ft
more. What is the new depth of the submarine?

At 3 P.M., the temperature was 9°F. By 11 PM, it
had dropped 31°F. What was the temperature at 11
PM?

7(1/2 + ¾), -2(5 + ½), 7 ½ x 4/4, 3/2(1/8 + 2/16)

Write a story that would result in the problem:
(-3) + 6 + 5.7 - 8

2012
 Which day has the greatest difference between its high
and low temperatures?” Allow students to discover
the process using whatever solution strategies make
sense to them.
 Move onto larger number once students understand.
Possible use Earth’s Highest and Lowest Elevations.
Repeat with similar type questions.
 Ask students to develop a procedure for adding and
subtracting rational numbers.
 Have them apply their procedures to several practice
problems.
 Extend this concept to problems involving negative
fractions and decimals. Have students investigate if
the same procedures apply.
Cards:
 Use a deck of cards. Assign values to the Ace, King,
Queen, Jack.
 Have students play “war”.
 Evenly distribute the deck of cards within each group.
Each students flips two cards and finds the sum.
 The student with the largest sum gets all the cards.
Red cards are negative, black cards are positive.
Model the solution in two different ways.


Diminishing Return

Part and Whole
Distance:
 Generate a discussion about distance.
 Help students arrive at the idea that distance is always
positive.
 Display a classroom number line.
 Ask questions such as, “What if your house was at 7
and your friends house was at 2, how would you find
7.NS.1

The height of Tom’s house from ground level to the top
7
of the roof is 23 ft. The basement floor of his house is
8
3
7 ft below ground level. Tom wrote this number
4
sentence to find the distance between the top of the roof
and the basement floor:
23
7
3
– (- 7 ) =
4
8
What is the distance between the top of the roof and the
basement floor?
5
1
1
5
A) 31 * B) 16
C) 16
D) 31
8
8
8
8
2012
the distance? Does the distance change if we start at 7
or start at 2? Could we find the distance by
subtracting 7 from 2?”
 Introduce the concept of absolute value. Tell them
that since the distance is the same regardless of
direction, we use the absolute value symbols to
indicate that what we are looking for the distance.
Ask more questions such as “What if you lived at 2
and your grandmother lived at -8, how would you find
the distance? How far away would you be from your
grandmother? Is the distance from your house to your
grandmother’s house, the same as the distance from
your grandmother’s house to yours?” Emphasize they
can count the number of spaces or express it as |-82|or |2-(-8)|.
 Divide the students into pairs, provide each group
with a worksheet of different distances or altitudes,
have the students select and answer one problem then
share out with the class.
Card Values:
 Use a deck of cards. Assign values to the Ace, King,
Queen, Jack. Have students play “war”.
 Evenly distribute the deck of cards within each
group. Each students flips two cards and finds the
difference. The student with the largest sum gets all
the cards. Red cards are negative, black cards are
positive.
7.NS.1
2012
Examples of 7.NS.1
Comparing Freezing Points
Distances on the Number Line 2
Operations on the Number Line
grade 7 addition subraction rational numbers.doc
Equipment Needed:
Teacher Resources:
Interactive Whiteboard
http://www.illustrativemathematics.org/standards/k8
Calculators
http://insidemathematics.org/index.php/7th-grade
Stocks
Deck of Cards
Algebra counters
Vertical Number lines
Horizontal number lines
http://www.nyscirs.org/CCSS%20Toolkit/Math%20Toolkit/
Exemplars/
http://www.schools.utah.gov/CURR/mathsec/Core/7thGrade-Core/7NS.aspx
http://www.ncpublicschools.org/acre/standards/commoncore-tools/
http://illuminations.nctm.org/