Download 7.NS.2 final

7.NS.2
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.2 Apply and extend previous understanding of multiplication and division and of fractions to multiply and
divide rational numbers.
Essential Questions
What models and
relationships help you
make sense of multiplying
and dividing positive and
negative numbers?
Content Statements
Apply the rules for
multiplying integers.
Review the Commutative
Property of Multiplication.
Multiply rational numbers.
Divide integers, recognize
when a quotient is
undefined.
Express a quotient of
integers as a rational
Enduring Understandings
Understand that multiplication
and division of whole numbers is
extended to integers by requiring
that operations continue to
satisfy properties of operations.
Activities, Investigation, and Student Experiences
Refer to 7.NS.2.a-7.NS.2.d
7.NS.2
number.
Write a rational number as
a quotient of integers.
Apply previous
understandings of division
of factions to write division
by a rational number as
multiplication by the
reciprocal.
Apply properties of
operations as strategies to
multiply and divide rational
numbers.
Simplify complex fractions
involving rational numbers.
Apply the distributive
property to multiplying
rational numbers.
Solve real-world problems
involving more than one
operation with rational
numbers.
Assessments
2012
7.NS.2
Refer to 7.NS.2.a-7.NS.2.d
Equipment Needed:
Teacher Resources:
Spinners
Holt McDougal Lessons 2-4, 3-2, 3-6
Deck of cards
Dice
2012
7.NS.2
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.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
Essential Questions
How does knowing how to
add positive and negative
integers help you multiply
positive and negative
integers?
Enduring Understandings
There are similarities and
differences between multiplying
rational numbers and
multiplying fractions and
decimals.
How do properties of
addition and multiplication
help you multiply positive
and negative integers?
The rules for multiplying
rational numbers.
Content Statements
Apply the rules for
multiplying integers.
Review the Commutative
Property of Multiplication.
Multiply rational numbers.
Activities, Investigation, and Student Experiences
Create a real-world situation that will help students to discover
the procedures for multiplying rational numbers. For example,
“You have a bank account that you forgot about and it currently
has a balance of $0. The bank charges a service fee of $3 every
month. What would the balance be after 5 months?” Hold a
brief discussion about what the equation used to solve this
problem would look like (5(-3). Which number is negative?
Why? Have students work with a partner to solve and share out
with the class. How did they know if the answer was negative
or positive? Challenge the students by telling them the bank
wants to refund the money. Have each pair of students
determine a new equation (-5)(-3), solve and share out with the
class. Again, how did they know if the answer was positive or
negative? Present students with several other problems 3(-2),
(-3)(-2), (-3)2. Encourage students to look for patterns. Have
students create rules for multiplying with negative numbers. In
what situations is the answer negative? positive?
Brainstorm a list of real-world scenarios in which students will
need to multiply negative numbers.
Use a spinner, dice OR number cards to build numbers to
7.NS.2
Assessments
The temperature in Bar Harbor, Maine, was -3 °F. It then
dropped during the night to be four times as cold. What was
the temperature then?
2012
multiply. Give students parameters to follow such as how many
digits each number must include. Student will spin to create
their number, and then spin to determine whether it is negative
or positive. (Odds can represent a negative, evens can represent
a positive). Students partner with a classmate to play . The
winner is the student who has the largest/smallest product.
Equipment Needed:
Have students play “war” with a deck of cards. The red cards
are negatives, black cards are positive. Students deal out the
cards, flip two cards each, multiply, and the student with the
larger product receives the cards. Assign number values to the
Ace, King, Queen, and Jack.
Teacher Resources:
Real world scenarios
Holt McDougal Lessons 2-4, 3-2, 3-6
Spinner, Dice or number cards
Deck of cards
7.NS.2
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.2.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, the –(p/q) = (-p)/q = p/(-q). Interpret quotients
of rational numbers by describing real-world contexts.
Essential Questions
How does the relationship
between multiplication and
division help you divide
integers and other rational
numbers?
Content Statements
Divide integers, recognize
when a quotient is
undefined.
Express a quotient of
integers as a rational
number.
Write a rational number as
a quotient of integers.
Apply previous
understandings of division
of factions to write division
by a rational number as
multiplication by the
reciprocal.
Enduring Understandings
Ability to explore and justify the
result of division by 0.
Ability to apply and extend
knowledge of addition and
subtraction of integers (ie two
color counters, arrows on a
number line) to extend to
division.
Ability to use patterns and
concrete models to devise a
general rule for dividing.
Activities, Investigation, and Student Experiences
Pair up students. Present –(8/2). Ask for answer, (-4). Present
(-8)/4. Again ask for volunteer to answer, (-4). Ask how they
know the answer is negative. Present 8/(-2). Ask for answer
and how they know. Have a brief discussion about the three
problems. What do the three problems have in common? What
conclusions can you draw about dividing negative numbers?
Work in pairs to solve several sets of problems similar to…
Ex. –(12/3), -(12)/3, 12/(-3), -12/-3
Generate a class discussion about the problems. Have students
make generalizations about dividing negative numbers and
create a set of rules detailing how to divide negative numbers.
Play a game where students use a spinner (or number cards).
Students spin to select numbers and create a division problem.
Challenge them to manipulate the negative sign to create as
many different problems as they can that will all have the same
answer.
Present additional problems to students that include decimals
and fractions and challenge students to discover whether the rule
they established still applies.
7.NS.2
Assessments
A teacher has 5 cups of M&M’s to be shared equally with 6
students. How many cups would each student receive.
-5/6 = ___/-6 Find the missing value.
Equipment Needed:
Teacher Resources:
Paper
Holt McDougal Lessons 2-4, 3-3,3-7
Standards Solution
Pencils
Division Problems
2012
7.NS.2
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.2.c. Apply properties of operations as strategies to multiply and divide rational numbers.
Essential Questions
What models and
relationships help you
make sense of multiplying
and dividing positive and
negative rational numbers?
Content Statements
Apply properties of
operations as strategies to
multiply and divide rational
numbers.
Simplify complex fractions
involving rational numbers.
Apply the distributive
property to multiplying
rational numbers.
Solve real-world problems
involving more than one
operation with rational
numbers.
Enduring Understandings
Deciding the order in which to
carry out the operations when a
problem consists of more than
one operation.
Ability to identify and apply the
Distributive, Associative,
Commutative, and Identity
Properties.
Activities, Investigation, and Student Experiences
Create four sets of problems with 5 problems in each set. Ex.
3(5+4), 4 ( ½ + ¼), 1/3 (6+3), -5(-3 + 2), -3/4 (1/2 – ¼). Have
students complete one set of problems with a partner. Once
students are finished, put students into groups of 8 so that all of
the problem sets are represented. Ask each pair to present their
problems to the larger group and share their strategies and
methods. Hold a class discussion to summarize the properties
they applied and how they used their prior knowledge to solve
the more complex ones. How did they treat fractions? How did
they decide which answers were negative and which were
positive?
7.NS.2
Assessments
A recipe calls for 2 ¾ cups of whole wheat flour. If Ms.
Ambrose wanted to triple the recipe, how many cups of flour
would she need?
Mr. Mischel wants to divide 3 ½ containers of fertilizer
equally amongst 8 flower beds. How many containers will
he need each day if he plans on filling 2 flower beds per day?
Equipment Needed:
Teacher Resources:
Problem sets
Holt McDougal Lessons 2-4,3-7
Paper
Pencils
2012
7.NS.2
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.2.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.
Essential Questions
Why do rational numbers
in decimal form either
terminate or repeat?
Content Statements
Write fractions as decimals
and vice versa.
Enduring Understandings
Ability to recognize that when
rational numbers in fractional
form are converted to decimals
they either terminate or repeat.
Determine whether a
decimal is terminating or
repeating.
Assessments
Provide students with one terminating decimal, one repeating
decimal in fraction form, and a number line. Have students
graph the given rational numbers on the number line,
determine one repeating and one terminating decimal
between the given rational numbers, identify those that are
terminating and repeating and explain why.
Activities, Investigation, and Student Experiences
Partner students up. Give each pair of students a baggie.
Students will match the fractions to their decimal equivalents.
Once students have found the ten matched pairs, have a class
discussion about strategies students used to find the answers.
Make sure students are able to articulate what process and
operation they used. What did they do when there weren’t any
more digits in the dividend but needed to avoid a remainder?
What did they do when they came across a repeating decimal?
Have students summarize the process for converting fractions to
decimals, using their journals.
***Sample fractions: ½, 3/8, ¼, 2/5, 5/8, 1/3, 2/3, ¾, 5/6, 4/5.
7.NS.2
Equipment Needed:
Baggie of 10 fractions and corresponding decimals.
Teacher Resources:
Holt McDougal Lesson 2-6
Standards Solution
2012