Download 1.2 Multiplying and Dividing Rational Numbers

7th Grade Math Unit 1: Operations with Rational Numbers
Length of Unit: 22 days
Standards:
Apply and extend previous understandings of operations with fractions to add, subtract, multiply
and divide rational numbers.
MCC7.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.
MCC7.NS.1a Describe situations in which opposite quantities combine to make 0.
MCC7.NS.1b Understand as the number located a distance from, in the positive or negative
direction depending on whether 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.
MCC7.NS.1c Understand subtraction of rational numbers as adding the additive inverse. 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.
MCC7.NS.1d Apply properties of operations as strategies to add and subtract rational numbers.
MCC7.NS.2 Apply and extend previous understandings of multiplication and division of
fractions to multiply and divide rational numbers.
MCC7.NS.2a 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.
MCC7.NS.2b 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. Interpret quotients of
rational numbers by describing real-world contexts.
MCC7.NS.2c Apply properties of operations as strategies to multiply and divide rational
numbers
MCC7.NS.2d Convert a rational number to a decimal using long division; know that the decimal
form of a rational number terminates in 0’s or eventually repeats.
MCC7.NS.3 Solve real-world and mathematical problems involving the four operations with
rational numbers.
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Enduring Understandings:


Solve real-world problems with accuracy
Select the numerical process needed to compute rational numbers
Common Misconceptions:




Absolute values are opposites.
The product of two negative numbers is negative.
Integer rules for addition are the same as multiplication /division.
The greater the absolute value of a negative number, the larger the number (for example,
-7 is greater than -2)
Topics:
1.1 Adding and subtracting rational numbers
1.2 Multiplying and Dividing Rational Numbers
1.3 Solving real-world Problems
Key Vocabulary:
Absolute value
Integers
Zero Pairs
Additive Inverse
Positive numbers
Negative numbers
Number line
Natural Numbers
Opposite Numbers
Rational Numbers
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Unit Calendar
Monday
Tuesday
Wednesday
preassessment
and overview
1.1.1a
absolute value
1.1.1b
1.1.1c
additive inverse opposites
1.1.2a
+/- with counters
1.1.2b
+ with
number line
1.1.2c
- with number
line
1.1.2d
sums of
rational
numbers
1.1.2e
difference of
absolute
values
1.1.2f
+/- rational
numbers
Week 1.2.1a
3
x/÷ fractions
Aug
18-22
1.2.1b
properties of
x/÷ fractions
applied to
integers
1.2.1c
x/÷ integers
1.2.1d
interpret x/÷
of rational
numbers
1.2.2a
identify order of
operations to x/÷
rational numbers
Week
4
Aug
25-29
1.2.3a
convert
rational
number to
decimal
1.2.3b
terminating and
repeating
decimals
1.3.1a
solve realworld rational
number
problems with
all operations
1.3.1b
create real-world
rational number
problems with all
operations
Week
1
Aug
4-8
Week
2
Aug
11-15
1.2.2b
apply order
of operations
to x/÷
rational
Thursday
Friday
3
numbers
Week HOLIDAY
5
Sept
1-5
Review
postassessment
4
Unit Structure
By the end of the unit, students should be able to answer the following questions:
Unit EQ’s
1. How can I
use previous
understanding
of operations
with fractions
to add,
subtract,
multiply,
divide rational
numbers?
Topic EQ’s
1.1
How can using
models deepen
my
understanding
of addition and
subtraction?
Lesson EQ’s
1.1.1 How can
knowing absolute
value help me
understand
operations on
rational numbers?
Daily EQ’s
1.1.1a What is absolute value and
why is it always positive?
1.1.1b How can I show that a
number and its opposite have a sum
of zero (additive inverse)?
1.1.1c How do I describe situations
in which opposite quantities
combine to make 0?
1.1.2 How do I show
addition and
subtraction using
vertical and
horizontal lines?
1.1.2a How can using colored
counters help me understand the
operations of addition and
subtraction?
1.1.2b How can I use a vertical or
horizontal number line to show
addition?
1.1.2c How can I use a vertical or
horizontal number line to show
subtraction?
1.1.2d How can I interpret sums of
rational numbers by describing realcontext?
1.1.2e How can I show that the
distance between two rational
numbers on a number line is the
absolute value of their difference,
and apply this principle in real world
context?
1.1.2f How can I use my
understanding of addition and
subtraction and apply to rational
numbers, such as fractions, integers
and decimals?
Topic 1.2
1.2.1 How do I apply 1.2.1a How can I demonstrate
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How do I
extend previous
understanding
of
multiplication
and division of
fractions to
multiply and
divide rational
numbers?
rules for
multiplication and
division to integers?
multiplying and dividing fractions?
1.2.1b How do the properties of
multiplication\division of fractions
apply to integers?
1.2.1c How can I show my
understanding of multiplication and
division of integers?
1.2.1d How can I interpret the
products and quotients of rational
numbers by describing real-world
contexts?
Topic 1.3
What methods
can I use to
solve real-world
and
mathematical
problems
involving the
four operations
with rational
numbers?
1.2.2 How do I apply
the rules for
multiplication and
division to rational
numbers such as
decimals?
1.2.2a How can I identify how
properties of operations can be used
to multiply and divide rational
numbers?
1.2.3 How can I
convert rational
numbers to decimals;
repeating/terminating
decimals?
1.2.3a How can I convert a rational
number to a decimal using long
division?
1.3.1 How can I
interpret the four
operations of rational
numbers using real
world contexts?
1.3.1a How can I solve real-world
mathematical problems by adding,
subtracting, multiplying and
dividing rational numbers, including
fractions?
1.2.2b How can I apply properties of
operations as strategies to multiply
and divide rational numbers?
1.2.3b How can I explain the process
of converting a rational number to
decimal form that terminates or
repeats?
1.3.1b How can create real-world
mathematical problems using
adding, subtracting, multiplying and
dividing rational numbers, including
fractions?
Unit Assessment
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