Download CMS Curriculum Guides 2011-2012 7th Grade Math Unit Title

CMS Curriculum Guides 2011-2012
7th Grade Math
Unit Title: Accentuate the Negative
Suggested Time: 20 days
Enduring understanding (Big Idea): Use appropriate notation to indicate positive & negative numbers; Compare & order positive and negative rational numbers
(fractions, decimals, and zero) and locate them on a number line; Understand the relationship between a positive or negative and its opposite (additive inverse);
Develop algorithm for adding, subtracting, multiplying, and dividing positive and negative numbers; Write mathematical sentences to show relationships; Write
and use related fact families for addition/subtraction and multiplications/division to solve simple equations; Use parentheses and rules for the order of operations
in computations; Understand and use Commutative Property for addition and multiplication; Apply the Distributive Property to simplify expressions and solve
problems; Graph points in four quadrants; Use positive and negative numbers to model and answer questions about situations
Essential Questions: How do negative and positive numbers help in describing the situation? What will addition, subtraction, multiplication, or division of
positive and negative numbers tell about the problem? What model(s) for positive and negative numbers would help in showing the relationships in the problem
situation?
Unit Plans
Common Core Standards Alignment
Connection to 2003 Standards
Investigation 1-Extending the Number System
7.NS.1.b
Objective: 1.02
Problems 1.1, 1.2, 1.3, 1.4, & Math Reflections
Assign specific ACE problems
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.EE.3
Solve multi-step real-life and mathematical
problems posed with positive and negative rational
numbers in any form (whole numbers, fractions,
and decimals), using tools strategically. Apply
properties of operations to calculate with numbers
in any form; convert between forms as appropriate;
and assess the reasonableness of answers using
mental computation and estimation strategies.
Investigation 2 -Adding and Subtracting Integers
Problems 2.1, 2.2, 2.3, 2.4. 2.5 & Math Reflections
Assign specific ACE problems
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
Objective: 1.02
CMS Curriculum Guides 2011-2012
7th Grade Math
7.NS.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.3
Solve real-world and mathematical problems
involving the four operations with rational numbers.


7.EE.3
Solve multi-step real-life and
mathematical problems posed with positive and
negative rational numbers in any form (whole
numbers, fractions, and decimals), using tools
strategically. Apply properties of operations to
calculate with numbers in any form; convert
between forms as appropriate; and assess the
reasonableness of answers using mental
computation and estimation strategies.
Investigation 3 - Multiplying and Dividing Integers
7.NS.2
Problems 3.1, 3.2, 3.3, 3.4, & Math Reflections
Apply and extend previous understandings of
multiplication and division and of fractions to
multiply and divide rational numbers.
Assign specific ACE problems
7.NS.2.a
Understand that multiplication is extended from
fractions to rational numbers by requiring that
operations continue to satisfy the properties of
Objective: 1.02, 1.03
CMS Curriculum Guides 2011-2012
7th Grade Math
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 realworld contexts.
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, then –(p/q) = (–p)/q
= p/(–q). Interpret quotients of rational numbers by
describing real world contexts.
7.NS.2.c
Apply properties of operations as strategies to
multiply and divide rational numbers
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.
7.NS.3
Solve real-world and mathematical problems
involving the four operations with rational numbers.


Investigation 4- Properties of Operations
Problems 4.1, 4.2, 4.3
Math Reflections
7.EE.3
Solve multi-step real-life and
mathematical problems posed with positive and
negative rational numbers in any form (whole
numbers, fractions, and decimals), using tools
strategically. Apply properties of operations to
calculate with numbers in any form; convert
between forms as appropriate; and assess the
reasonableness of answers using mental
computation and estimation strategies.
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.
Objective: 1.02, 1.03
CMS Curriculum Guides 2011-2012
7th Grade Math
Looking Back & Looking Ahead
7.NS.1.d
Assign specific ACE problems
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.c
Apply properties of operations as strategies to
multiply and divide rational numbers
7.NS.3
Solve real-world and mathematical problems
involving the four operations with rational numbers.


7.EE.3
Solve multi-step real-life and
mathematical problems posed with positive and
negative rational numbers in any form (whole
numbers, fractions, and decimals), using tools
strategically. Apply properties of operations to
calculate with numbers in any form; convert
between forms as appropriate; and assess the
reasonableness of answers using mental
computation and estimation strategies.

Mathematical Practices Standards for Common Core
1-Make sense of problems and persevere in solving them 2-Reason abstractly and quantitatively 3-Construct viable arguments and critique the reasoning of
others 4-Model with mathematics 5-Use appropriate tools strategically 6-Attend to precision 7-Look for and make use of structure 8-Look for and express
regularity in repeated reasoning
Prior Knowledge:
Developing understanding of whole numbers and rational numbers; Using models to develop understanding of mathematical concepts; Understanding and
applying arithmetic operations with rational numbers; Using a coordinate grid with positive coordinates; Using a number line to develop equivalence and
operations of fractions and decimals; Developing understanding of the Commutative Property using whole numbers and rational numbers; Using the order of
operations to solve problems in a context
CMS Curriculum Guides 2011-2012
7th Grade Math
Essential Terms Developed in This Unit
Useful Terms Referenced in This Unit
Terms Developed in Previous Unit
Commutative Property
Distributive Property
Integers
Negative Numbers
Opposites
Order of Operations
Positive Numbers
Rational Numbers
Absolute Value
Additive Inverse
Associative Property
Expanding
Factoring
Quadrant I, II, III, IV
Algorithm
Area*
Coordinate Grid
Decimals*
Expressions
Fact Family*
Fractions*
Income/Profit
Mathematical Sentence*
Number Line*
Operations*
Ordered Pair
Variable
* Denotes in previous year
Resources
Lab-Sheet
Additional Practice/Skills Worksheets
CMP2 Website –online & technology resources
Formal Assessment
 Check-Ups
 Partner Quiz
 Unit Test
Assessment Options
 Notebook check
 Multiple-Choice
 Question Bank
 ExamView CD-ROM
Parent Guide-Unit Letters
Spanish Assessment Resources
PHSchool.com
TeacherExpress CD-ROM
LessonLab Online Courses
Unit Technology Tips