MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 7
Unit Description
Big Idea(s)
What enduring
understandings are
essential for
application to new
situations within or
beyond this
content?
Essential
Question(s)
What questions will
provoke and
sustain student
engagement while
focusing learning?
Standards
Unit 1
Integers
Suggested Length: 3 weeks
Enduring Understandings
Understand Operations of Rational Numbers
Enduring Skills Rubric measures competency of the following skills:
 Apply understandings of addition and subtraction for rational numbers.
 Represent addition and subtraction on a number line diagram
(horizontal or vertical)
 Apply understandings of multiplication and division for rational numbers.
 Solve Real-world and mathematical problems involving the four
operations with rational numbers.
 How can you add and subtract integers to solve real-world problems?
 How can you multiply and divide integers to solve real-world problems?
 How can you use integers to solve multi-step real-world problems?
Standards for Mathematical Practice
1 - Make sense of problems and persevere in solving them.
2 - Reason abstractly and quantitatively.
4 - Model with mathematics.
5 – Use appropriate tools strategically.
6 - Attend to precision.
7 - Look for and make use of structure.
Standards for Mathematical Content
7.NS.1a 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.
7.NS.1b 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.1c 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.1d Apply properties of operations as strategies to add and subtract
Curriculum and Instruction
2015-2016
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MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 7
rational numbers.
7.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.
7.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. 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.2c Apply properties of operations as strategies to multiply and divide
rational numbers.
Supporting
Standard(s)
Which related
standards will be
incorporated to
support and
enhance the
enduring
standards?
7.NS.3 Solve real-world and mathematical problems involving the four
operations with rational numbers. (NOTE: Computations with rational numbers
extend the rules for manipulating fractions to complex fractions.)
6th Grade Enduring Understanding – Number
6.NS.1 Interpret and compute quotients of fractions, and solve word problems
involving division of fractions by fractions, e.g., by using visual fraction models
and equations to represent the problem. For example, create a story context
for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the
relationship between multiplication and division to explain that (2/3) ÷ (3/4) =
8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much
chocolate will each person get if 3 people share 1/2 lb of chocolate equally?
How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a
rectangular strip of land with length 3/4 mi and area 1/2 square mi?
6.NS.2 Fluently divide multi-digit numbers using the standard algorithm.
6.NS.3 Fluently add, subtract, multiply, and divide multi-digit decimals using
the standard algorithm for each operation.
6.NS.4 Find the greatest common factor of two whole numbers less than or
equal to 100 and the least common multiple of two whole numbers less than or
equal to 12. Use the distributive property to express a sum of two whole
numbers 1–100 with a common factor as a multiple of a sum of two whole
numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2).
Instructional
Outcomes
What must students
learn and be able
to do by the end of
Curriculum and Instruction
I am learning to….


describe situations in which opposite quantities combine to make 0.
(7.NS.1a)
show that a number and its opposite have a sum of 0 (are additive
inverses). (7.NS.1b)
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MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 7
the unit to
demonstrate
mastery?




interpret sums of rational numbers by describing real-world contexts.
(7.NS.1b)
show that the distance between two integers (rational numbers) on the
number line is the absolute value of their difference. (7.NS.1c)
apply the principle of an additive inverse in a real-world context. (7.NS.1c)
operations as strategies to add and subtract integers (rational numbers).
(7.NS.1d)





know and apply the sign rules to multiply rational numbers. (7.NS.2a)
interpret products of integers (rational numbers) by describing real-world
contexts. (7.NS.2a)
know and apply the sign rules to divide with integers, provided that the
divisor is not 0. (7.NS.2b)
interpret quotients of integers (rational numbers) by describing real-world
contexts. (7.NS.2b)
operations as strategies to multiply and divide integers (rational numbers).
(7.NS.2c)


Vocabulary
What vocabulary
must students know
to understand and
communicate
effectively about
this content?
apply the order of operations to multiply and divide integers (rational
numbers). (7.NS.2c)
add, subtract, multiply, and divide integers (rational numbers) in real-world
and mathematical problems. (7.NS.3)
Essential Vocabulary
additive inverse, absolute value, integers, Additive Identity, Associative
Property, Commutative Property, Distributive Property, estimate, evaluate,
expression, factor, Multiplicative Property of Zero, Multiplicative Identity,
number line, signed number, quotient
Supporting Vocabulary
Difference, dividend, divisor, Order of Operations, product
Resources/Activitie
s
What resources
could we use to
best teach this
unit?
Curriculum and Instruction
Resources/Activities
 From www.georgiastandards.org look for the tasks. Some fall into this
unit and others into unit 2. https://www.georgiastandards.org/CommonCore/Common%20Core%20Frameworks/CCGPS_Math_7_7thGrade_Unit
1.pdf
 Ann Shannon Formative Assessment Lessons (search by standard)
http://map.mathshell.org/lessons.php?gradeid=22
 Shodor Activities by Content Strand http://www.shodor.org/interactivate/standards/organization/354/
 EngageNY Lessons by Strand https://www.engageny.org/resource/grade-7-mathematics
 NCTM Illuminations – search for games, lessons and interactives by grade
level and content http://illuminations.nctm.org
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MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 7
Common
Misconceptions
Curriculum and Instruction
Remember there are other sources in your school that may not be listed on this
common resources list due to variation in each individual school. Examples of
other great resources your school may have access to include: GoMath,
Connected Math, IXL, Compass, MobyMax, Laying the Foundation, Carnegie,
etc. The Kentucky Numeracy Project is also a great resource that can be
searched by CCSS and grade level K-4 for RTI and gap closure purposes. Find
this resource at http://knp.kentuckymathematics.org/#!/page_knphome.
Kentucky teachers can use it for free. Just put in your school email address and
the username “mathfun”, and password is “859”.
 Students may not understand that additive inverses, opposite numbers,
and zero pairs all have the same outcome.
 Students may confuse the absolute value symbol with parentheses.
 Students may not realize that l l is a math symbol.
 Students may try to use opposite numbers and absolute value
interchangeably. Some will think that a numbers absolute value is always
its opposite.
 Students may not realize that the distance between two numbers on a
number line is the absolute value of their distance.
 Students can often confuse the properties when applying them to
problems.
 Students can often forget to distribute to all terms in the parenthesis.
 Students can sometimes forget to apply the integer sign rules when
applying the properties of numbers.
 Students often confuse the values of negative numbers and misinterpret
the value when comparing.
 Students can misinterpret the sign rules due to a lack of understanding
why the products/quotients should be negative (incorrect mathematical
reasoning).
 For multi-step problems, students can sometimes confuse the order of
operations.
 Students often have a difficult time interpreting word problems to
determine the task and the information needed.
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Curriculum and Instruction
2015-2016
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