MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 7
Unit Description
Unit 2
Rational Numbers
Suggested Length: 3 weeks
Big Idea(s)
What enduring
understandings are
essential for
application to new
situations within or
beyond this
content?
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Essential
Question(s)
What questions will
provoke and
sustain student
engagement while
focusing learning?
Enduring Standards:
Which standards
provide endurance
beyond the course,
leverage across
multiple disciplines,
and readiness for
the next level?
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Operation Meanings and Relationships – The same number sentence
(e.g. 12-4 = 8) can be associated with different concrete or real-world
situations, AND different number sentences can be associated with the
same concrete or real-world situations.
Properties – For a given set of numbers there are relationships that are
always true, and these are the rules that govern arithmetic and algebra.
Basic Facts and Algorithms – Basic facts and algorithms for operations
with rational numbers use notions of equivalence to transform
calculations into simpler ones.
How can you add and subtract rational numbers to solve real-world
problems?
How can you multiply and divide rational numbers to solve real-world
problems?
How can you use rational numbers to solve multi-step, real-world
problems?
Enduring Understandings
Understand operations of rational numbers
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.1b 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
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
Curriculum and Instruction
2015-2016
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MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 7
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.
7.NS.2d 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. (NOTE: Computations with rational numbers
extend the rules for manipulating fractions to complex fractions.)
Supporting
Standard(s):
Which related
standards will be
incorporated to
support and
enhance the
enduring
standards?
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.
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).
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MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 7
Instructional
Outcomes
What must students
learn and be able
to do by the end of
the unit to
demonstrate
mastery?
I am learning to….
 convert a rational number to a decimal using long division (7.NS.2d)
 explain that the decimal form of a rational number terminates (stops) in
zeroes or repeats (7.NS.2d)
 add rational numbers and interpret sums of rational numbers by describing
real world contexts (7.NS.1b)
 subtract rational numbers and apply the principle of subtracting rational
numbers in real world contexts (7.NS.1c)
 recognize that the process for multiplying fractions can be used to multiply
rational numbers including integers. (7.NS. 2a)
 know and describe the rules when multiplying signed numbers. (7.NS.2a)
 multiply rational numbers and interpret the products of rational numbers by
describing real world contexts (7.NS.2a)
 apply properties of operations to multiply rational numbers (7.NS.2c)
 explain why integers can be divided except when the divisor is 0. (7.NS.2b)
 describe why the quotient or integers is always a rational number (7.NS.2b)
 know and describe the rules when dividing signed numbers (7.NS.2b)
 recognize that –(p/q) = -p/q = p/-q (7.NS.2b)
 divide rational numbers and interpret the quotient of rational numbers by
describing real world contexts (7. NS. 2b)
 identify and apply properties of operations to add, subtract, multiply and
divide rational numbers (such as distributive, multiplicative inverse,
multiplicative identity, commutative for multiplication, associative for
multiplication, etc. (7.NS.1d and 2c)
 solve real world and mathematical problems by adding, subtracting,
multiplying and dividing rational numbers, including complex fractions
(7.NS.3)
Vocabulary
What vocabulary
must students know
to understand and
communicate
effectively about
this content?
Essential Vocabulary
Irrational number, rational number, complex fraction, long division, repeating
decimal, terminating decimal
Supporting Vocabulary
Additive Identity, Associative Property, Commutative Property, Distributive
Property, Order of Operations, dividend, divisor, factor, integer, multiplicative
inverse, product, quotient, Multiplicative Property of Zero, Multiplicative
Identity, dividend, divisor, estimate, evaluate, expression
Resources/Activities
Resources/Activitie
s
What resources
could we use to
best teach this
unit?
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Curriculum and Instruction
From www.georgiastandards.org Use the following unit to access tasks
and instructional strategies specific to rational numbers concepts.
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 2015-2016
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MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 7
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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
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”.
Common
Misconceptions
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Curriculum and Instruction
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).
Students can sometimes forget to apply the integer sign rules when
applying the properties of numbers.
Students often think that the last number on a calculator is the ending of
a number.
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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