Math Unit Template
El Rancho Unified School District
Topic/Main Idea:
Operating with Rational Numbers
CCSS: 7.NS.1-3
Timeline: Quarter 1, 4-5 weeks
Objectives/Concept/Skill (DOK):
 Apply and extend previous understandings of addition and
subtraction to add, subtract, multiply and divide rational
numbers (including integers, decimals and fractions)
 Apply properties of operations as strategies to add, subtract,
multiply and divide rational numbers (e.g., additive inverse when
adding or subtracting integers).
 Converting a rational number (i.e., a fraction to a decimal)
 Solve real world problems involving the four operations with
rational numbers
Performance Task/Activity (DOK):
CCSS 7NS1-3, Grade 7, “ASB Student Treasurer”, DOK 3
Connections to earlier and next grade levels:
Grades 3-6: Fractions Concepts
Grades 4-6: Decimal Concepts
Grades 5-6: Integer Concepts
Grade 8: Rational vs. irrational numbers and converting
repeating decimal expansion to a rational number
Relevance/Rationale:
Understanding rational number concepts and how to
operate on rational numbers of all types will be critical
to successfully problem solving in real life contexts
well as a necessary foundation for more abstract
problem solving in future math courses.
SBAC Assessment Item References:
MAT.07.SR.1.000NS.B.163
Academic Vocabulary:
Sum, difference, product, quotient, additive inverse, rational
number, integers, opposites, absolute value, distributive
property, non-zero divisor, decimal fraction
Textbook References (i.e., Homework Resources):
CGP Sections 2.1, 1.3, 2.4, 2.6; CPM Making Connections FFA
Sections 1.2, 1.3, 2.1
Materials/Manipulatives: integer tiles, number lines, fraction
rulers/bars, and base 10 grids/play money
Mathematical Practices
__X__ 1.
__X__ 2.
__X__ 3.
__X__ 4.
Makes sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with Mathematics.
Explanation:
Lesson Topic:
Integer Concepts
Adding & Subtracting Integers
Additive Inverse
Multiplying & Dividing Integers
Distributive Property
Properties of Operations (i.e.,
properties of rational numbers)
Fraction Concepts
LOL (Learning
__X__ 5.
__X__ 6.
_____ 7.
_____ 8.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.
Objective with Language):
We will learn how to use different
representations for integers to model values.
Students will learn how to add and subtract
integers using models to develop patterns and
explain their solutions.
Students will learn how to use the additive
inverse property to rewrite integer subtraction
problems as integer addition problems.
Students will learn how to multiply and divide
fractions using a model to develop patterns for
multiplication and apply those patterns to develop
patterns for division.
Students will models to understand distributive
property and apply that understanding to solving
problems using distributive property.
Students will learn the remaining properties of
operations and use them to justify strategies
used to add, subtract, multiply and divide rational
numbers.
Students will use fraction models to represent,
compare, order and find equivalent fractions.
Resources (Instructional
Strategies,
Textbook References, etc.):
 Integer tiles, number lines (horizontal and
vertical)
 Build it, draw it, record it (ALPHA website)
 Problem-solving using integer tiles, number
lines, temperature, money, etc.
 Build it, draw it, record it (ALPHA website)
 Problem-solving using integer tiles, number
lines, temperature, money, etc.
 Inverse operations to establish patterns for
division.
 Algebra tiles and area models
 Fraction bars, number lines and area models.
Add, Subtract, Multiply and
Divide Fractions
Converting Fractions to Decimals
Add, Subtract, Multiply and
Divide Decimals
Rational and Irrational Numbers
Operating with varying rational
numbers
Summative Performance Task
Students will use fraction models to add,
subtract, multiply and divide fractions, justify
their solutions and develop an understanding of
common algorithms.
Students will use their understanding of place
value concepts (i.e., decimal fractions) to convert
fraction to decimal using varying methods.
Students will use decimal models to add, subtract,
multiply and divide decimals and develop an
understanding of common algorithms.
Students will understand that every number has a
decimal expansion, that rational numbers have a
decimal expansion that eventually repeats or
terminates, and that numbers that are not
rational are called irrational.
Students will perform all four operations on a
combination of rational numbers.
Students will solve real-world and mathematical
problems involving the four operations with
rational numbers.
 Problem solving using fraction bars, number
lines and area models.
Dividing numerator by denominator
Finding equivalent decimal fractions (e.g.,
n/10s, n/100s, n/1000s, etc.)
 Problem solving using number lines, base 10
play money, area models (i.e., decimal grids)
and estimation.


 SBAC item: MAT.07.SR.1.000NS.B.163
 “ASB Treasurer”