Unit Overview
Content Area: Math
Unit Title: Rational Numbers Unit:2
Target Course/Grade Level: Seventh Grade Timeline: 3 weeks
Unit Summary:Students develop an understanding of rational numbers and their different forms. They express fractions as decimals and decimals as fractions. As with integers, students learn how to add, subtract, multiply, and divide fractions. Students solve real-world problems with rational numbers.
Primary interdisciplinary connections: Language Arts and Technology
9.1 21st-Centuries Life & Career Skills
Standard 9.1 All students will demonstrate the creative, critical thinking, collaboration, and problem-solving skills needed to function successfully as both global citizens and workers in diverse ethnic and organizational cultures.
Strand: A. Critical Thinking and Problem Solving
B. Creativity and Innovation
C. Collaboration, Teamwork and Leadership
Content Statement:
9.1.8: A The ability to recognize a problem and apply critical thinking skills and problem
solving skills to solve the problem is a lifelong skill that develops over time.
9.1.8: B Gathering and Evaluating knowledge and information from a variety of sources,
including global perspective, fosters creativity and innovative thinking.
9.1.8: C Collaboration and team work enable individuals or groups to achieve common goals
with greater efficiency.
Leadership abilities develop over time through participation in group and or teams that
that are engaged in challenging or competitive activities.
21st Century themes and skills: Critical Thinking and Problem Solving, Collaboration, Teamwork and
Leadership, Creativity and Innovation
Mathematical Practices:
7.MP.1 Make sense of problems and persevere in solving them.
7.MP.2 Reason abstractly and quantitatively.
7.MP.3 Construct viable arguments and critique the reasoning of others.
7.MP.4 Model with mathematics.
7.MP.6 Attend to precision.
7.MP.7 Look for and make use of structure.
7.MP.8 Look for and express regularity in repeated reasoning.
Learning Targets
Domain: The Number System
Cluster: Apply and extend previous understandings of numbers to the system of rational numbers
Standard # / Standards
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.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.2 / Apply and extend previous understandings of multiplication and
division and of fractions to multiply and divide 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 realworld
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.1
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. For example: If a woman
making $25 an hour gets a 10% raise, she will make an additional 1/10 of
her salary an hour, or $2.50, for a new salary of $27.50. If you want to place
a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches
wide, you will need to place the bar about 9 inches from each edge; this
estimate can be used as a check on the exact computation.
9.1.8.A.1 / Develop strategies to reinforce positive attitudes and productive behaviors that impact critical thinking and problem-solving skills.
9.1.8.A.2 / Implement problem-solving strategies to solve a problem in school or the community.
9.1.8.B.2 / Assess data gathered to solve problems for which there are varying perspective (e.g., cross cultural, gender specific, generational, etc.) and determine how the data can best be used to design the multiple solutions.
9.1.8.C.1 / Determine an individual’s responsibility for personal actions and contributions to group activities.
9.1.8.C.2 / Demonstrate the use of compromise, consensus and community building strategies for carrying out different task, assignments and projects.
9.1.8.C.3 / Model leadership skills during classroom and extracurricular activities.
Unit Essential Questions
  • What are rational numbers?
  • Describe the relationship between rational numbers, integers, and whole numbers.
  • How is adding unlike fractions similar to adding like fractions? How is it different?
  • How is multiplying fractions different from adding fractions? How is it similar?
/ Unit Enduring Understandings
  • A rational number is any number that can be written as a fraction a/b where b≠0 A repeating or terminating decimal that can be written as a fraction is a rational number.
  • Number that neither terminate or repeat are irrational numbers.
  • When adding and subtracting fractions, one must get a common denominator. An answer must always be in simplest form, which means the GCF of the numerator and denominator is 1.
  • When dividing fractions, multiply by its reciprocal or multiplicative inverse.

Unit Learning Targets
Students will ...
  • Graph rational numbers and order and compare rational numbers
  • Change fractions to decimals and visa-versa
  • Add and subtract fractions with like and unlike denominators
  • Add and subtract with mixed numbers
  • Multiply and divide fractions and mixed numbers

Evidence of Learning
Summative Assessment
  • Express rational numbers as terminating and repeating decimals
  • Compare and order fractions, decimals and percents
  • Add, subtract, multiply and divide rational numbers

Equipment needed: grid paper, smartboard, elmo, whiteboards and markers
Teacher Instructional Resources: Textbook (To be determined)
Study Island
Khan Academy Videos
Formative Assessments
  • Skill sheets
  • Quizzes/Tests
  • Student workbook
/
  • Homework
  • Math games
  • Study Island

Integration of Technology:
  • Smart Board to play online games, utilize online resources, generate models with Smart Software.
  • Kahn Academy Videos
  • Elmo – for demonstration
  • Study Island

Technology Resources:

– Interactive 2.0 instructional and practice site. Students can view instructional videos and complete practice modules for additional practice/remediation.
- Web-based instruction, practice, assessment and reporting built from NJ standards.
- IXL 7th grade online interactive activities for the students to complete
- AAA math 7th grade – online interactive activities and problems for the student to complete.
– Grade level material for practice, lessons, games, etc.
Opportunities for Differentiation:
Decelerate: use decimals out to the hundredths for calculating
Use simple common denominators
Have students write multiplication as repeated addition
Accelerated: Havestudents create an expression involving multiplying or dividing polynomials with negative exponents.
Teacher Notes: