Unit _4
Rational Numbers
Mathematics
Grade 6
School Year: 2013-14
Unit Duration: Six Weeks
Domains—Students
The Number System (6.NS.6.7.8)
Statistics and Probability (6.SP.4.5a,b)
 Apply and extend previous understandings of
 Develop understanding of statistical
multiplication and division to divide fractions
variability.
by fractions.
 Summarize and describe distributions.
 Compute fluently with multi-digit numbers and
find common factors and multiples.
Geometry (6.G.3)
 Apply and extend previous understandings of
 Solve real-world and mathematical problems
numbers to the system of rational numbers.
involving area, surface area, and volume.
Standards for Mathematical Practice
 Make sense of problems and persevere in solving them.
 Reason abstractly and quantitatively.
 Construct viable arguments and critique the reasoning of others.
 Model with mathematics.
 Use appropriate tools strategically.
 Attend to precision.
 Look for and make use of structure.
 Look for and express regularity in repeated reasoning.
Overview/Rationale
The standards included in units 3 and 4 were strategically placed for their impact on ratios and proportional
reasoning which is found in unit 5.
Standard(s)
(6.NS.6)— Understand a rational number as a point on the number line. Extend number line diagrams and
coordinate axes familiar from previous grades to represent points on the line and in the plane with negative
number coordinates.
a. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number
line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that
0 is its own opposite.
b. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate
plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related
by reflections across one or both axes.
c. Find and position integers and other rational numbers on a horizontal or vertical number line diagram;
find and position pairs of integers and other rational numbers on a coordinate plane.
(6.NS.7)— Understand ordering and absolute value of rational numbers.
a. Interpret statements of inequality as statements about the relative position of two numbers on a
number line diagram. For example, interpret –3 > –7 as a statement that –3 is located to the right of –7
on a number line oriented from left to right.
b. Write, interpret, and explain statements of order for rational numbers in real-world contexts. For
example, write –3oC > –7oC to express the fact that –3oC is warmer than –7oC.
c. Understand the absolute value of a rational number as its distance from 0 on the number line; interpret
absolute value as magnitude for a positive or negative quantity in a real-world situation. For example,
for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars.
d. Distinguish comparisons of absolute value from statements about order. For example, recognize that
an account balance less than –30 dollars represent a debt greater than 30 dollars.
(6.NS.8)— Solve real-world and mathematical problems by graphing points in all four quadrants of the
coordinate plane. Include the use of coordinates and absolute value to find distances between points with the
same first coordinate or the same second coordinate.
(6.G.3) Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the
length of a side joining points with the same first coordinate or the same second coordinate. Apply these
techniques in the context of solving real-world and mathematical problems.
(6.SP.4)— Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
(6.SP.5a,b)—Summarize numerical data sets in relation to their context, such as by:
a. Reporting the number of observations.
b. Describing the nature of the attribute under investigation, including how it was measured and its
units of measurement.
Technology Standard(s)
8.1.A
The use of technology and digital tools requires
knowledge and appropriate use of operations and
related applications.
4.A.1: Demonstrate effective input of text and data
using an input device.
4.A.2: Create a document with text formatting and
graphics using a word processing program.
4.A.3: Create and present a multimedia presentation
that includes graphics.
4.A.4: Create a simple spreadsheet, enter data, and
interpret the information.
4.A.5: Determine the benefits of a wide range of
digital tools by using them to solve problems.
Technology Common Core Standards
Interdisciplinary Standard(s)
Common Core Science Grade 6-Grade8
Common Core History & Social Issues Grade 6-8
Common Core Reading Informational Text
Essential Question(s)
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If we didn’t have variables, what would we use?
What purposes do variable expressions serve?
What are some advantages to being able to describe a pattern using variables?
Why does the order of operations exist?
What other task/processes require the use of a strict order of steps?
How many parts does a number have?
What is the best way to compare amounts or sizes?
Why is it useful to know how to combine and separate parts of numbers?
How do you apply finding factors and multiples to real life?
Why do we need different ways to say the same thing?
When is it appropriate to use estimates and when should you compute exactly?
What is a real-world situation that can be modeled using positive and negative rational numbers?
What is the absolute value of a number and when do we use it?
How does the number line extend in order to incorporate negative numbers?
How does the coordinate plane extend in order to incorporate negative numbers?
How do you know which quadrant a coordinate pair will be in?
How do you decide which of two numbers is greater when both numbers are positive? Both are
negative? One number is positive and one number is negative?
Why is being able to convert rational numbers between fractions, decimals and percents important
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Why is it important to be able to relate absolute value inequalities to real world situations?
Why is it useful for me to know the absolute value of a number?
What are opposites and how are they shown on a number line?
How do I compare and order integers?
What are opposites and what characteristics do they have on the number line?
How are opposites and absolute value related?
How can I use models to prove that opposites combine to 0?
What real life situations combine to make 0?
How are the characteristics of a polygon different from other shapes?
How do we use polygon shapes in the real world?
How can a frequency table be used to determine the number of outcomes of given event?
How can a line plot be used to determine the number of outcomes of a given event?
How does using a frequency table or line plot make understanding the data easier to understand?
Enduring Understandings
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Algebraic expressions can be used to generalize properties of arithmetic.
Variables can be used as unique unknown values or as quantities that vary.
Algebraic expressions may be used to represent and generalize mathematical problems and real life
situations.
Use values from specified sets to make an equation or inequality true.
Develop an initial conceptual understanding of different uses of variables.
Graphs can be used to represent all of the possible solutions to a given situation.
Many problems encountered in everyday life can be solved using proportions, equations or inequalities.
In this unit plan, the following 21st Century themes and skills are addressed.
21
√
Check all that apply.
st
Century Themes
Global Awareness
Indicate whether these skills are E-Encouraged, T-Taught, or AAssessed in this unit by marking E, T, A on the line before the
appropriate skill.
21 s t Century Skills
A
Creativity and Innovation
Environmental Literacy
T
Critical Thinking and Problem Solving
Health Literacy
E
Communication
E
Collaboration
Civic Literacy
Financial, Economic, Business, and
Entrepreneurial Literacy
√
Student Learning Targets/Objectives/SLOs
1. Locate positive and negative rational numbers on the number line and explain the meaning of
absolute value of a rational number as indicating locations on opposite sides of zero on the number
line.
2. Write and compare rational numbers using inequality signs.
3. Plot ordered pairs in all four quadrants on the coordinate plane and describe their reflections.
4. Interpret and explain absolute value as magnitude for a positive or negative quantity in a real-world
situation.
5. Solve real world problems mathematically by graphing points in all four quadrants of the coordinate
plane. Use the absolute value of the differences of their coordinates to find distances between points
with the same first coordinate or same second coordinate.
6. Draw polygons in the coordinate plane given the coordinates of the vertices and use the coordinates
to solve real world distance, perimeter, and area problems.
7. Display numerical data in plots on the number line (including dot plots, histograms, and box plots)
and summarize in relation to their context.
Assessments
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NWEA--Diagnostic
Exit Tickets, Do Nows, skill check list, --Formative (Monitor student progress)
Model Curriculum Unit Testing, Unit Project, Extended Response Questions—Summative
(evaluate student learning)
Authentic Tasks, Math Notebook, Other Evidence
Interactive Assessment Practice
CMP2 Testing Activities Grade 6
Instructor Code: amk-5500
Student Code: amk-0099
Grade 6 Math Skill Practice
Interactive math skill builders - Sixth grade at I4C
6th Grade Math Test Skills Practice
Portfolio
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Authentic Tasks
Extended Response Questions
Short Response Questions
DOL Samples
Enrichment
ELL
Test Box
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Unit Tests
Quiz Samples
NWEA Data
SAMS Data
Differentiated Activities
Bits & Pieces I: Applications. Pg. 14 #13-#15.
Bits & Pieces I: Extensions. Pg. 33 #69
Bits & Pieces I: Connections. Pg. 51 #52
Bits & Pieces I: Extensions. Pg. 66 #37-#39.
Bits & Pieces II: Extensions. Pg. 14 #43-#46
Bits & Pieces II: Connections. Pg. 26 #28
Covering & Surrounding: Extensions. Pg. 35 #29
Data About Us: Connections. Pg. 43 #11
Value Student Backgrounds to Improve Performance
Be aware of and draw from your ELL students' prior knowledge. You should:
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Make sure ELL students know that their experiences and culture are
valued. This will help their attitudes and increase their motivation.
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Focus on meaning. When your ELL students share answers and present
ideas, remember to focus on the meaning they are conveying, not on their
grammar and usage.
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Be flexible with student use of native language. You may want to have
the ELL student record answers or solution steps in their own native
language. You can have their work translated, if desired. This will help
ELL students focus on the concepts and reasoning involved, without
being slowed or hindered by their developing language skills.
Readings:
Helping English Language Learners in the Classroom
Intervention
US Department of Education--Intervention--What Works!
Strategies to help struggling students
Teaching and Learning Actions
Instructional Strategies
Activities/Experiences
Compare & Contrast: Venn diagrams, Number line placement, plot and graph
comparison
Note Taking: Student organized notebook by unit.
Reinforcing Effort & Providing Feedback: Using rubrics to guide student work;
display student work with relevant comments.
Homework & Practice: Focus practice on difficult concepts; Homework is an
extension of class work. Word problems that require student to choose the
correct strategy.
Setting objectives & Providing Feedback: Specific objective and DOL for each
lesson; Rubrics comparison as feedback. (Given a word problem, the student will
be able to complete the division algorithm to find the solution)
Generating & Testing Hypotheses: Using a general rule to make a prediction.
(Rounding to add/subtract/multiply/divide decimals)
Cues, Questions, Advance Organizers: Use of lists, tables to collect data, the
efficient use of an algorithm.
Constructing a Number Line
Graphing Decimals on the Coordinate Plane
Absolute Value
Data Project
(Connect to TE Resource Wiki)
Resources
Key Terms
Content Vocabulary
Integers
Rational
Coordinate
Ordered pairs
Horizontal
Vertical
Quadrants
Absolute value
Number line diagram
Magnitude
Dot plots
Histograms
Box plots
Academic Vocabulary
Compose
Decompose
Context
evaluate
Visual
Relationship
Interpret
Value
Verbal model
Numerical data sets
observations
Readings
Progression through the Grades
University of Arizona Progression documents to support the Common Core
Kansas Assoc. of Teacher of Mathematics--Flip Books
“Flip Books” are intended to help teachers understand what each standard
means in terms of what students must know and be able to do. It provides only
a sample of instructional strategies and examples. The “Flip Books” support a
teacher’s goal to guide students in understanding and making sense of
mathematics.
Supporting Text
Connected Math 2
6.NS.6.7.8: Bits & Pieces I: Inv. 2.3.4.
Sharing and Comparing Fractions;
Moving Between Fraction and
Decimals, Working with Percents;
Bits & Pieces II: Inv. 2.3.4 Adding,
Subtracting, Multiplying, Dividing
Fractions;
Bits & Pieces III: Decimals—More or
Less, Decimal Times, The Decimal
Divide, Using Percents.
Cc Transition Kit: Inv. 3. Integers and
the Coordinate Plane. Inv. 2. Changing
Area, Changing Perimeter;
Shapes and Designs: Inv. 3. Integers
and the Coordinate Plane
Data About Us: Inv. 1. Looking at
Data; Inv. 2. Using graphs to explore
data.
Inv. 3. What do we mean by mean?
(6.SP.5a) How Likely is it? Inc.
1.2.3.4: A First Look at Chance,
Experimental and Theoretical
Probability, Making Decisions with
Probability, Probability, Genetics, and
Games.
6.SP.5b: Inv. 1. Looking at Data; Inv.
2. Using Graphs to Explore Data; Data
About Us: Inv. 2. Using Graphs to
Explore Data.
Supplemental Materials
Video/Presentation Links
Teacher Resource Links
Ready Common Core Math 6—Student Workbook
Lesson 12: Understand Positive and Negative Numbers
Lesson 13: Absolute Value and Ordering Numbers
Lesson 14: The Coordinate Plane
Math Connects, Course 1: Problem-Solving Practice Homework Book
http://www.mathplayground.com/mathvideos.html
http://math.pppst.com/
Understand Positive & Negative Numbers: LearnZillion
Absolute Value & the Coordinate Plane: LearnZillion
The Coordinate Plane | Coordinate plane | Khan Academy
(Connect to TE Resource Wiki)
CMP2 Transition Kit
Pearson Transition Kit Grade 6
Connected Math Online:
http://www.phschool.com/cmp2/
Master Codes: CMP2 Student Grade 6: amk 0099 Teacher: amk 5500
Sadlier-Oxford Online Practice & Activities
Coordinate Worksheets: Math-Aids
Illuminations: Finding Your Way Around the Coordinate Plane
Quantitles Grade 6 Database
(For More Resources Connect to TE Resource Wiki)
Student Resource Links
Sixth Grade Interactive Math Skills - Coordinate Plane
Absolute Value Worksheet Generator: Math-Aids
Submitted by: ____________________________________
Date:
Curriculum and Instruction Administration:
Approved
Date: March 11, 2014
Board of Education:
Approved
Date: March 25, 2014