Common Core Mathematics 6 (CCM-6) Starting Points
Unit 2: The Number System
Essential Questions:
o How does division of fractions relate to multiplication of fractions?
o How is division of fractions used in the real world?
o Why is the quotient greater than the divided when dividing by a value less than one?
o How does repeated subtraction or equal groups relate to the measurement concept?
o How much is one as it relates to the partition concept?
o What is the difference between factors and multiples?
o What is the meaning of positive and negative numbers and zero in real-life situations?
o How and why are rational numbers ordered? How and why is absolute value ordered?
o What is the definition of coordinate plane terminology and where are the quadrants
located?
o What is the conceptual understanding of absolute value and in terms of a real-world
context?
Curriculum Standards:
6.NS.A Apply and extend previous understandings of multiplication and division to divide
fractions by fractions.
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.
6.NS.B Compute fluently with multi-digit numbers and find common factors and multiples.
2. Fluently divide multi-digit numbers using the standard algorithm.
3. Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm
for each operation.
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.
6.NS.C Apply and extend previous understandings of numbers to the system of rational
numbers.
5. Understand that positive and negative numbers are used together to describe quantities
having opposite directions or values (e.g. temperature above/below zero, elevation
above/below sea level, credits/debits, positive/negative electric charge); use positive and
negative numbers to represent quantities in real-world contexts, explaining the meaning of 0
in each situation.
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.
This document represents one sample starting points for the unit. It is not all-inclusive and is only one
planning tool. Please refer to the wiki for more information and resources.
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.
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.
b. Write, interpret, and explain statements of order for rational numbers in real-world
contexts.
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.
d. Distinguish comparisons of absolute value from statements about order.
8. Solve real-world and mathematical problems by graphing points in all four quadrants of the
coordinate plane. Include use of coordinates and absolute value to find distances between
points with the same first coordinate or the same second coordinate
Approximate Length of Unit: 50 days
Note: Pre-assess understanding of the 5.NF standards. Address any misconceptions and
gaps in student understanding as you introduce this unit. These days should be included in
the 50 days.
Standard(s)
6.NS.1
Days
7-10
Notes
Big ideas:
Compute quotients using models and equations.
Solve word problems involving division of fractions and
mixed numbers.
Resources:
 Lesson: Dividing Fractions & Linked ppt (HCPSS
Wiki)
 Dividing Fractions Tic-Tac-Toe (HCPSS Wiki)
 Activity: Father’s Day Blueberry Surprise
 Illustrative Mathematics: How many _____ are
in…?
Assessment Items:
 Illustrative Mathematics: Baking Cookies
 Illustrative Mathematics: Drinking Juice: Variation
This document represents one sample starting points for the unit. It is not all-inclusive and is only one
planning tool. Please refer to the wiki for more information and resources.






6.NS.2
3-4
2
Illustrative Mathematics: Drinking Juice Variation
3
Illustrative Mathematics: Making Hot Cocoa:
Variation 1
Illustrative Mathematics: Making Hot Cocoa:
Variation 2
Illustrative Mathematics: Video Game Credits
Illustrative Mathematics: Cup of Rice
Illustrative Mathematics: Dan’s Division Strategy
Big ideas:
Divide multi-digit whole numbers (Fluency Standard).
Resources:
 Lesson: Dividing Multi-Digit Numbers (HCPSS
Wiki)
Assessment Items:
 Illustrative Mathematics: Setting Goals
6.NS.3
7-10
Big ideas:
Compute with decimals using all four operations (Fluency
Standard).
Resources:
 Task: The Road Taken (HCPSS Wiki)
 Task: How Much is That (HCPSS Wiki)
 Task: School Store (HCPSS Wiki)
 Illustrative Mathematics: Reasoning about
Multiplication & Division Place Value Part 1, Part
2
Assessment Items:
 Illustrative Mathematics: Pennies to Heaven
 Illustrative Mathematics: Buying Gas
 Illustrative Mathematics: Gifts from Grandma:
Variation 3
 Illustrative Mathematics: Movie Tickets
6.NS.4
* Consider
combining
this standard
with 6.EE.3.
3-4
Big ideas:
Determine greatest common factor of two whole numbers.
Rewrite the sum of two whole numbers using the
distributive property.
This document represents one sample starting points for the unit. It is not all-inclusive and is only one
planning tool. Please refer to the wiki for more information and resources.
Resources:
 Task: It All Adds Up (HCPSS Wiki)
 Illustrative Mathematics: Factors & Common
Factors
 Illustrative Mathematics: Multiples & Common
Multiples
Assessment Items:
 Illustrative Mathematics: Bake Sale
 Illustrative Mathematics: The Florist Shop
6.NS.5, 6a
5-8
Big ideas:
Represent positive and negative numbers from real-world
scenarios.
Be able to explain the meaning of zero in a scenario.
Understand opposite numbers.
Plot rational numbers on a number line.
Resources:
 Lesson: Contest Winner (HCPSS Wiki)
 Lesson: Opposite Numbers on a Number Line
(HCPSS Wiki)
Assessment Items:
 Illustrative Mathematics: Mile High
6.NS.7c, d
3-4
Big ideas:
Understand absolute value is a measure of distance from
zero.
Interpret absolute value in real world scenarios.
Understand how absolute value can be used to order
rational numbers.
Resources:
 Task: Moving the Ball (HCPSS Wiki)
 Lesson: Illustrating Values (HCPSS Wiki)
Assessment Items:
 PARCC Prototype: Cake Weighing
This document represents one sample starting points for the unit. It is not all-inclusive and is only one
planning tool. Please refer to the wiki for more information and resources.
6.NS.7a, b
9-11
Pretest on
fraction,
decimal,
percent
equivalency
to help with
ordering
Big ideas:
Use inequality symbols to compare numbers (include all
rational numbers).
Use inequality symbols to represent real-world scenarios.
Resources:
 Lesson: Inequality Exploration (HCPSS Wiki)
Assessment Items:
 Illustrative Mathematics: Fractions on a Number
Line
6.NS.6b, 6c,
6.NS.8
Extend from
plotting in
quadrant one
in 5th grade
6-8
Big ideas:
Plot ordered pairs on a coordinate grid.
Recognize when ordered pairs will be reflections of each
other on the axis.
Use coordinates and absolute value to determine distances
between two points in mathematical and real-world
problems.
Resources:
 Task: Amusement Park (HCPSS Wiki)
 Lesson: Battleship (HCPSS Wiki)
 Online Game: Billy Bug
Assessment Items:
 Illustrative Mathematics:
 Task: Outdoor Ed (HCPSS Wiki)
Culminating Task: Outdoor Ed
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has
licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0
Unported License.
This document represents one sample starting points for the unit. It is not all-inclusive and is only one
planning tool. Please refer to the wiki for more information and resources.