### Grade 6 Module 3 Focus PPT

```NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Ratios
A Story of Ratios
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Ratios
Session Objectives
• Examine the development of mathematical
understanding across the module using a focus on
concept development within the lessons.
• Identify the big idea within each topic in order to
support instructional choices that achieve the lesson
objectives while maintaining rigor within the
curriculum.
NYS COMMON CORE MATHEMATICS CURRICULUM
Agenda
Introduction to the Module
Concept Development
Module Review
A Story of Ratios
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Ratios
Curriculum Overview of A Story of Ratios
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Ratios
Module’s Foundation
• Standards: 6.NS.C.5, 6.NS.C.6, 6.NS.C.7, 6.NS.C.8
• Pages 7 – 8 in the Progressions Document (The Number System, 6-8) serves
as a foundation.
• Directed measurement --- a rational number’s position on the number line
is found using length and direction.
• The opposite of a number a, is –a. Both a and –a are located an equal
distance from zero, in opposite directions.
• Rational numbers represent real-world situations.
NYS COMMON CORE MATHEMATICS CURRICULUM
G6-M3: Module Overview
A Story of Ratios
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Ratios
G6-M3: Vocabulary and Representations
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Ratios
G6-M3 Rational Numbers – Topic Overview
Topic A: Understanding Positive and Negative Numbers on the
Number Line
Topic B: Order and Absolute Value
Topic C: Rational Numbers and The Coordinate Plane
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Ratios
Topic A: Understanding Positive and Negative Numbers on
the Number Line
NYS COMMON CORE MATHEMATICS CURRICULUM
Agenda
Introduction to the Module
Concept Development – Topic A
Module Review
A Story of Ratios
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Ratios
Positive and Negative Numbers on the Number
Line: Opposite Direction and Value
Outcomes:
• Students extend their understanding of the number line,
which includes zero and numbers to the right, that are
above zero, and numbers to the left, that are below zero.
• Students use positive integers to locate negative
integers, moving in the opposite direction from zero.
• Students understand that the set of integers is the set of
whole numbers and their opposites, and understand that
zero is its own opposite.
Lesson 1
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Ratios
Positive and Negative Numbers on the Number Line:
Opposite Direction and Value
• The number line extends to include negative numbers.
• Lengths on the right-side and left-side of zero are the same for a
number and its opposite. (Use a compass for the construction.)
• The set of whole numbers and their opposites
(zero is its own opposite) are called integers.
• The order of the set of integers is: …-5,-4,-3,-2,-1,0,1,2,3,4,5…
Lesson 1
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Ratios
Positive and Negative Numbers on the Number Line: Opposite
Direction and Value
• Draw a horizontal line. Place a point on the line and label it 0.
• Use a compass to locate and label the next point 1, thus creating a scale.
(Continue to locate other whole numbers to the right of zero using the
same unit measure.)
• Using the same process, locate the opposite of each number on the left
side of zero. Label the first point to the left of zero, -1.
Lesson 1/Activity
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Ratios
Real World Positive and Negative Numbers and
Zero
Outcomes:
• Students use positive and negative numbers to indicate a change
(gain or loss) in elevation with a fixed reference point, temperature,
and the balance in a bank account.
•
Students use vocabulary precisely when describing and
representing situations involving integers; for instance, an elevation
of −10 feet is the same as 10 feet below the fixed reference point.
•
Students will choose an appropriate scale for the number line when
given a set of positive and negative numbers to graph.
Lessons 2-3
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Ratios
Real World Positive and Negative Numbers and Zero
• Use positive and negative numbers and zero to represent
situations.
• Graph integers on a number line, using an appropriate
scale and relating points to real-world situations.
• Explain the meaning of zero in the context of a situation.
Lessons 2-3
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Ratios
Real World Positive and Negative Numbers and
Zero
Lesson 3 /Exit Ticket
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Ratios
The Opposite of a Number’s Opposite
Outcomes:
• Students understand that, for instance, the opposite
of −5 is denoted −(−5) and is equal to 5. In
general, they know that the opposite of the opposite
is the original number; e.g., −(−) = .
• Students locate and position opposite numbers on a
number line.
Lesson 5
NYS COMMON CORE MATHEMATICS CURRICULUM
The Opposite of a Number’s Opposite
Lesson 5/Example
A Story of Ratios
NYS COMMON CORE MATHEMATICS CURRICULUM
The Opposite of a Number’s Opposite
Lesson 5/Activity
A Story of Ratios
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Ratios
Rational Numbers on the Number Line
Lesson 6
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Ratios
Rational Numbers on the Number Line
Lesson 6/Exercise 1
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Ratios
Rational Numbers on the Number Line
Lesson 6/Exercise 1
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Ratios
Rational Numbers on the Number Line
Lesson 6/Exit Ticket
NYS COMMON CORE MATHEMATICS CURRICULUM
Agenda
Introduction to the Module
Concept Development – Topic B
Module Review
A Story of Ratios
NYS COMMON CORE MATHEMATICS CURRICULUM
Topic B: Order and Absolute Value
A Story of Ratios
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Ratios
Ordering Integers and Other Rational Numbers
Outcomes:
• Students write, interpret, and explain statements of
order for rational numbers in real world contexts.
• Students recognize that if a < b, then -a > -b, because
a number and its opposite are equal distances from
zero; and moving along the horizontal number line to
the right means the numbers are increasing.
Lesson 7
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Ratios
Ordering Integers and Other Rational Numbers
What is the Value of Each Number and Which is Larger?
1) The first number is 8 ½ units to the right of -5. The second number is 3
units to the right of 0.
First Number: 3.5; Second Number: 3; 3.5 is larger than 3.
2) The first number is ¼ unit to the left of -7.
The second number is 8 units to the left of 1.
First Number: −7.25; Second Number: −7; −7 is larger than −7.25.
3) The opposite of the first number is 2 units to the right of 3.
The opposite of the second number is 2 units to the left of -3.
First Number: −5; Second Number: 5; 5 is larger than −5.
Lesson 7
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Ratios
Ordering Integers and Other Rational Numbers
Outcomes:
• Students write, interpret, and explain statements of
order for rational numbers in the real-world.
• Students recognize that if  < , then − > −,
because a number and its opposite are equal
distances from zero; and moving along the horizontal
number line to the right means the numbers are
increasing.
Lesson 8
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Ratios
Writing and Interpreting Inequality Statements Involving
Rational Numbers
Inequalities Fluency Builder
Lesson 10
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Ratios
Absolute Value – Magnitude and Distance
• Complete Exercises 1- 3
• How do we want Grade 6 students to conceptualize absolute value?
• Complete Exercises 6 – 19
• Discuss how students display an understanding of
absolute value as magnitude and distance.
Lesson 11/Exercises
NYS COMMON CORE MATHEMATICS CURRICULUM
Mid-Module Assessment
Question 3
A Story of Ratios
NYS COMMON CORE MATHEMATICS CURRICULUM
Agenda
Introduction to the Module
Concept Development – Topic C
Module Review
A Story of Ratios
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Ratios
Topic C: Rational Numbers and the Coordinate Plane
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Ratios
You’re the Expert!
• Go to the appropriate table as designated by the number on your card.
• You will have ten minutes to discuss with your group the following:
• Lesson Study
• Modeling of an Essential Portion of the Lesson
• Concerns/Scaffolding Beyond Teacher’s Edition
• Each group will have ten minutes to model essential portion
• Lesson progression
• Prerequisite/Foundation Skills
Lessons 14 - 19
NYS COMMON CORE MATHEMATICS CURRICULUM
End-of-Module Assessment
Questions 1 and 5
A Story of Ratios
NYS COMMON CORE MATHEMATICS CURRICULUM
Agenda
Introduction to the Module
Concept Development
Module Review
A Story of Ratios
NYS COMMON CORE MATHEMATICS CURRICULUM
Biggest Takeaway
Turn and Talk:
• What questions were answered for you?
• What new questions have surfaced?
A Story of Ratios
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Ratios
Key Points
• Directed measurement --- a rational number’s position on the number line
is found using length and direction.
• The opposite of a number a, is –a. Both a and –a are located an equal
distance from zero, in opposite directions.
• Rational numbers represent real-world situations. We can write and
explain statements of order for rational numbers in real-world contexts.
• The absolute value of a number is its distance from zero; and can be used
in the context of a situation to show magnitude. We can use absolute
value and the symmetry of the coordinate plane to solve problems related
to distance.