American International School, Hong Kong
MTH06C
Middle School > Grade 6 > Mathematics > MTH06C > Week 15 ­ Week 19
Rational Numbers
Collaboration
Stage 1 - Desired Results (Standards and Benchmarks)
Established Goals
CCSS: Mathematics
CCSS: Grade 6
The Number System
6.NS.C. Apply and extend previous understandings of numbers to the system of rational numbers.
6.NS.C.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 real­world contexts, explaining the meaning of 0 in each situation.
6.NS.C.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.
6.NS.C.6a. 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.
6.NS.C.6b. 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.
6.NS.C.6c. 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.C.7. Understand ordering and absolute value of rational numbers.
6.NS.C.7a. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram.
6.NS.C.7b. Write, interpret, and explain statements of order for rational numbers in real­world contexts.
6.NS.C.7c. 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 real­world situation.
6.NS.C.7d. Distinguish comparisons of absolute value from statements about order.
6.NS.C.8. Solve real­world 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.
Problem Solving Rubric & Questions
7th Accelerated Math Standards Unpacked
Pacing Guide Grade 6 Math
Middle School Math Scope & Sequence Overview
7th Accelerated Math Standards
Math websites
Understandings
Essential Questions
Students will understand that . . .
1. Positive and negative numbers are used together to describe
quantities having opposite directions or values ­ eg temperature
2. A rational number is a point on the number line.
3. Signs of numbers in ordered pairs indicate locations in quadrants.
4. The relative position of integers and rational numbers on the number
line/coordinate plane.
5. The absolute value of a number is its distance from 0 on a number
line.
6. Rotating about the origin results in changing the ordered pairs. 90
deg, swop x/y rotating 180 deg; x,y opposites.
1. How are fractions, decimals and percents related?
2. Why are there negative numbers?
3. How do we compare and contrast numbers?
4. What is the relationship between rational numbers and integers?
Content or Knowledge
Learning Outcomes or Skills
Students will know . . .
Students will be able to . . .
Rational number ­ a number that can be written as a ratio or fraction, in
which both the numerator and the denominator are whole numbers.
(repeating decimals, finite decimals, integers) Irrational Number ­ number that never terminates or repeats. Integers are the set of whole numbers and their opposites. Whole numbers
greater than zero are called positive integers. Whole numbers less than zero
are called negative integers.
Negative integer ­ numbers less than zero. Positive integer ­ numbers greater than zero. Opposite ­ numbers that are equal distance from zero. Zero ­ an integer that is neither positive or negative.
Absolute value ­ a numbers distance from zero.
Origin ­ The point where the x­axis and the y­axis intersect on the
coordinate plane. The coordinates of the origin are (0,0). Ordered Pair ­ A pair of numbers used to locate a point on a coordinate
grid, such as (5,­2). The x­axis coordinate is always first because “x” comes
before “y” alphabetically. Coordinates ­ One of the numbers in an ordered pair. The x value is the first
coordinate of the pair and the y value is the second coordinate.
Use rational numbers (fractions, decimals, and integers) to represent
real­world contexts and understand the meaning of 0 in each
situation.
Plot rational numbers and integers on a number line.
Order integers and rational numbers.
Express relationships between two rational numbers using
inequalities.
Write statements using < or > to compare rational number in a real­
world context.
Find absolute value of integers and rational numbers.
Order absolute value.
Graph rational number and integers.
Find the distance between points when ordered pairs have the same
x­coordinate (vertical) or same y­coordinate (horizontal).
Stage 2 - Assessment Evidence
Performance Task/Standards Based Assessments
Assessments
Rational Numbers Assessment
Summative: Common Assessment
13_Rational Unit Test.docx
Stage 3 - Learning Activities
Learning Activities
Unit Project
As part of this unit, students participated in a real­life simulation. Each
student selected a profession: Graphic Designer, Engineer, Assistant
Marketing Officer, Forensic Technician, or Journalist and earned a salary
according to their profession. Students tracked their monthly spending and
saving in a Google Sheets Current and Saving Account. Based on their
salaries, they selected an apartment and cell phone plan. Each week, they
calculated their taxes, saving, and monthly expenses using formulas. To
determine how they spend their residual income, students selected four
Chance Card a week. Expenses ranged from unexpected medical costs to
buying shoes for work or taking a vacation. They earned or lost additional
income by completing homework and coming to class prepared and on time.
In the week three of the game, students got married and had kids, which
required them to increase their food costs, purchase life and medical
insurance, and select two additional Chance Cards per week. Each week,
students reflected on what they had learned and how they would apply their
learning in next week.
Lesson 1 ­ Real­life Integers
O/T: Where do you see integers in real­life?
1. Students review bank statement and make observations
Learning Resources and Reflection
NY Engage Integers Unit
practice_b.pdf
Rational Numbers Engage.pdf
2. Introduce & define banking terms: deposit, debit, credit, withdrawal,
fee
3. Integer notes ­ plotting on the number line
4. Student read banking scenario, write the integer that represents the
situation, and model it on the number line.
Lesson 2 ­ Ordering Integers
O/T: Convert decimals to fraction and fractions to decimals.
1. Compare and order set of numbers. Discuss common errors in
ordering and strategies for comparing numbers ­ benchmark,
common denominators/numerators.
2. Students work in groups to order 5 sets of numbers.
HW: Lesson 7 ­ Engage ordering rational numbers.
Lesson 3 ­ Absolute Value and Magnitude
O/T: Students categorize rational numbers and integers
1. Absolute value notes: magnitude, absolute value
2. Absolute value practice ­ Engage lesson ­ 11
HW: Engage practice problems
Lesson 4 ­ Inequalities ­ engage lesson 10
Lesson ­ 5 ­ Adding Integers
Students model addition of integers using yellow chips and a number line.
Lesson 6 ­ Subtracting integers
O/T ­ Model subtraction problem with number line (positive numbers)
Students work in pairs to model subtraction of integers with chips and
a number line and then rewrite problem to add the opposite.
Lesson 7 ­ Coordinate Planes ­ Body Graphing
O/T: read scenario about finding a seat in a stadium using a pair of numbers,
students identify what each coordinates means ­ section, seat.
1. Notes on graphing coordinates
2. Body graphing ­ students work in pairs to graph a point on the floor
grid
3. Students then graph the point on graph paper.
Lesson 8 ­ Coordinate Battleship
Students arrange 5 battleships on a coordinate plan. They work to
sink their partners ship by guessing the coordinates of the ship's
location.
Lesson 9 ­ Test Review
Lesson 9 ­ Unit Test
TransformationsColoringActivity (1).pdf
CoordinateBattleshipLevels.pdf
1_Ticket out Opposites.docx
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