Rational Number Operations

Essential Questions

• How are positive and negative numbers similar and different?
• How is absolute value used to solve real problems?
• How do you use a number line to determine the location of a rational number compared to another?
• How do you order rational numbers:
• How do inequality symbols help to compare rational numbers?
• How do you find the distance between two points?
• What is the relationship between addition and subtraction of positive and negative numbers?
• How can you add and subtract negative and positive rational numbers?
• How can you model the product or quotient of two integers?
• How do multiplication and division of rational numbers relate to each other?
• How can you multiply and divide rational numbers?

What You Need To Know

• Absolute value of a number is the number's distance from zero and is always positive
• Negative numbers are simply positive numbers on the opposite side of zero

What You Need To Be Able To Do

• Determine the direction of positive and negative numbers on a number line in reference to zero.
• Describe positive and negative quantities as having opposite direction or value.
• Determine the location of a rational number as a point on the number line.
• Interpret statements of inequality as statements about the relative position of two numbers on a number line.
• Write, interpret, and explain statements of comparison of ration numbers.
• Recognize the absolute value of a rational number as its distance from 0 and its magnitude for a positive and negative quantity on a number line.
• Determine order based on distance from 0.
• Solve problems adding and subtracting negative rational numbers.
• Represent addition and subtraction on a horizontal and a vertical number line.
• Show that the sum of a number and its opposite is equal to zero.
• Use properties of operations (associative, commutative, distributive, identity) to add and subtract rational numbers.
• Use additive inverse to subtract rational numbers.
• Demonstrate the distance between two numbers as the difference of their absolute values.
• Know that p_q as t he number located a distance |q| from p, in the positive or negative direction depending on if q is positive or negative.
• Apply and extend previous understanding of multiplicatoin and division to negative rational numbers including complex fractions.
• Develop and use rules for multiplying and dividing signed (+/-) numbers to find products or quotients.
• Know -(p/q)=(-p/q)=(p/-q).

Unit Syllabus - Identifies the planned topic, notes and homework for each day in the month. This plan may change in order to meet student needs. Sometimes they need more/less time on a given topic.

Day 1: Compare/Order Numbers

Homework Accentuate the Negative ACE Inv 1: 9-19

Day 2: Absolute Value

Homework Handt 4, 6, 7, 9, 11-13, 56-61, 63-66

Day 3: Graph in 4 Quadrants

Day 4: Distance Between Points

Homework Handout 37-55

Day 5: Classifying Rational Numbers

Day 6: Chip Model

Homework Accentuate the Negative ACE Inv 1: 32-35, 40-47

Day 7: Adding/Subtracting on the Number Line

Homework Accentuate the Negative ACE Inv 2: 1-3, 30

Day 8: Subtracting Integers

Homework Accentuate the Negative ACE Inv 2: 4-6, 8, 31-37

Day 9: Rewriting subtraction as addition

Homework Accentuate the Negative ACE Inv 2: 10-16 & Additional Practice Handout

Day 10: Multiply Integers

Homework Accentuate the Negative ACE Inv 3: 1-6

Day 11: Dividing Integers

Homework Accentuate the Negative ACE Inv 3: 7-8, 22, 27-28

Day 12: Order of Operations with rational numbers

Homework Accentuate the Negative ACE Inv 4: 1-2, 8-25

Day 13: Distributive Property with rational numbers

Homework Accentuate the Negative ACE Inv 4: 5-7, 33-35

Day 14: Review

Day 15: Test

Homework Performance Task