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# Unit 1: Number Sense - PowerPoint PPT Presentation

Unit 1: Number Sense. Minds On. Solve for the variables: 3x + 12 = 0 12x – 9 = 15 (3 + x) 4 = 7. Unit 1: Number Sense. Lesson 1 – Introduction to Rational Numbers. Learning Goals: I can convert between mixed and improper fractions I can perform all four operations with fractions

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Minds On

Solve for the variables:

3x + 12 = 0

12x – 9 = 15

(3 + x) 4 = 7

Lesson 1 – Introduction to Rational Numbers

• Learning Goals:

• I can convert between mixed and improper fractions

• I can perform all four operations with fractions

• I can reduce fractions to lowest terms

Lesson 1 – Introduction to Rational Numbers

Numbers are grouped together based on their characteristics:

Natural Numbers (Counting numbers): {1, 2, 3, …}

Whole Numbers (including 0): {0, 1, 2, 3,…}

Integers ( Positive or negative whole numbers):

{…-2, -1, 0, 1, 2…}

Rational Numbers: All numbers in the form where a and b are integers and b

(Ex. 0, ,

Lesson 1 – Introduction to Rational Numbers

Whole

Rational

Natural

Integers

0.5, -5.89

1, 2, 3

0

-1, -2

Lesson 1 – Introduction to Rational Numbers

Types of Fractions:

1. Proper: When the numerator (top number) is less than the denominator (bottom number)

2. Improper: When the numerator (top number) is greater than the denominator (bottom number)

3. Mixed: When a whole number is combined with a fraction

Lesson 1 – Introduction to Rational Numbers

Lowest terms: A fraction is in lowest terms when there are no common factors between the numerator and the denominator.

Examples:

Lesson 1 – Introduction to Rational Numbers

Equivalent Fractions: two fractions that are the same.

• Success Criteria for making equivalent fractions:

• Multiply or divide

• What you do to the top you must do to the bottom

Lesson 1 – Introduction to Rational Numbers

Example: Find an equivalent fraction to

Lesson 1 – Introduction to Rational Numbers

Example: A

Lesson 1 – Introduction to Rational Numbers

• Success Criteria for converting Mixed Fractions to Improper Fractions:

• Multiply the whole number by the denominator and add the numerator. This gives you the numerator for your improper fraction

• Keep the denominator the same

• Negative signs out front of the fraction are not involved in the calculation

Lesson 1 – Introduction to Rational Numbers

Example: Convert 4

Lesson 1 – Introduction to Rational Numbers

• Success Criteria for converting Improper Fractions to Mixed Fractions:

• Count how many times the denominator will go into the numerator. This gives you your whole number to put in front of the fraction

• Take the remainder and use it as your numerator

• Your denominator stays the same

• Leave negative signs out front

Lesson 1 – Introduction to Rational Numbers

Example: Convert

Lesson 1 – Introduction to Rational Numbers

• Success Criteria for Adding and Subtracting Fractions:

• Convert mixed fractions into improper fractions first

• Find a common denominator

• Keep the denominator the same

Lesson 1 – Introduction to Rational Numbers

Example: 2

Lesson 1 – Introduction to Rational Numbers

• Success Criteria for Multiplying Fractions

• Convert mixed fractions into improper fractions first

• You DO NOT need a common denominator

• Whole numbers have an imaginary denominator of 1

• Multiply the numerators

• Multiply the denominators

Lesson 1 – Introduction to Rational Numbers

Example: 3

Lesson 1 – Introduction to Rational Numbers

• Success Criteria for Dividing Fractions

• Convert mixed fractions into improper fractions first

• You DO NOT need a common denominator

• Change the division sign to a multiplication sign

• Flip the second fraction

• Multiply the numerators

• Multiply the denominators

Lesson 1 – Introduction to Rational Numbers

Example:

Lesson 1 – Introduction to Rational Numbers

• Practice

• Pg. 186 Q# 6

• Read top of pg. 14

• Pg. 14 Q# 1 bcefhi, 2-7 parts bcef for all, 8ab