Unit 1: Number Sense
Minds On
Solve for the variables:
a) 3x + 12 = 0
b) 12x – 9 = 15
c) (3 + x) 4 = 7
Unit 1: Number Sense
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
Unit 1: Number Sense
Lesson 1 – Introduction to Rational Numbers
Numbers are grouped together based on their characteristics:
1.Natural Numbers (Counting numbers): {1, 2, 3, …}
2.Whole Numbers (including 0): {0, 1, 2, 3,…}3.Integers ( Positive or negative whole
numbers): {…-2, -1, 0, 1, 2…}4. Rational Numbers: All numbers in the form
where a and b are integers and b (Ex. 0, ,
Unit 1: Number Sense
Lesson 1 – Introduction to Rational Numbers
Natural1, 2, 3
Whole
0Integers
-1, -2
Rational
0.5, -5.89
Unit 1: Number Sense
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
Unit 1: Number Sense
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:
Unit 1: Number Sense
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
Unit 1: Number Sense
Lesson 1 – Introduction to Rational Numbers
Example: Find an equivalent fraction to
Unit 1: Number Sense
Lesson 1 – Introduction to Rational Numbers
Example: A
Unit 1: Number Sense
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
Unit 1: Number Sense
Lesson 1 – Introduction to Rational Numbers
Example: Convert 4
Unit 1: Number Sense
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
Unit 1: Number Sense
Lesson 1 – Introduction to Rational Numbers
Example: Convert
Unit 1: Number Sense
Lesson 1 – Introduction to Rational Numbers
Success Criteria for Adding and Subtracting Fractions:• Convert mixed fractions into improper
fractions first• Find a common denominator• Add the numerators• Keep the denominator the same
Unit 1: Number Sense
Lesson 1 – Introduction to Rational Numbers
Example: 2
Unit 1: Number Sense
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
Unit 1: Number Sense
Lesson 1 – Introduction to Rational Numbers
Example: 3
Unit 1: Number Sense
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
Unit 1: Number Sense
Lesson 1 – Introduction to Rational Numbers
Example:
Unit 1: Number Sense
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