unit 1: number sense minds on. unit 1: number sense learning goals: i can convert between mixed and...

$: Unit 1: Number Sense Minds On. Unit 1: Number Sense Learning Goals: I can convert between mixed and improper fractions I can perform all four operations$
Unit 1: Number Sense

Minds On

Solve for the variables:

a) 3x + 12 = 0

b) 12x – 9 = 15

c) (3 + x) 4 = 7


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:

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, ,



Natural1, 2, 3

Whole

0Integers

-1, -2

Rational

0.5, -5.89



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



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

Examples:



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



Example: Find an equivalent fraction to



Example: A



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



Example: Convert 4



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



Example: Convert



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



Example: 2



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



Example: 3



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



Example:



Practice

Pg. 186 Q# 6 Read top of pg. 14

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

unit 1: number sense minds on. unit 1: number sense learning goals: i can convert between mixed and...

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