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Unit 1: Number Sense

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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Unit 1: Number Sense

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  1. Unit 1: Number Sense Minds On Solve for the variables: 3x + 12 = 0 12x – 9 = 15 (3 + x) 4 = 7

  2. 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 • I can reduce fractions to lowest terms

  3. Unit 1: Number Sense 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, ,

  4. Unit 1: Number Sense Lesson 1 – Introduction to Rational Numbers Whole Rational Natural Integers 0.5, -5.89 1, 2, 3 0 -1, -2

  5. 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

  6. 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:

  7. 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

  8. Unit 1: Number Sense Lesson 1 – Introduction to Rational Numbers Example: Find an equivalent fraction to

  9. Unit 1: Number Sense Lesson 1 – Introduction to Rational Numbers Example: A

  10. 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

  11. Unit 1: Number Sense Lesson 1 – Introduction to Rational Numbers Example: Convert 4

  12. 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

  13. Unit 1: Number Sense Lesson 1 – Introduction to Rational Numbers Example: Convert

  14. 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

  15. Unit 1: Number Sense Lesson 1 – Introduction to Rational Numbers Example: 2

  16. 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

  17. Unit 1: Number Sense Lesson 1 – Introduction to Rational Numbers Example: 3

  18. 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

  19. Unit 1: Number Sense Lesson 1 – Introduction to Rational Numbers Example:

  20. 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

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