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Fraction Friday!

In this lesson, students explore concepts of real numbers, square roots, and grouping symbols through various practice problems. The warm-up activities challenge students to use grouping symbols in equations and analyze patterns in geometric figures. Students will learn to classify numbers into sets, understand perfect squares, and utilize Venn diagrams to illustrate relationships between different number categories. Homework will reinforce these concepts with targeted exercises, focusing on inequalities and relationships among numbers.

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Fraction Friday!

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  1. Fraction Friday! • 1. 3. • 2. 4. • 5. Use grouping symbols to make the following equation true. 53 5 + 20 = 5

  2. Warm-Up • 1. If the pattern continues, which will be the first figure to contain more than 200 square units? Explain. • 2. Use grouping symbols to make the following equation true. 120+10÷2=65

  3. Homework Review • P. 13 # 10-32E, 36-42E, 46-52E, 55 • 10. 64 • 12. 100,000,000 • 14. 1/16 • 16. 2401 • 18. 11 • 20. 18 • 22. 92 • 24. 6 • 26. 322 • 28. 30 • 30. 512 • 32. 0 • 36. a) 24 in3 b) 2.0 in3 • 38. 36 • 40. 55/8 • 42. 70/9 • 46. 1.75 • 48. 196 • 50. 33 • 52. 5/9 • 55. 20; 14 – 5(3) + 32

  4. 1.3 Real Numbers and the Number Line SWBAT classify real numbers SWBAT approximate square roots

  5. Square Root • A number a is a square root of a number b if a2 = b • In other words, if you’re looking for the square root of a number you are asking yourself what number can be multiplied by itself to get the original number • Ex: 7 is the square root of 49 because 72 = 49

  6. Radical • The mathematical symbol for a square root is called a radical and looks like this

  7. Examples

  8. Perfect Squares • Notice that all of these answers came out to be whole numbers, that is because the numbers under the radical was a perfect square • Perfect Squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 169, 196…

  9. Estimate • In your groups and without a calculator, estimate • Be prepared to explain how you figured it out

  10. Sets • You can classify numbers using sets. • A set is a defined collection of objects • For example, if you were looking at the set of people that use Twitter in our class it would include everyone except Mrs. DeSmith.

  11. Sets of Numbers • Natural Numbers: 1, 2, 3, … • Whole Numbers: 0, 1, 2, 3, … • Integers: … -2, -1, 0, 1, 2, 3… • Rational Numbers: any number that can be written as a fraction • Irrational Numbers: any decimal that goes on forever without a pattern or repetition

  12. Venn Diagram • A Venn Diagram shows relationships between sets of objects • Example: Dogs Cats Spotted Dogs Dogs with long tails Dalmatians

  13. Group Work • In your groups, come up with a Venn Diagram that shows how the sets of numbers relate.

  14. Examples • Name the subset(s) of the real numbers to which each number belongs • 2/3 • -1 • √3

  15. Inequalities • When comparing numbers that are unequal we can use inequality symbols • <, ≤ , > ,≥

  16. Example • Compare the numbers using an inequality symbol

  17. Ordering

  18. Homework • P.20 #9-13, 19-23, 39-42, 45-46, 52-54E

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