1 / 55

Math 8

Math 8. Unit 1: Square Roots and the Pythagorean Theorem. Unit 1: Square Roots and the Pythagorean Theorem. What you’ll learn: Determine the square of a number Determine the square root of a number Determine the approximate square root of a non-perfect square

shayla
Download Presentation

Math 8

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Math 8 Unit 1: Square Roots and the Pythagorean Theorem

  2. Unit 1: Square Roots and the Pythagorean Theorem What you’ll learn: • Determine the square of a number • Determine the square root of a number • Determine the approximate square root of a non-perfect square • Develop and apply the Pythagorean Theorem

  3. Unit 1: Square Roots and the Pythagorean Theorem Why it’s important • Used in construction to ensure 900 corners • Used in surveying • Used to determine the distance between two locations (video games)

  4. Unit 1: Square Roots and the Pythagorean Theorem 1.1 Square Numbers and Area Models

  5. 1.1 Square Numbers and Area Models • Focus: Relate the area of a square and square numbers

  6. 1.1 Square Numbers and Area Models On a piece of grid paper draw as many different rectangles as you can with an area of: • 4 squares • 6 squares • 8 squares • 9 squares

  7. 1.1 Square Numbers and Area Models • What are the differences and similarities between squares and rectangles? Differences Rectangle sides have length and width Square has all four sides the same Similarities Quadrilaterals, parallelograms: 4 sides 90o (right) corners Parallel sides

  8. 1.1 Square Numbers and Area Models • Use grid paper to draw several different squares. • How does the side length relate to the area?

  9. 1.1 Square Numbers and Area Models • What are the square numbers from 0 to 100?

  10. 1.1 Square Numbers and Area Models • What is the equation for the perimeter of a square? S S S S

  11. 1.1 Square Numbers and Area Models • Homework

  12. Unit 1: Square Roots and the Pythagorean Theorem 1.2 Squares and Square Roots

  13. 1.2 Squares and Square Roots • Focus: Find the squares and square roots of whole numbers

  14. 1.2 Squares and Square Roots • What numbers have only two factors? • What are these numbers called? • Which numbers have an even number of factors, but more than 2 factors? • Which numbers have an odd number of factors? • What are these numbers called?

  15. 1.2 Squares and Square Roots • Remember division: quotient dividend divisor

  16. 1.2 Squares and Square Roots • Draw a square with an area of 36 squares. • What is the side length?

  17. 1.2 Squares and Square Roots • The square root of a number is when the divisor and quotient of a number are the same. • The square root is the opposite of the square.

  18. 1.2 Squares and Square Roots • Homework

  19. Unit 1: Square Roots and the Pythagorean Theorem 1.3 Measuring Line segments

  20. 1.3 Measuring Line Segments • Focus: Use the area of a square to find the length of a line segment

  21. 1.3 Measuring Line Segments • Do the investigate questions

  22. 1.3 Measuring Line Segments • Try example 1

  23. 1.3 Measuring Line Segments • Try example 2

  24. 1.3 Measuring Line Segments • Not all numbers have whole number square roots. • If it doesn’t have a whole number root than leave the number as a root.

  25. 1.3 Measuring Line Segments • Homework

  26. Unit 1: Square Roots and the Pythagorean Theorem 1.4 Estimating square roots

  27. 1.4 Estimating Square Roots • Focus: Develop strategies for estimating a square root.

  28. 1.4 Estimating Square Roots • Investigate • Estimate the square roots of 2, 5, 11, 18, and 24

  29. 1.4 Estimating Square Roots • Homework

  30. Unit 1: Square Roots and the Pythagorean Theorem 1.5 The Pythagorean Theorem

  31. 1.5 The Pythagorean Theorem • Focus: Discover a relationship among the side lengths of a right triangle

  32. 1.5 The Pythagorean Theorem • Draw a right angle with legs 3 cm and 4 cm long. Measure the length of the diagonal. • Draw a right angle with legs 12 cm and 5 cm long. Measure the length of the diagonal. • Draw a right angle with legs 12 cm and 16 cm long. Measure the length of the diagonal 5 cm 13 cm 20 cm

  33. 1.5 The Pythagorean Theorem Right angle triangle Hypotenuse (diagonal, opposite the right angle, longest side) Right angle

  34. 1.5 The Pythagorean Theorem • Pythagorean Theorem a and b are legs and c must be the hypotenuse c a b

  35. Pythagorean triples • Whole number triples that satisfy the Pythagorean theorem. • 3, 4, 5 • 5, 12, 13 • 7, 24, 25 • 8, 15, 17 • 9, 40, 41

  36. 1.5 The Pythagorean Theorem Example • What is the length of the hypotenuse of a triangle with legs 6 cm and 10 cm? c a = 6 cm b = 10cm

  37. 1.5 The Pythagorean Theorem • Homework

  38. Unit 1: Square Roots and the Pythagorean Theorem 1.6 Exploring the Pythagorean Theorem

  39. 1.6 Exploring the Pythagorean Theorem • Focus: Use the Pythagorean Theorem to identify right triangle

  40. 1.6 Exploring the Pythagorean Theorem There are many different types of triangles. (some overlap) • Right Triangle – has a 90o angle • Isosceles Triangle – two sides are the same length and two angles are the same • Obtuse Triangle – one internal angle is obtuse (>90o) • Acute Triangle – all angles are less than 90o • Scalene Triangle – all three sides are different lengths

  41. 1.6 Exploring the Pythagorean Theorem Investigate Work in a group of 4 with four different triangles

  42. 1.6 Exploring the Pythagorean Theorem • Homework

  43. Unit 1: Square Roots and the Pythagorean Theorem 1.7 Applying the Pythagorean Theorem

  44. 1.7 Applying the Pythagorean Theorem • Focus: Solve problems using the Pythagorean Theorem

More Related