Math 8

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

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

14. 1.2 Squares and Square Roots • Focus: Find the squares and square roots of whole numbers

15. 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?

16. 1.2 Squares and Square Roots • Remember division: quotient dividend divisor

17. 1.2 Squares and Square Roots • Draw a square with an area of 36 squares. • What is the side length?

18. 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.

19. 1.2 Squares and Square Roots • Homework

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

22. 1.3 Measuring Line Segments • Focus: Use the area of a square to find the length of a line segment

23. 1.3 Measuring Line Segments • Do the investigate questions

24. 1.3 Measuring Line Segments • Try example 1

25. 1.3 Measuring Line Segments • Try example 2

26. 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.

27. 1.3 Measuring Line Segments • Homework

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

30. 1.4 Estimating Square Roots • Focus: Develop strategies for estimating a square root.

31. 1.4 Estimating Square Roots • Investigate • Estimate the square roots of 2, 5, 11, 18, and 24

32. 1.4 Estimating Square Roots • Homework

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

35. 1.5 The Pythagorean Theorem • Focus: Discover a relationship among the side lengths of a right triangle

36. 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

37. 1.5 The Pythagorean Theorem Right angle triangle Hypotenuse (diagonal, opposite the right angle, longest side) Right angle

38. 1.5 The Pythagorean Theorem • Pythagorean Theorem a and b are legs and c must be the hypotenuse c a b

39. 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

40. 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

41. 1.5 The Pythagorean Theorem • Homework

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

44. 1.6 Exploring the Pythagorean Theorem • Focus: Use the Pythagorean Theorem to identify right triangle

45. 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

46. 1.6 Exploring the Pythagorean Theorem Investigate Work in a group of 4 with four different triangles

47. 1.6 Exploring the Pythagorean Theorem • Homework

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

50. 1.7 Applying the Pythagorean Theorem • Focus: Solve problems using the Pythagorean Theorem