1. Module 3 Lesson 1 Investigating Perimeter and Area Formulas.

2.  After this lesson you will be able to:  Know the formula and how to find the perimeter of a rectangle.  Know the formula and how to find the area of a rectangle. Lesson Objective

3. What do you notice about this rectangle?

4. Did you notice that one side is 4 and the other is 6?

5. Did you know that the 4 represents the width?

6. Did you know that the 6 represents the length?

7. If I were to walk along the outside of this rectangle how many units would I travel?

8. Did you get 20? 4 6

9. What would this be called? 4 6

10. The Perimeter 4 6

11. Now let’s look at the squares inside of the rectangle. What do these represent?

12. The squares represent the area! How could I find the area for this rectangle?

13. We could count each individual square.

14. We could count each individual square and get 24. 12 3 7 11 5 6 8 4 9 10 12 1314 15 16 17 18 19202122 23 24

15. Let’s try finding the Perimeter and Area of this rectangle. What do I need to know to get the perimeter?

16. Let’s try finding the Perimeter and Area of this rectangle. The length and width!

17. Let’s try finding the Perimeter and Area of this rectangle. What is the length of this rectangle?

18. Let’s try finding the Perimeter and Area of this rectangle. Now what is the width of this rectangle? 8

19. Let’s try finding the Perimeter and Area of this rectangle. What do I do to find the perimeter? 8 3

20. Let’s try finding the Perimeter and Area of this rectangle. We need to add up all the sides! 8 3 8 3

21. Let’s try finding the Perimeter and Area of this rectangle. Does it matter the order in which I add the numbers? 8 3 8 3

22. Let’s try finding the Perimeter and Area of this rectangle.  8 + 3 = 11; 11 + 8 = 19; 19 + 3 = 22  8 + 8 = 16; 3 + 3 = 6; 16 + 6 = 22  8 + 3 = 11; 8+ 3 = 11; 11 + 11 = 22 8 3 8 3

23. Can you think of an easier way to find the perimeter?  8 + 3 = 11; 11 + 8 = 19; 19 + 3 = 22  8 + 8 = 16; 3 + 3 = 6; 16 + 6 = 22  8 + 3 = 11; 8+ 3 = 11; 11 + 11 = 22 8 3 8 3

24. Can you think of an easier way to find the perimeter?  8 + 3 = 11; 11 + 8 = 19; 19 + 3 = 22  8 + 8 = 16; 3 + 3 = 6; 16 + 6 = 22  8 + 3 = 11; 8+ 3 = 11; 11 + 11 = 22 8 3 8 3 We could multiply instead of adding!

25. Can you think of an easier way to find the perimeter?  8 + 8 = 16; 3 + 3 = 6; 16 + 6 = 22  We could do (8 x 2) + (3 x 2).  This formula is: 2L + 2W. 8 3 8 3

26. Can you think of an easier way to find the perimeter?  8 + 3 = 11; 8+ 3 = 11; 11 + 11 = 22  We could do (8 + 3) x 2  This formula is: 2 x (L + W) 8 3 8 3

27. You have discovered the formulas for finding the perimeter! 2 x (L + W) 2L + 2W 8 3 8 3

28. Now let’s look at the area! How do we find the area? 8 3 8 3

29. Now let’s look at the area! We can count all of the boxes. 8 3 8 3

30. Now let’s look at the area! 8 3 8 3 1 23 4 5 6 7 8 9 10 11 12 13 1415 16 17 18 19 20 21 22 23 24

31. Now let’s look at the area! 8 3 8 3 1 23 4 5 6 7 8 9 10 11 12 13 1415 16 17 18 19 20 21 22 23 24 Is there a quicker way to find the area of the rectangle.

32. What if we skip count by 8? 8 3 8 3 1 23 4 5 6 7 8 Is there a quicker way to find the area of the rectangle.

33. What if we skip count by 8? 8 3 8 3 1 23 4 5 6 7 8 Is there a quicker way to find the area of the rectangle. 9 10 11 12 13 1415 16

34. What if we skip count by 8? 8 3 8 3 1 23 4 5 6 7 8 Skip counting is the same as… 9 10 11 12 13 1415 16 17 18 19 20 21 22 23 24

35. What if we skip count by 8? 8 3 8 3 1 23 4 5 6 7 8 Skip counting is the same as… Multiplying! 9 10 11 12 13 1415 16 17 18 19 20 21 22 23 24

36. Area Formula!  We can multiply 8 x 3 and get 24.  The formula for area is L x W 8 3 8 3

37. Let’s try out the formulas!  Let’s use the formulas we just learned to find the perimeter and area of the following rectangle.

38. First we need to find…  Before we can use the formulas, we need to find the L and W.

39. First we need to find…  Before we can use the formulas, we need to find the L and W.  The L is 4 4

40. First we need to find…  Before we can use the formulas, we need to find the L and W.  The L is 4  The W is 4 4 4

41. First we need to find…  Before we can use the formulas, we need to find the L and W.  The L is 4  The W is 4  Let’s find the perimeter 4 4

42. Let’s find the Perimeter 4 4 Use the formula you want and solve. 2 x (L + W) 2L + 2W

43. Let’s find the Perimeter 2 x (L + W)  (2 x 4) + (2 x 4) =  8 + 8 =  16  2 x (4 + 4) =  2 x 8 =  16 2L + 2W

44. Now let’s find the area. 4 4  Use the formula and solve. L x W

45. Now let’s find the area. 4 4 L x W 4 x 4 = 16

46. Now it’s your turn! Find the Perimeter and Area of the following rectangles 3 7 5 6

47. 3 7 Perimeter: 20 Area: 21

48. Now it’s your turn! Find the Perimeter and Area of the following rectangles 5 6 Perimeter: 22 Area: 30