Area of the Lovely El

1. Area of the Lovely El “Area” means the space taken up by this shape… … so really, we should imagine it ‘filled in.’ (You could shade it in with your pencil too  )

2. Area of the Lovely El How many square spaces does it taketo fill up this shape?

3. Area of the Lovely El 1 2 This one has twenty.Yup! We could just count them. Let’s try to think of area as something real, taking up space Let’s make the formula make sense! 3 4 6 5 8 7 10 9 11 12 13 14 15 16 17 18 19 20

4. Area of the Lovely El 1 2 One of the best ways to figure out something complicatedis to break it into simpler pieces, figure them out, *and then* finish the job by putting the pieces together. (This is not to be confused with “well, this is too hard, soI’ll do something simpler and hope it’s good enough.” 3 4 6 5 8 7 10 9 11 12 13 14 15 16 17 18 19 20

5. Area • “I DON’T KNOW HOW TO FIGURE OUT THE AREA OF A WEIRD SHAPED BLOCK!” • … okay, what *do* you know how to figure out? 1 2 3 4 6 5 8 7 10 9 11 12 13 14 15 16 17 18 19 20

6. Area 2cm • We can break this up into rectangles. • The big rectangle has two squares of space in the first row… 1 2 3 4 6 5 8 7 10 9 11 12 13 14 15 16 17 18 19 20

7. Area 2cm • We can break this up into rectangles. • The big rectangle has two squares of space in the first row… 1 2 3 4 6 5 8 7 10 9 11 12 13 14 15 16 17 18 19 20

8. Area 2cm • there are 8 rows of two squares each… here’s another place where “of” is showing multiplication 1 2 3 4 6 5 8cm 8 7 10 9 11 12 13 14 15 16 17 18 19 20

9. Area 2cm • there are 8 rows of two squares each… here’s another place where “of” is showing multiplication 1 2 3 4 6 5 8cm 8 7 10 9 11 12 13 14 15 16 17 18 19 20

10. Area 2cm • there are 8 rows of two squares each… here’s another place where “of” is showing multiplication 1 2 3 4 6 5 8cm 8 7 10 9 11 12 13 14 15 16 17 18 19 20

11. Area 2cm • there are 8 rows of two squares each… here’s another place where “of” is showing multiplication 1 2 3 4 6 5 8cm 8 7 10 9 11 12 13 14 15 16 17 18 19 20

12. Area 2cm • there are 8 rows of two squares each… here’s another place where “of” is showing multiplication 1 2 3 4 6 5 8cm 8 7 10 9 11 12 13 14 15 16 17 18 19 20

13. Area 2cm • there are 8 rows of two squares each… here’s another place where “of” is showing multiplication 1 2 3 4 6 5 8cm 8 7 10 9 11 12 13 14 15 16 17 18 19 20

14. Area 2cm • there are 8 rows of two squares each… here’s another place where “of” is showing multiplication • This rectangle’s area is 16cm2 1 2 3 4 6 5 8cm 8 7 10 9 11 12 13 14 15 16 17 18 19 20

15. Area 2cm • Think “area: square ya!” • Since we’re measuring squares – two dimensions – our unit is raised to the second power. 1 2 3 4 6 5 8cm 8 7 10 9 11 12 13 14 15 16 17 18 19 20

16. Area 2cm • What about the other guy? • It’s 4 x 1 or 4cm2 1 2 3 4 6 5 8cm 8 7 10 9 11 12 4cm 13 14 1cm 2 4 3 15 16 1

17. Area 2cm • So, together… this shape has 20 cm2 1 2 3 4 6 5 8cm 8 7 10 9 11 12 4cm 13 14 1cm 2 4 3 15 16 1

18. Area 2cm • So, together… this shape has 20 cm2 1 2 3 4 6 5 8cm 8 7 10 9 11 12 13 14 19 15 16 17 18 20

19. Breaking into rectangles 2cm But how can you tell where to break it up? 7cm 8cm 4cm 1cm 6cm

20. Breaking into rectangles 2 We can break this “el” into two rectangles. This one… but what numbers are its length and width? 7 8 4 1 6

21. Breaking into rectangles • It’s the 8 and the 2 • Trace the rectangle … • The six goes further than the base of the rectangle… 2 1 2 3 4 6 5 7 8 8 7 10 9 11 12 4 13 14 1 15 16 6 Should stop here!!!

22. Breaking into rectangles • It’s the 8 and the 2 • The six goes further than the base of the rectangle… • And the 7 doesn’t go to the end. 2 1 2 3 4 6 5 7 8 8 7 Should end here! 10 9 11 12 4 13 14 1 15 16 6

23. Breaking into rectangles 2 1 2 3 4 6 This rectangle is left… And the six is too big here, too! It’s 1 x 4, or 4. 5 7 8 8 7 10 9 11 12 4 13 14 1 15 16 6

24. 2 1 2 So our area is 16 + 4, which is 20… 3 4 6 5 7 8 8 7 10 9 11 12 4 13 14 1 15 16 17 18 19 20 6

25. 2 1 2 Or, we could have split it this way: 7 x 2 (the 8 is too long!) 3 4 6 5 7 8 8 7 10 9 11 12 4 13 14 1 15 16 17 18 19 20 6

26. 2 1 2 Or, we could have split it this way: 7 x 2 + 6 x 1 = 14 + 6 = 20 -- different ways to get the same answer. 3 4 6 5 7 8 8 7 10 9 11 12 4 13 14 1 15 16 17 18 19 20 6

27. Area of the Lovely El 6 cm Back to this harder one – no, it’s not the same! (Centimeters are really bigger than this; this is a picture of it, so it’s smaller.) 25 cm 20 cm 14 cm 5 cm 20 cm

28. Area of the Lovely El 6 cm Break it up and find the right sides to multiply. You don’t have to solve it – just set it up! Don’t click ‘til you’ve made your equation  25 cm 20 cm 14 cm 5 cm 20 cm

29. Area of the Lovely El 6 cm Break it up and find the right sides to multiply. You don’t have to solve it – just set it up! It should be 20 x 6 + 20 x 5 = 120 + 100 = 220 cm OR>>>> 25 cm 20 cm 14 cm 5 cm 20 cm

30. Area of the Lovely El 6 cm Break it up and find the right sides to multiply. You don’t have to solve it – just set it up! It could also be 25 x 6 + 5 x 14 150 + 70 = 220 25 cm 20 cm 14 cm 5 cm 20 cm