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 take to fill up this shape?

3. Area of the Lovely El 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! 12 34 5 6 7 8 9 10 1112 1314 151617181920

4. Area of the Lovely El One of the best ways to figure out something complicated is 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, so I’ll do something simpler and hope it’s good enough.” 12 34 5 6 7 8 9 10 1112 1314 151617181920

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? 12 34 5 6 7 8 9 10 1112 1314 151617181920

6. Area We can break this up into rectangles. The big rectangle has two squares of space in the first row… 12 34 5 6 7 8 9 10 1112 1314 1516 17181920 2 cm

7. Area We can break this up into rectangles. The big rectangle has two squares of space in the first row… 12 34 5 6 7 8 9 10 1112 1314 1516 17181920 2 cm

8. Area there are 8 rows of two squares each… here’s another place where “of” is showing multiplication 12 34 5 6 7 8 9 10 1112 1314 1516 17181920 2 cm 8 cm

9. Area there are 8 rows of two squares each… here’s another place where “of” is showing multiplication 12 34 5 6 7 8 9 10 1112 1314 1516 17181920 2 cm 8 cm

10. Area there are 8 rows of two squares each… here’s another place where “of” is showing multiplication 12 34 5 6 7 8 9 10 1112 1314 1516 17181920 2 cm 8 cm

11. Area there are 8 rows of two squares each… here’s another place where “of” is showing multiplication 12 34 5 6 7 8 9 10 1112 1314 1516 17181920 2 cm 8 cm

12. Area there are 8 rows of two squares each… here’s another place where “of” is showing multiplication 12 34 5 6 7 8 9 10 1112 1314 1516 17181920 2 cm 8 cm

13. Area there are 8 rows of two squares each… here’s another place where “of” is showing multiplication 12 34 5 6 7 8 9 10 1112 1314 1516 17181920 2 cm 8 cm

14. Area there are 8 rows of two squares each… here’s another place where “of” is showing multiplication This rectangle’s area is 16cm 2 12 34 5 6 7 8 9 10 1112 1314 1516 17181920 2 cm 8 cm

15. Area Think “area: square ya!” Since we’re measuring squares – two dimensions – our unit is raised to the second power. 12 34 5 6 7 8 9 10 1112 1314 1516 17181920 2 cm 8 cm

16. Area What about the other guy? It’s 4 x 1 or 4cm 2 12 34 5 6 7 8 9 10 1112 1314 1516 2 cm 8 cm 1 cm 4 cm 1 2 3 4

17. Area So, together… this shape has 20 cm 2 12 34 5 6 7 8 9 10 1112 1314 1516 2 cm 8 cm 1 cm 4 cm 1 2 3 4

18. Area So, together… this shape has 20 cm 2 12 34 5 6 7 8 9 10 1112 1314 1516 19 171820 2 cm 8 cm

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

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

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 6 1 4 8 7 12 34 5 6 7 8 9 10 1112 1314 1516 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 6 1 4 8 7 12 34 5 6 7 8 9 10 1112 1314 1516 Should end here!

23. Breaking into rectangles 2 6 1 4 8 7 12 34 5 6 7 8 9 10 1112 1314 1516 This rectangle is left… And the six is too big here, too! It’s 1 x 4, or 4.

24. So our area is 16 + 4, which is 20… 2 6 1 4 8 7 12 34 5 6 7 8 9 10 1112 1314 151617181920

25. Or, we could have split it this way: 7 x 2 (the 8 is too long!) 2 6 1 4 8 7 12 34 5 6 7 8 9 10 1112 1314 151617181920

26. Or, we could have split it this way: 7 x 2 + 6 x 1 = 14 + 6 = 20 -- different ways to get the same answer. 2 6 1 4 8 7 12 34 5 6 7 8 9 10 1112 1314 151617181920

27. Area of the Lovely El 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 6 cm 20 cm 5 cm 20 cm 14 cm

28. Area of the Lovely El 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 6 cm 20 cm 5 cm 20 cm 14 cm

29. Area of the Lovely El 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 6 cm 20 cm 5 cm 20 cm 14 cm

30. Area of the Lovely El 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 6 cm 20 cm 5 cm 20 cm 14 cm