1. Numerations Systems 999nnn IIIIII 9n n IIIII 125 was written as 336 would be written as

2. Roman Numerals IVXLCDM 1 510501005001000 M D CCC L V I IV = 4IX = 9 XL = 40CD = 400 CM= M CM L IX =

3. Base 10 Sticks in Bundles Unifix Cubes Units, Strips, Mats Base Ten Blocks

4. Homework Pg 159 # 1,2,13,14,16,17,18,26-29

5. Different Base Systems Base Five Digits used 0,1,2,3,4 Decimal Value of Positions 5 4 = 625 5 3 = 1255 2 = 25 5 1 = 5 5 0 = 1 1 3 2 4 2 Five 625 + 3 x 125 + 2 x 25 + 4 x 5 + 2 x 1 = 625 + 375 + 50 + 20 + 2 = 1072

6. Base 6 Digits used 0,1,2,3,4,5 Decimal Value of Position 6 4 = 1296 6 3 = 216 6 2 = 36 6 1 = 6 6 0 = 1 1 2 3 5 2 six =

7. Base Seven Base 7 Digits used 0,1,2,3,4,5,6 Decimal Value of Position 7 4 = 2401 7 3 = 343 7 2 = 49 7 1 = 7 7 0 = 1 1 2 3 5 2 seven =

8. Base 2 Digits used 0,1 Decimal Value of Position 2 5 = 32 2 4 = 16 2 3 = 8 2 2 = 4 2 1 = 2 2 0 = 1 1 0 1 1 0 1 two =

9. Convert to Base 10 notation 413 five 2004 five 100 five 214 seven 213 six 415 eight 2E4 twelve 1TE twelve

10. Homework Pg 165 # 1,5,9,10,11,13

11. Addition Algorithm Making exchanges with Units, Strips, Mats 15 units, 11 strips, and 2 mats. What exchanges must be made in order to represent the same number but with the smallest number of pieces? Pg 166

12. Units, Strips, Mats Adding 1 mats, 3 strips, and 5 units +2 mats, 4 strips, and 3 units 3 mats, 7 strips, and 8 units

13. Add 3 mats, 5 strips, 7 units +2 mats, 7 strips, 4 units 5 mats, 12 strips, 11 units Exchange 5 mats, 13 strips, 1 unit Exchange 6 mats, 3 strips, 1 unit

14. Use Mats, strips, and Units 457 + 265 =

15. Subtraction Algorithm 9 – 5 = 9 take away 5 =

16. 3 mats, 7 strips, 5 units -2 mats, 4 strips, 3 units 1 mat, 3 strips, 2 units

17. 375 – 189 =

18. 375 – 189 36 (15) – 189

19. 375 – 189 36 (15) – 189 =

20. 375 – 189 36 (15) – 189 2(100) + 16(10) + 15(1)

21. 375 – 189 2(100) + 16(10) + 15(1) – 189= 186

22. 324 - 156 100s10s1s 3 2 4 - 1 5 6 3 1 14 - 1 5 6 2 11 14 - 1 5 6 1 6 8 Exchange

23. 3 hours 24 minutes 54 seconds +2 hours 47 minutes 38 seconds 6 hours 12 minutes32 seconds 7 hours 46 minutes 29 seconds -3 hours 27 minutes 52 seconds 4 hours 18 minutes 37 seconds

24. Adding & Subtracting in Other Bases 143 five +234 five

25. 25s5s1s 143 five + 234 five 3 12 12 five 4 3 2 five

27. Add 231 five 434 five 144 five 243 five 430 five 1232 five

28. Subtract 231 five 434 five 144 five 243 five 32 five 141 five

29. What Base ? 231344 534 +414 +143 +245 1200 1042 1112 1020 572 - 203 - 144 312427

30. Homework Pg 181 #1a,3,5,6,7,21,33-36,

31. Multiplying Whole Numbers 9 times 3 = 3+3+3+3+3+3+3+3+3 2 groups of 10 and 7 ones = 27

32. Multiplying Whole Numbers 9 times 3 = 3+3+3+3+3+3+3+3+3 Use Sticks in Bundles Unifix Cubes Units, Strips, Mats Base Ten Blocks

33. Multiplying Whole Numbers 3 times 213 = 213+213+213 Use Sticks in Bundles Unifix Cubes Units, Strips, Mats Base Ten Blocks

34. Multiplying Whole Numbers 4 times 243 = 243+243+243 Use Sticks in Bundles Unifix Cubes Units, Strips, Mats Base Ten Blocks

35. 15 x 324 324 15 20 100 1500 40 200 3000 4860 5 x 4 5 x 20 5 x 300 10 x 20 10 x 4 10 x 300

36. Final Algorithm 1 2 324 x 15 1620 324 4860

37. x300204 10300020040 5150010020 Sum = 4860

38. 324 x 15 324 1 5

39. 463 x 34 463 3 4

40. 527 x 43 527 4 3

41. Division A ÷ B A/B B  A Meaning of Division: – How many groups? – How many in each group?

42. How many groups? A ÷ B 8 ÷ 2 8 objects are divided into groups with 2 objects in each group. “How many Groups?”

43. How many in each group? A ÷ B 8 ÷ 2 How many objects are in each group when 8 objects are divided into 2 groups.

44. Division Algorithms Standard Method Scaffold Method Repeated Subtraction

45. Homework Pg 192 # 1a,7,10,11,13,14,17,35-38 Pg 183 #21,22,23a,d,e, Finish Wkst.

46. Mental Arithmetic & Properties 35 + 7+ 15 (Comm.) 8+3+4+6+7+12+4+3+6+3 (add to 10s) 25 x 8 4 x 99

47. Rounding Numbers Determine to which position your are rounding If the digit immediately to the right of this position is 5 or more, add 1 to the digit in the position to which you are rounding. Otherwise leave the digit unchanged. Replace with 0s all digits to the right of the position to which you are rounding, up to the decimal point.

48. Homework Pg 206 # 1,2,4,5,28 – 31 Review Packet on Web