Get Ahead of the Curve: Algebra

1. Get Ahead of the Curve: Algebra

2. baltimoresun.comA failing grade for Md. mathWhat is taught in high schools seen as insufficient for collegeBy Liz Bowie July 12, 2009Maryland's public schools are teaching mathematics in such a way that many graduates cannot be placed in entry-level college math classes because they do not have a grasp of the basics, according to education experts and professors.College math professors say there is a gap between what is taught in the state's high schools and what is needed in college. Many schools have de-emphasized drilling students in basic math, such as multiplication and division, they say.

3. "We have hordes of students who come in and have forgotten their basic arithmetic," said Donna McKusick, dean for developmental education at the Community College of Baltimore County. College professors say students are taught too early to rely on calculators. "You say, 'What is seven times seven?' and they don't know," McKusick said.Ninety-eight percent of Baltimore students signing up for classes at Baltimore City Community College had to pay for remedial classes to learn the material that should have been covered in high school. Across Maryland, 49 percent of the state's high school graduates take remedial classes in college before they can take classes for credit.

4. And the problem has been getting worse. The need for remedial math classes among Maryland high school graduates who had taken a college preparatory curriculum and went on to one of the state's two- or four-year colleges rose from 23 percent in 1997 to 32 percent in 2007, according to an Abell Foundation report released this spring.

5. I think that math is … • Great • Fun • Challenging • Interesting • OK • Hard • A way of solving problems for real-life situations • Annoying • Difficult

6. Homework

7. 1. List three occupations or professions for which algebra is necessary. (Consider using a search engine like Google and a search phrase like “professions requiring algebra”.) Try to list at least one occupation or profession that no other student identifies.

8. 4. Use a computer search engine like Google to find divisibility rules for the following. For each, write a number at least four digits in length that demonstrates the rule and a second number at least four digits in length that is not divisible by the given number. • Divisibility rule for 4

9. 4. Use a computer search engine like Google to find divisibility rules for the following. For each, write a number at least four digits in length that demonstrates the rule and a second number at least four digits in length that is not divisible by the given number. • Divisibility rule for 6

10. 4. Use a computer search engine like Google to find divisibility rules for the following. For each, write a number at least four digits in length that demonstrates the rule and a second number at least four digits in length that is not divisible by the given number. • Divisibility rule for 9

11. 4. Use a computer search engine like Google to find divisibility rules for the following. For each, write a number at least four digits in length that demonstrates the rule and a second number at least four digits in length that is not divisible by the given number. • Divisibility rule for 10

12. 4. Use a computer search engine like Google to find divisibility rules for the following. For each, write a number at least four digits in length that demonstrates the rule and a second number at least four digits in length that is not divisible by the given number. • Divisibility rule for 11

13. Fill in the missing numbers in the following arithmetic sequences. • 1 4 7 10 _____ _____

14. Fill in the missing numbers in the following arithmetic sequences. • 1 4 7 10 13 16

15. Fill in the missing numbers in the following arithmetic sequences. • 1 4 7 10 13 16 • 11 15 ______ 23 ______

16. Fill in the missing numbers in the following arithmetic sequences. • 1 4 7 10 13 16 • 11 15 19 23 27 • 3 ______ 17 ______ 31

17. Fill in the missing numbers in the following arithmetic sequences. • 1 4 7 10 13 16 • 11 15 19 23 27 • 3 10 17 24 31 • ______ ______ 23 32 41

18. Fill in the missing numbers in the following arithmetic sequences. • 1 4 7 10 13 16 • 11 15 19 23 27 • 3 10 17 24 31 • 514 23 32 41 • 6 ______ ______ ______ 14

19. Fill in the missing numbers in the following arithmetic sequences. • 1 4 7 10 13 16 • 11 15 19 23 27 • 3 10 17 24 31 • 514 23 32 41 • 6 81012 14 • 7 ______ ______ ______

20. What is the 100th term of the sequence 2 5 8 11 14 . . .? Instead of writing all the numbers in the sequence, we can find a pattern. Use the pattern to predict the 100th term of the sequence.

21. Fill in the missing numbers in the following geometric sequences. • 4 12 36 ______ ______

22. Fill in the missing numbers in the following geometric sequences. • 4 12 36 108324

23. Fill in the missing numbers in the following geometric sequences. • 4 12 36 108324 • 2 14 ________ 686

24. Fill in the missing numbers in the following geometric sequences. • 4 12 36 108324 • 2 14 98 686 • ______ ______ 18 54 162

25. Fill in the missing numbers in the following geometric sequences. • 4 12 36 108324 • 2 14 98 686 • 26 18 54 162 • 5 ______ 20 ______ 80

26. Fill in the missing numbers in the following geometric sequences. • 4 12 36 108324 • 2 14 98 686 • 26 18 54 162 • 5 10 20 40 80

27. Fill in the missing numbers in the following geometric sequences. • 4 12 36 108324 • 2 14 98 686 • 26 18 54 162 • 5 10 20 40 80 • 0 ______ ______ ______

28. Fill in the missing numbers in the following geometric sequences. • 4 12 36 108324 • 2 14 98 686 • 26 18 54 162 • 5 10 20 40 80 • 0 000

29. In 1935 a chain letter craze started in Denver and swept across the country. It worked like this. You receive a letter with a list of five names. You send a dime to the person named at the top, cross out that name, and add your own name at the bottom. Then you send out five copies of the letter to your friends with instructions to do the same. When your five friends send out five letters each, there will be 25 in all. If none of the 25 persons getting these letters breaks the chain, 125 more letters will be sent, and so on. If no one broke the chain, how much money could you expect to receive?

30. In 1935 a chain letter craze started in Denver and swept across the country. It worked like this. You receive a letter with a list of five names. You send a dime to the person named at the top, cross out that name, and add your own name at the bottom. Then you send out five copies of the letter to your friends with instructions to do the same. When your five friends send out five letters each, there will be 25 in all. If none of the 25 persons getting these letters breaks the chain, 125 more letters will be sent, and so on. If no one broke the chain, how much money could you expect to receive?

31. Two students are in a group. Before they start to work, they shake hands with each other. In a different group there are three students. Students A and B shake hands, students A and C shake hands, and students B and C shake hands for three total handshakes. If four students are in a group, the number of handshakes will be six: A and B A and C A and D B and C B and D C and D If five students are in the group, the number of handshakes will be 10. A and B A and C A and D A and E B and C B and D B and E C and D C and E D and E List the handshakes for groups of 6 and 7.

32. Complete the chart and describe a rule for determining the number of handshakes in a group of any size.

33. Complete the chart and describe a rule for determining the number of handshakes in a group of any size.

34. Multiplication Practice QUIZ

35. 3 x 4 14 ÷ 2 13 x 24 2 x 12 21 ÷ 7 32 x 51 8 x 9 144 ÷ 12 81 x 12 7 x 7 55 ÷ 5 63 ÷ 9 11 x 9 5 x 7 24 ÷ 4 132 ÷ 11 6 x 8 7 x 6 27 ÷ 3 9 x 9 32 ÷ 4 10 x 3 2 ÷ 1 3 x 8 18 ÷ 6

36. 12 7 312 24 3 1632 72 12 972 49 11 7 99 35 6 12 48 42 9 81 8 30 2 24 8

37. Multiplying Two Digit Numbers 32 x 51 3 x 5 15 2 x 5 13 + 3 x 1 2 x 1 2 1 5 1 3 0 2 1 6 3 2

38. 34 x56 1 5 3 8 2 4 1 9 0 4

39. 81 x19 0 8 7 3 0 9 1 5 3 9

40. More Number Sequences 1 4 9 16 25 36 ___ ___ ___ ___ Where did we see this sequence last week?

41. Square Numbers 1 x 1 = 1 2 x 2 = 4 3 x 3 = 9 4 x 4 = 16 5 x 5 = 25 6 x 6 = 36 7 x 7 = 49 8 x 8 = 64 9 x 9 = 81 10 x 10 = 100 11 x 11 = 121 12 x 12 = 144

42. Square Numbers – Using Exponents 12 = 1 x 1 = 1 22 =2 x 2 = 4 32 = 3 x 3 = 9 42 = 4 x 4 = 16 52 = 5 x 5 = 25 62 = 6 x 6 = 36 72 = 7 x 7 = 49 82 = 8 x 8 = 64 92 = 9 x 9 = 81 102 = 10 x 10 = 100 112 = 11 x 11 = 121 122 = 12 x 12 = 144

43. A Meaning for Squares

44. My Swimming Pool 9 Feet If I walk around my pool, how far do I travel? 9 feet

45. My Swimming Pool 9 Feet If I get a cover for my pool, how big will it be? 9 feet

46. The Perfect Squares

47. Cubes 1 x 1 x 1 = 1 2 x 2 x 2 = 8 3 x 3 x 3 = 27 4 x 4 x 4 = 64 5 x 5 x 5 = 125 6 x 6 x 6 = 216 7 x 7 x 7 = 343 8 x 8 x 8 = 512 9 x 9 x 9 = 729 10 x 10 x 10 = 1000 11 x 11 x 11 = 1331 12 x 12 x 12 = 1728

48. Cubes – Using Exponents 13 = 1 x 1 x 1 = 1 23 = 2 x 2 x 2 = 8 33 = 3 x 3 x 3 = 27 43 =4 x4 x 4 = 64 53 = 5 x 5 x 5 = 125 63 = 6 x 6 x 6 = 216 73 =7 x 7 x 7 = 343 83 =8 x 8 x 8 = 512 93 = 9 x 9 x 9 = 729 103 =10 x 10 x 10 = 1000 113 = 11 x 11 x 11 = 1331 123 =12 x 12 x 12 = 1728

49. My Swimming Pool 9 feet 9 feet 9 feet How much water is needed to fill my pool?

50. SummaryLinear MeasureSquare MeasureCubic Measure