get ahead of the curve: algebra

Get Ahead of the Curve:

Algebra

baltimoresun.comA failing grade for Md. mathWhat is taught in high schools seen as insufficient for collegeBy Liz Bowie July 12, 2009

Maryland'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.

"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.

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.

I think that math is …• Great• Fun• Challenging• Interesting• OK• Hard• A way of solving problems

for real-life situations• Annoying• Difficult

Homework

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.

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.

a. Divisibility rule for 4

Fill in the missing numbers in the following arithmetic sequences.

a. 1 4 7 10 _____ _____


a. 1 4 7 10 13 16


a. 1 4 7 10 13 16b. 11 15 ______ 23 ______


a. 1 4 7 10 13 16b. 11 15 19 23 27

c. 3 ______ 17 ______ 31


a. 1 4 7 10 13 16b. 11 15 19 23 27c. 3 10 17 24 31

d. ______ ______ 23 32 41


a. 1 4 7 10 13 16b. 11 15 19 23 27c. 3 10 17 24 31d. 5 14 23 32 41

e. 6 ______ ______ ______ 14


a. 1 4 7 10 13 16b. 11 15 19 23 27c. 3 10 17 24 31d. 5 14 23 32 41e. 6 8 10 12 14

f. 7 ______ ______ ______

6. 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.

Term 1st 2nd 3rd 4th 5th 6th 7th 8th

Value 2 5 8 11 14 17 20 23

Formula 2 2 +1x3 2 + 2x3 2 + 3x3 2 + 4x3 2 + 5x3 2 + 6x3 2 + 7x3

Fill in the missing numbers in the following geometric sequences.

a. 4 12 36 ______ ______


a. 4 12 36 108 324


a. 4 12 36 108 324b. 2 14 ________ 686


a. 4 12 36 108 324b. 2 14 98 686

c. ______ ______ 18 54 162


a. 4 12 36 108 324b. 2 14 98 686

c. 2 6 18 54 162d. 5 ______ 20 ______ 80


a. 4 12 36 108 324b. 2 14 98 686

c. 2 6 18 54 162d. 5 10 20 40 80


a. 4 12 36 108 324b. 2 14 98 686

c. 2 6 18 54 162d. 5 10 20 40 80

e. 0 ______ ______ ______


a. 4 12 36 108 324b. 2 14 98 686

c. 2 6 18 54 162d. 5 10 20 40 80

e. 0 0 0 0

8. 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.

Name Position Number of LettersFifth 5

Fourth 25Third 125

SecondTop

If no one broke the chain, how much money could you expect to receive?

8. 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.

Name Position Number of LettersFifth 5

Fourth 25Third 125

Second 625Top 3125

If no one broke the chain, how much money could you expect to receive?

9. 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 CB 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.

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

Number of Students in Group Number of Handshakes2 13 34 65 106789

10

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

Number of Students in Group Number of Handshakes2 13 34 65 106 157 218 289 36

10 45

Multiplication Practice QUIZ

Multiplication Division Big Numbers1 12 23

2 13 24

3 14 25

4 15

5 16

6 17

7 18

8 19

9 20

10 21

11 22

3 x 4

2 x 12

8 x 9

7 x 7

11 x 95 x 7

6 x 87 x 6

63 ÷ 9

10 x 3

3 x 8

14 ÷ 2

21 ÷ 7

144 ÷ 12

55 ÷ 5

24 ÷ 4

9 x 9

132 ÷ 11

27 ÷ 3

32 ÷ 4

2 ÷ 1

18 ÷ 6

13 x 24

32 x 51

81 x 12

Multiplication Division Big Numbers1 12 23

2 13 24

3 14 25

4 15

5 16

6 17

7 18

8 19

9 20

10 21

11 22

12

24

72

49

9935

4842

7

30

24

7

3

12

11

6

81

12

9

8

2

8

312

1632

972

Multiplying Two Digit Numbers 32x 51 1st operation 2nd operation 3rd operation

3 x 515

2 x 5 + 3 x 113 2 x 12

0th operation 1st operation 2nd operation 3rd operation

1 5

1 3

0 21 6 3 2

34x56


1 5

3 8

2 41 9 0 4

81x19


0 8

7 3

0 91 5 3 9

More Number Sequences

1 4 9 16 25 36 ___ ___ ___ ___Where did we see this sequence last week?

Square Numbers

1 x 1 = 12 x 2 = 43 x 3 = 9

4 x 4 = 165 x 5 = 256 x 6 = 36

7 x 7 = 498 x 8 = 649 x 9 = 81

10 x 10 = 10011 x 11 = 12112 x 12 = 144

Square Numbers – Using Exponents

12 = 1 x 1 = 122 =2 x 2 = 432 = 3 x 3 = 9

42 = 4 x 4 = 1652 = 5 x 5 = 2562 = 6 x 6 = 36

72 = 7 x 7 = 4982 = 8 x 8 = 6492 = 9 x 9 = 81

102 = 10 x 10 = 100112 = 11 x 11 = 121122 = 12 x 12 = 144

A Meaning for Squares

My Swimming Pool

9 feet

9 Fe

etIf I walk around my pool, how far do I travel?

My Swimming Pool

9 feet

9 Fe

etIf I get a cover for my pool, how big will it be?

The Perfect Squares

Cubes

1 x 1 x 1 = 12 x 2 x 2 = 8

3 x 3 x 3 = 274 x 4 x 4 = 64

5 x 5 x 5 = 1256 x 6 x 6 = 216

7 x 7 x 7 = 3438 x 8 x 8 = 5129 x 9 x 9 = 729

10 x 10 x 10 = 100011 x 11 x 11 = 133112 x 12 x 12 = 1728

Cubes – Using Exponents

13 = 1 x 1 x 1 = 123 = 2 x 2 x 2 = 8

33 = 3 x 3 x 3 = 2743 = 4 x 4 x 4 = 64

53 = 5 x 5 x 5 = 12563 = 6 x 6 x 6 = 216

73 = 7 x 7 x 7 = 34383 = 8 x 8 x 8 = 51293 = 9 x 9 x 9 = 729

103 = 10 x 10 x 10 = 1000113 = 11 x 11 x 11 = 1331123 = 12 x 12 x 12 = 1728

My Swimming Pool9 feet

9 feet

9 feet

How much water is needed to fill my pool?

SummaryLinear MeasureSquare MeasureCubic Measure

Identifying Perfect Squares

and Perfect Cubes

Identify the Perfect Square

A. 32B. 49C. 50D. 99

E. 111


A. 10B. 24C. 39D. 81

E. 156


A. 100B. 45C. 55D. 66E. 88


A. 32B. 48C. 56D. 66

E. 121

Identify the Perfect Cube

A. 4B. 9

C. 36D. 64

E. 100


A. 16B. 25C. 27

D. 144E. 200


A. 800B. 900

C. 1000D. 1200E. 1500


A. 81B. 121C. 144D. 216E. 524


A. 200B. 300C. 400D. 500E. 600


A. 2000B. 4000C. 6000D. 8000

E. 10000

Using Exponents

35

Base

Exponent

Practice with Exponents

1. 54

2. 26

3. 34

4. 45

5. 107

5x5x5x52x2x2x2x2x23x3x3x34x4x4x4x410x10x10x10x10x10x10

62564

911024

10000000

Amazing Number Trick #1

1. Choose a number.2. Add 5.3. Double the result.4. Subtract 4.5. Divide by 2.6. Subtract the number you started with.


1. Choose a number.2. Add 3.3. Multiply by 2.4. Add 4.5. Divide by 2.6. Subtract your original number.


1. Choose a number.2. Add the next larger number.3. Add 7.4. Divide by 2.5. Subtract your original number.

Amazing Number Trick #1Choose a number.Add 5.Double the result.Subtract 4.Divide by 2.Subtract the number you started with.

NEXT WEEK: Bring a Calculator

get ahead of the curve: algebra

Documents

given number

divisibility rules

divisibility rule f

college professors

college math professors

computer search engine

remedial math classes

remedial classes