Get Ahead of the Curve: Algebra
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Transcript of Get Ahead of the Curve: Algebra
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Get Ahead of the Curve:
Algebra
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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.
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"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.
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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.
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I think that math is …• Great• Fun• Challenging• Interesting• OK• Hard• A way of solving problems
for real-life situations• Annoying• Difficult
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Homework
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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.
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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
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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 6
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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 9
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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 10
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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 11
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Fill in the missing numbers in the following arithmetic sequences.
a. 1 4 7 10 _____ _____
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Fill in the missing numbers in the following arithmetic sequences.
a. 1 4 7 10 13 16
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Fill in the missing numbers in the following arithmetic sequences.
a. 1 4 7 10 13 16b. 11 15 ______ 23 ______
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Fill in the missing numbers in the following arithmetic sequences.
a. 1 4 7 10 13 16b. 11 15 19 23 27
c. 3 ______ 17 ______ 31
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Fill in the missing numbers in the following arithmetic sequences.
a. 1 4 7 10 13 16b. 11 15 19 23 27c. 3 10 17 24 31
d. ______ ______ 23 32 41
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Fill in the missing numbers in the following arithmetic sequences.
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
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Fill in the missing numbers in the following arithmetic sequences.
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 ______ ______ ______
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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
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Fill in the missing numbers in the following geometric sequences.
a. 4 12 36 ______ ______
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Fill in the missing numbers in the following geometric sequences.
a. 4 12 36 108 324
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Fill in the missing numbers in the following geometric sequences.
a. 4 12 36 108 324b. 2 14 ________ 686
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Fill in the missing numbers in the following geometric sequences.
a. 4 12 36 108 324b. 2 14 98 686
c. ______ ______ 18 54 162
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Fill in the missing numbers in the following geometric sequences.
a. 4 12 36 108 324b. 2 14 98 686
c. 2 6 18 54 162d. 5 ______ 20 ______ 80
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Fill in the missing numbers in the following geometric sequences.
a. 4 12 36 108 324b. 2 14 98 686
c. 2 6 18 54 162d. 5 10 20 40 80
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Fill in the missing numbers in the following geometric sequences.
a. 4 12 36 108 324b. 2 14 98 686
c. 2 6 18 54 162d. 5 10 20 40 80
e. 0 ______ ______ ______
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Fill in the missing numbers in the following geometric sequences.
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
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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?
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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?
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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.
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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
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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
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Multiplication Practice QUIZ
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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
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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
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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
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34x56
0th operation 1st operation 2nd operation 3rd operation
1 5
3 8
2 41 9 0 4
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81x19
0th operation 1st operation 2nd operation 3rd operation
0 8
7 3
0 91 5 3 9
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More Number Sequences
1 4 9 16 25 36 ___ ___ ___ ___Where did we see this sequence last week?
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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
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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
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A Meaning for Squares
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My Swimming Pool
9 feet
9 Fe
etIf I walk around my pool, how far do I travel?
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My Swimming Pool
9 feet
9 Fe
etIf I get a cover for my pool, how big will it be?
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The Perfect Squares
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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
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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
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My Swimming Pool9 feet
9 feet
9 feet
How much water is needed to fill my pool?
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SummaryLinear MeasureSquare MeasureCubic Measure
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Identifying Perfect Squares
and Perfect Cubes
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Identify the Perfect Square
A. 32B. 49C. 50D. 99
E. 111
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Identify the Perfect Square
A. 10B. 24C. 39D. 81
E. 156
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Identify the Perfect Square
A. 100B. 45C. 55D. 66E. 88
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Identify the Perfect Square
A. 32B. 48C. 56D. 66
E. 121
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Identify the Perfect Cube
A. 4B. 9
C. 36D. 64
E. 100
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Identify the Perfect Cube
A. 16B. 25C. 27
D. 144E. 200
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Identify the Perfect Cube
A. 800B. 900
C. 1000D. 1200E. 1500
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Identify the Perfect Cube
A. 81B. 121C. 144D. 216E. 524
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Identify the Perfect Square
A. 200B. 300C. 400D. 500E. 600
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Identify the Perfect Cube
A. 2000B. 4000C. 6000D. 8000
E. 10000
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Using Exponents
35
Base
Exponent
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Practice with Exponents
1. 54
2. 26
3. 34
4. 45
5. 107
5x5x5x52x2x2x2x2x23x3x3x34x4x4x4x410x10x10x10x10x10x10
62564
911024
10000000
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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.
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Amazing Number Trick #2
1. Choose a number.2. Add 3.3. Multiply by 2.4. Add 4.5. Divide by 2.6. Subtract your original number.
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Amazing Number Trick #3
1. Choose a number.2. Add the next larger number.3. Add 7.4. Divide by 2.5. Subtract your original number.
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Amazing Number Trick #1Choose a number.Add 5.Double the result.Subtract 4.Divide by 2.Subtract the number you started with.
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NEXT WEEK: Bring a Calculator