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Get Ahead of the Curve: Algebra

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baltimoresun.com A failing grade for Md. math What is taught in high schools seen as insufficient for college By 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 16 b.11 15 ______ 23 ______

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Fill in the missing numbers in the following arithmetic sequences. a.1 4 7 10 13 16 b.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 16 b.11 15 19 23 27 c.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 16 b.11 15 19 23 27 c.3 10 17 24 31 d.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 16 b.11 15 19 23 27 c.3 10 17 24 31 d.5 14 23 32 41 e.6 8 10 12 14 f.7 ______ ______ ______

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6.What is the 100 th 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 100 th term of the sequence. Term1 st 2 nd 3 rd 4 th 5 th 6 th 7 th 8th Value2581114172023 Formula22 +1x32 + 2x32 + 3x32 + 4x32 + 5x32 + 6x32 + 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 36 108 324 b.2 14 ________ 686

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Fill in the missing numbers in the following geometric sequences. a.4 12 36 108 324 b.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 36 108 324 b.2 14 98 686 c.2 6 18 54 162 d.5 ______ 20 ______ 80

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Fill in the missing numbers in the following geometric sequences. a.4 12 36 108 324 b.2 14 98 686 c.2 6 18 54 162 d.5 10 20 40 80

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Fill in the missing numbers in the following geometric sequences. a.4 12 36 108 324 b.2 14 98 686 c.2 6 18 54 162 d.5 10 20 40 80 e.0 ______ ______ ______

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Fill in the missing numbers in the following geometric sequences. a.4 12 36 108 324 b.2 14 98 686 c.2 6 18 54 162 d.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 PositionNumber of Letters Fifth5 Fourth25 Third125 Second Top 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 PositionNumber of Letters Fifth5 Fourth25 Third125 Second625 Top3125 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 BA and CA and DB and C B and DC and D If five students are in the group, the number of handshakes will be 10. A and BA and CA and DA and E B and CB and D B and EC and D C and ED 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 GroupNumber of Handshakes 21 33 46 510 6 7 8 9

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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 GroupNumber of Handshakes 21 33 46 510 615 721 828 936 1045

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Multiplication Practice

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MultiplicationDivisionBig Numbers 11223 21324 31425 415 516 617 718 819 920 1021 1122 3 x 4 2 x 12 8 x 9 7 x 7 11 x 9 5 x 7 6 x 8 7 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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MultiplicationDivisionBig Numbers 11223 21324 31425 415 516 617 718 819 920 1021 1122 12 24 72 49 99 35 48 42 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 32 x 51 1 st operation2 nd operation3 rd operation 3 x 515 2 x 5+3 x 1132 x 12 0 th operation1 st operation2 nd operation3 rd operation 15 13 02 1632

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34 x56 0 th operation1 st operation2 nd operation3 rd operation 15 38 24 1904

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81 x19 0 th operation1 st operation2 nd operation3 rd operation 08 73 09 1539

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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 = 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

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

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A Meaning for Squares

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

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My Swimming Pool 9 feet 9 Feet If 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 = 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

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

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

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Summary Linear Measure Square Measure Cubic Measure

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Identifying Perfect Squares and Perfect Cubes

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Identify the Perfect Square A.32 B.49 C.50 D.99 E.111

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Identify the Perfect Square A.10 B.24 C.39 D.81 E.156

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Identify the Perfect Square A.100 B.45 C.55 D.66 E.88

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Identify the Perfect Square A.32 B.48 C.56 D.66 E.121

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Identify the Perfect Cube A.4 B.9 C.36 D.64 E.100

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Identify the Perfect Cube A.16 B.25 C.27 D.144 E.200

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Identify the Perfect Cube A.800 B.900 C.1000 D.1200 E.1500

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Identify the Perfect Cube A.81 B.121 C.144 D.216 E.524

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Identify the Perfect Square A.200 B.300 C.400 D.500 E.600

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Identify the Perfect Cube A.2000 B.4000 C.6000 D.8000 E.10000

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Using Exponents 3535 Base Exponent

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Practice with Exponents 1.5 4 2.2 6 3.3 4 4.4 5 5.10 7 5x5x5x5 2x2x2x2x2x2 3x3x3x3 4x4x4x4x4 10x10x10x10x10x10x10 625 64 91 1024 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 #1 Choose 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

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