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2 x 1 = 2 x 1 = 22 Main Menu

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2 x 2 = 2 x 2 = 44 Main Menu

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2 x 3 = 2 x 3 = 66 Main Menu

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2 x 4 = 2 x 4 = 88 Main Menu

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2 x 5 = 2 x 5 = 1010 Main Menu

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2 x 6 = 2 x 6 = 1212 Main Menu

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2 x 7 = 2 x 7 = 1414 Main Menu

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2 x 8 = 2 x 8 = 1616 Main Menu

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2 x 9 = 2 x 9 = 1818 Main Menu

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2 x 10 = 2 x 10 = 2020 Main Menu

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3 x 1 = 3 x 1 = 33 Main Menu

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3 x 2 = 3 x 2 = 66 Main Menu

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3 x 3 = 3 x 3 = 99 Main Menu

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3 x 4 = 3 x 4 = 1212 Main Menu

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3 x 5 = 3 x 5 = 1515 Main Menu

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3 x 6 = 3 x 6 = 1818 Main Menu

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3 x 7 = 3 x 7 = 2121 Main Menu

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3 x 8 = 3 x 8 = 2424 Main Menu

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3 x 9 = 3 x 9 = 2727 Main Menu

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3 x 10 = 3 x 10 = 3030 Main Menu

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4 x 1 = 4 x 1 = 44 Main Menu

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4 x 2 = 4 x 2 = 88 Main Menu

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4 x 3 = 4 x 3 = 1212 Main Menu

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4 x 4 = 4 x 4 = 1616 Main Menu

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4 x 5 = 4 x 5 = 2020 Main Menu

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4 x 6 = 4 x 6 = 2424 Main Menu

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4 x 7 = 4 x 7 = 2828 Main Menu

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4 x 8 = 4 x 8 = 3232 Main Menu

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4 x 9 = 4 x 9 = 3636 Main Menu

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4 x 10 = 4 x 10 = 4040 Main Menu

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5 x 0 = 5 x 0 = 00 Main Menu

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5 x 1 = 5 x 1 = 55 Main Menu

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5 x 2 = 5 x 2 = 1010 Main Menu

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5 x 3 = 5 x 3 = 1515 Main Menu

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5 x 4 = 5 x 4 = 2020 Main Menu

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5 x 5 = 5 x 5 = 2525 Main Menu

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5 x 6 = 5 x 6 = 3030 Main Menu

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5 x 7 = 5 x 7 = 3535 Main Menu

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5 x 8 = 5 x 8 = 4040 Main Menu

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5 x 9 = 5 x 9 = 4545 Main Menu

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5 x 10 = 5 x 10 = 5050 Main Menu

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6 x 0 = 6 x 0 = 00 Main Menu

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6 x 1 = 6 x 1 = 66 Main Menu

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6 x 2 = 6 x 2 = 1212 Main Menu

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6 x 3 = 6 x 3 = 1818 Main Menu

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6 x 4 = 6 x 4 = 2424 Main Menu

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6 x 5 = 6 x 5 = 3030 Main Menu

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6 x 6 = 6 x 6 = 3636 Main Menu

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6 x 7 = 6 x 7 = 4242 Main Menu

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6 x 8 = 6 x 8 = 4848 Main Menu

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6 x 9 = 6 x 9 = 5454 Main Menu

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6 x 10 = 6 x 10 = Main Menu

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6 x 10 = 6 x 10 = 6060 Main Menu

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7 x 0 = 7 x 0 = 00 Main Menu

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7 x 1 = 7 x 1 = 77 Main Menu

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7 x 2 = 7 x 2 = 1414 Main Menu

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7 x 3 = 7 x 3 = 2121 Main Menu

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7 x 4 = 7 x 4 = 2828 Main Menu

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7 x 5 = 7 x 5 = 3535 Main Menu

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7 x 6 = 7 x 6 = 4242 Main Menu

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7 x 7 = 7 x 7 = 4949 Main Menu

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7 x 8 = 7 x 8 = 5656 Main Menu

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7 x 9 = 7 x 9 = 6363 Main Menu

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7 x 10 = 7 x 10 = Main Menu

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7 x 10 = 7 x 10 = 7070 Main Menu

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8 x 0 = 8 x 0 = 00 Main Menu

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8 x 1 = 8 x 1 = 88 Main Menu

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8 x 2 = 8 x 2 = 1616 Main Menu

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8 x 3 = 8 x 3 = 2424 Main Menu

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8 x 4 = 8 x 4 = 3232 Main Menu

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8 x 5 = 8 x 5 = 4040 Main Menu

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8 x 6 = 8 x 6 = 4848 Main Menu

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8 x 7 = 8 x 7 = 5656 Main Menu

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8 x 8 = 8 x 8 = 6464 Main Menu

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8 x 9 = 8 x 9 = 7272 Main Menu

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8 x 10 = 8 x 10 = Main Menu

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8 x 10 = 8 x 10 = 8080 Main Menu

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9 x 0 = 9 x 0 = 00 Main Menu

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9 x 1 = 9 x 1 = 99 Main Menu

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9 x 2 = 9 x 2 = 1818 Main Menu

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9 x 3 = 9 x 3 = 2727 Main Menu

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9 x 4 = 9 x 4 = 3636 Main Menu

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9 x 5 = 9 x 5 = 4545 Main Menu

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9 x 6 = 9 x 6 = 5454 Main Menu

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9 x 7 = 9 x 7 = 6363 Main Menu

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9 x 8 = 9 x 8 = 7272 Main Menu

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9 x 9 = 9 x 9 = 8181 Main Menu

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9 x 10 = 9 x 10 = Main Menu

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9 x 10 = 9 x 10 = 9090 Main Menu

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10 x 0 = 10 x 0 = 00 Main Menu

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10 x 1 = 10 x 1 = 1010 Main Menu

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10 x 2 = 10 x 2 = Main Menu

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10 x 2 = 10 x 2 = 2020 Main Menu

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10 x 3 = 10 x 3 = Main Menu

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10 x 3 = 10 x 3 = 3030 Main Menu

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10 x 4 = 10 x 4 = Main Menu

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10 x 4 = 10 x 4 = 4040 Main Menu

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10 x 5 = 10 x 5 = Main Menu

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10 x 5 = 10 x 5 = 5050 Main Menu

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10 x 6 = 10 x 6 = Main Menu

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10 x 6 = 10 x 6 = 6060 Main Menu

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10 x 7 = 10 x 7 = Main Menu

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10 x 7 = 10 x 7 = 7070 Main Menu

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10 x 8 = 10 x 8 = Main Menu

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10 x 8 = 10 x 8 = 8080 Main Menu

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10 x 9 = 10 x 9 =

Main Menu

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10 x 9 = 10 x 9 = 9090 Main Menu

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10x10 = 10x10 = Main Menu

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10x10 = 10x10 = 100100 Main Menu

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1111x 3x 3 3333


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1212x 1x 1 1212


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1212x 2x 2 2424


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1212x 3x 3 3636


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1212x 4x 4 4848


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1212x 5x 5 6060


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1212x 6x 6

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1212x 6x 6 7272


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1212x 7x 7

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1212x 7x 7 8484


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1212x 8x 8

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1212x 8x 8 9696


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1212x 9x 9108108


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1212x10x10120120


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1313x 1x 1 1313


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1313x 2x 2 2626


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1313x 3x 3 3939


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1313x 4x 4 5252


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1313x 5x 5 6565


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1313x 6x 6 7878


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1313x 7x 7 9191


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1313x 9x 9117117


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1414x 0x 0


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1414x 1x 1

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1414x 1x 1 1414


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1414x 2x 2 2828


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1414x 3x 3

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1414x 3x 3 4242


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1414x 4x 4

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1414x 4x 4 5656


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1414x 5x 5

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1414x 5x 5 7070


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1414x 6x 6

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1414x 6x 6 8484


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1414x 7x 7

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1414x 7x 7 9898


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1414x 8x 8

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1414x 9x 9

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1414x 9x 9126126


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1414x10x10140140


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1515x 0x 0


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1515x 1x 1

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1515x 1x 1 1515


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1515x 2x 2

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1515x 2x 2 3030


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1515x 3x 3

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1515x 3x 3 4545


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1515x 4x 4

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1515x 4x 4 6060


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1515x 5x 5

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1515x 5x 5 7575


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1515x 6x 6

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1515x 6x 6 9090


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1515x 7x 7

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1515x 7x 7105105


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1515x 8x 8120120


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1515x 9x 9135135


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1515x10x10150150


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6 x 7 = 6 x 7 =

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Main Menu

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6 x 7 = 6 x 7 = 4242

STOPSTOP


MDPSTOPSTOP


8 x 6 = 8 x 6 = 4848 Main Menu

MDPSTOPSTOP


MDPSTOPSTOP


9 x 8 = 9 x 8 = 7272 Main Menu

MDPSTOPSTOP


MDPSTOPSTOP


5 x 7 = 5 x 7 = 3535 Main Menu

MDPSTOPSTOP


MDPSTOPSTOP


6 x 4 = 6 x 4 = 2424 Main Menu

MDPSTOPSTOP


MDPSTOPSTOP


9 x 9 = 9 x 9 = 8181 Main Menu

MDPSTOPSTOP


MDPSTOPSTOP


7 x 9 = 7 x 9 = 6363 Main Menu

MDPSTOPSTOP


MDPSTOPSTOP


1 x 6 = 1 x 6 = 66 Main Menu

MDPSTOPSTOP


MDPSTOPSTOP


8 x 4 = 8 x 4 = 3232 Main Menu

MDPSTOPSTOP


MDPSTOPSTOP


4 x 3 = 4 x 3 = 1212 Main Menu

MDPSTOPSTOP


MDPSTOPSTOP


7 x 4 = 7 x 4 = 2828 Main Menu

MDPSTOPSTOP


MDPSTOPSTOP


6 x 5 = 6 x 5 = 3030 Main Menu

MDPSTOPSTOP


MDPSTOPSTOP


2 x 9 = 2 x 9 = 1818 Main Menu

MDPSTOPSTOP


MDPSTOPSTOP


3 x 6 = 3 x 6 = 1818 Main Menu

MDPSTOPSTOP


MDPSTOPSTOP


7 x 6 = 7 x 6 = 4242 Main Menu

MDPSTOPSTOP


MDPSTOPSTOP


8 x 5 = 8 x 5 = 4040 Main Menu

MDPSTOPSTOP


MDPSTOPSTOP


7 x 8 = 7 x 8 = 5656 Main Menu

MDPSTOPSTOP


MDPSTOPSTOP


3 x 8 = 3 x 8 = 2424 Main Menu

MDPSTOPSTOP


MDPSTOPSTOP


4 x 0 = 4 x 0 = 00 Main Menu

MDPSTOPSTOP


MDPSTOPSTOP


9 x 4 = 9 x 4 = 3636 Main Menu

MDPSTOPSTOP


MDPSTOPSTOP


8 x 9 = 8 x 9 = 7272 Main Menu

MDPSTOPSTOP


MDPSTOPSTOP


9 x 6 = 9 x 6 = 5454 Main Menu

MDPSTOPSTOP


MDPSTOPSTOP


7 x 2 = 7 x 2 = 1414 Main Menu

MDPSTOPSTOP


MDPSTOPSTOP


8 x 7 = 8 x 7 = 5656 Main Menu

MDPSTOPSTOP


MDPSTOPSTOP


8 x 3 = 8 x 3 = 2424 Main Menu

MDPSTOPSTOP

9 x 10 = 9 x 10 = Main Menu

MDPSTOPSTOP


9 x 10 = 9 x 10 = 9090 Main Menu

MDPSTOPSTOP


MDPSTOPSTOP


5 x 9 = 5 x 9 = 4545 Main Menu

MDPSTOPSTOP


MDPSTOPSTOP


9 x 7 = 9 x 7 = 6363 Main Menu

MDPSTOPSTOP

8 x 10 = 8 x 10 = Main Menu

MDPSTOPSTOP


8 x 10 = 8 x 10 = 8080 Main Menu

MDPSTOPSTOP


MDPSTOPSTOP


7 x 0 = 7 x 0 = 00 Main Menu

MDPSTOPSTOP


MDPSTOPSTOP


9 x 2 = 9 x 2 = 1818 Main Menu

MDPSTOPSTOP


MDPSTOPSTOP


7 x 3 = 7 x 3 = 2121 Main Menu

MDPSTOPSTOP


MDPSTOPSTOP


9 x 5 = 9 x 5 = 4545 Main Menu

MDPSTOPSTOP


MDPSTOPSTOP


7 x 7 = 7 x 7 = 4949 Main Menu

MDPSTOPSTOP


MDPSTOPSTOP


2 x 7 = 2 x 7 = 1414 Main Menu

MDPSTOPSTOP


MDPSTOPSTOP


8 x 1 = 8 x 1 = 88 Main Menu

MDPSTOPSTOP


MDPSTOPSTOP


9 x 3 = 9 x 3 = 2727 Main Menu

MDPSTOPSTOP


MDPSTOPSTOP


4 x 4 = 4 x 4 = 1616 Main Menu

MDPSTOPSTOP

Main Menu

Main Menu

Division Division Drill PracticeDrill Practice

Division Division Drill PracticeDrill Practice

Level I Level II

STOPSTOP

16 16 ÷ 4÷ 4 = = Main Menu

DDP


STOPSTOP

16 16 ÷ 4÷ 4 = = 44 Main Menu

DDP


STOPSTOP

72 72 ÷ 8÷ 8 = = Main Menu

DDPSTOPSTOP

72 72 ÷ 8÷ 8 = = 99 Main Menu

DDPSTOPSTOP

64 64 ÷ 8÷ 8 = = Main Menu

DDPSTOPSTOP

64 64 ÷ 8÷ 8 = = 88 Main Menu

DDPSTOPSTOP

42 42 ÷ 7÷ 7 = = Main Menu

DDPSTOPSTOP

42 42 ÷ 7÷ 7 = = 66 Main Menu

DDPSTOPSTOP

36 36 ÷ 4÷ 4 = = Main Menu

DDPSTOPSTOP

36 36 ÷ 4÷ 4 = = 99 Main Menu

DDPSTOPSTOP

54 54 ÷ 9÷ 9 = = Main Menu

DDPSTOPSTOP

54 54 ÷ 9÷ 9 = = 66 Main Menu

DDPSTOPSTOP

49 49 ÷ 7÷ 7 = = Main Menu

DDPSTOPSTOP

49 49 ÷ 7÷ 7 = = 77 Main Menu

DDPSTOPSTOP

18 18 ÷ 3÷ 3 = = Main Menu

DDPSTOPSTOP

18 18 ÷ 3÷ 3 = = 66 Main Menu

DDPSTOPSTOP

27 27 ÷ 3÷ 3 = = Main Menu

DDPSTOPSTOP

27 27 ÷ 3÷ 3 = = 99 Main Menu

DDPSTOPSTOP

63 63 ÷ 7÷ 7 = = Main Menu

DDPSTOPSTOP

63 63 ÷ 7÷ 7 = = 99 Main Menu

DDPSTOPSTOP

12 12 ÷ 4÷ 4 = = Main Menu

DDPSTOPSTOP

12 12 ÷ 4÷ 4 = = 33 Main Menu

DDPSTOPSTOP

24 24 ÷ 6÷ 6 = = Main Menu

DDPSTOPSTOP

24 24 ÷ 6÷ 6 = = 44 Main Menu

DDPSTOPSTOP

56 56 ÷ 7÷ 7 = = Main Menu

DDPSTOPSTOP

56 56 ÷ 7÷ 7 = = 88 Main Menu

DDPSTOPSTOP

48 48 ÷ 8÷ 8 = = Main Menu

DDPSTOPSTOP

48 48 ÷ 8÷ 8 = = 66 Main Menu

DDPSTOPSTOP

28 28 ÷ 4÷ 4 = = Main Menu

DDP

“Click” to go to Level II“Click” to go to Level II

STOPSTOP

28 28 ÷ 4÷ 4 = = 77 Main Menu

DDP

“Click” to go to Level II“Click” to go to Level II

STOPSTOP

39 39 ÷ 3÷ 3 = = Main Menu

DDP


STOPSTOP

39 39 ÷ 3÷ 3 = = 1313 Main Menu

DDP


STOPSTOP

99 99 ÷ 11÷ 11 = = Main Menu

DDPSTOPSTOP

99 99 ÷ 11÷ 11 = = 99 Main Menu

DDPSTOPSTOP

78 78 ÷ 3÷ 3 = = 78 78 ÷ 3÷ 3 = = Main Menu

DDPSTOPSTOP

78 78 ÷ 3÷ 3 = = 78 78 ÷ 3÷ 3 = = 2626 Main Menu

DDPSTOPSTOP

51 51 ÷ 3÷ 3 = = Main Menu

DDPSTOPSTOP

51 51 ÷ 3÷ 3 = = 1717 Main Menu

DDPSTOPSTOP

93 93 ÷ 3÷ 3 = = Main Menu

DDPSTOPSTOP

93 93 ÷ 3÷ 3 = = 3131 Main Menu

DDPSTOPSTOP

60 60 ÷ 12÷ 12 = = Main Menu

DDPSTOPSTOP

60 60 ÷ 12÷ 12 = = 55 Main Menu

DDPSTOPSTOP

74 74 ÷ 2÷ 2 = = Main Menu

DDPSTOPSTOP

74 74 ÷ 2÷ 2 = = 3737 Main Menu

DDPSTOPSTOP

57 57 ÷ 3÷ 3 = = Main Menu

DDPSTOPSTOP

57 57 ÷ 3÷ 3 = = 1919 Main Menu

DDPSTOPSTOP

48 48 ÷ 4÷ 4 = = Main Menu

DDPSTOPSTOP

48 48 ÷ 4÷ 4 = = 1212 Main Menu

DDPSTOPSTOP

60 60 ÷ 4÷ 4 = = Main Menu

DDPSTOPSTOP

60 60 ÷ 4÷ 4 = = 1515 Main Menu

DDPSTOPSTOP

60 60 ÷ 10÷ 10 = = Main Menu

DDPSTOPSTOP

60 60 ÷ 10÷ 10 = = 66 Main Menu

DDPSTOPSTOP

70 70 ÷ 2÷ 2 = = Main Menu

DDPSTOPSTOP

70 70 ÷ 2÷ 2 = = 3535 Main Menu

DDPSTOPSTOP

36 36 ÷ 12÷ 12 = = Main Menu

DDPSTOPSTOP

36 36 ÷ 12÷ 12 = = 33 Main Menu

DDPSTOPSTOP

64 64 ÷ 2÷ 2 = = Main Menu

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64 64 ÷ 2÷ 2 = = 3232 Main Menu

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90 90 ÷ 2÷ 2 = = Main Menu

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90 90 ÷ 2÷ 2 = = 4545 Main Menu

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AcuteAngle

AcuteAngle DiameterDiameterCongruent

Figures

CongruentFigures

CompositeNumber

CompositeNumberAreaArea

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EquilateralTriangle

IsoscelesTriangle

IsoscelesTriangle

GreatestCommon

Factor

GreatestCommon

FactorFactorsFactorsExpanded

Form

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AACUTE CUTE AANGLENGLE – – An angle with a measure less An angle with a measure less than 90°than 90°

AACUTE CUTE AANGLENGLE – – An angle with a measure less An angle with a measure less than 90°than 90°

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This angle is an acute angle because it is smaller than a “right” angle (90°).

AAREAREA – – The number of square units needed to The number of square units needed to cover a regioncover a region

AAREAREA – – The number of square units needed to The number of square units needed to cover a regioncover a region

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6 inches6 inches

4 inches4 inches

Since this rectangle is 6 inches by 4 inches, the Since this rectangle is 6 inches by 4 inches, the areaarea is 24 inches squared (or 24 in²) is 24 inches squared (or 24 in²)

CCOMPOSITE OMPOSITE NNUMBERUMBER – – A whole number A whole number greater than one that has more than two factorsgreater than one that has more than two factors

CCOMPOSITE OMPOSITE NNUMBERUMBER – – A whole number A whole number greater than one that has more than two factorsgreater than one that has more than two factors

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36 and 24 are examples of composite numbers because they each have more than two factors.

36:

24:

36 and 24 are examples of composite numbers because they each have more than two factors.

36:

24: 1, 2, 3, 4, 6, 9, 12, 18, 36

1, 2, 3, 4, 6, 8, 12, 24

CCONGRUENT ONGRUENT FFIGURESIGURES – – Figures that have Figures that have the same size and shapethe same size and shape

CCONGRUENT ONGRUENT FFIGURESIGURES – – Figures that have Figures that have the same size and shapethe same size and shape

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These two items are congruent because they have the exact same shape and size.

These two items are congruent because they have the exact same shape and size.

These two items are not congruent because they do not have the exact same shape and size.

These two items are not congruent because they do not have the exact same shape and size.

DDIAMETERIAMETER – – A line segment that passes through A line segment that passes through the center of a circle and has both endpoints on the the center of a circle and has both endpoints on the circlecircle

DDIAMETERIAMETER – – A line segment that passes through A line segment that passes through the center of a circle and has both endpoints on the the center of a circle and has both endpoints on the circlecircle

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This is the diameter of the circle.This is the diameter of the circle.

EEQUILATERAL TRIANGLEQUILATERAL TRIANGLE – A triangle with all – A triangle with all sides and angles equalsides and angles equal

EEQUILATERAL TRIANGLEQUILATERAL TRIANGLE – A triangle with all – A triangle with all sides and angles equalsides and angles equal

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All angles All angles measure measure

60°,60°,and each and each side has side has the exact the exact

same same length.length.

60° 60°

60°

EEXPANDED FORMXPANDED FORM –– A number written as the A number written as the sum of the values of its digitssum of the values of its digits

EEXPANDED FORMXPANDED FORM –– A number written as the A number written as the sum of the values of its digitssum of the values of its digits

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1,368,902 =1,368,902 =

56,923 =56,923 =

4,978 =4,978 =

39 = 39 =

The The expanded formexpanded form of each number is highlighted below. of each number is highlighted below.

30 + 9

4,000 + 900 + 70 + 8

50,000 + 6,000 + 900 + 20 + 3

1,000,000 + 300,000 + 60,000 + 8,000 + 900 + 2

FFACTORSACTORS – The numbers that are multiplied to give – The numbers that are multiplied to give a producta product

FFACTORSACTORS – The numbers that are multiplied to give – The numbers that are multiplied to give a producta product

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15 x 7 = 10515 x 7 = 105

In a multiplication problem, the In a multiplication problem, the factorsfactors are the are the numbers that are multiplied to get a product.numbers that are multiplied to get a product.15 & 7 are both 15 & 7 are both factorsfactors in this problem. in this problem.

20:20:

FactorsFactors for a given number are often listed in order for a given number are often listed in order from least to greatest. The from least to greatest. The factorsfactors for 20 are for 20 are highlighted below.highlighted below.

1, 2, 4, 5, 10, 20

GGREATESTREATEST C COMMONOMMON F FACTOR (GCF)ACTOR (GCF) –– The greatest number that is a factor of each of two or The greatest number that is a factor of each of two or more numbersmore numbers

GGREATESTREATEST C COMMONOMMON F FACTOR (GCF)ACTOR (GCF) –– The greatest number that is a factor of each of two or The greatest number that is a factor of each of two or more numbersmore numbers

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15: 1, 3, 5, 15

18: 1, 2, 3, 6, 9, 18

27: 1, 3, 9, 27

15: 1, 3, 5, 15

18: 1, 2, 3, 6, 9, 18

27: 1, 3, 9, 27

Common factors of 15, 18 and 27 are Common factors of 15, 18 and 27 are shown in red. 3 is the shown in red. 3 is the greatest greatest common factorcommon factor and is circled. and is circled.

IISOSCELES SOSCELES TTRIANGLERIANGLE – – A triangle with two A triangle with two congruent sidescongruent sides

IISOSCELES SOSCELES TTRIANGLERIANGLE – – A triangle with two A triangle with two congruent sidescongruent sides

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Two sides are Two sides are exactly the exactly the same length in same length in an an isosceles isosceles triangletriangle..

6 cm 6 cm

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LeastCommon

Denominator

LeastCommon

DenominatorMedianMedianMeanMeanMaximumMaximum

LeastCommonMultiple

LeastCommonMultiple

MinimumMinimum ObtuseAngle

ObtuseAngle

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NegativeNumberMultipleMultipleModeMode

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LLEAST EAST CCOMMON OMMON DDENOMINATOR (LCD)ENOMINATOR (LCD) – – The least common multiple of the denominators of two or more fractions

LLEAST EAST CCOMMON OMMON DDENOMINATOR (LCD)ENOMINATOR (LCD) – – The least common multiple of the denominators of two or more fractions

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In order to solve the problem 3/4 + 5/8, you must first find a common denominator. In this example we will find the LCD. Since “8” is the lowest shared multiple of the denominators (4 & 8), it is the LCD. To change the 4 to an 8, we must multiply by 2. Notice in the example that the numerator is also multiplied by 2. This is because whatever you do to the denominator, you must also do to the numerator.

In order to solve the problem 3/4 + 5/8, you must first find a common denominator. In this example we will find the LCD. Since “8” is the lowest shared multiple of the denominators (4 & 8), it is the LCD. To change the 4 to an 8, we must multiply by 2. Notice in the example that the numerator is also multiplied by 2. This is because whatever you do to the denominator, you must also do to the numerator.

Fractions with different denominators CANNOT be added together without first finding a common denominator. Fractions with different denominators CANNOT be added together without first finding a common denominator.

3 x 2 = 6

4 x 2 = 8

+

5 5

8 8

11

8

3 x 2 = 6

4 x 2 = 8

+

5 5

8 8

11

8

=

or 1 3/8

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LLEAST EAST CCOMMON OMMON MMULTIPLEULTIPLE – – The least common number, other than zero, that is a multiple of each of two or more numbers

LLEAST EAST CCOMMON OMMON MMULTIPLEULTIPLE – – The least common number, other than zero, that is a multiple of each of two or more numbers

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5: 5, 10, 15, 20, 25, 30, 35

6: 6, 12, 18, 24, 30, 36, 42

3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30

5: 5, 10, 15, 20, 25, 30, 35

6: 6, 12, 18, 24, 30, 36, 42

3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30

30 is the least common multiple and is shown in red.

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MMAXIMUMAXIMUM – – the largest or highest amount; greatest amount possible

MMAXIMUMAXIMUM – – the largest or highest amount; greatest amount possible

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There are only 25

seats on the bus, so the maximum allowable number of passengers

is 25.

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MMEANEAN – – the average of the numbers in a set of data

MMEANEAN – – the average of the numbers in a set of data

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Mr. Johnson’s math class received the following scores on their chapter test: 95, 75, 88, 100, 63 and 89. To calculate the mean, complete the following steps:

Mr. Johnson’s math class received the following scores on their chapter test: 95, 75, 88, 100, 63 and 89. To calculate the mean, complete the following steps:

1. Add up all of the numbers (scores)95+75+88+100+63+89=510

1. Add up all of the numbers (scores)95+75+88+100+63+89=510

2. Divide the sum (510) by the number of scores (6).510 6 = 85

The mean (or average) test score is 85

2. Divide the sum (510) by the number of scores (6).510 6 = 85

The mean (or average) test score is 85

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MMEDIANEDIAN – – The middle number, or average of the two middle numbers, in a collection of data when the data are arranged in order

MMEDIANEDIAN – – The middle number, or average of the two middle numbers, in a collection of data when the data are arranged in order

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The following numbers are the ages of seven individuals in a room: 66, 3, 14, 19, 9, 5, 59

The following numbers are the ages of seven individuals in a room: 66, 3, 14, 19, 9, 5, 59

To find the median age, you must first list the numbers in order:3, 5, 9, 14, 19, 59, 66

To find the median age, you must first list the numbers in order:3, 5, 9, 14, 19, 59, 66

Next, simply find the number that is in the middle position. The median age here is 14 because there are 3 people that are younger (3, 5, & 9), and there are three people that are older (19, 59 & 66).3, 5, 9, 14, 19, 59, 66

Next, simply find the number that is in the middle position. The median age here is 14 because there are 3 people that are younger (3, 5, & 9), and there are three people that are older (19, 59 & 66).3, 5, 9, 14, 19, 59, 66

MMINIMUMINIMUM – – the least possible amountMMINIMUMINIMUM – – the least possible amount

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The roller coaster will not leave its station unless it has at least 15 passengers.

The roller coaster will not leave its station unless it has at least 15 passengers.

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In other words, the minimum number of passengers that can ride the roller coaster is 15.

In other words, the minimum number of passengers that can ride the roller coaster is 15.

MMODEODE – – The number or numbers that occur most often in a set of data

MMODEODE – – The number or numbers that occur most often in a set of data

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Mr. Johnson’s students went on a nature field trip, and each student recorded the number of wild animals that they saw. Their results are listed below:

9, 7, 6, 11, 9, 5, 8, 9, 13, 9, 4, 5, 6, 8, 7, 9

Mr. Johnson’s students went on a nature field trip, and each student recorded the number of wild animals that they saw. Their results are listed below:

9, 7, 6, 11, 9, 5, 8, 9, 13, 9, 4, 5, 6, 8, 7, 9

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“9” was the most common response, so the mode is 9. “9” was the most common response, so the mode is 9.

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MMULTIPLEULTIPLE – – The product of a whole number and any other whole number

MMULTIPLEULTIPLE – – The product of a whole number and any other whole number

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6 x 8 = 48 6 x 8 = 48

48 is a multiple of both 6 and 8. It is considered a multiple because each of the numbers above (6 & 8) “go into” 48. Other multiples of 6 and 8 are listed below.

48 is a multiple of both 6 and 8. It is considered a multiple because each of the numbers above (6 & 8) “go into” 48. Other multiples of 6 and 8 are listed below.

6 : 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 64 …

8 : 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88 …

6 : 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 64 …

8 : 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88 …

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NNEGATIVEEGATIVE N NUMBERUMBER – – A number whose value is less than zero

NNEGATIVEEGATIVE N NUMBERUMBER – – A number whose value is less than zero

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The numbers to the left of zero (0) on a number line are considered negative numbers. They each have a value that is less than zero.

The numbers to the left of zero (0) on a number line are considered negative numbers. They each have a value that is less than zero.

0 1 2 3 4 5 6 7 8-7 -6 -5 -4 -3 -2 -1

Negative numbers

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OOBTUSEBTUSE A ANGLE NGLE – – An angle with a measure greater than 90° but less than 180°

OOBTUSEBTUSE A ANGLE NGLE – – An angle with a measure greater than 90° but less than 180°

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This angle is an obtuse angle because it is greater than a “right” angle (90°).

This angle is an obtuse angle because it is greater than a “right” angle (90°).

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ParallelLines

ParallelLines PerpendicularPerpendicularPerimeterPerimeterPatternsPatternsParallelogramParallelogram

PolygonPolygon QuadrilateralQuadrilateralProbabilityProbabilityPrimeNumbers

PrimeNumbers

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PPARALLEL ARALLEL LLINESINES – Lines in the same plane that never intersect

PPARALLEL ARALLEL LLINESINES – Lines in the same plane that never intersect

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If extended, these lines would never intersect, so they are parallel lines.

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PPARALLELOGRAMARALLELOGRAM – – A quadrilateral with each pair of opposite sides parallel and congruent

PPARALLELOGRAMARALLELOGRAM – – A quadrilateral with each pair of opposite sides parallel and congruent

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Side A

Side B

Sid

e C

Side

D

Sides A and B are congruent and parallel to one another, and Sides C and D are congruent and parallel to one another.

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PPATTERNATTERN – An arrangement of items or objects (colors, shapes, numbers etc…) that continues or can be predicted

PPATTERNATTERN – An arrangement of items or objects (colors, shapes, numbers etc…) that continues or can be predicted

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Different examples of patterns are shown below.Different examples of patterns are shown below.

A, B, C, B, A, B, C, B, A, B, C, B, A, B, C, B …

1, 2, 4, 7, 11, 16, 22, 29, 37, 46, 56, 67, 79 …

EXAMPLE 1

EXAMPLE 2

EXAMPLE 3

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PPERIMETERERIMETER – The distance around a polygonPPERIMETERERIMETER – The distance around a polygon

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Each side of this hexagon is 4 units long. If you add up all of the sides, you get a perimeter of 24 units.

4 units

A

B

CD

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PPERPENDICULARERPENDICULAR – lines, or line segments, that intersect at right (90°) angles

PPERPENDICULARERPENDICULAR – lines, or line segments, that intersect at right (90°) angles

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AB and DC are perpendicular because they intersect at a 90° angle.

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PPOLYGONOLYGON – A closed plane figure with line segments as sides

PPOLYGONOLYGON – A closed plane figure with line segments as sides

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Examples of some common polygons are shown below.Examples of some common polygons are shown below.

triangle

quadrilateral

pentagon

hexagon

octagon

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PPRIME RIME NNUMBERSUMBERS – A whole number greater than 1 with only two factors – itself and 1

PPRIME RIME NNUMBERSUMBERS – A whole number greater than 1 with only two factors – itself and 1

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17 and 31 are examples of prime numbers because they each have only two factors.

17:

31:

17 and 31 are examples of prime numbers because they each have only two factors.

17:

31:

1, 17

1, 31

Other common prime numbers are:2, 3, 5, 7, 11, 13, 19, 23, 29, 37, 43

Other common prime numbers are:2, 3, 5, 7, 11, 13, 19, 23, 29, 37, 43

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PPROBABILITYROBABILITY – The ratio of the number of favorable outcomes to all outcomes of an experiment (usually expressed as a fraction)

PPROBABILITYROBABILITY – The ratio of the number of favorable outcomes to all outcomes of an experiment (usually expressed as a fraction)

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The probability of rolling a “5” is 1/6 (1 out of 6).

The probability of rolling a “5” is 1/6 (1 out of 6).

The probability of this coin landing on “heads” is 1/2

(1 out of 2).

The probability of this coin landing on “heads” is 1/2

(1 out of 2).

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QQUADRILATERALUADRILATERAL – A polygon with four sidesQQUADRILATERALUADRILATERAL – A polygon with four sides

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Examples of some common quadrilaterals are shown below.Examples of some common quadrilaterals are shown below.

square rectangle

rhombus trapezoid

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RangeRange ScaleneTriangle

ScaleneTriangle

RightTriangle

RightTriangle

RightAngle

RightAngle

SimilarFigures

SimilarFigures

TrapezoidTrapezoidTessellationTessellationSymmetricalSymmetrical VolumeVolumeTriangleTriangle

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RRANGEANGE – The difference between the greatest and least numbers in a set of data

RRANGEANGE – The difference between the greatest and least numbers in a set of data

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Mrs. Stevens had her students record their height (in inches) on a piece of paper. Their heights are listed below:61”, 58”, 49”, 55”, 58”, 65”, 60”, 59”, 57”, and 62”

Mrs. Stevens had her students record their height (in inches) on a piece of paper. Their heights are listed below:61”, 58”, 49”, 55”, 58”, 65”, 60”, 59”, 57”, and 62”

To find the range, simply subtract the smallest number (49”) from the largest number (65”). 65 - 49 = 16, so the range of this set of data is 16”.

To find the range, simply subtract the smallest number (49”) from the largest number (65”). 65 - 49 = 16, so the range of this set of data is 16”.

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RRIGHT IGHT AANGLENGLE – An angle that measures 90°RRIGHT IGHT AANGLENGLE – An angle that measures 90°

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The measure of this angle is 90°, so it is considered a right angle.

The measure of this angle is 90°, so it is considered a right angle.

This square denotes a 90° angle.

Can you think of any capital letters in the alphabet that have

90° angles?

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RRIGHT IGHT TTRIANGLERIANGLE – A triangle with one right angle

RRIGHT IGHT TTRIANGLERIANGLE – A triangle with one right angle

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It is not possible for a triangle to have more than one right angle.

It is not possible for a triangle to have more than one right angle.

This triangle has a 90° angle (or a right

angle), so it is considered a right

triangle.

Did you know?

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SSCALENECALENE T TRIANGLERIANGLE – A triangle that has no congruent sides

SSCALENECALENE T TRIANGLERIANGLE – A triangle that has no congruent sides

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In a scalene triangle, each side is a different length.In a scalene triangle, each side is a different length.

10 cm

8 cm

4 cm

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SSIMILAR IMILAR FFIGURESIGURES – Figures that have the same shape but not necessary the same size

SSIMILAR IMILAR FFIGURESIGURES – Figures that have the same shape but not necessary the same size

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These two items are similar figures because they are the same shape, but not the same size.

These two items are similar figures because they are the same shape, but not the same size.

These two items are not similar figures because they are not even the same shape.

These two items are not similar figures because they are not even the same shape.

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SSYMMETRICALYMMETRICAL – A figure that can be folded along a line so that the two resulting parts match exactly

SSYMMETRICALYMMETRICAL – A figure that can be folded along a line so that the two resulting parts match exactly

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The items shown below are symmetrical. The lines that they can be folded along are called “lines of symmetry” (shown as dotted lines).

The items shown below are symmetrical. The lines that they can be folded along are called “lines of symmetry” (shown as dotted lines).

This item can be folded four different ways.

This item can be folded four different ways.

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TTESSELLATIONESSELLATION – An arrangement of congruent figures in a plane in such a way that no figures overlap, and there are no gaps

TTESSELLATIONESSELLATION – An arrangement of congruent figures in a plane in such a way that no figures overlap, and there are no gaps

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The pattern that you see in the background is a tessellation because each of the triangles are congruent to one another, there are no gaps between them, and they do not overlap.

The pattern that you see in the background is a tessellation because each of the triangles are congruent to one another, there are no gaps between them, and they do not overlap.

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TTRAPEZOIDRAPEZOID – A quadrilateral with only one pair of opposite sides parallel

TTRAPEZOIDRAPEZOID – A quadrilateral with only one pair of opposite sides parallel

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The following shapes are trapezoids because they each have only one pair of opposites sides that are parallel.

The following shapes are trapezoids because they each have only one pair of opposites sides that are parallel.

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TTRIANGLERIANGLE – A polygon with three sidesTTRIANGLERIANGLE – A polygon with three sides

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Not all triangles look the same. The following are just a few examples of what triangles could look like:

Not all triangles look the same. The following are just a few examples of what triangles could look like:

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VVOLUMEOLUME – The number of cubic units that fit inside a “space figure”

VVOLUMEOLUME – The number of cubic units that fit inside a “space figure”

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A space figure is often referred to as a “3-dimensional object.”A space figure is often referred to as a “3-dimensional object.”

This space figure is made up of 72 cubes, so it has a volume of 72 cubic units (72 units³).

Helpful HintsHelpful HintsHelpful HintsHelpful Hints

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Parents, the following are practical ways for you to help your child to be more successful on their 5th grade standardized tests:

Don’t wait until testing time to talk to your student about the importance of doing their best.

Don’t wait until testing time to talk to your student about the importance of doing their best.

Establish a time and a place that homework should be done each day.Establish a time and a place that homework should be done each day.

Make every effort to attend school functions such as Open House, Back to School Night etc…

Make every effort to attend school functions such as Open House, Back to School Night etc…

Schedule at least one Parent / Teacher conference to discuss your child’s strengths and weaknesses. Ask what you can do at home to help your child to be as successful as possible.

Schedule at least one Parent / Teacher conference to discuss your child’s strengths and weaknesses. Ask what you can do at home to help your child to be as successful as possible.

Assist your child with their homework when appropriate. Don’t do it for them, but offer advice and encouragement. Keep the tone positive, and try to help develop a strong work ethic. ☺

Assist your child with their homework when appropriate. Don’t do it for them, but offer advice and encouragement. Keep the tone positive, and try to help develop a strong work ethic. ☺

Communicate with your child’s teacher(s). Find out when tests are scheduled, and help your child prepare for them.

Communicate with your child’s teacher(s). Find out when tests are scheduled, and help your child prepare for them.

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Students, the following may help you when the time comes to take your fifth grade standardized tests:

ASK QUESTIONS!!! If you don’t understand something, there’s a good chance that others are also confused.

ASK QUESTIONS!!! If you don’t understand something, there’s a good chance that others are also confused.

Keep your school materials organized during the year. Your teacher and your parents can assist you if you need help.

Keep your school materials organized during the year. Your teacher and your parents can assist you if you need help.

Make sure that you write down homework assignments accurately. If you forget part of an assignment, call a friend for details. You’ll be glad you did.

Make sure that you write down homework assignments accurately. If you forget part of an assignment, call a friend for details. You’ll be glad you did.

Do your best on every homework assignment. Don’t blow an opportunity to better understand a concept just so that you can play ball or video games. If you are truly stuck on something, do your best, and ask your parents or teacher about it as soon as you are able.

Do your best on every homework assignment. Don’t blow an opportunity to better understand a concept just so that you can play ball or video games. If you are truly stuck on something, do your best, and ask your parents or teacher about it as soon as you are able.

Take advantage of any extra help that you can get at home or school. Even when you think you fully comprehend a concept, you may be able to learn more about it.

Take advantage of any extra help that you can get at home or school. Even when you think you fully comprehend a concept, you may be able to learn more about it.

55thth Grade Grade Skills ReviewSkills Review55thth Grade Grade

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Get your scrap paper ready! Get your scrap paper ready! “Click” on a link above to go to “Click” on a link above to go to worksheets for each category.worksheets for each category.

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Numbers and Numbers and Number RelationshipsNumber Relationships

Numbers and Numbers and Number RelationshipsNumber Relationships

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Numbers and Number RelationshipsNumbers and Number RelationshipsWorksheet #1Worksheet #1


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AnswerKey #1

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Directions: Determine the place of the underlined digit.

1. 108 2. 17

3. 2,496 4. 97

5. 5,983 6. 758

7. 9,961 8. 14,773

9. 3,350 10. 482

11. 555,698 12. 98,523,223

13. 923,835 14. 848,383,490

15. 1,332,460 16. 1,456,893,001

17. 554,679,261 18. 747,585

19. 901,835,762 20. 4,123,567,890

Click on the answer key link above to check your answers.

Directions: Determine the place of the underlined digit.

1. 108 (tens) 2. 17 (ones)

3. 2,496 (thousands) 4. 97 (tens)

5. 5,983 (ones) 6. 758 (hundreds)

7. 9,961 (tens) 8. 14,773 (ten thousands)

9. 3,350 (hundreds) 10. 482 (hundreds)

11. 555,698 (hundred thousands) 12. 98,523,223 (ten millions) 13. 923,835 (tens) 14. 848,383,490 (hundred millions)

15. 1,332,460 (ten thousands) 16. 1,456,893,001 (billions)

17. 554,679,261 (ten millions) 18. 747,585 (hundreds thousands)

19. 901,835,762 (thousands) 20. 4,123,567,890 (billions)

Numbers and Number RelationshipsNumbers and Number RelationshipsWorksheet #1 – Worksheet #1 – ANSWER KEYANSWER KEY


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Directions: Determine the value of the underlined digit.

1. 108 2. 17

3. 2,496 4. 97

5. 5,983 6. 758

7. 9,961 8. 14,773

9. 3,350 10. 482

11. 555,698 12. 98,523,223

13. 923,835 14. 848,383,490

15. 1,332,460 16. 1,456,893,001

17. 554,679,261 18. 747,585

19. 901,835,762 20. 4,123,567,890

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STOPSTOP SRNumbers and Number RelationshipsNumbers and Number RelationshipsWorksheet #2 – Worksheet #2 – ANSWER KEYANSWER KEY


Directions: Determine the value of the underlined digit.

1. 108 (0) 2. 17 (7)

3. 2,496 (2,000) 4. 97 (90)

5. 5,983 (3) 6. 758 (700)

7. 9,961 (60) 8. 14,773 (10,000)

9. 3,350 (300) 10. 482 (400)

11. 555,698 (500,000) 12. 98,523,223 (90,000,000)

13. 923,835 (30) 14. 848,383,490 (800,000,000)

15. 1,332,460 (30,000) 16. 1,456,893,001 (1,000,000,000)

17. 554,679,261 (50,000,000) 18. 747,585 (700,000)

19. 901,835,762 (5,000) 20. 4,123,567,890 (4,000,000,000)

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Directions: For questions 1-4, write the standard form of each.

1. 4,000+300+20+7 2. 4 thousand+3 hundred+seven

3. 100,000+8,000+700+30+5 4. Seventy-five thousand, sixteen

Directions: For questions 5-8, find the GCF of the numbers listed.

5. 45, 9 6. 15, 20

7. 12,15, 18 8. 25, 100, 1000

Directions: For questions 9-12, find the LCM of the numbers listed.

9. 4, 5 10. 3, 5

11. 3, 4, 10 12. 5, 8, 20

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Directions: For questions 1-4, write the standard form of each.

1. 4,000+300+20+7 (4,327) 2. 4 thousand+3 hundred+seven (4,307)

3. 100,000+8,000+700+30+5 (108,735) 4. Seventy-five thousand, sixteen (75,016)

Directions: For questions 5-8, find the GCF of the numbers listed.

5. 45, 9 (9) 6. 15, 20 (5)

7. 12,15, 18 (3) 8. 25, 100, 1000 (25)

Directions: For questions 9-12, find the LCM of the numbers listed.

9. 4, 5 (20) 10. 3, 5 (15)

11. 3, 4, 10 (60) 12. 5, 8, 20 (40)

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AnswerKey #4




Directions: Answer each question.

1. The temperature rose from –4° F to 15° F. How many degrees did the temperature go up?

2. What is always true about a prime number?

3. What is the decimal equivalent to 3/5?

4. Steve took 3 shirts and 4 pair of shorts on vacation. How many different outfits (or shirt/short combinations) can Steve wear?

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1. The temperature rose from –4° F to 15° F. How many degrees did the temperature go up?

The temperature went up 19 °.

2. What is always true about a prime number?

A prime number only has two factors – “1” and itself.

3. What is the decimal equivalent to 3/5?

The decimal equivalent to 3/5 is .60.

4. Steve took 3 shirts and 4 pair of shorts on vacation. How many different outfits (or shirt/short combinations) can Steve wear?

Steve can create 12 different outfits to wear.

Computation and Computation and EstimationEstimation

Computation and Computation and EstimationEstimation

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Computation and EstimationComputation and EstimationWorksheet #1Worksheet #1


Directions: Find each sum.

1. 399 + 251 = 2. 49 + 32 =

3. 600 + 302 = 4. 4,392 + 3, 209 =

5. 11, 684 + 7,995 = 6. 5,698 + 4,328 =

7. 17,843 + 308 = 8. 1,259 + 567 =

9. 427 + 999 = 10. 789 + 943 =

11. 3,908 + 2, 889 = 12. 459 + 396 = 13. 187 + 469 = 14. 4, 972 + 99 =

15. 6,008 + 3,992 = 16. 27 + 798 =

17. 654 + 3,499 = 18. 5,987 + 7,598 =

19. 3,759 + 348 = 20. 6,432 + 7,945 =

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Computation and EstimationComputation and EstimationWorksheet #1 - Worksheet #1 - ANSWER KEYANSWER KEY


Directions: Find each sum.

1. 399 + 251 = 650 2. 49 + 32 = 81

3. 600 + 302 = 902 4. 4,392 + 3,209 = 7,601

5. 11,684 + 7,995 = 19,679 6. 5,698 + 4,328 = 10,026

7. 17,843 + 308 = 18,151 8. 1,259 + 567 = 1,826

9. 427 + 999 = 1,426 10. 789 + 943 = 1,732

11. 3,908 + 2,889 = 6,797 12. 459 + 396 = 855 13. 187 + 469 = 656 14. 4,972 + 99 = 5,071

15. 6,008 + 3,992 = 10,000 16. 27 + 798 = 825

17. 654 + 3,499 = 4,153 18. 5,987 + 7,598 = 13,585

19. 3,759 + 348 = 4,107 20. 6,432 + 7,945 = 14,377

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Directions: Find each difference.

1. 650 – 267 = 2. 400 – 234 =

3. 482 – 383 = 4. 698 – 133 =

5. 501 – 387 = 6. 3,349 – 1,870 =

7. 9,807 – 799 = 8. 1000 – 677 =

9. 2,334 – 109 = 10. 648 – 355 =

11. 8,790 – 2,334 = 12. 7,688 – 5,679 = 13. 457 – 261 = 14. 602 - 499 =

15. 509 – 200 = 16. 2,333 – 684 =

17. 266 – 97 = 18. 590 – 392 =

19. 1,832 – 589 = 20. 6,571 – 4,490 =

Check your work with a calculator, or simply click on the answer key link above.

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Directions: Find each difference.

1. 650 – 267 = 383 2. 400 – 234 = 166

3. 482 – 383 = 99 4. 698 – 133 = 565

5. 501 – 387 = 114 6. 3,349 – 1,870 = 1,479

7. 9,807 – 799 = 9,008 8. 1000 – 677 = 323

9. 2,334 – 109 = 2,225 10. 648 – 355 = 293

11. 8,790 – 2,334 = 6,456 12. 7,688 – 5,679 = 2,009 13. 457 – 261 = 196 14. 602 - 499 = 103

15. 509 – 200 = 309 16. 2,333 – 684 = 1,649

17. 266 – 97 = 169 18. 590 – 392 = 198

19. 1,832 – 589 = 1,243 20. 6,571 – 4,490 = 2,081

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AnswerKey #3

Directions: Find each product.

1. 17 x 9 = 2. 115 x 9 =

3. 49 x 6 = 4. 627 x 5 =

5. 77 x 4 = 6. 6,550 x 0 =

7. 4,578 x 3 = 8. 5 x 115 =

9. 33 x 45 = 10. 57 x 32 =

11. 576 x 43 = 12. 367 x 34 = 13. 357 x 241 = 14. 679 x 352 =

15. 474 x 552 = 16. 999 x 0 =

17. 795 x 21 = 18. 433 x 4 =

19. 60 x 59 = 20. 499 x 67 =


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Directions: Find each product.

1. 17 x 9 = 153 2. 115 x 9 = 1,035

3. 49 x 6 = 294 4. 627 x 5 = 3,135

5. 77 x 4 = 308 6. 6,550 x 0 = 0

7. 4,578 x 3 = 13,734 8. 5 x 115 = 575

9. 33 x 45 = 1,485 10. 57 x 32 = 1,824

11. 576 x 43 = 24,768 12. 367 x 34 = 12,478 13. 357 x 241 = 86,037 14. 679 x 352 = 239,008

15. 474 x 552 = 261,648 16. 999 x 0 = 0

17. 795 x 21 = 16,695 18. 433 x 4 = 1,732

19. 60 x 59 = 3,540 20. 499 x 67 = 33,433

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AnswerKey #4

Directions: Find each quotient.

1. 72 ÷ 8 = 2. 117 ÷ 9 =

3. 49 ÷ 7 = 4. 625 ÷ 25 =

5. 77 ÷ 7 = 6. 6,550 ÷ 655 =

7. 4,578 ÷ 3 = 8. 750 ÷ 6 =

9. 33 ÷ 11 = 10. 558 ÷ 18 =

11. 576 ÷ 9 = 12. 408 ÷ 34 = 13. 368 ÷ 16 = 14. 1000 ÷ 8 =

15. 476 ÷ 4 = 16. 999 ÷ 1 =

17. 795 ÷ 5 = 18. 575 ÷ 25 =

19. 60 ÷ 4 = 20. 1,824 ÷ 32 =


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Directions: Find each quotient.

1. 72 ÷ 8 = 9 2. 117 ÷ 9 = 13

3. 49 ÷ 7 = 294 4. 625 ÷ 25 = 25

5. 77 ÷ 7 = 11 6. 6,550 ÷ 655 = 10

7. 4,578 ÷ 3 = 1,526 8. 750 ÷ 6 = 125

9. 33 ÷ 11 = 3 10. 558 ÷ 18 = 31

11. 576 ÷ 9 = 64 12. 408 ÷ 34 = 12 13. 368 ÷ 16 = 23 14. 1000 ÷ 8 = 125

15. 476 ÷ 4 = 119 16. 999 ÷ 1 = 999

17. 795 ÷ 5 = 159 18. 575 ÷ 25 = 23

19. 60 ÷ 4 = 15 20. 1,824 ÷ 32 = 57

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MeasurementMeasurementand Estimationand EstimationMeasurementMeasurement

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Directions: Solve.

1. What is the perimeter of an octagon with a side of 7 inches? Show your work.

2. What is the area of a living room wall that is 25 ft. by 8 ft.? Show your work.

3. If John went to the mall at 9:30am and returned at 1:00pm, how long was he gone? Show your work.

4. If there are 36 inches in a yard, and a football field is 100 yards long, how many inches are there in a football field? Show your work.


Measurement and EstimationMeasurement and EstimationWorksheet #1 - Worksheet #1 - ANSWER KEYANSWER KEY


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Directions: Solve.

1. What is the perimeter of an octagon with a side that measures 7 inches? Show your work.

2. What is the area of a living room wall that is 25 ft. by 8 ft.? Show your work.

3. If John went to the mall at 9:30am and returned at 1:00pm, how long was he gone? Show your work.

4. If there are 36 inches in a yard, and a football field is 100 yards long, how many inches are there in a football field? Show your work.

The perimeter of an octagon with a side that measures 7 inches is 56 inches. (7 in x 8 = 56 in)

The area of a living room wall that is 25 ft x 8 ft is 200 ft squared. (25 ft x 8 ft = 200 ft squared)

If John was gone from 9:30am until 1:00pm, then he was gone for 3 ½ hours. (9:30am to 10:00am = ½ hr; 10:00am to 1:00pm = 3 hrs; 3 + ½ = 3 ½ hrs)

A football field is 3,600 inches long. (36 x 100 = 3,600)



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1. 5 kilometers is = __________ meters

2. 5 yards and 2 feet = __________ feet

3. 65 inches = __________ feet

4. 156 weeks = __________ years

5. 4 days and 6 hours = __________ hours

6. 12 cups = __________ pints

7. 3 gallons = __________ quarts

8. 8 pints = __________ gallons

9. 6,000 pounds = __________ tons

10. 48 ounces = __________ pounds

Directions: Convert the following measurements.



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1. 5 kilometers is = __________ meters

2. 5 yards and 2 feet = __________ feet

3. 60 inches = __________ feet

4. 156 weeks = __________ years

5. 4 days and 6 hours = __________ hours

6. 12 cups = __________ pints

7. 3 gallons = __________ quarts

8. 8 pints = __________ gallons

9. 6,000 pounds = __________ tons

10. 48 ounces = __________ pounds

Directions: Convert the following measurements.

5,000

17

5

3

102

6

12

1

3

3



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Directions: Choose the best unit of measure for each example.

1. Steve wants to know the total area of a standard sheet of paper. Whatunit should he use?

a. miles b. inches c. yards d. days

2. Rashaad is training to run in a race. Which unit should he use to keeptrack of his training?

a. miles b. centimeters c. inches d. millimeters

3. Marcia is helping her father fill the swimming pool. Which unit shouldthey use to keep track of how much water they are using?

a. ounces b. cups c. teaspoons d. gallons

4. What unit of measurement would most likely be used in baking a dozencookies?

a. tons b. pounds c. teaspoons d. months



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Directions: Choose the best unit of measure for each example.

1. Steve wants to know the total area of a standard sheet of paper. Whatunit should he use?

a. miles b. inches c. yards d. days

2. Rashaad is training to run in a race. Which unit should he use to keeptrack of his training?

a. miles b. centimeters c. inches d. millimeters

3. Marcia is helping her father fill the swimming pool. Which unit shouldthey use to keep track of how much water they are using?

a. ounces b. cups c. teaspoons d. gallons

4. What unit of measurement would most likely be used in baking a dozencookies?

a. tons b. pounds c. teaspoons d. months

Mathematical ReasoningMathematical ReasoningMathematical ReasoningMathematical Reasoning

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Directions: Use the information below to answer questions 1-3.

1. Which is required to find out the total amount of fruit to use? a. The party is at the park. b. He hopes that he succeeds.c. He spent $8.89. d. The recipe calls for 5 large apples.

3. How would you determine the total amount of fruit to be used?

a. ask someone. b. add up the amounts of the required fruits.c. subtract the price of the fruit from the other ingredients.

Steve is baking a fruit pie for a picnic at the park. The recipe calls for 5 large apples, a cup of blueberries, 4 peaches and some other ingredients. He spent $8.89 on the ingredients. He hopes that he succeeds!

2. Which is NOT required to find out the total amount of fruit to use? a. The recipe calls for 1 cup of blueberries.b. The recipe calls for 4 peaches.c. He spent $8.89.d. The recipe calls for 5 large apples.

Mathematical ReasoningMathematical Reasoning Worksheet #1 – Worksheet #1 – ANSWER KEYANSWER KEY


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Directions: Use the information below to answer questions 1-3.

1. Which is required to find out the total amount of fruit to use? a. The party is at the park. b. He hopes that he succeeds.c. He spent $8.89. d. The recipe calls for 5 large apples.

3. How would you determine the total amount of fruit to be used?

a. ask someone. b. add up the amounts of the required fruits.c. subtract the price of the fruit from the other ingredients.

Steve is baking a fruit pie for a picnic at the park. The recipe calls for 5 large apples, a cup of blueberries, 4 peaches and some other ingredients. He spent $8.89 on the ingredients. He hopes that he succeeds!

2. Which is NOT required to find out the total amount of fruit to use? a. The recipe calls for 1 cup of blueberries.b. The recipe calls for 4 peaches.c. He spent $8.89.d. The recipe calls for 5 large apples.



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Directions: Solve.

1. Which statement is true?

a. All numbers that end in 6 are divisible by 3.b. Some numbers that end in 6 are divisible by 3.c. Numbers that end in 6 are not divisible by 3.

2. Michael does yard work for his neighbor. He earns $7.95/hr, and he worked for 12 hours last weekend. How much money did Michael earn last weekend?

a. $19.95b. $95.40c. $23.85

3. What is the perimeter of a square with a side length of 8cm?

a. 32cmb. 64 cmc. 8cm

1. Which statement is true?

a. All numbers that end in 6 are divisible by 3.b. Some numbers that end in 6 are divisible by 3.c. Numbers that end in 6 are not divisible by 3.

2. Michael does yard work for his neighbor. He earns $7.95/hr, and he worked for 12 hours last weekend. How much money did Michael earn last weekend?

a. $19.95b. $95.40c. $23.85

3. What is the perimeter of a square with a side length of 8cm?

a. 32cmb. 64 cmc. 8cm



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Directions: Solve.



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Directions: Solve.

1. The Collector’s Store sells baseball cards in packs of 25. How many packs would it take to have 11,475 cards? Show your work.

2. If Jasmine sells lemonade for 35 cents per cup, how much will she make if she sells 400 cups? Show your work.

3. Tashina rode her bike 11 miles a day for 4 weeks. How many miles did she ride in all? Show your work.



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It would take 459 packs to have 11,475 cards in all. I solved this problem by doing the following: 11,475 ÷ 25 = 459

Tashina rode 308 miles in all. My work is shown below.4 weeks = 28 days, 11 X 28 = 308

Jasmine would make $140.00 if she sold 400 cups at $0.35 each. I solved this problem by doing the following: 400 x $0.35 = $140.00

Directions: Solve.

1. The Collector’s Store sells baseball cards in packs of 25. How many packs would it take to have 11,475 cards? Show your work.

2. If Jasmine sells lemonade for 35 cents per cup, how much will she make if she sells 400 cups? Show your work.

3. Tashina rode her bike 11 miles a day for 4 weeks. How many miles did she ride in all? Show your work.

Statistics and Statistics and Data AnalysisData AnalysisStatistics and Statistics and Data AnalysisData Analysis

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Statistics and Data AnalysisStatistics and Data AnalysisWorksheet #1Worksheet #1

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Month Snowfall (in inches)

November 4

December 12

January 17

February 26

March 9

Directions: Use the chart above to answer the questions below.

1. Which month received the least amount of snowfall?

2. How much less snow fell in March than in February?

3. How much snow fell between November and March? (include November and March when calculating your answer)

Statistics and Data AnalysisStatistics and Data Analysis Worksheet #1 – Worksheet #1 – ANSWER KEYANSWER KEY


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Directions: Use the chart above to answer the questions below.

1. Which month received the least amount of snowfall?

2. How much less snow fell in March than in February?

3. How much snow fell between November and March? (include November and March when calculating your answer)

Month Snowfall (in inches)

November 4

December 12

January 17

February 26

March 9

November received the least amount of snowfall. (4 inches)

17 fewer inches of snow fell in March. (26 – 9 = 17)

68 inches of snow fell between November and March. (4 + 12 + 17+ 26 + 9 = 68)

Statistics and Data AnalysisStatistics and Data Analysis Worksheet #2Worksheet #2


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Sara's "Back to School Budget" (Dollars Spent)

50

50100

20

Shirts

Pants

Shoes

Accessories

Directions: Use the pie graph to answer the questions below.

1. How much did Sara spend?

3. What percentage of Sara’s money was spent on shirts?

2. How many times more money was spent on shoes than on accessories?



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Sara's "Back to School Budget" (Dollars Spent)

50

50100

20

Shirts

Pants

Shoes

Accessories


1. How much did Sara spend?

3. What percentage of Sara’s money was spent on shirts?

2. How many times more money was spent on shoes than on accessories?

Sara spent a total of $220.00.

Sara spent 5 times more money on shoes than accessories.

22.7% of Sara’s money was spent on shirts (50/220 = .227 = 22.7%)



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Extreme Skate Shop Sales (2003)

0

50

100

150

200

250

300

W SP SU F

Seasons

SkateboardsSold

Directions: Use the line graph to answer the questions below.

1. How many more skateboards were sold in the Summer than Fall?

3. Explain the results of the line graph?

2. How many skateboards were sold in all during 2003?



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150 more skateboards were sold in the Summer. (250 – 100 = 150)

500 skateboards were sold in 2003. (50 + 100 + 250 + 100 = 500)

The warmer the season, the more skateboards are sold.

Extreme Skate Shop Sales

0

50

100

150

200

250

300

W SP SU F

Seasons

SkateboardsSold

1. How many more skateboards were sold in the Summer than Fall?

3. Give a possible explanation for the results of the line graph?

2. How many skateboards were sold in all during 2003?



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Friday ☺ ☺ ☺ ☺ ☺ ☺Saturday ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺Sunday ☺ ☺ ☺ ☺ ☺Each ☺ equals 20 customers.

Directions: Use the pictograph to answer the questions below.

1. How many customers did the local ice cream shop have on Friday?

3. What was the total number of customers served? (Friday-Sunday)

2. Which night should have the most workers to assist customers?

Ice Cream Shop Customers



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Ice Cream Shop Customers

Directions: Use the pictograph to answer the questions below.

Friday ☺ ☺ ☺ ☺ ☺ ☺Saturday ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺Sunday ☺ ☺ ☺ ☺ ☺Each ☺ equals 20 customers.

1. How many customers did the local ice cream shop have on Friday?

2. Which night should have the most workers to assist customers?

The ice cream shop had 120 customers on Friday.

Saturday had the most customers, so it should also have the most workers.

360 customers were served.

3. What was the total number of customers served? (Friday-Sunday)

Probability and Probability and PredictionsPredictions

Probability and Probability and PredictionsPredictions

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1. There are 10 blocks in a container. Three are blue, two are green, one is black, and four are red. Which color block has the highest probability of being chosen?

2. Fifteen boys and ten girls put their names in a hat. Each student hopes to have their name pulled from the hat. What is the probability that a girl will have her name picked?

3. What is the probability that a quarter will be chosen from a bowl that contains 11 pennies, 4 nickels, 5 dimes, and 1 quarter?


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1. There are 10 blocks in a container. Three are blue, two are green, one is black, and four are red. Which color block has the highest probability of being chosen?

2. Fifteen boys and ten girls put their names in a hat. Each student hopes to have their name pulled from the hat. What is the probability that a girl will have her name picked?

3. What is the probability that a quarter will be chosen from a bowl that contains 11 pennies, 4 nickels, 5 dimes, and 1 quarter?

A red block has the highest probability of being chosen.

The probability that a girl’s name will be picked is 10/25 or 2/5.

The probability that a quarter will be chosen is 1/21.

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1. Julie flipped a coin 100 times. It landed on “heads” 41 times, and it landed on “tails” 59 times. If she flipped it again, what would be the probability of flipping another “heads”?

2. When rolling a standard die, the probability of rolling a “six” is 1/6. What is the probability of rolling a “six” 2 times in a row?

3. In a standard deck of 52 playing cards, there are 12 “face” cards. What is the probability of picking a card out of the deck that is NOT a face card?


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The probability of Julie rolling another “heads” is 1/2.

The probability of rolling a “six” 2 times in a row is 1/36.

The probability of picking a non-face card is 40/52 or 10/13.

1. Julie flipped a coin 100 times. It landed on “heads” 41 times, and it landed on “tails” 59 times. If she flipped it again, what would be the probability of flipping another “heads”?

2. When rolling a standard die, the probability of rolling a “six” is 1/6. What is the probability of rolling a “six” 2 times in a row?

3. In a standard deck of 52 playing cards, there are 12 “face” cards. What is the probability of picking a card out of the deck that is NOT a face card?

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A D

B C

I E

H G

1. What is the probability of spinning the letter “G”?

2. What is the probability of spinning the letter “B” OR the letter “E”?

3. What is the probability of spinning a vowel?

Directions: Use the spinner to answer the questions below.



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A D

B C

I E

H G

Directions: Use the spinner to answer the questions below.

1. What is the probability of spinning the letter “G”?

2. What is the probability of spinning the letter “B” OR the letter “E”?

3. What is the probability of spinning a vowel?

The probability of spinning the letter “G” is 1/8.

The probability of spinning the letter “B” or the letter “E” is 2/8 or 1/4.

The probability of spinning a vowel is 3/8.

Algebra and FunctionsAlgebra and FunctionsAlgebra and FunctionsAlgebra and Functions

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Algebra and FunctionsAlgebra and FunctionsWorksheet #1Worksheet #1


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AnswerKey #1

Directions: Solve for n.

1. n + 19 = 32 2. 23 + 6 = n

3. 98 - n = 55 4. 73 - n = 43

5. n + 23 = 73 6. 77 + n = 90

7. 99 ÷ n = 11 8. n ÷ 3 = 12

9. 33 ÷ 11 = n 10. 36 ÷ 6 = n


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1. n + 19 = 32 (n = 13) 2. 23 + 6 = n (n = 29)

3. 98 - n = 55 (n = 43) 4. 73 - n = 43 (n = 30)

5. n + 23 = 73 (n = 50) 6. 77 + n = 90 (n = 13)

7. 99 ÷ n = 11 (n = 9) 8. n ÷ 3 = 12 (n = 36)

9. 33 ÷ 11 = n (n = 3) 10. 36 ÷ 6 = n (n = 6)

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1. 14 x 3 = n 2. 7 x n = 56 3. 55 + 19 = n 4. 72 + 82 = n

5. 5n = 45 6. 7n = 14

7. 9n = 63 8. 36n = 36

9. 12n = 0 10. 15n = 60


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1. 14 x 3 = n (n = 42) 2. 7 x n = 56 (n = 8) 3. 55 + 19 = n (n = 74) 4. 72 + 82 = n (n = 154)

5. 5n = 45 (n = 9) 6. 7n = 14 (n = 2)

7. 9n = 63 (n = 7) 8. 36n = 36 (n = 1)

9. 12n = 0 (n = 0) 10. 15n = 60 (n = 4)

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Directions: Fill in the blank in each pattern.

1. 2, 4, 6, 8, ____ 2. 1, 3, 5, 7, ____ 3. 5, 15, 25, 35, ____ 4. 56, 52, 48, ____

5. 12, 21, 30, 39, ____ 6. 100, 90, 70, 40, ____

7. 2, 3, 5, 7, 11, ____ 8. 80, 40, 20, 10, ____

9. 2, 4, 8, 14, 22, ____ 10. 1, 2, 4, 7, ____


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1. 2, 4, 6, 8, ____ (10) 2. 1, 3, 5, 7, ____ (9) 3. 5, 15, 25, 35, ____ (45) 4. 56, 52, 48, ____ (44)

5. 12, 21, 30, 39, ____ (48) 6. 100, 90, 70, 40, ____ (0)

7. 2, 3, 5, 7, 11, ____ (17- primes) 8. 80, 40, 20, 10, ____ (5)

9. 2, 4, 8, 14, 22, ____ (32) 10. 1, 2, 4, 7, ____ (11)

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Algebra and FunctionsAlgebra and FunctionsWorksheet #4 Worksheet #4

Algebra and FunctionsAlgebra and FunctionsWorksheet #4 Worksheet #4

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1. 2, 2, 4, 12, 48, ___ 2. 3, 4, 6, 9, 13, ____ 3. a, c, e, g, ____ 4. a, b, a, b, c, b, c, d, ____

5. ____ 6. 2, 4, 16, ____

7. 5, 8, 6, 9, 7, 10 ____ 8. a, b, d, g, k, ____

9. I, O, I, I, O, O, I, I, I, ____ 10. z, x, v, t, ____


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1. 2, 2, 4, 12, 48, ___ (240) 2. 3, 4, 6, 9, 13, ____ (18) 3. a, c, e, g, ____ (i) 4. a, b, a, b, c, b, c, d, ____ (c)

5. ___( ) 6. 2, 4, 16, ____ (256)

7. 5, 8, 6, 9, 7, 10 ____ (8) 8. a, b, d, g, k, ____ (p)

9. I, O, I, I, O, O, I, I, I, ____ (O) 10. z, x, v, t, ____ (r)

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GeometryGeometryWorksheet #1Worksheet #1


Directions: Fill in the blank.

1. A polygon with 5 sides is called a

2. Any polygon with 8 sides is called an

3. A three-sided polygon is called a

4. Polygons with four sides are called

5. A polygon in which all sides have the same length is called a regular polygon.

6. A trapezoid is a quadrilateral with only one pair of parallel sides.

7. Squares and rectangles are both examples of a special quadrilateral called a

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GeometryGeometryWorksheet #1 – Worksheet #1 – ANSWER KEYANSWER KEY

GeometryGeometryWorksheet #1 – Worksheet #1 – ANSWER KEYANSWER KEY

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Directions: Fill in the blank.

1. A polygon with 5 sides is called a pentagon.

2. Any polygon with 8 sides is called an octagon.

3. A three-sided polygon is called a triangle.

4. Polygons with four sides are called quadrilaterals.

5. A polygon in which all sides have the same length is called a regular polygon.

6. A trapezoid is a quadrilateral with only one pair of parallel sides.

7. Squares and rectangles are both examples of a special quadrilateral called a parallelogram.

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Directions: Name the “space figure”, or three-dimensional object, that best describes the object given.

1. A can of soup 2. A box of cereal

3. An ice cream cone 4. A tent

5. A six-sided die 6. A roll of quarters

7. A video tape 8. One of the pyramids in Egypt

9. A globe 10. A funnel

Click on the answer key link above to check your answers..

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Geometry Geometry Worksheet #2 – Worksheet #2 – ANSWER KEYANSWER KEY


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Directions: Name the “space figure”, or three-dimensional object, that best describes the object given.

1. A can of soup 2. A box of cereal

a cylinder a rectangular prism

3. An ice cream cone 4. A tent a cone a pyramid or a triangular

prism

5. A six-sided die 6. A roll of quarters a cube a cylinder

7. A video tape 8. One of the pyramids in Egypt a rectangular prism a pyramid

9. A globe 10. A funnel a sphere a cone

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Geometry Geometry Worksheet #3Worksheet #3


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Directions: Solve.

1. If a circle has a radius of 3.5 inches, what is the diameter

2. If the circumference of a circle is approximately 3 times its diameter, what is the circumference of the circle in problem #1?

3. What is the radius of a swimming pool with a diameter of 24 ft?

4. What is the area of a rectangle with a width of 4cm and a length of 6cm?

5. What is the volume of a cube with a length of 6 inches?

6. What is the perimeter of a square with a side that measures 8m?


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Directions: Solve.

1. If a circle has a radius of 3.5 inches, what is the diameter The diameter is 7 inches.

2. If the circumference of a circle is approximately 3 times its diameter, what is the circumference of the circle in problem #1? The circumference is approximately 21 inches.

3. What is the radius of a swimming pool with a diameter of 24 ft? The radius is 12 feet.

4. What is the area of a rectangle with a width of 4cm and a length of 6cm? The area is 24 square centimeters.

5. What is the volume of a cube with a length of 6 inches? The volume is 216 cubic inches.

6. What is the perimeter of a square with a side that measures 8m? The perimeter is 32 meters.

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For #s 1-3, classify each triangle by its sides.

1.

3.

2.

For #s 4-6, classify each triangle by its angles.

4.

5.

6.

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For #s 1-3, classify each triangle by its sides.

1. isosceles

3. scalene

2. equilateral

For #s 4-6, classify each triangle by its angles.

4. acute

5. right

6. obtuse

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TrigonometryTrigonometryTrigonometryTrigonometry

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TrigonometryTrigonometry Worksheet #1Worksheet #1


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DirectionsDirections: : Answer each question.Answer each question.

1. How would you define an acute angle?1. How would you define an acute angle?

2. How would you define a right angle?2. How would you define a right angle?

3. What is a hypotenuse?3. What is a hypotenuse?

4. What is the sum of all of the angles in any triangle?4. What is the sum of all of the angles in any triangle?

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1. How would you define an acute angle?1. How would you define an acute angle? An acute angle is an angle that measures less than 90°.

2. How would you define a right angle?2. How would you define a right angle?

A right angle is an angle with a measure of 90°.

3. What is a hypotenuse?3. What is a hypotenuse?

A hypotenuse is the longest side of a right triangle. It is also the side directly across from the right angle.

4. What is the sum of all of the angles in any triangle?4. What is the sum of all of the angles in any triangle?

The sum of the angles in any triangle is 180°.

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1. What tool is useful in measuring angles?1. What tool is useful in measuring angles? a. a telescope b. a ruler c. a protractor

2. If the sum of two angles in a triangle is 120°, what is the 2. If the sum of two angles in a triangle is 120°, what is the measure of the third angle?measure of the third angle?

a. 90° b. 60° c. 45°

3. What is the greatest number of right angles that a triangle 3. What is the greatest number of right angles that a triangle can have?can have?

a. 1 b. 3 c. 2

4. Which angle has the greatest measure?4. Which angle has the greatest measure?

a. an acute angle b. a right angle c. an obtuse angle

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DirectionsDirections: : Choose the best answer.Choose the best answer.

1. What tool is useful in measuring angles?1. What tool is useful in measuring angles? a. a telescope b. a ruler c. a protractor

2. If the sum of two angles in a triangle is 120°, what is the 2. If the sum of two angles in a triangle is 120°, what is the measure of the third angle?measure of the third angle?

a. 90° b. 60° c. 45°

3. What is the greatest number of right angles that a triangle 3. What is the greatest number of right angles that a triangle can have?can have?

a. 1 b. 3 c. 2

4. Which angle has the greatest measure?4. Which angle has the greatest measure?

a. an acute angle b. a right angle c. an obtuse angle

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Concepts of CalculusConcepts of CalculusConcepts of CalculusConcepts of Calculus

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Concepts of CalculusConcepts of CalculusWorksheet #1Worksheet #1


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DirectionsDirections: : For questions 1-6, fill in the blank with one of the following For questions 1-6, fill in the blank with one of the following phrases: phrases: “is less than,” “is equal to,” or “is greater than”“is less than,” “is equal to,” or “is greater than”

1. 5,324 _____5,2341. 5,324 _____5,234 2. 392+79_____4712. 392+79_____471 3. 27 x 2_____553. 27 x 2_____55

4. 519 _____5194. 519 _____519 5. 834_____4385. 834_____438 6. 140-16_____1256. 140-16_____125

Directions: Directions: For questions 7-12, fill in the blank with one of the following For questions 7-12, fill in the blank with one of the following symbols: symbols: “<“ “=” or “>”“<“ “=” or “>”

7. 140÷2 _____757. 140÷2 _____75 8. 500_____500.08. 500_____500.0 9. 7,218_____7,000+2189. 7,218_____7,000+218

10. 5.05 _____5.50010. 5.05 _____5.500 11. 8.6_____8½ 11. 8.6_____8½ 12. 1/10 _____.100 12. 1/10 _____.100

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DirectionsDirections: : For questions 1-6, fill in the blank with one of the following For questions 1-6, fill in the blank with one of the following phrases: phrases: “is less than,” “is equal to,” or “is greater than”“is less than,” “is equal to,” or “is greater than”

1. 5,324 _____5,2341. 5,324 _____5,234 2. 392+79_____4712. 392+79_____471 3. 27 x 2_____553. 27 x 2_____55 is greater than is equal to is less than

4. 519 _____5194. 519 _____519 5. 834_____4385. 834_____438 6. 140-16_____1256. 140-16_____125 is equal to is greater than is less than

Directions: Directions: For questions 7-12, fill in the blank with one of the following For questions 7-12, fill in the blank with one of the following symbols: symbols: “<“ “=” or “>”“<“ “=” or “>”

7. 140÷2 _____757. 140÷2 _____75 8. 500_____500.08. 500_____500.0 9. 7,218_____7,000+2189. 7,218_____7,000+218 < = =

10. 5.05 _____5.50010. 5.05 _____5.500 11. 8.6_____8½ 11. 8.6_____8½ 12. 1/10 _____.100 12. 1/10 _____.100 < > =

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Directions: Solve each problem.

1. Alex can read 120 pages in 3 hours. How many pages does he read on average per hour?

2. How many pages can he read 12 hours if he continues at the same rate?

3. Mike can run 8 miles in 2 hours. How many miles does he run on average per hour?

4. How long would it take Mike to run 32 miles at this rate?

5. A bakery makes 144 muffins per hour. How many can they make in 6 hours?

6. How many muffins can be made in 30 minutes?



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Directions: Solve each problem.

1. Alex can read 120 pages in 3 hours. How many pages does he read on average per hour?

2. How many pages can he read 12 hours if he continues at the same rate?

3. Mike can run 8 miles in 2 hours. How many miles does he run on average per hour?

4. How long would it take Mike to run 32 miles at this rate?

5. A bakery makes 144 muffins per hour. How many can they make in 6 hours?

6. How many muffins can be made in 30 minutes?

Alex can read 40 pages per hour. Alex can read 480 pages in 12 hours.

Mike runs 4 miles per hour. It would take 8 hours to run 32 miles.

The bakery can make 864 muffins in 6 hours.

72 muffins can be made in 30 minutes.

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Word ProblemsWord Problems

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Problem#1

Problem#1

Problem#2

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Problem#3

Problem#3

Problem#4

Problem#4

Problems are presented in order of difficulty.Problems are presented in order of difficulty.Problems are presented in order of difficulty.Problems are presented in order of difficulty.

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Justin is helping his dad put up a fence around their backyard. The perimeter of their backyard is 506 feet. If the store sells fence in sections of 6 feet, how many sections will they need to buy in order to complete the job?

“Click” to see a sample answer.


Sample AnswerSample Answer



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Justin is helping his dad put up a fence around their backyard. The perimeter of their backyard is 506 feet. If the store sells fence in sections of 6 feet, how many sections will they need to buy in order to complete the job?

To determine how many sections of fence Justin and his father will need to buy, you must divide the total perimeter (506 ft.) by the length of one individual section. (506 ÷ 6 = 84.3). It will take just over 84 sections to complete the job, but be careful! The store will not sell part of a section, so 85 sections must be purchased.

Don’t forget to restate your answer: Justin and his father will need to buy 85 sections of fence

in order to complete the job.

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Madison wants to buy a new leather jacket that costs $125.00. To earn money, she took a job that pays $5.00 an hour. If she works 5 hours per week, how many weeks will she have to work before she has enough money to purchase the jacket?





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Madison wants to buy a new leather jacket that costs $125.00. To earn money, she took a job that pays $5.00 an hour. If she works 5 hours per week, how many weeks will she have to work before she has enough money to purchase the jacket?

If Madison works 5 hours a week at $5.00 per hour, that means she earns $25.00 per week. The following list shows how much money she’ll have at the end of each week:

Week 1 - $25.00 Week 3 - $75.00 Week 5 - $125.00Week 2 - $50.00 Week 4 - $100.00

Don’t forget to restate your answer: Madison will need to work for 5 weeks before she has

enough money to purchase the jacket.

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A travel agency offered a trip to Orlando, Florida to visit a popular amusement park. If they received 124 reservations, and their buses hold 41 passengers each, how many buses must they use in order to take all of their customers?






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A travel agency offered a trip to Orlando, Florida to visit a popular amusement park. If they received 124 reservations, and their buses hold 41 passengers each, how many buses must they use in order to take all of their customers?

Divide 124 (the total number of passengers) by 41 (the number of passengers that can ride on a single bus). 124 ÷ 41 = 3 R1. This means that even if three buses are filled, there will be one passenger left over. Since the travel agency wants to make sure that every passenger is able to go, they must take 4 buses.

Don’t forget to restate your answer: The travel agency must use 4 buses in order to take all

of their customers.

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Rashaun has hired a company to install a 30ft x 50ft in-ground pool. He is having another company landscape the remaining space in his backyard at a charge of $1.50 per square foot. If Rashaun’s backyard is 8,000 sq. ft, how much will he need to budget in order to pay the landscaping company?






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Rashaun has hired a company to install a 30ft x 50ft in-ground pool. He is having another company landscape the remaining space in his backyard at a charge of $1.50 per square foot. If Rashaun’s backyard is 8,000 sq. ft, how much will he need to budget in order to pay the landscaping company?

Step 1: Establish the square footage that will need to be landscaped. To figure this out, you must first calculate the square footage of the swimming pool (30ft x 50ft = 1,500 square feet) and subtract it from the total backyard space (8,000 sq ft – 1,500 sq ft. = 6,500 sq ft).

Step 2: Determine the cost to landscape 6,500 square feet. Remember, for each square foot, Rashaun will need to budget $1.50. By multiplying the total square footage to be landscaped (6,500 sq ft) by $1.50, you arrive at a budget price of $9,750.

Don’t forget to restate your answer: Rashaun will need to budget $9,750.00 in order to pay

the landscaping company.

Possible solution:

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Connect your computer to the internetConnect your computer to the internet, and then , and then “click” on a link above to go directly to the website. “click” on a link above to go directly to the website.

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Math StandardsMath StandardsMath StandardsMath Standards

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While the 5th grade standards displayed here are specific to Pennsylvania, it is important to note that they are based on national standards. Pennsylvania’s Academic Standards for Mathematics have been divided into eleven categories. To view the categories, and examples of what is entailed with each, click on the links below. After viewing a category, click on the MS link to return to this page.

While the 5th grade standards displayed here are specific to Pennsylvania, it is important to note that they are based on national standards. Pennsylvania’s Academic Standards for Mathematics have been divided into eleven categories. To view the categories, and examples of what is entailed with each, click on the links below. After viewing a category, click on the MS link to return to this page.

2.1Numbers, Number

Systems andRelationships

2.2Computation

andEstimation

2.3Measurement

andEstimation

2.4MathematicalReasoning andConnections

2.5Mathematical

Problem Solving& Communication

2.6Statistics

andData Analysis

2.7Probability

andPredictions

2.8Algebra

andFunctions

2.9Geometry

2.10Trigonometry

2.11Concepts

ofCalculus

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Math Standard 2.1Math Standard 2.1Math Standard 2.1Math Standard 2.1

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Numbers, Number Systems, and Numbers, Number Systems, and Number RelationshipsNumber Relationships

A. . Types of numbers 1. whole

2. prime

3. irrational

4. complex

B. . Equivalent forms 1. fractions

2. decimals

3. percents

Numbers, Number Systems, and Numbers, Number Systems, and Number RelationshipsNumber Relationships

A. . Types of numbers 1. whole

2. prime

3. irrational

4. complex

B. . Equivalent forms 1. fractions

2. decimals

3. percents

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Computation and EstimationComputation and Estimation

A. . Basic functions 1. addition

2. subtraction

3. multiplication

4. division

B. . Reasonableness of answers

C. . Use of calculators

Computation and EstimationComputation and Estimation

A. . Basic functions 1. addition

2. subtraction

3. multiplication

4. division

B. . Reasonableness of answers

C. . Use of calculators

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Measurement and EstimationMeasurement and Estimation

A. . Types of measurement 1. length

2. time

B. . Units and tools of measurement

C. . Computing and comparing measurements

Measurement and EstimationMeasurement and Estimation

A. . Types of measurement 1. length

2. time

B. . Units and tools of measurement

C. . Computing and comparing measurements

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Mathematical Reasoning and ConnectionsMathematical Reasoning and Connections

A. . Using inductive and deductive reasoning B. . Validating arguments 1. if…then statements

2. proofs

Mathematical Reasoning and ConnectionsMathematical Reasoning and Connections

A. . Using inductive and deductive reasoning B. . Validating arguments 1. if…then statements

2. proofs

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Mathematical Problem Solving Mathematical Problem Solving and Communicationand Communication

A. . Problem solving strategies B. . Representing problems in various ways

C. . Interpreting results

Mathematical Problem Solving Mathematical Problem Solving and Communicationand Communication

A. . Problem solving strategies B. . Representing problems in various ways

C. . Interpreting results

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Statistics and Data AnalysisStatistics and Data Analysis

A. . Collecting and reporting data 1. charts

2. graphs

B. . Analyzing data

Statistics and Data AnalysisStatistics and Data Analysis

A. . Collecting and reporting data 1. charts

2. graphs

B. . Analyzing data

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Probability and PredictionsProbability and Predictions

A. . Validity of data B. . Calculating probability to make predictions

Probability and PredictionsProbability and Predictions

A. . Validity of data B. . Calculating probability to make predictions

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Algebra and FunctionsAlgebra and Functions

A. . Equations B. . Patterns and functions

Algebra and FunctionsAlgebra and Functions

A. . Equations B. . Patterns and functions

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GeometryGeometry

A. . Shapes and their properties B. . Using geometric principles to solve problems

GeometryGeometry

A. . Shapes and their properties B. . Using geometric principles to solve problems

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TrigonometryTrigonometry

A. . Right angles

B. . Measuring and computing with triangles

C. . Use of graphing calculators

TrigonometryTrigonometry

A. . Right angles

B. . Measuring and computing with triangles

C. . Use of graphing calculators

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Concepts of CalculusConcepts of Calculus

A. . Comparing Quantities and Values B. . Graphing Rates of Change

C. . Continuing Patterns Infinitely

Concepts of CalculusConcepts of Calculus

A. . Comparing Quantities and Values B. . Graphing Rates of Change

C. . Continuing Patterns Infinitely

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