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  • How Many Ghosts Do You See? - Mathwire.com · How Many Ghosts Do You See? Instructions: • This lesson builds upon the Pascal’s Pumpkins or Pascal’s Triangle ex- perience. •
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How Many Ghosts Do You See? Instructions: • This lesson builds upon the Pascal’s Pumpkins or Pascal’s Triangle ex- perience. • Explain to students that the question asks how many different ways they can spell GHOSTS using the letter arrangement on the handout. • Use an overhead to model the process. It is important that students un- derstand that they can only move to one of the two pumpkins directly below any pumpkin. This follows Pascal Pumpkin rules. There are, however, many different ways of spelling GHOSTS. • Model two DIFFERENT ways to spell GHOSTS following these rules. • Encourage students to find all of the others. They will need to use a very orderly approach (systematic counting) to actually come up with the correct answer. Supply students with 2 copies of the Ghosts re- cording sheet and ask them to mark one path in each box. • ANSWER: Since GHOSTS has 6 letters, there will be 32 different ways of spelling GHOSTS since 32 is the sum of the numbers in the 6th row of Pascal’s triangle. • CHALLENGE: Superimpose Pascal’s Triangle on the GHOSTS triangle and challenge students to find one way to get to each end pumpkin, 5 ways to get to the next pumpkin and 10 ways to get to each inner pumpkin. G H H O O O S S S S T T T T T S S S S S S G H H O O O S S S S T T T T T S S S S S S Pascal's Ghosts 1 [email protected]

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Page 1: How Many Ghosts Do You See? - Mathwire.com · How Many Ghosts Do You See? Instructions: • This lesson builds upon the Pascal’s Pumpkins or Pascal’s Triangle ex- perience. •

How Many Ghosts Do You See?

Instructions: • This lesson builds upon the Pascal’s Pumpkins or Pascal’s Triangle ex-

perience. • Explain to students that the question asks how many different ways

they can spell GHOSTS using the letter arrangement on the handout. • Use an overhead to model the process. It is important that students un-

derstand that they can only move to one of the two pumpkins directly below any pumpkin. This follows Pascal Pumpkin rules. There are, however, many different ways of spelling GHOSTS.

• Model two DIFFERENT ways to spell GHOSTS following these rules.

• Encourage students to find all of the others. They will need to use a very orderly approach (systematic counting) to actually come up with the correct answer. Supply students with 2 copies of the Ghosts re-cording sheet and ask them to mark one path in each box.

• ANSWER: Since GHOSTS has 6 letters, there will be 32 different ways of spelling GHOSTS since 32 is the sum of the numbers in the 6th row of Pascal’s triangle.

• CHALLENGE: Superimpose Pascal’s Triangle on the GHOSTS triangle and challenge students to find one way to get to each end pumpkin, 5 ways to get to the next pumpkin and 10 ways to get to each inner pumpkin.

G H H

O O O S S S S

T T T T T S S S S S S

G H H

O O O S S S S

T T T T T S S S S S S

Pascal's Ghosts 1 [email protected]

Page 2: How Many Ghosts Do You See? - Mathwire.com · How Many Ghosts Do You See? Instructions: • This lesson builds upon the Pascal’s Pumpkins or Pascal’s Triangle ex- perience. •

G H H 0 0 0

S S S S T T T T T

S S S S S S

How many

GHOSTS do you

see?

Pascal's Ghosts 2 [email protected]

Page 3: How Many Ghosts Do You See? - Mathwire.com · How Many Ghosts Do You See? Instructions: • This lesson builds upon the Pascal’s Pumpkins or Pascal’s Triangle ex- perience. •

1 1 1

1 2 1 1 3 3 1

1 4 6 4 1 1 5 10 10 5 1

How many

GHOSTS do you

see?

Pascal's Ghosts 3 [email protected]

Page 4: How Many Ghosts Do You See? - Mathwire.com · How Many Ghosts Do You See? Instructions: • This lesson builds upon the Pascal’s Pumpkins or Pascal’s Triangle ex- perience. •

G H H

O O O S S S S

T T T T T S S S S S S

G H H

O O O S S S S

T T T T T S S S S S S

G H H

O O O S S S S

T T T T T S S S S S S

G H H

O O O S S S S

T T T T T S S S S S S

G H H

O O O S S S S

T T T T T S S S S S S

G H H

O O O S S S S

T T T T T S S S S S S

G H H

O O O S S S S

T T T T T S S S S S S

G H H

O O O S S S S

T T T T T S S S S S S

G H H

O O O S S S S

T T T T T S S S S S S

G H H

O O O S S S S

T T T T T S S S S S S

G H H

O O O S S S S

T T T T T S S S S S S

G H H

O O O S S S S

T T T T T S S S S S S

G H H

O O O S S S S

T T T T T S S S S S S

G H H

O O O S S S S

T T T T T S S S S S S

G H H

O O O S S S S

T T T T T S S S S S S

G H H

O O O S S S S

T T T T T S S S S S S

How Many Ghosts Do You See? Recording Sheet

Name:

Pascal's Ghosts 4 [email protected]


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