binomial theorem jigsaw

7/24/2019 Binomial Theorem Jigsaw

1/5

JIGSAW ACTIVITY, TASK #1

Your job is to multiply and find all the terms in ( )+4

1x .

Recall that this means ( ) ( ) ( ) ( )+ + + +1 1 1 1x x x x .

Start by multiplying: ( ) ( )+ +1 1x x . Write your answer in the space below.

Now multiply this answer by ( )+ 1x combine li!e terms write your answer in the spacebelow.

"inally multiply this result by ( )+ 1x combine li!e terms write your answer in the spacebelow.

#a!e sure your answer in written in the correct order. $ighest powers of % should comefirst down to the lowest powers.

What are the coefficients of % in your answer& Write these coefficients in the bo%es

below.

'()S*+,NS ",R -/SS 0+S-(SS+,N

1. redict the number of terms in ( )2

1+x

3. What do you thin! ( )4

+x y would loo! li!e when e%panded&


2/5

JIGSAW ACTIVITY, TASK #2

+n how many ways can 4 coins be tossed& "or e%ample one way is *ails $eads$eads *ails. (sing *s to represent tails and $s to represent heads write the samplespace for this situation in the space below.

+f 4 coins are tossed how many ways are there to get 5 heads&





Write the answers to these 7uestions in order in the bo%es below.

'()S*+,NS ",R -/SS 0+S-(SS+,N

1. +n how many ways can 2 coins be tossed& 8 coins&

3. +f 2 coins are tossed in how many ways can e%actly 1 head appear& 3 heads&


3/5

JIGSAW ACTIVITY,TASK #3

9elow is a blan! ersion of a famous mathematical pattern ascals *riangle. +t hasbeen studied for hundred of years by mathematicians and students and contains manyinteresting patterns. *he concept behind the triangle is simple: each ;cell< in the triangle

is the sum of the two numbers aboe it. *he first few rows hae been filled in for you.Your job is to fill in the remaining rows of the triangle.

'uestion 1. What is the sum of theentries for each row of the triangle&"ind each sum and write it at theend of the row. $ow are thesenumbers related&

'uestions 3. What are the entries inrow 4 of the triangle& Row 4 is the row which has 2 entries =note: the top row isconsidered row 5>. Write your answer in the bo%es below.

'()S*+,NS ",R -/SS 0+S-(SS+,N

1. 0escribe patterns that e%ist along the different diagonals in the triangle.

3. Write a formula for the sum of the terms in any particular row.


4/5

JIGSAW ACTIVITY,TASK #4

CALCULATORS ARE BANNED FOR THIS TASK. WRITE OUT ALL FORMULAS

ractice computing combinations and permutations. (se the formulas you !now to

compute each of the following. You may use a scientific calculator to chec! youranswers but all wor! must be shown.

1. "ind the alue of each of the following: 35-3and 35-1?

3. "ind the alue of each of the following: 18-4and 18-13

0eelop a rule that demonstrates the pattern in problems 1 and 3.

6. -ompute each of the following writing your answers in the bo%es below.

4-5 4-1 4-3 4-6 4-4

4. What is the sum of the answers in problem 6&

2. "ind the sum of K2 5 2 1 2 3 2 2- - - - &

8. "ind the sum of K8 5 8 1 8 3 8 8- - - - &

0eelop a rule that demonstrates the pattern in problems 2 and 8.

'()S*+,NS ",R -/SS 0+S-(SS+,N

1. Name a combination that is e7ual to 12-3.

3. What is the sum of all combinations where n @ 13&


5/5

PROBABILITY AND STATISTICS, JIGSAW ACTIVITY, CONNECTIONS

Now that you hae e%plored each tas! and discussed the results ta!e a step bac! andnote the connections that e%ist between the tas!s. With your group write a sentence ortwo which describes the connections between each of the following:

1. -ombinations and ascals triangle

3. -oin flipping and ascals triangle

6. #ultiplying binomials and combinations

4. -ombinations and coin flipping

(se your new !nowledge to e%plore the following 7uestions.

1. 15 coins are tossed. What is the probability that e%actly 2 of them are heads& *hate%actly ? of them are heads&

3. )%pand: ( )

?

1+x

binomial theorem jigsaw

Documents