Pascal's Patterns

Here

1

1

1

1

2

1

1

3

3

1

1

4

6

4

1

1

5

10

10

5

1

1

6

15

20

15

6

1

1

7

21

35

35

21

7

1

1

8

28

56

70

56

28

8

1

1

9

36

84

126

126

84

36

9

1

1

10

45

120

210

252

210

120

45

10

1

1

11

55

165

330

462

462

330

165

55

11

1

1

12

66

220

495

792

924

792

495

220

66

12

1

1

13

78

286

715

1287

1716

1716

1287

715

286

78

13

1

1

14

91

364

1001

2002

3003

3432

3003

2002

1001

364

91

14

1

1

15

105

455

1365

3003

5005

6435

6435

5005

3003

1365

455

105

15

1

1

16

120

560

1820

4368

8008

11440

12870

11440

8008

4368

1820

560

120

16

1

1

17

136

680

2380

6188

12376

19448

24310

24310

19448

12376

6188

2380

680

136

17

1

1

18

153

816

3060

8568

18564

31824

43758

48620

43758

31824

18564

8568

3060

816

153

18

1

1

19

171

969

3876

11628

27132

50388

75582

92378

92378

75582

50388

27132

11628

3876

969

171

19

1

1

20

190

1140

4845

15504

38760

77520

125970

167960

184756

167960

125970

77520

38760

15504

4845

1140

190

20

1

1

21

210

1330

5985

20349

54264

116280

203490

293930

352716

352716

293930

203490

116280

54264

20349

5985

1330

210

21

1

Clear

There are many wonderful patterns in Pascal's triangle and some of them are described above. Take time to explore the creations when hexagons are displayed in different colours according to the properties of the numbers they contain.

You can either tick some of the check boxes above or click the individual hexagons multiple times to change their colour.

Here is an idea for a whole class activity if everyone has access to technology and can display this page. The teacher creates a pattern (not too complex) and displays it on the white board. Each person in the class tries to recreate that pattern without seeing the instructions.

Suggested

Pascal's Triangle

Pascal's Triangle

Get to know this famous number pattern with some revealing learning activities including the Binomial Theorem.

The short web address is:

Transum.org/go/?to=pascals

Related

Xmas Toggle Tree

Xmas Toggle Tree

Find the right combination of button presses to turn all of the Christmas tree lights on.

The short web address is:

Transum.org/go/?to=xmastoggle

Recommended

Pascal's Xmas Tree

Xmas Tree Trim

Light up the Christmas Tree by flashing numbered lights according your own number pattern.

The short web address is:

Transum.org/go/?to=pascaltree

Transum.org

This web site contains over a thousand free mathematical activities for teachers and pupils. Click here to go to the main page which links to all of the resources available.

Please contact me if you have any suggestions or questions.

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Mathematicians are not the people who find Maths easy; they are the people who enjoy how mystifying, puzzling and hard it is. Are you a mathematician?

Comment recorded on the 24 May 'Starter of the Day' page by Ruth Seward, Hagley Park Sports College:

"Find the starters wonderful; students enjoy them and often want to use the idea generated by the starter in other parts of the lesson. Keep up the good work"

Comment recorded on the 28 May 'Starter of the Day' page by L Smith, Colwyn Bay:

"An absolutely brilliant resource. Only recently been discovered but is used daily with all my classes. It is particularly useful when things can be saved for further use. Thank you!"

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Featured Activity

Number Crunch Saga

Number Crunch Saga

A lively numeracy game requiring you to align three numbers to create the given target sum or product. There are five levels to this online game and a virtual Transum Trophy available for each level.

Numeracy

"Numeracy is a proficiency which is developed mainly in Mathematics but also in other subjects. It is more than an ability to do basic arithmetic. It involves developing confidence and competence with numbers and measures. It requires understanding of the number system, a repertoire of mathematical techniques, and an inclination and ability to solve quantitative or spatial problems in a range of contexts. Numeracy also demands understanding of the ways in which data are gathered by counting and measuring, and presented in graphs, diagrams, charts and tables."

Secondary National Strategy, Mathematics at key stage 3

Go Maths

Learning and understanding Mathematics, at every level, requires learner engagement. Mathematics is not a spectator sport. Sometimes traditional teaching fails to actively involve students. One way to address the problem is through the use of interactive activities and this web site provides many of those. The Go Maths main page links to more activities designed for students in upper Secondary/High school.

Teachers

If you found this activity useful don't forget to record it in your scheme of work or learning management system. The short URL, ready to be copied and pasted, is as follows:

Alternatively, if you use Google Classroom, all you have to do is click on the green icon below in order to add this activity to one of your classes.

It may be worth remembering that if Transum.org should go offline for whatever reason, there are mirror site at Transum.info that contains most of the resources that are available here on Transum.org.

When planning to use technology in your lesson always have a plan B!

Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.

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© Transum Mathematics :: This activity can be found online at:
www.Transum.org/go/?Num=778