Pascal's Christmas Tree

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

Design your Christmas light display: Pattern:

Every: Starting at: Colour: Add

Run Light Show Clear Instructions

There are many wonderful patterns in Pascal's triangle and they make excellent designs for Christmas tree lighting. Choose a number pattern from the drop-down box above, set the timing and colour then add it to the instructions for the lighting display. Press the Run Light Show button to see your creation.

During your display each light will stay on for one second so setting a light to come on every 1 second effectively means that light stays on for the whole display time.

Patterns chosen further down the drop-down list may overwrite some of the lights in the patterns chosen higher up the list.

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

Xmas Tree Trim

Xmas Tree Trim

Use the lights provided to decorate each of the Christmas trees so that no two trees are the same.

The short web address is:

Transum.org/go/?to=xmastrim

Don't miss out on other great Festive mathematical activities. Click the link below.

CHRISTMATHS

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.

Email address

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 17 June 'Starter of the Day' page by Mr Hall, Light Hall School, Solihull:

"Dear Transum,

I love you website I use it every maths lesson I have with every year group! I don't know were I would turn to with out you!"

Comment recorded on the 23 September 'Starter of the Day' page by Judy, Chatsmore CHS:

"This triangle starter is excellent. I have used it with all of my ks3 and ks4 classes and they are all totally focused when counting the triangles."

Each month a newsletter is published containing details of the new additions to the Transum website and a new puzzle of the month.

The newsletter is then duplicated as a podcast which is available on the major delivery networks. You can listen to the podcast while you are commuting, exercising or relaxing.

Transum breaking news is available on Twitter @Transum and if that's not enough there is also a Transum Facebook page.

Featured Activity

Newsletter

Newsletter

The Transum Newsletter for April 2025 has just been published. Click on the image above to read about the latest developments on this site and try to solve the puzzle of the month. You can read the newsletter online or listen to it by downloading the podcast.

Save Your Light Show

The saved lighting display is in the form of a URL that you can send to your friends, family or people at school so that they too can enjoy your lighting display. In fact it could be sent as a Christmas card by email, saving you the cost of stamps!

Click the button below to create a URL for your Pascal's Christmas Tree lighting display. This URL can be shared with others and pasted into the comments below so that we can all enjoy your creativity.

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!

Transum,

Thursday, October 18, 2018

"Creating this activity was the most interesting project I have tackled for ages. I discovered many more patterns in Pascal's triangle than I thought were there. Creating the algorithms and formulas to identify the hexagons that need to light up for any chosen pattern was a great example of Maths in action and a very satisfying experience. Here is the first light show I created on completing the project: First Light Show. I'm sure you can do much better. Have fun!"

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=775