Pascal's Triangle

Level 1 Level 2 Level 3 Level 4 Level 5 Level 6 Binomial Theorem Description Help More...

Check

1. The row of Pascal’s Triangle containing just two ones is normally referred to as row 1. The solitary one at the top of the triangle is row zero. Row two contains the numbers 1,2 and 1 in that order.

What is the number in row 5 next to the one?

Correct Wrong

2. What is the sum of all the numbers in row 4?

Correct Wrong

3. What is the sum of all the numbers in rows 0 to 6?

Correct Wrong

4. The sum of the numbers in a particular row add up to \( x \). What do the numbers in the row below this row add up to?

Correct Wrong

5. A calculator can be used to find any number in Pascal’s Triangle given the row number and the position of the number from the left of the row [noting that the first number in a row is in position zero]. Click the HELP tab above for information about using a calculator for the following questions:

Use a calculator to find the number in row 20, position 4.

Correct Wrong

6. Use a calculator to find the number in row 41, position 5.

Correct Wrong

7. The number in row 27, position 3 can be represented as \( \begin{pmatrix}27\\3\\ \end{pmatrix} \)

Find \( \begin{pmatrix}27\\3\\ \end{pmatrix} \)

Correct Wrong

8. Find \( \begin{pmatrix}53\\50\\ \end{pmatrix} \)

Correct Wrong

9. The calculation \( \begin{pmatrix}5\\3\\ \end{pmatrix} \) can be written as 5C3 (pronounced five choose three) and can be used to find the number ways of choosing three items from five.

How many ways are there of choosing 2 players from a team of 11?

Correct Wrong

10. How many different ways can seven cakes be chosen from a tray containing ten cakes?

Correct Wrong

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 5 April 'Starter of the Day' page by Mr Stoner, St George's College of Technology:

"This resource has made a great deal of difference to the standard of starters for all of our lessons. Thank you for being so creative and imaginative."

Comment recorded on the 9 May 'Starter of the Day' page by Liz, Kuwait:

"I would like to thank you for the excellent resources which I used every day. My students would often turn up early to tackle the starter of the day as there were stamps for the first 5 finishers. We also had a lot of fun with the fun maths. All in all your resources provoked discussion and the students had a lot of fun."

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

23 or Bust

23 or Bust

A game involving mental arithmetic and strategy for two players or one player against the computer. It is possible to beat the computer but you need a well thought out strategy.

Answers

There are answers to this exercise but they are available in this space to teachers, tutors and parents who have logged in to their Transum subscription on this computer.

A Transum subscription unlocks the answers to the online exercises, quizzes and puzzles. It also provides the teacher with access to quality external links on each of the Transum Topic pages and the facility to add to the collection themselves.

Subscribers can manage class lists, lesson plans and assessment data in the Class Admin application and have access to reports of the Transum Trophies earned by class members.

If you would like to enjoy ad-free access to the thousands of Transum resources, receive our monthly newsletter, unlock the printable worksheets and see our Maths Lesson Finishers then sign up for a subscription now:

Subscribe

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!

Steven Strogatz, Twitter

Friday, February 18, 2022

Apple

©1997-2024 WWW.TRANSUM.ORG

© Transum Mathematics :: This activity can be found online at:
www.Transum.org/go/?Num=773

Description of Levels

Close

Close

Level 1 - Fill in the numbers on a blank triangular grid

Level 2 - Colour in the even numbers to produce a surprising pattern

Level 3 - Colour in the multiples of 3 to produce a surprising pattern

Level 4 - Colour in the remainders when dividing by four in different colours

Level 5 - Colour in sets of six connected hexagons that have given sums

Level 6 - Use a calculator to find particularly large numbers from Pascal's Triangle

Exam Style Questions - A collection of problems in the style of GCSE or IB/A-level exam paper questions (worked solutions are available for Transum subscribers).

More on this topic including lesson Starters, visual aids, investigations and self-marking exercises.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

Log in Sign up

Recommended

Sieve of Eratosthenes

Sieve of Eratosthenes

A self checking, interactive version of the Sieve of Eratosthenes method of finding prime numbers.

The short web address is:

Transum.org/go/?to=sieve

Suggested

Number Grids

Number Grids

Investigate the properties of number with these interactive number grids which can be coloured in.

The short web address is:

Transum.org/go/?to=grids

Related

Plinko Probability

Plinko Probability

A simulation of a Quincunx (Galton Board) which can be used to create the bell shaped curve of the normal distribution.

The short web address is:

Transum.org/go/?to=plinko

Festive

Pascal's Patterns

Pascal's Patterns

See the number patterns on Pascal's Triangle with this colourful, interactive application.

The short web address is:

Transum.org/go/?to=pascalpatterns

Using a Scientific Calculator

The function to work out a number in Pascal's Triangle appears as nCr where:

nCr Formula nCr button on calculator

Using a Graphic Display Calculator

With a GDC you can work out a whole row of Pascal's Triangle using the combinations function. Here is a screenshot of the TI Nspire.

Combinations function

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

Log in Sign up

Close

Close