##### Level 1Level 2Level 3Level 4Level 5Level 6Binomial TheoremDescriptionHelpMore...

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 1. The row of Pascalâ€™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? 2. What is the sum of all the numbers in row 4? 3. What is the sum of all the numbers in rows 0 to 6? 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? 5. A calculator can be used to find any number in Pascalâ€™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. 6. Use a calculator to find the number in row 41, position 5. 7. The number in row 27, position 3 can be represented as $$\begin{pmatrix}27\\3\\ \end{pmatrix}$$Find $$\begin{pmatrix}27\\3\\ \end{pmatrix}$$ 8. Find $$\begin{pmatrix}53\\50\\ \end{pmatrix}$$ 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? 10. How many different ways can seven cakes be chosen from a tray containing ten cakes?

## Transum.org

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#### Digital Darts

An online darts game for one or two players requiring skill, strategy and mental arithmetic. It provides an enjoyable way to practise adding and subtracting two and three digit numbers.

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## 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

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Friday, February 18, 2022

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## Description of Levels

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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).

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#### 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

#### 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

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:

#### 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:

## 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.

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