**"Number patterns"**

## Magic Numbers

*By toni On 6 October, 2021 · Leave a Comment*

What patterns do you see in them?

Suppose you have to share 9872 gold coins between 8 people.

You give the coins out in thousands until there are less than 8000 left.

Then you give out one hundred at a time until there are less than 800, then […]

## Money Bags

*By toni On 1 September, 2021 · 2 Comments*

Ram had 15 coins, all the same kind, and he put them into 4 bags.

He labelled each bag with the number of coins inside it.

He could then pay any sum of money from 1 coin to 15 coins using one or more of the bags without opening any of the bags.

How […]

1. What do you see in this picture?

Give a proof linked to this picture of the formula $a^2 – b^2 = (a + b)(a – b)$ .

2. What do you notice about the difference between squares of consecutive numbers?

Compare the differences between squares of numbers that differ by 1 […]

## Triangle Number Picture

*By toni On 5 February, 2021 · Leave a Comment*

Is a picture worth a thousand words (as the saying goes)?

This picture shows how you can fit 2 identical copies of a triangle together to form a rectangle.

Can you use it to find the number of dots in the fifth triangle number without counting the dots?

Can you find any […]

## Blocks, Bricks and Boxes

*By toni On 5 February, 2021 · Leave a Comment*

Find a cuboid (with edges of integer values) that has a surface area of exactly 100 square units.

Is there more than one?

It is quite easy to find a few solutions. The big challenge is to find all possible solutions.

Can you provide a convincing argument that you have found […]

## Magic of 37

*By toni On 1 February, 2021 · Leave a Comment*

First complete the number sentences by putting = + – x or ÷ in the boxes. Then explain why the pattern occurs.

Explore the pattern you get when you carry on these multiplications up to 37 × 54.

Click here for MAGIC OF 37 worksheet.

Click here for the Notes […]

## Mystic Rose

*By toni On 31 January, 2021 · Leave a Comment*

What can you see in this diagram?

Could you draw it? Could you draw a similar diagram with just 5 or 6 points around the outside? Try it?

How many lines are there in your diagrams? How many lines are there in the original diagram? Can you find a way of working out […]

## Prime Sieve

*By toni On 7 January, 2021 · Leave a Comment*

You might like to start by investigating the patterns you get when you shade multiples of a number on a grid. Download here

For the prime sieve investigation use a 100 square grid (download here):

Circle the number 2. Put a line through every multiple of 2 up to 100.

[…]

Can you find the chosen number from this square using the clues below?

1. The number is odd.

2. It is a multiple of three.

3. It is smaller than 7 x 4.

4. It has an even tens digit.

5. It is the greater of the two possibilities.

[…]

## Fibonacci’s Rabbits

*By toni On 20 August, 2020 · Leave a Comment*

Fibonacci (in the year 1202) investigated a problem about how fast a population of rabbits would grow in the following circumstances, starting with just one pair of rabbits:

Suppose a newly-born pair of rabbits, one male, one female, are put in a field. Rabbits are able to mate at the age of […]

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