# Maths Mysteries **click graphic for print version**

## The Missing 8

###### 123 456 788 876 543 211

Challenge:

Complete these:

#### Without the 8…..

1) 12 345 679 x 45 =           2) 12 345 679 x 54 =         3) 12 345 679 x 63 =

4) 12 345 679 x 72 =           5) 12 345 679 x 81 =

#### With the 8….

6)   123 456 789 x 45 =       7)   123 456 789 x 54 =       8)   123 456 789 x 63 =

9)   123 456 789 x 72 =       10) 123 456 789 x 81 =

The ‘without 8’ pattern continues below:

12 345 679 x 90   =   1 111 111 110

12 345 679 x 99   =   1 222 222 221

12 345 679 x 108 =   1 333 333 332

Fill in the answers to these:

11) 12 345 679 x 117 =       12) 12 345 679 x 126 =       13) 12 345 679 x 135 =

14) 12 345 679 x 144 =       15) 12 345 679 x 153 =       16) 12 345 679 x 162 =

The ‘with the  8’ pattern continues below:

123 456 789 x 90 =  11 111 111 010

123 456 789 x 99 =  12 222 222 111

123 456 789 x 108 =13 333 333 212

Now fill in the answers to these:

17) 123 456 789 x 117 =       18) 123 456 789 x 126 =       19) 123 456 789 x 135 =

20) 123 456 789 x 144 =       21) 123 456 789 x 153 =       22) 123 456 789 x 162 =

Solutions to The Missing 8

## Multiples of 9

987 654 321 x   9 =   8 888 888 889

987 654 321 x 18 = 17 777 777 778

987 654 321 x 27 = 26 666 666 667

987 654 321 x 36 = 35 555 555 556

987 654 321 x 45 = 44 444 444 445

Challenge:

1) What do you notice about the first and last digits of the product?

Complete these:

2) 987 654 321 x 54 =

3) 987 654 321 x 63 =

4) 987 654 321 x 72 =

5) 987 654 321 x 81 =

Solutions to Multiples of 9

1) Same as the multiplier        2) 53 333 333 334
3) 62 222 222 223                    4) 71 111 111 112
5) 80 000 000 001

# Curiosities & Perplexities **click graphic for print version**

## Odd Numbers Greater Than 7

#### Solutions to Odd Numbers Greater Than 7 (in cases where there are multiple solutions up to three solutions are given) 1. 3+7+31, 5+13+23, 7+11+23 2. 3+7+19, 5+5+19, 3+3+23 3. 3+7+13, 5+5+13, 5+7+11 4. 3+7+43, 3+13+37, 5+5+43 5. 5+19+19, 11+13+19, 11+15+17 6. 7+13+41, 3+17+41, 3+5+53 7. 11+19+37, 13+17+37, 7+23+37 8. 5+13+29, 7+11+29, 7+17+23 9. 5+7+47, 31+23+5, 17+19+23 10. 7+7+17, 3+11+17, 5+7+19 11. 3+31+37, 29+11+31, 29+29+13 12. 7+31+41, 19+19+41, 19+23+27 13. 11+31+41, 13+29+41, 33+37+13 14. 11+37+41, 7+41+41, 5+41+43 15. 19+37+41, 23+37+37, 29+31+37 16. 19+41+41, 23+37+41, 29+31+41 17. 23+37+43, 19+41+43, 19+31+53 18. 23+37+53, 19+41+53, 5+7+101 19. 37+37+53, 3+5+119, 7+11+109 20. 37+41+53, 5+7+119, 5+19+107

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# Divisibility Rules

## The Divisibility Rules

#### 114 (it is even, and 1+1+4=6 and 6÷3 = 2) Yes

308 (it is even, but 3+0+8=11 and 11÷3 = 3 2/3) No

#### The sum of the digits is divisible by 9

(Note: you can apply this rule to that answer again if you want)

# Famous Mathematicians **click Pascal’s pic for print version**

## Blaise Pascal

#### He died in 1662.

 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1

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###### Send feedback to info[at]australianteacher.org

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### 11 Responses to Maths

1. Peter Fedder says:

These resources are great. Some of the most practical and useful I have had sent to me for quite some time. All were useful not just ‘one out of the bunch’. Thanks again.

• Thank you Peter.

Glad you’re getting something out of the website and thanks so much for taking the time to write.

Best wishes,

Ron and Jacqueline

2. Sue MacGibbon says:

Great looking resources and even better being able to download/ share these with other teachers,

Thanks, keep up the good work,

Sue

• Thanks Sue.

Glad you’re getting good use out of them.

Have a great year!

Best,

Ron & Jacqueline

3. Steve Thornton says:

There are some nice activities here. Thanks.
The activity about even numbers being the sum of two odd primes is called Goldbach’s conjecture, and is a famous unproved conjecture in mathematics. This is a really nice example that shows mathematics as a living subject, with problems for which we don’t yet have an answer. Researching some of the historical aspects of primes and Goldbach’s conjecture is a great cross-curriculum activity.
Also, if Goldbach’s conjecture for even numbers happens to be true, the result about odd numbers greater than 7 being the sum of 3 odd primes follows logically. Why? This is a good exercise in logical reasoning for children.

• Thanks for your kind words and your very interesting contribution Steve.

Wiki tells us, “Since if every even number greater than 4 is the sum of two odd primes, merely adding 3 to each even number greater than 4 will produce the odd numbers greater than 7.”

You’re right…this would indeed be a great exercise for not-too-young maths students.

Many thanks again.

Ron and Jacqueline

• Hi again Steve,

You may have seen this already…
http://au.news.yahoo.com/thewest/a/-/world/14831400/mathematician-proof-prime-numbers/

All the best,

Ron

PS
I know it’s not the same conjecture you discussed in your comment above.

4. dev says:

The study mat for children is great!! I am from India and my six-year-old is bright in maths. (usually Indians are great at mathematics (although not much in research part). I hope this material helps my kid to understand the nuances of maths in order to delve deep into it.
Thanks and all the best

Dev

• Thank you Dev.

It’s nice to know that some of our maths material is being used in India, a nation that has produced some of the world’s great mathematicians.

Best wishes to you and your little six year old.

Warm regards,

Ron and Jacqueline

5. Jaki says:

These are great! Haven’t used them yet but I can definitely see them in my maths groups. Thanks a lot.

• Many thanks for your positive comment Jaki.

We hope to put more maths activities up on the website soon.

All the best,

Ron and Jackie