#    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

——————————————————-

# ## Pythagoras

#### Look at the diagram below. # 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

# Fractions (Conversions) ** click graphic for printable lessons** # —————————————————————

### 13 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

6. Lori says:

Thanks so much for these amazing resources! We are homeschoolers and appreciate the time you have put into these activities. We especially appreciate the care and consideration you have when explaining each lesson.