Shaking Hands Solution

3 people = 3 handshakes
4 people = 6 handshakes
5 people = 10 handshakes

The answers are all triangular numbers.  If you do not know what triangular numbers are, go and look them up.

Painted Cubes ***

A 3 x 3 x 3 cube is painted red on the outside.  If it is broken up into 1 x 1 x1 – unit cubes, how many of these small cubes have 3 faces painted?  Two faces painted?  One face painted?  No faces painted? 

Hint: Imagine or draw a cube with each face looking like the 3 x 3 grid below.  (Unfortunately the picture I had of a cube will not show up here.)  You could even build one with small blocks!

  

Extend your thinking *****

What about if you start out with a larger cube?  Can you come up with a general rule for an n x n x n cube?

I would very much like to see any answers you are able to come up with!

Happy Easter,

Mrs Hopkins

Sequence ****

What is the next number in the following sequence?

15, 78, 456, 2724...

Hint: Two operations (out of adding, subtracting, multiplying, dividing) are needed to get to the next term.

Sequence Solution

16, 332 is the next number.  The term-to-term rule is subtract 2 then multiply by 6.

Domino Jigsaws ****

Can you arrange a set of dominoes (up to double sixes) onto these mats.  Each number refers to the number of dots on each domino. 

4	5	3	1
3	3	3	3

0	5	5	1
0	3	1	1
0	0	0	1

4	4	6	6
1	1	6	3
1	2	2	3

0	4	4	2
4	4	4	2
5	5	5	5

0	0	6	6
2	2	6	6
2	2	6	5

If you find a solution, draw it out and show it to Mrs Hopkins.  Do you think there is more than one solution?

Countdown Solutions

Using the numbers 2, 3 and 6, and any of the four mathematical operations:

6 + 3 + 3 = 11

2 x 3 + 6 = 12

6 x 2 + 3 = 15

6 + 3 - 2 = 7

6 x 3 + 2 = 20

3 x 2 x 6 = 36

6 - 3 - 2 = 1 or (6/3) / 2 = 1

6 - (3 - 2) = 1

(3 + 6) x 2 = 18
(6 + 2) x 3 = 24

You might have found some different solutions that work as well.

Multiple Choice Maths **

Find the answers to these problems.  Challenge yourself to calculate the solutions mentally.

1. A tree was planted in 1998.  How old will it be in 2020?

A – 12 years old

B – 22 years old

C – 32 years old

D – 42 years old

2. Which number is nearest to 1000?

A – 909

B – 960

C – 1039

D – 1049

3. What is half of 56?

A – 29

B – 28

C – 27

D – 26

4. My book has 144 pages.  I have read 40 pages.  How many pages do I need to read until I am halfway through the book?

A – 31 pages

B – 32 pages

C – 72 pages

D – 188 pages