### Consecutive Numbers

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

### Roll These Dice

Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possible answers?

### Domino Square

Use the 'double-3 down' dominoes to make a square so that each side has eight dots.

# Build it Up

##### Age 7 to 11 Challenge Level:

We had a very large number of solutions come in for this challenge. Here are a selection for you to consider.
Primary 6 at Victoria Primary School in Scotland sent in this very thorough solution

Firstly, we looked at the 4 numbers at the bottom and tried to work out how to get to 15.  As a class we agreed that this would take too long for us to try and work out  all the 4 digit numbers.  So next we worked out a system...

We started at the top and worked out all the 2 digit numbers that make 15 which were

14 + 1; 13 + 2; 12 + 3; 11 + 4; 10 + 5; 9 + 6; 8 + 7; 7 + 8; 6 + 9; 5 + 10; 4 + 11; 3 + 12; 1+ 14;

Then we looked at next row down and worked out that we couldn't have 1 + 14 and 14 + 1 because we we couldn't use 0 so nothing adds up to 0.  We took a pair of numbers each and worked out some of the group of 3 numbers which were:

 making 15 making the two totals 9 + 6 8,1,5 7,2,3 6,3,2 5,4,3 4,5,1 5 + 10 4,1,9 3,2,8 2,3,7 1,4,6 12 + 3 11,1,2 10,2,1 6 + 9 3,3,6 2,4,5 1,5,4 4,2,7 11 + 4 10,1,3 9,2,2, 8,3,1 8 + 7 7,1,6 6,2,5 5,3,4 4,4,3 3,5,2 2,6,1 7 + 8 3,4,5 5,2,6 6,1,7 10 + 5 9,1,4 8,2,3 7,3,2 6,4,1 3 + 12 1,2,10 2,1,11 13 + 2 12,1,1 4 + 11 3,1,10 2,2,9 1,3,8

And from that we were able to do the exact same to work out the four
numbers which are:

2221; 8111; 4122; 421152123211; 5211; 4122; 7112; 5114; 3213; 3123; 7112; 2131; 7112; 7223; 5211; 2214; 2311; 8231; 1312; 6113; 1127; 1118; 4212;

We really enjoyed the challenge and our (something? brains? hands? minds ?) hurts after it but in a good way.
We really needed to keep a growth mindset.
This has been explained very well but now have a look at the ones I've put in italics (and underlined) what do you think about them?

We also had a number of solutions sent in from  Peak School in  Hong Kong

Alyssa wrote:

I found that all of my solutions always had a 1 in the bottom row, and the
total of all the numbers in the bottom row was always an odd number.

Victoria K & F wrote:

These are our solutions:

Rules:
There has to always be a 1 in the bottom row.
In the bottom row will always be a number repeated twice.
The bottom row must equal an odd number.
The second to bottom row must equal 11, 12 or 13.
There must be a combination of odd and even numbers in every row.

Mathias wrote:

I found out 9 different ways to get 15 using different numbers.

Sophie and Dorika wrote:

We think that the bottom line has to add up to an odd number.
We also found out that there has to be a one in in the bottom row.
The middle line can't have a one in it.
The second to bottom row will equal to 11, 12, 13.
On the bottom row a number will always be repeated twice or three times.
There are only 4 pairs of numbers that can be used in the second row.

Extension:
We combined your idea and we did our own version using decimal points

15
9  6
6  3  3
4  2  1  2
2.5 1.5 .5 .5 1.5
1.25 1.25 .25 .25 .25 1.25
.125 1.125 .125 .125 .125 .125 1.125

Chloé, Holly and Anna wrote:

We found these solutions by starting from the top row and working our way
to the bottom:

We found some rules after finding the solutions:

-The bottom row must equal an odd number (7, 9, 11)
-The second to bottom row equal 11,12 or 13
-On the bottom row there will always be a number repeated twice
-There has to be be one in the bottom row